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<title>Boom Effects with Short 3-Element 146-MHz Yagis</title>
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<h1><img src="../images/yagicad.gif" align="middle" width="125" height="62" border="2" vspace="5" hspace="10"> Notes on Boom Effects with Short 3-Element 146-MHz Yagis <img src="../images/w4rnlwwr.gif" align="middle" width="99" height="83" border="2" vspace="5" hspace="10"></h1>
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<h3>L. B. Cebik, W4RNL</h3>
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<p>There is a long-standing question concerning the effects of directly connecting Yagi elements to a boom vs. having them well insulated and isolated from the boom. The empirical evidence shows that the boom connection requires an adjustment to element lengths relative to the use of insulated elements (or a non-conductive boom). However, at least two questions remain. 1. Can NEC show the difference? 2. What are the currents along the boom relative to those on the active elements?</p>
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<p>As a preliminary investigation, I used 2 of a series of 3-element optimized utility Yagis and remodeled them to show element-to-boom connections. NEC (-2/-4) is limited in its ability to model such situations, since it develops errors if there are angular junctions of dissimilar-diameter materials. However, since I had optimized the designs for a number of element diameters, I selected the models using 0.5"-diameter elements. This selection permitted the use of a 0.5"-diameter boom for the NEC-4 modeling tests.</p>
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<p>Each modeling test proceeded in 4 steps:</p>
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<p>1. The initial model using no boom</p>
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<p>2. Pre-boom model adjustments: The adjustments included a. moving the driver 1" above the plane of the antenna to maintain its insulation from the boom, b. dividing the elements into wires joining along the array centerline, and finally c. optimizing the segmentation at a value of about 0.85 segments per inch of wire element.</p>
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<p>3. Adding a boom extending from the reflector junction to the director junction, using the same segmentation as in step 2.</p>
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<p>4. Adding 1.7" extensions from the reflector back and from the director forward, with 2 segments each.</p>
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<p>The following notes provide the modeling data for the tests.</p>
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<p><b>1. 23FB-50: A 2-meter, 3-element Yagi optimized for maximum front-to-back ratio at 146 MHz</b></p>
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<p><i>Step 1</i>. The following dimensions apply to the initial (no-boom) model of the max FB design. Element lengths are in half-length units to simplify replication of the model. All element diameter values will be 0.5" (radius = 0.25"). Each element used 31 segments. The material is aluminum. The environment is free-space.</p>
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<pre>Element Length Distance from Reflector
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Reflector +/- 20.06" -----
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Driver +/- 18.16" 13.39"
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Director +/- 17.21" 25.10" (11.71" from driver)</pre>
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<p>Performance report:</p>
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<pre> 144 MHz 146 MHz 148 MHz
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Gain 7.66 dBi 7.81 8.02
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Front-back 23.34 dB 56.80 22.82
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Source Z 65.90 + j 8.24 50.17 - j 0.60 33.41 - j 1.76
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50-Ohm SWR 1.364 1.012 1.500</pre>
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<p>The reverse curve of source reactance stems from the use of a beta match consisting of a transmission-line stub across the source after shortening the driver to show the requisite capacitive reactance.</p>
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<p><i>Step 2</i>. The model was revised to use 2 wires for the reflector and director elements, with 17 segments per half reflector and 15 segments per half director. The driver was elevated 1" with 31 segments. The following performance figures resulted from the revisions.</p>
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<p>Performance report:</p>
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<pre> 144 MHz 146 MHz 148 MHz
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Gain 7.65 dBi 7.79 8.00
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Front-back 23.57 dB 56.50 22.57
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Source Z 65.56 + j 8.24 49.86 - j 0.46 33.21 - j 1.52
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50-Ohm SWR 1.358 1.010 1.508</pre>
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<p>I consider the performance differences between the initial and the Step-2 model insignificant, but the latter forms the baseline for the following steps.</p>
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<p><i>Step 3</i>. The model added a 0.5"-diameter aluminum boom from the reflector to the director, using 21 segments. The resulting performance report was identical to that shown for Step 2, with no changes even in the last decimal place.</p>
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<p>The currents are interesting. The driver was given a current source of relative magnitude 1.0 and phase angle 0 degrees. Because the source has a transmission line stub across it to effect a match to a 50-Ohm feedline, the driver current value will be other than 1.0 at 0 degrees, as shown in the following short table of values for 146 MHz. The element currents are identical to those that appear for Step 2.</p>
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<p>Relative current magnitude and phase at 146 MHz at element centers and boom junctions:</p>
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<pre>Reflector: 4.17E-1//172.31 deg Boom junction: 6.5E-7//105.83 deg
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Driver: 1.37E+0//42.48
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Director: 9.25E-1//-93.54 Boom junction: 4.6E-7//-54.68</pre>
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<p><i>Step 4</i>. The Step-3 model added 1.7"-long 0.5"-diameter boom extensions to simulate construction realities, but permit the use of 2 segments, each the same length as others in the model. The performance report did not change. However, the boom-to-element junction current changed somewhat.</p>
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<p>Relative current magnitude and phase at 146 MHz at element centers and boom junctions:</p>
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<pre>Reflector: 4.17E-1//172.31 deg Boom junction: 4.97E-7//96.27 deg
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Driver: 1.37E+0//42.48
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Director: 9.25E-1//-93.54 Boom junction: 6.6E-7//-69.82</pre>
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<p>Nowhere along the booms in Steps 3 and 4 did the relative current magnitude exceed 6.6E-7, about 6 orders of magnitude below the current peaks recorded on the parasitic elements.</p>
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<p><b>2. 23WB-50: A 2-meter, 3-element Yagi for wide-band operation from 144-148 MHz</b></p>
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<p><i>Step 1</i>. The following dimensions apply to the initial (no-boom) model of the wide-band design. Element lengths are in half-length units to simplify replication of the model. All element diameter values will be 0.5" (radius = 0.25"). Each element used 31 segments. The material is aluminum. The environment is free-space.</p>
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<pre>Element Length Distance from Reflector
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Reflector +/- 20.46" -----
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Driver +/- 19.15" 18.10"
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Director +/- 16.80" 28.60" (10.50" from driver)</pre>
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<p>Performance report:</p>
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<pre> 144 MHz 146 MHz 148 MHz
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Gain 7.04 dBi 7.14 7.30
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Front-back 19.78 dB 23.20 26.42
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Source Z 52.58 - j 7.78 49.95 - j 0.76 46.30 + j 7.58
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50-Ohm SWR 1.173 1.015 1.191</pre>
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<p>The driver source impedance shows a normal curve because the antenna was designed for direct feed by a 50-Ohm coaxial cable.</p>
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<p><i>Step 2</i>. The model was revised to use 2 wires for the reflector and director elements, with 17 segments per half reflector and 14 segments per half director. The driver was elevated 1" with 33 segments. The following performance figures resulted from the revisions.</p>
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<p>Performance report:</p>
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<pre> 144 MHz 146 MHz 148 MHz
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Gain 7.04 dBi 7.14 7.30
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Front-back 19.85 dB 23.26 26.33
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Source Z 52.56 - j 7.68 49.94 - j 0.61 46.31 + j 7.78
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50-Ohm SWR 1.171 1.012 1.196</pre>
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<p>I consider the performance differences between the initial and the Step-2 model insignificant, but the latter forms the baseline for the following steps.</p>
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<p><i>Step 3</i>. The model added a 0.5"-diameter aluminum boom from the reflector to the director, using 21 segments. The resulting performance report was again identical to that shown for Step 2, with no changes even in the last decimal place.</p>
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<p>The currents reflect the situation with the first Yagi design. The driver was given a current source of relative magnitude 1.0 and phase angle 0 degrees, as shown in the following short table of values for 146 MHz. The element currents are identical to those that appear for Step 2.</p>
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<p>Relative current magnitude and phase at 146 MHz at element centers and boom junctions:</p>
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<pre>Reflector: 2.72E-1//98.38 deg Boom junction: 2.1E-7//50.20 deg
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Driver: 1.00E+0//0.0
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Director: 7.24E-1//-132.3 Boom junction: 7.1E-7//120.46</pre>
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<p><i>Step 4</i>. The Step-3 model added 1.7"-long 0.5"-diameter boom extensions to simulate construction realities, but permit the use of 2 segments, each the same length as others in the model. The performance report did not change. However, the boom-to-element junction current changed somewhat.</p>
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<p>Relative current magnitude and phase at 146 MHz at element centers and boom junctions:</p>
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<pre>Reflector: 2.72E-1//98.38 deg Boom junction: 4.0E-7//62.84 deg
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Driver: 1.00E+0//0.0
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Director: 7.24E-1//-132.3 Boom junction: 5.0E-7//122.32</pre>
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<p>Nowhere along the booms in Steps 3 and 4 did the relative current magnitude exceed 7.1E-7, about 6 orders of magnitude below the current peaks recorded on the parasitic elements. However, we may note that the boom-to-director current phase differs on the wide-band model relative to the max F-B model. It does not reflect the phase angle of the director (a negative value on the max F-B design), but has a high positive value in a progression running from the reflector forward.</p>
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<p><i>Special note</i>: On the wide-band design, I pressed the segmentation limit by increasing the number of segments uniformly by a factor of about 1.5. Hence, the reflector halves used 25 segments, the director halves used 21, while the driver used 49. The main boom used 37 segments, with the end extensions using 3 each. In the pre-boom adjusted model (Step 2), the results varied by no more than a digit or two in the last decimal column, relative to the model with conservative segmentation. The highly segmented version of the design achieved an AGT of 1.000, although pressing further to double the original segmentation yielded core and program based warnings.</p>
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<p>The pre-boom (Step 2) model and the boom + extensions (Step 4) model of the highly segmented design produced identical performance reports to the last decimal place. The following table of current reports reflects that fact that the element and boom junction currents are closer to the actual junction than in the conservatively segmented model.</p>
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<p>Relative current magnitude and phase at 146 MHz at element centers and boom junctions:</p>
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<pre>Reflector: 2.73E-1//98.10 deg Boom junction: 1.4E-6//-132.1 deg
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Driver: 1.00E+0//0.0
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Director: 7.23E-1//-132.4 Boom junction: 1.1E-6//50.75</pre>
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<p>The table appears anomalous, because the current phases for the boom junctions appears to be reversed from what one might expect. However, in the region of the boom below the driver--with its current at 1.0 and 0.0 degrees--the boom current is about 1.1E-7 at 180 degrees.</p>
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<p>The current magnitudes reported for the boom junctions--actually the segment centers for the segment forming the junction--is nearly an order of magnitude higher than for the conservatively segmented model.</p>
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<p>The next step was to question whether the exact centering of the boom--and its identify in diameter to the elements--might be a reason for the identity of results between the boomless and boomed models. So I moved the boom to a position 0.51" below the parasitic elements. This situation provided a clearance of 0.01" (0.00012 wavelength) between the boom and element surfaces. The performance reports remained unchanged.</p>
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<p>I then transported this model with higher segmentation density to MININEC, and included a pre-boom adjusted model for comparison. The implementation of MININEC was Antenna Model. It is necessary to specify the implementation of MININEC, since the core is quite variably modified by each available implementation. Antenna Model has passed numerous benchmark tests involving areas where raw MININEC shows deficiencies. It has passed more tests than any other implementation.</p>
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<p>The MININEC version of the model differs from the NEC version only by having 48 segments on the driver in order to place the source at the exact center on a pulse (segment junction).</p>
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<p>Performance report--both pre-boom and full boom + extension models:</p>
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<pre> 144 MHz 146 MHz 148 MHz
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Gain 6.97 dBi 7.04 7.20
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Front-back 19.06 dB 22.11 25.35
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Source Z 53.94 - j 9.05 51.76 - j 2.11 48.49 + j 6.13
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50-Ohm SWR 1.209 1.055 1.137</pre>
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<p>Since MININEC does not suffer the NEC weakness with angular junctions with dissimilar diameter wires, I increased the boom diameter to 1", reducing the segmentation in the extension to avoid segment-length/diameter warnings. Increasing the boom diameter created no change in the performance reports</p>
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<p>The current at element junctions with the boom in MININEC is the current in the junction itself, since MININEC places pulses of current maximums at segment ends. For the 0.5" and the 1" booms, the current reports are as follows:</p>
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<p>Relative current magnitude and phase at 146 MHz at element centers and boom junctions:</p>
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<pre>0.5" boom:
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Reflector: 2.81E-1//97.11 deg Boom junction: 5.2E-6//10.88 deg
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Driver: 1.00E+0//0.0
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Director: 7.08E-1//-131.2 Boom junction: 5.0E-6//167.0
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1.0" boom:
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Reflector: 2.81E-1//97.11 deg Boom junction: 5.7E-6//8.94 deg
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Driver: 1.00E+0//0.0
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Director: 7.08E-1//-131.2 Boom junction: 6.3E-6//166.3</pre>
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<p>As expected, the element center current magnitude and phase do not change as we change to boom diameter. However, the boom currents do change slightly. Nevertheless, the boom current magnitudes are generally in accord with NEC results for the more highly segmented model, although the phase angles do not coincide.</p>
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<p><b>3. Ruminations on the results</b></p>
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<p>1. The models were all given an average gain test (AGT) and returned values of 1.000, an unusually perfect score that likely resulted from the careful segmentation of the elements and boom parts. Hence, within the terms internal to NEC-4 and a highly corrected version of MININEC, the models are fully adequate, with no detectable defects.</p>
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<p>2. The segment lengths are 1.17" (with very small variations from one model wire to another). The NEC current report for each segment is centered within the middle 1/3 of the segment. Junction surface penetration along a segment length is 0.25" maximum or about 21% into the segment length. This value is well short of the penetration needed to disturb segment currents during calculation, as evidenced by the AGT values. The segment lengths are restricted to the lengths shown to ensure a segment-length-to-radius ratio of over 4:1 (actual, about 4.7:1) in order to preserve model adequacy as registered in the AGT score. MININEC models are not limited by exactly the same set of phenomena, but the segment length should be at least 1.25 times the wire diameter for maximum reliability. The more highly segmented versions of the models press both NEC and MININEC to the limit of reliable performance with respect to element-length/element-diameter, but both programs return results considered reliable.</p>
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<p>3. Nothing in the model itself exceeds any limitations of the programs, and there is a variance between modeled results and building experience for element-to-boom connections. Hence, one must look elsewhere for the reason why there is no difference in performance reports with or without a conductive boom connected between the parasitic elements. In the NEC-2 Manual, we find the following:</p>
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<p>"In the thin-wire kernel, the current on the surface of a segment is reduced to a filament of current on the segment axis. In the extended thin-wire kernel, a current uniformly distributed around the surface is assumed. . . In either of these approximations [used in the kernel of the electric field integral equations], only currents in the axial direction on a segment are considered, and there is no allowance for variation of the current around the wire circumference." (pp. 3-4)</p>
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<p>The axial current (along the element axis) does not yield a detectable interaction with the conductive boom. The only unaccounted current remaining as the source of that interaction is the current around the circumference of the wire, which is caused to vary by the presence of the boom from the level normally accompanying an element not connected to a conductive boom. IF this inference is correct, then several likely facts follow:</p>
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<p>a. The region of interaction in terms of the total length of the boom is likely to be quite small, since the axial and the circumferential currents are inter-related and controlled largely by the axial currents, which are controlled, in turn, by the driver (or in larger arrays, the adjacent elements). If the current on the boom (except at the junction) were large, then current division would occur, and the general operation of a parasitic array would be thrown off by an amount that simple element-length adjustments could not overcome. In a 3-element Yagi, the source impedance due to significant current division (even of a 10:1 element-to-boom current division ratio) would not return to normal with an element-length adjustment. However, empirical evidence from building and testing Yagis suggests that element length adjustments are satisfactory to compensate for direct element-boom connections.</p>
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<p>b. The most likely effect of circumferential current interaction with the boom would be to enlarge the current region at the point and very near to the connection, thus creating the effect of a stepped-diameter element. The requisite adjusted element length would be longer than for an independent element. Hence, it is likely that the technique of empirically deriving larger-diameter element insert corrections for boom-to-element assemblies and connections is a generally correct one.</p>
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<p>c. An alternative interpretation based upon axial current occurs in the Guy Fletcher, "Effects of Boom and Element Diameters on Yagi Element Lengths at 144, 432, and 1296 MHz," <i>QEX</i> (Jan/Feb, 2001, pp. 16-22. In this account, as interpreted by the journal editor, the axial currents set up around the element circumferential magnetic field lines that intercept the boom. Although the mechanisms are speculative, the results "can be represented as a pure negative reactance, the value of which depends also to a lesser extent on the element diameter. [The effect is to require an] increase in [element] length to compensate for this reactance" (p. 20). Nevertheless, if the speculative mechanism is an accurate account and in fact controlled by axial currents, then it should produce results within NEC and/or MININEC. However, as the modeling evidence shows, no such effects appear. Although field influence is undoubtedly involved--especially in cases where the boom and elements are close but not touching--it seems more likely to be a function of circumferential currents, since NEC already accounts for variations in axial current. See also the work of Lief Asbrink, SM5BSZ, much of which is at the commercial web site, <a href="https://web.archive.org/web/20030330235241/http://www.antennspecialisten.com/" target="_blank">www.antennspecialisten.com</a> (web.archive.org).</p>
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<p>d. Until or unless NEC or MININEC adopts algorithms for integral equations that include circumferential currents as well as axial currents, there will be no straightforward way of actually calculating directly the exact boom-to-element interaction. Hence, these notes are speculative and deserve discarding to the degree that the process of elimination and the subsequent inferences can be shown to be faulty.</p>
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<p><i>Updated 10-22-2003. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.</i></p>
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<p><a href="../radio.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Go to Amateur Radio Page</a></p>
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<p class="topics-footer">Topics: <a href='../topics.html#boom-effects'>Boom Effects</a>, <a href='../topics.html#vhf-uhf'>VHF / UHF</a>, <a href='../topics.html#yagi'>Yagi</a></p><br>
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<meta name="keywords" content="Vertical, VHF / UHF">
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<title>The Coaxial Folded Monopole</title>
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<h1>The Coaxial Folded Monopole:<br>
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A Modeling Adventure</h1>
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<center>
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<h3>L. B. Cebik, W4RNL</h3>
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</center><br>
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<p>The coaxial folded monopole lies at the base of the coaxial collinear array and a number of other antennas. The difficulty that designers and analysts have with the antenna lies partly in our inability to effectively model the relatively simple device. However, in principle, the antenna is as easy to understand as a simple folded monopole. <b>Fig. 1</b> outlines the basic considerations.</p>
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<center>
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<img src="cofd-1.gif" width="250" height="275" border="2" vspace="5" hspace="9">
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</center>
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<p>The antenna has two "legs." One extends from the ground upward to the top of the structure and bridges to a second conductor running back to the ground. Here, the term "ground" may mean a ground-plane assembly of radials, a perfect ground in models, or a mirror of the upper structure to form a coaxial dipole. In our efforts to model the coaxial monopole, we shall use perfect ground for simplicity. Any changes that we make in length to set the antenna at resonance will not depend upon the radius of a radial set. Hence, we may easily compare one model to the next.</p>
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<p>What differentiates the coaxial monopole from a standard folded monopole is the fact that the conductors have a concentric arrangement, with one conductor wholly inside the larger one. Like any folded monopole, the coaxial monopole has two sets of currents. One set is the transmission-line current, where at any given point along the length, the currents on the two conductors are equal in magnitude and opposite in polarity. These currents exist on the outer surface of the inner conductor and the inner surface of the outer conductor. As well, the coaxial monopole should exhibit radiation currents, which in principle have the same polarity on both conductors. However, skin effect places the radiation current on the outer surface of the outer conductor. In principle, the coaxial monopole should have the same gain as a simple single-wire monopole.</p>
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<p><b>Fig. 1</b> shows the source terminals in series with the bottom edge of the two coaxial conductors. Efforts to model the coaxial monopole cannot proceed with the actual layout of the final product because neither MININEC nor NEC can handle coaxial structures effectively. Rather than using an outer solid-wall tube as the outer conductor, most models employ a number of wires that are parallel to the inner or center wire, each equally spaced from the center conductor and from each other. <b>Fig. 2</b> shows the general layout used in most models.</p>
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<center>
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<img src="cofd-2.gif" width="250" height="340" border="2" vspace="5" hspace="9">
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</center>
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<p>The sketch shows the outline of the type of model that has proven most successful and that also has numerous implementations in actual practice. The source connects to each of the outer wires in parallel. The perimeter wire at the base of the monopole only suggests the parallel connection, but does not show the best method for achieving as close to a true parallel connection as possible in a model. At the top, bridge wires connect each outer wire to the center wire that returns to the ground. Theoretically, we may reverse the source connection. We may place it on the base of the center wire, with each of the outer wires returned to ground. Herein lies a problem.</p>
|
||||
<p>Casual models of the center-fed coaxial dipole appear to produce very disheartening results. If we believe such models, the center-fed coaxial monopole should not be worth the effort of building. Nevertheless, many coaxial collinear vertical arrays are in service and appear to perform to specification. In the past, a number of large arrays of coaxial dipoles were built for narrow-beam radar use. (The patents for the coaxial collinear array go back to Germany in the 1930s.) Either something is wrong with the casual models or something is wrong with the antenna design.</p>
|
||||
<p>The plan for these notes is to examine the basic modeling requirements that affect models of coaxial monopoles and then to review some data drawn from the version of the antenna that has proven relatively reliable. Only after looking in some detail at the outer-wire-fed coaxial dipole will we be positioned to approach the center-fed version with some idea of what may count as successful modeling.</p>
|
||||
<p><b>Some Basic Constraints and Specifications</b></p>
|
||||
<p>The models in this exercise will use a test frequency of 299.7025 MHz, where 1 meter = 1 wavelength. All dimensions will be in millimeters to allow for an easy conversion of element lengths to a fraction of a wavelength. All models will use a perfect ground in NEC to allow for ready comparisons among models.</p>
|
||||
<p>All wires in the assemblies will be 5-mm in diameter, using both perfect or lossless wire and copper wire in tabulated results. (At the test frequency and element diameter selected, we normally find only minuscule differences in the reported performance numbers, so that departures from that condition may prove instructive.) The center-to-center spacing between the fed wire(s) and the return wire(s) will be 20-mm, about 0.8". If the outer wires are numerous enough to form a rough approximation of a circle, the diameter will be about 40-mm. As we shall discover, 6 wires is enough to approach but not quite reach the status of a full circle enclosing the center wire.</p>
|
||||
<p>Wherever relevant, we shall adjust the length of the center and outer wires together to reach a resonant length with no more than +/-j1 Ohm of reactance at the feedpoint. The values that we obtain in the first series of tests will provide a guide for what sort of feedpoint impedance emerges from a sensible model that uses a center-fed wire.</p>
|
||||
<p>Besides this condition, we shall be very interested in several model properties. The Average Gain Test (AGT) is critical to testing the models and to adjusting reported values of both gain and feedpoint resistance. We shall use the AGT score to correct the feedpoint resistance value, and we shall use the AGT converted to dB to provide a corrected gain report. Some appearances of both superior and inferior performance will disappear once we make the corrections. However, we must also be aware that the AGT score is also a measure of a model's reliability or adequacy as a model. Some suggested interpretations of AGT scores supply the following meanings to attach to the numbers.</p>
|
||||
<blockquote>
|
||||
<pre>
|
||||
AGT Value Meaning
|
||||
0.95 to 1.05 Highly reliable model
|
||||
0.90-0.95 and 1.05-1.10 Good model, adequate for most purposes
|
||||
0.85-0.90 and 1.10-1.15 Fair model, broadly adequate but may be refined
|
||||
<0.85 or >1.15 Poor model, inadequate for most purposes
|
||||
</pre>
|
||||
</blockquote>
|
||||
<p>We shall also be interested in the current magnitude distribution along the wires of the model. Some erroneous models of coaxial dipoles reveal their deficiency by showing both aberrant feedpoint impedance vales and an inappropriate set of current magnitude curves.</p>
|
||||
<p><b>Outer-Wire-Fed Multi-Wire Folded Dipoles</b></p>
|
||||
<p>The folded monopole need not consist simply of two vertical wires with a bridge wire at the top. Because the most familiar form of folded monopole performs an upward impedance transformation to a value that many user do not wish, some designers have increased the number of wires to form 3-, 4-, 5-, and 6-feed-wire assemblies. Rarely do we need to go beyond three outer fed wires to obtain a source impedance compatible with common coaxial cables (50 Ohms). Nevertheless, I extended this exercise to 6 outer fed wires to prepare the way for later models.</p>
|
||||
<p>In fact, the exercise begins with a single-wire monopole as a reference point. Then it proceeds to models with 2 through 6 outer fed wires, all using the same spacing from the center return wire and all forming a regular polygon around the center wire. Each vertical wire uses 25 segments, for a segment length between 9 and 10 mm, depending upon the particular model. Each top bridge wire is the same diameter as the outer wires and the center wire to eliminate errors due to NEC angular junctions of wires having dissimilar diameters.</p>
|
||||
<center>
|
||||
<img src="cofd-m1.gif" width="690" height="317" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>Fig. M-1 shows the EZNEC wire table for one of the models in the series. It uses 4 outer fed wires with a center return wire. The segmentation of the wires is clear, along with the equal spacing of the outer wires. At the bottom of the list is a very short (5-mm long) 1-mm diameter wire. Its function is to serve as the source wire.</p>
|
||||
<center>
|
||||
<img src="cofd-m2.gif" width="660" height="189" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>A single perimeter wire with a single feedpoint does not normally produce equal current magnitudes at the bases of all of the conductors. Even with lossless wire, the length of the wire between the source segment and the bottom of each outer wire differs enough to produce unequal current magnitudes at each corresponding segment among the 4 wires. To ensure parallel feeding of all four outer wires, I use a short wire separated physically from the antenna by an amount sufficient to prevent significant interaction between the antenna structure and the new wire. Between the source wire and each vertical leg to be fed, I run a transmission line, using the NEC TL facility. <b>Fig. M-2</b> shows the lines relevant to the model in <b>Fig. M-1</b>. The significant aspect of the lines is our ability to select a length independent of the actual physical distance between the new wire and the outer wires. Hence, each line has the same length. Moreover, each line is exceptionally short: 0.001-mm in this case. Such a line length is too short to exhibit any impedance transformation relative to the specified source magnitude and phase angle. Hence, the characteristic impedance (Zo) is arbitrary within very broad limits. The 20-Ohm value shows no differences when changed to 50 Ohms, for example. The net effect is to create a virtual short circuit between the source wire and the base segment of each fed leg. Therefore, for a source current magnitude of 1.0, the current magnitude on each base segment is 1/n, where n is the number of fed legs. At the same time, the reported source impedance, within the limits of the AGT value, is the parallel combination of all outer legs.</p>
|
||||
<p>The short-TL method of deriving parallel feedpoints is not strictly necessary. You can place a source in the lowest segment of each out wire, take the average value of all 6 sources and then divide by 6 for a net feedpoint source. The result will be the same. For example, I converted the 7-wire/6-feed model into separate sources and obtained a reported feedpoint impedance of 41.0 Ohms, the same value that appears in the tabulated values below. The short-TL technique simply saves some post-modeling calculations by letting the program do the work.</p>
|
||||
<p>The exercise using models of multi-wire folded dipoles fed on the outer wires produced both reliable models and interesting numbers. <b>Table 1</b> provides the relevant tabular data.</p>
|
||||
<center>
|
||||
<img src="cofd-t1.gif" width="833" height="257" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>Perhaps the most important columns in the table are the ones devoted to the AGT. The single-wire monopole and the 2-wire folded monopole achieve AGT values of 1.000. As we add more fed wires, the AGT values depart from the ideal value, but the more outer and bridge wires that we add, the closer to ideal the AGT becomes. No AGT value is any worse than good, which gives us confidence in applying the correctives. The gain corrective consists of subtracting the converted AGT score (10*log(10)AGT) from the reported gain. The corrected feedpoint resistance results from multiplying the AGT times the reported source resistance value.</p>
|
||||
<p>Although the raw NEC reports might suggest that there are small but noticeable differences in the far-field performance of the various models, the correct gain values show a remarkable equality of gain. The absence of differences between the zero-loss wire models and the copper models gives us greater confidence in this result. The corrected feedpoint impedance values show numerical differences but no operationally significant differences relative to the raw values. The impedance ratio between the single-wire monopole and the 2-wire folded monopole is 3.92:1, where a theoretically perfect value would be 4:1. However, the theoretical calculation does not take into account the 20-mm bridge wire.</p>
|
||||
<center>
|
||||
<img src="cofd-3.gif" width="611" height="407" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p><b>Fig. 3</b> shows two different facets of the series of folded monopoles from 2 to 7 wires total (1 to 6 fed outer wires). First, the required length of the monopole does not change more than about 1% over the sampled range. Second, the resonant source resistance values--both raw and adjusted--undergo an interesting progression downward as we add more fed outer wires. Moving from a 2-wire to a 3-wire model results in a 50% reduction in the feedpoint impedance. However, the impedance ratio for additional fed wires does not keep pace with the increase in the number of fed wires that gradually enclose the center return wire. We might innocently expect the 6-fed-wire model (7 total wires) to show 1/6 the impedance of the 2-wire folded monopole. However, the impedance is about 29% of the 2-wire model value at 41 Ohm reported and 41.9 Ohms corrected.</p>
|
||||
<p>It is likely that the feedpoint impedance of the multi-wire folded dipole could not go below the 36-Ohm value for a single wire monopole. The 6-outer-wire/7-total-wire model does not approach that value largely because it does not provide complete virtual coverage of the center return wire. (If the models had provided complete coverage, the resulting coaxial cable would have a Zo of approximately 115 to 125 Ohms, depending on the exact virtual position of the inner surface of the outer ring of wires.) Nevertheless, the 41-Ohm source impedance of the 7-wire model represents a good benchmark value for use when evaluating other kinds of models of this antenna structure. Part of this status results from its emergence from a model that we may rate as highly reliable by reference to the AGT score.</p>
|
||||
<p>As we increase the number of outer wires, we may also note a change in the current magnitude distribution along the wires, with special attention to the difference between the curves for the fed wires and for the center return wire. <b>Fig. 4</b> shows the progression of relative current magnitudes on each of the sampled models. The single wire monopole provides a standard current distribution that runs from 1.0 at the base to about 0.1 at the top. The reported current does not go to zero in a NEC model, since the virtual sampling point is in the middle of the topmost segment, not at the wire tip. In contrast and easily expected are the current magnitude curves for the 2-wire folded monopole. The curves do not approach zero due to the fact that the assembly yields both radiating and transmission-line currents. The latter reach a peak value at the antenna top end, as the radiating current goes toward zero.</p>
|
||||
<center>
|
||||
<img src="cofd-4.gif" width="500" height="370" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>As we add more outer fed wires to the assembly, we may note changes in the overall current magnitude distribution of the center wire. The 2-wire model shows maximum current on the return wire at the antenna base. The 3-wire model shows nearly equal overall current magnitudes at both ends. By the time we reach 4 wires, the center return wire shows maximum current at the top and minimum current at the base. Additional coverage with outer fed wires simply increases the ratio of top current magnitude to bottom current magnitude. <b>Table 3</b> shows some of the differences as numerical values of the current magnitudes for 2-wire, 3-wire, 4-wire, and 7-wire models. The progression skips a few steps since the rate of change shows dramatically after the assembly consists of at least 4 wires. The table shows the top 6 segments and the bottom 6 segments of each sampled wire or wire set. Note that "top" and "bottom" reverse positions in this extraction from the NEC current tables.</p>
|
||||
<center>
|
||||
<img src="cofd-t2.gif" width="577" height="497" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>The sum of the fed wires results simply from multiplying the current magnitude on 1 of the outer wires by the number of fed wires. The procedure is accurate within the limits of the table. As we increase the number of fed wires, we may note that maximum current does not occur on the lowest segment of the fed-wire set. Rather, it occurs 1 to 2 segments higher. This condition results from the fact that the transmission-line component of the current does not change magnitude or phase angle at the same rate as the radiating current. Therefore, the highest vector sum of these current may not always occur on the source segment.</p>
|
||||
<p>As we move up the fed-wire set of current values, we find that the composite current on the topmost segment (1) systematically decreases as we add more outer fed wires. The same situation occurs at the top of the return wire at the other end of the bridge wires. As we move down the return wire, the 3-wire system's return-wire currents barely manage parity between the top and bottom segments. However, from the 4-wire system upward, the bottom segment of the turn wire shows less current magnitude than the top, and the reduction increases with the number of outer wires.</p>
|
||||
<p>The situation suggests that the behavior of the assembly changes with respect at least to transmission-line currents as we more completely surround the return wire, that is, as we approach a coaxial situation. One way to view the difference quantitatively is to sort the radiating and the transmission-line currents from at least two examples. The first sample uses the 2-wire folded monopole, the current patterns for which should be reasonably familiar. <b>Table 3</b> separates the radiating and transmission-line currents for all 25 segments of the 2-wire folded monopole.</p>
|
||||
<center>
|
||||
<img src="cofd-t3.gif" width="577" height="561" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>The radiating-current column shows a pattern that exactly parallels the current distribution on the single-wire monopole. The only significant difference is that the folded monopole radiating currents change phase angle more than do the single-wire monopole currents (about 13 degrees for the folded monopole and 9 degrees for the single-wire monopole). The transmission-line current on this model shows its highest value at the top end of the structure and the lowest value at the ground plane. The phase angle is nearly a constant 90 degrees with respect to the phase angle of the source current in the model.</p>
|
||||
<p>To apply the same sorting process to the 7-wire model requires that we again multiply the current magnitudes (but not phase angles) of a sample fed wire by 6 to obtain a very close approximation of the total current in the fed wires. We may use the return wire without change. The results appear in <b>Table 4</b>.</p>
|
||||
<center>
|
||||
<img src="cofd-t4.gif" width="577" height="561" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>If we examine the radiating-current column, we find a progression that is almost the same as for the 2-wire folded monopole. Of course, we might wish to increase the maximum value to 1.0, but on a strictly relative scale, we may simply use the values shown and trace the curve from bottom to top. The curve is essentially a typical monopole curve of current magnitude along the wire assembly. The phase angle for the radiating current changes somewhat more radically as we added outer fed wires and reaches about 24 degrees for the 7-wire model.</p>
|
||||
<p>The greatest difference between a standard 2-wire folded monopole and the 7-wire model appears in the transmission-line columns. The 2-wire model showed large changes in magnitude but almost no change in phase angle. The model that approaches (but does not reach) the status of a coaxial assembly reverses the trends. The transmission-line current magnitude shows only a very small change (about 0.15), while the phase angle undergoes nearly a 75-degree change. It is likely that a perfect coaxial system (assuming a velocity factor of 1.0) would show slightly over 80 degrees of phase shift for a structure that is just under 90% of a quarter wavelength. (The bridge wires, at 20-mm each, are more than trivially long.) Although we must be cautious in evaluating the level of success in the model capturing a coaxial system, the small difference between the theoretical limit of phase change and the level achieved in the model is one preliminary measure of success.</p>
|
||||
<p>Hypothetically, we might continue the modeling process by adding further outer wires. However, practical systems that I have encountered have not risen to a 6-fed-outer-wire system. Moreover, such systems generally use thin wires around a large-diameter center return structure (such as a tower), which would present a massive difficulty for NEC. Finally, the use of 6 outer wires results in a spacing between each pair of outer wires that is the same as the spacing between the center wire and each outer wire. The sense of symmetry adds an aesthetic reason for closing the book (at least temporarily) on outer-fed quasi-coaxial systems.</p>
|
||||
<p><b>Center-Wire-Fed Multi-Wire Folded Monopoles</b></p>
|
||||
<p>In theory, we need only shift the position of the source within the 7-wire model to obtain a model of the coaxial monopole with a source on the inner wire so that the outer wires become the returns to the perfect ground. Since all outer wires terminate at the ground, we likely need not retain the TL-based parallel short-circuit among the lowest segments on the outer wires. I shall presume that some such arrangement underlies the models of a coaxial monopole that I have heard about from time to time. Accompanying reports of such models have been commentaries to the effect that the arrangement tends to have a low performance level, almost as if the outer return wires were trapping the energy within the structure. Admittedly, such comments have a casual basis, and the models are not available to me. So at most, we can only see if we can find a reason (not necessarily the reason) why one might reach such a conclusion.</p>
|
||||
<p>Therefore, I constructed a series of models, of which we shall sample two that I classify as potential casual models of a center-wire-fed coaxial monopole with 6 outer wires. The wires and model environment are identical to the conditions set for the outer-feed structures that we have explored. The first sample appears in the EZNEC wire table shown in <b>Fig. M-3</b>. The model uses no transmission lines. The bridge wires at the top of the structure are 20-mm long with the same diameter wire as the vertical legs of the structure. The segmentation is also the same as in earlier models.</p>
|
||||
<center>
|
||||
<img src="cofd-m3.gif" width="690" height="365" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>The outline of the structure appears on the left in <b>Fig. 5</b>. The figure also shows an alternative version of the structure. In order to ensure that the return wires electrically terminate at the end of the segment containing the source, I ended the vertical outer wires 5 mm above ground. From each "loose" end, I ran a 2-segment wire to the bottom of the center wire at the ground-plane level (Z=0). The right-hand outline in <b>Fig. 5</b> should make the plan clear. The wire table in <b>Fig. M-4</b> will confirm the wire structure.</p>
|
||||
<center>
|
||||
<img src="cofd-5.gif" width="359" height="314" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<center>
|
||||
<img src="cofd-m4.gif" width="690" height="464" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>Each of these models uses the vertical leg-length assigned to the 2-wire folded dipole. I did not proceed further in length adjustment because each of these models mis-performs beyond the limits of reliability of the AGT score. The top entries in <b>Table 5</b> show the situation. The model designated M-3 or Top Only has an AGT score of 0.538, when a sensible limit to even a poor but usable model is a score of about 0.85. The model reports an exceptionally low far-field gain value and perhaps underlies the sense that the outer wires somehow trap the energy in the center wire. The problem does not lie in the antenna, but rather in its model. If we use the AGT score as a correction on the gain value, we obtain a quite normal value for a monopole over perfect ground. We obtain further evidence of complete model inadequacy from the gain difference between the version using lossless wire and the version using copper wire. Ordinarily we expect a gain change no greater than about 0.01 dB. Any larger difference indicates significant trouble in the model, which the AGT score confirms.</p>
|
||||
<center>
|
||||
<img src="cofd-t5.gif" width="769" height="321" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>The model called M-4 or Top/Bot suffers an inverse but equal difficulty. The reported AGT score is 2.466, when the limits of a poor but usable model might be about 1.15. The raw gain report seems to promise nearly magical performance in the 9-dBi range. However, if we correct that gain value by reference to the AGT value, the gain drops to a more normal monopole level. Once more, we find an inordinate decrease in the gain of the model version using copper wire relative to the version using lossless wire, another indication of the model's inadequacy.</p>
|
||||
<p>In both casual models, the reported source data falls well outside of what we might expect, if we use our experience with outer-fed 7-wire models as a reference. Moreover, adding a corrected source resistance column would only exacerbate the difficulty. The low AGT value for M-3 would reduce the already low raw impedance value even further. Likewise, the high AGT value for M-4 would raise an already high value of source impedance. Moreover, the high value of reactance in the reported source impedance does not decrease to zero until the model height shrinks to the 80-85-mm region, and even then, the impedance is unstable. Very small changes in height create very large changes in the reactance value.</p>
|
||||
<p>The casual models, then, prove to be wholly inadequate to capture the performance of a center-wire-fed 7-wire monopole structure. <b>Table 5</b> also contains performance reports on three models (out of many that I constructed along the way) that may prove more useful. I modeled them to yield reasonable gain values, good AGT scores, and source impedance values that seem to be relatively typical for 7-wire folded structures. Hence, I call them careful models, but not necessarily ideal models. Each model records an AGT of 1.000, since nothing in the structure comes close to pressing any NEC limit. All of the wires use a simple straight uniform diameter geometry. <b>Fig. 6</b> shows some suggestive outlines.</p>
|
||||
<center>
|
||||
<img src="cofd-6.gif" width="400" height="350" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>Model Top-Bot forms the baseline for the series. At the top, it eliminates the bridge wires and replaces them with TL short circuits of the same type used for the feed system of the outer-fed monopoles. However, each top TL runs between the top segment of the outer wire and the top segment of the center wire. At the base of the model, I also used TL short circuits to connect together the lowest segments of the outer wires. The only difference between these TL entries and those of <b>Fig. M-2</b> is that the source is not on the external junction wire, but on the lowest segment of the center wire. This model forms perhaps the key comparator with the performance of the 7-wire outer-fed monopole.</p>
|
||||
<p>The data in <b>Table 5</b> shows very normal gain performance. The slightly high gain value (by 0.03 dB) results from the fact that the overall height of the model is taller than the models for the corresponding outer-fed monopole. In fact, the length is about as much longer than the single-wire monopole as the outer-fed systems are shorter than the single wire monopole. The extra length stems from replacing the bridge wires--which do affect current distribution--with TL shorts that have no practical length. The correlation cannot be precise because the TL connections extend from the virtual centers of the segments to which they are attached, and each segment is between 9 and 10 mm long.</p>
|
||||
<p>The reported feedpoint impedance is about 45.2 Ohms, only slightly higher than the value yielded by our final outer-fed model. As a consequence, we may account this model to be a reasonable facsimile of an actual center-fed 7-wire folded monopole. For functional analyses, the model may prove sufficient. However, it is not perfect, since the replacement of bridge wires at the top with TL shorts modifies the current distribution relative to a physical structure. The modification becomes more evident if we sort out the radiating and transmission-line currents, using the same method employed for the corresponding outer-fed 7-wire model. Compare <b>Table 4</b> with the data in <b>Table 6</b>.</p>
|
||||
<center>
|
||||
<img src="cofd-t6.gif" width="577" height="561" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>The radiating current column shows a progression of magnitude values not very different from the ones in the earlier table. Indeed, one might account any magnitude differences to the slight height differences between the two models. The change in radiating current phase angle is somewhat greater than in the outer-fed model, but does not reach suspicious or doubtful levels. The key difference lies in the transmission-line current columns, especially in the range of phase angles from bottom to top. The outer-fed system showed a considerable (74-degree) shift in phase angle, while the center-fed model shows slightly less than 45 degrees. It is likely that the bridge-wire replacement with TL shorts is the major source of the difference, but the degree of error attributable to each model remains unknown in the present context.</p>
|
||||
<p>Both the center-fed and the outer-wire-fed models show impedances in the 40-45-Ohm region. The curves shown by <b>Fig. 3</b> suggest that a truer coaxial structure would gradually approach the source impedance of the single-wire monopole. Therefore, I performed a 2-step experiment, adding TL shorting structures around the outer wires of the center-fed model. The first step added a set of shorts half way up the structure. The final step added two more encircling shorts at the one-quarter and three-quarter length points. <b>Fig. 6</b> shows the outlines of these models, while the final lines of <b>Table 5</b> provide the resulting data. Since the TLs add nothing to the actual geometry, they do not affect the AGT score.</p>
|
||||
<p>As we add the TLs, the resonant height of the structure decreases somewhat. As a consequence, the reported maximum far-field gain also decreases slightly. Perhaps more significant within this context is the continued decrease in the source impedance value. The final figure in the table is almost identical to the value for a single-wire monopole. However, we should not too quickly equate the two, since the effective diameter of the 70-wire model is many time the diameter of the single-wire monopole.</p>
|
||||
<p>The final models are an attempt (but not necessarily a fully successful one) at capturing the performance of a true coaxial monopole composed of a center wire and a virtually solid outer shell. The model suggests that the idea of a coaxial monopole is sound. The radiating (or common-mode) currents yield normal operation for a monopole. At the same time, the transmission-line currents remain within the structure, that is, between the outer surface of the inner conductor and the inner surface of the outer conductor. The short circuit at the monopole top ensures that the impedance at the bottom will be a parallel combination of a very high impedance value 1/4 wavelength from the short and the resonant monopole impedance. The result, under ideal conditions, would simply be the monopole impedance.</p>
|
||||
<p>The simplified impedance analysis presumes a velocity factor of 1.0 and no further geometric disturbances to the structure. However, bridge wires at the top of the structure modify the current distribution. If we add the normal material found within real coaxial cables, the current distribution may show further non-ideal conditions. Therefore, cutting a real coaxial monopole to length and still having a usable impedance value may prove to be a somewhat finicky task. Nevertheless, the existence of successful coaxial collinear monopoles and dipoles attest to that fact that the task is feasible.</p>
|
||||
<p><b>Conclusion</b></p>
|
||||
<p>Our goal has been to explore the possibility of modeling the coaxial monopole. To that end, we set up a test environment over perfect ground and created a series of models at 299.7925 MHz. The first series used well-established techniques for parallel feeding the outer wires of such systems while adhering to tight NEC guidelines for equality of diameter throughout the model. These models showed that we can model structures using up to 6 relatively fat outer wires and obtain results that both are reasonable and show a progression of feedpoint values and other transitions toward a true coaxial situation.</p>
|
||||
<p>We next turned to center-fed models and had to modify the antenna geometry and the method of connecting wires to avoid wholly unreasonable AGT values. One result was a model that replicated very closely the performance of the corresponding outer-fed model, while preserving an ideal AGT score. We further pressed the center-fed model toward true coaxial conditions, but remained cognizant of limitations other than the AGT score they may reduce the accuracy of the model relative to a physical implementation of a coaxial monopole.</p>
|
||||
<p>Since there is a theoretical (tight) and practical (rough) equality between the outer-fed and the center-fed 7-wire models, the choice of which to use within a more complex structure remains a modeler option. In some ways, the 7-wire outer-fed model may be simpler and more direct to use when modeling such arrays as the coaxial monopole or dipole. Notwithstanding, the exercise has demonstrated that there are ways to model both feedpoint positions with multi-wire folded monopoles.</p>
|
||||
<center>
|
||||
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
|
||||
</center>
|
||||
<p><i>Updated 03-01-2007. © L. B. Cebik, W4RNL. The original item appeared in</i> AntenneX <i>for February, 2007. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.</i></p>
|
||||
<center>
|
||||
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
|
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</center>
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<h1><img src="../images/yagicad.gif" align="left" width="125" height="62" border="2" vspace="5" hspace="25">Notes on Modeling and Convergence Testing <img src="../images/antbott.gif" align="right" width="150" height="77"></h1>
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<h3>L. B. Cebik, W4RNL</h3>
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Every commercial method of moments antenna modeling software manual warns the user to perform convergence testing to validate to the extent possible the reliability of the model. Many such packages also offer automatic wire segmentation, using algorithms developed from the basic NEC criteria for recommended minimum segment lengths. Unfortunately, for many users, the two facilities come into conflict, and convergence testing loses out. In fact, convergence testing should always take priority over the modeling speed made possible by automatic segmentation of wires.
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<p>Convergence testing is the process of increasing the number of segments in each wire of a model until the program output values change by only insignificant amounts relative to the purpose of modeling. Notice that what counts as satisfactory convergence may vary according to what the modeler wants to get out of the exercise. Among the most used outputs are gain, front-to-back ratio, feedpoint impedance, and antenna current magnitudes and phases.</p>
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<p>Every antenna model should be tested for convergence of results. Otherwise a model cannot be counted as a reliable indicator of antenna performance, with resultant uncertainties about construction, adjustment, or evaluation. However, convergence testing should only occur after certain basic good modeling practices have been employed. To the degree permitted by the antenna structure, antenna segments in parallel and almost parallel wires should be aligned. The wire containing the feedpoint should be examined to ensure the correct source type--single or split--according to the segmentation and desired source position. Segment length minimums should be checked at the highest frequency of interest. For greatest utility of all program outputs, segmentation should begin at one consistent end of each element and progress in the same direction until reaching the other end of the element. For some types of antennas with linear elements, the only difficulty posed by violating this practice may be reading the current levels and phases on each wire of the model. For antennas with phasing networks built into the model or with certain orders of complex geometry, almost all outputs may become erroneous if consistent wire construction practices are not followed.</p>
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<p>Once the model is in good order, convergence testing can begin. Some models may show convergence with the first increase in segmentation. Some may require only 2 or 3 test steps. Others may require many steps. Finally, some models may never converge. A model that fails to converge over critical performance outputs cannot be considered reliable at any segmentation without some external standard.</p>
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<p>Here are some examples of convergence results taken on EZNEC, which permits automatic segmentation at two levels: a level of absolute minimum numbers of segments per half wavelength (Smin) and a level of recommended or conservative numbers of segments per half wavelength (Scon). It is always tempting to model at the least possible number of segments, since every extra segments adds to the time required for NEC to make its matrix calculations. So we shall begin each sample model with the absolute minimum segmentation to see what happens. Besides Smin and Scon, we shall use the following abbreviations: Saligned = segments equalized in length and aligned with those of parallel elements; Sx## = the segmentation of Scon multiplied by the number ##.</p>
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<p>1. A dipole element for 20 meters with many steps in diameter. Note: many versions of NEC-2 contain a stepped-element diameter correction algorithm, since NEC-2 produces unreliable results without it. NEC-4 handles stepped diameters directly. In this example, NEC-2 results are used. We shall look only at the feedpoint impedance of this free space model</p>
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||||
<pre>Model Total Segmentation Feedpoint Z (R +/- jX) in ohms
|
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Smin 9 81.5 + 39.3
|
||||
Scon 15 81.1 + 39.5
|
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S aligned 21 81.3 + 40.2
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</pre>
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<p>Clearly, for most purposes, such as building the antenna element in question, data produced by the minimal model is quite reliable. This is generally true of one-element linear antennas, although for multi- wavelength antennas, higher levels of segmentation may be needed.</p>
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<p>2. To the element of example 1., we might install a center section 2 or more times the diameter of the adjacent sections to simulate boom mounting hardware.</p>
|
||||
<pre>Model Total Segmentation Feedpoint Z (R +/- jX) in ohms
|
||||
Smin 11 78.5 + 29.6
|
||||
Scon 15 79.7 + 31.8
|
||||
S aligned 21 80.0 + 32.5
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</pre>
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<p>Although the model seems sufficiently reliable for most purposes at all level of segmentation, note the differentials in values for each step of increase. The decrease of difference between the Scon and S aligned levels is precisely the definition of convergence. Here, the difference may make no practical difference, but it might for an antenna of which this element is but one of many.</p>
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<p>3. Let's look at a 5-element Yagi using the element in example 1 as the driven element.</p>
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||||
<pre>Model Total Gain F-B Ratio Feedpoint Z
|
||||
Segmentation in dBi in dB (R +/- jX) in ohms
|
||||
Smin 45 10.1 24.3 38.9 + 23.5
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||||
Scon 69 10.2 23.9 38.4 + 22.8
|
||||
S aligned 102 10.2 23.7 38.4 + 22.6
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</pre>
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<p>Since the Yagi elements are linear and gently tapered, the results achieve almost instant convergence at a practical level.</p>
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<p>4. Lest we grow overconfident that convergence is an easy thing to achieve, consider the following 2-element beam using an extended double Zepp driven element and a pair of reflectors, one at each extremity of the driven element. The elements are quite closely spaced. These figures are for a height over medium ground of 50 feet on 20 meters. Elements are #12 copper wire and begin well aligned.</p>
|
||||
<pre>Model Total Gain F-B Ratio Feedpoint Z
|
||||
Segmentation in dBi in dB (R +/- jX) in ohms
|
||||
Smin 24 12.9 12.1 93.6 - 1297
|
||||
Scon 46 12.8 12.5 80.3 - 1120
|
||||
S x 1.5 70 12.8 12.5 68.9 - 1016
|
||||
S x 2 92 12.8 12.4 66.6 - 992
|
||||
S x 2.5 114 12.8 12.4 64.9 - 976
|
||||
S x 3 138 12.8 12.4 62.5 - 956
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</pre>
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<p>In this exercise, checking only the gain and front-to-back ratio would have misled us into thinking that the model had achieve convergence at an early stage--perhaps between the Scon and S x 1.5 levels. However, suppose we plan to stub-tune the antenna. Stub construction requires a reasonably accurate measurement or forecast of feedpoint impedance. This particular model achieves convergence at the 1.5-2% level only as we increase segmentation considerably. Had we used the feed impedance provided by the conservative auto-segmented model, our initial stub would have been way off the mark. In short, before ended a convergence test, be sure to check all of the relevant output data.</p>
|
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<p>5. Let's try a single quad loop. To make matters interesting, we shall make it square, with the horizontal members made from 0.5" diameter tubing and the vertical members from #12 wire. We shall feed the center of the bottom horizontal section and place the whole thing in free space. Here is what we get within the limits of most ham versions of NEC-2.</p>
|
||||
<pre>Model Total Gain Feedpoint Z
|
||||
Segmentation in dBi (R +/- jX) in ohms
|
||||
Scon 28 3.61 154 + 81
|
||||
S x 1.5 44 3.60 158 + 91
|
||||
S x 3 84 3.59 164 + 108
|
||||
S x 4.5 124 3.58 168 + 119
|
||||
S x 9 244 3.57 175 + 140
|
||||
S x 16 444 3.56 183 + 161
|
||||
[MININEC 240 3.61 137 - 6]
|
||||
[MININEC 56 (tapered lengths)
|
||||
3.61 137 - 2]
|
||||
</pre>
|
||||
<p>In this example, convergence is never achieved with respect to feedpoint impedance, even though the gain stabilizes from the beginning. Consequently, there is no internal evidence produced by NEC-2 that any of the output data is reliable.</p>
|
||||
<p>By importing an external standard, we can judge that the smallest segmentation produces outputs closest to reality for cases in which NEC-2 encounters angularly joined wires of different diameters. MININEC is the standard used here, and by its internally correlated figures it suggests that at any level, the feedpoint impedance figures of NEC-2 are unreliable for this type of case.</p>
|
||||
<p>Knowing in what cases a modeling program yields unreliable data is just as important as making good use of reliable data. Convergence testing is one method of establishing the reliability of some data and the unreliability of other outputs.</p>
|
||||
<p>The examples, may be multiplied, and perhaps from time to time, I shall add others. In the meantime, I hope this little survey clarifies the principles of convergence testing and helps make it a part of every modeling exercise.<br>
|
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<br></p>
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<p><a href="../radio.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Return to Amateur Radio Page</a></p>
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<title>Notes on Dipole Convergence</title>
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<h1><img src="../images/w4rnlwwr.gif" align="left" width="99" height="83" border="2" vspace="5" hspace="10"><img src="../images/antbott.gif" align="right" width="150" height="77">Notes on Fat-Wire Dipole Convergence:<br>
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MININEC, NEC-2, NEC-4</h1>
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<h3>L. B. Cebik, W4RNL</h3>
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<p>A standard dipole at HF made from commonly used materials can be accurately modeled in any of the NEC-based programs using minimally recommended segmentation. Convergence testing (increasing the segmentation density) confirms the accuracy of the model for virtually any purpose the model might be used.</p>
|
||||
<p>Similar behavior is often expected from dipoles of increasing diameter, for example up to 1' at 14 MHz. 2 * PI * radius (circumference) / wavelength must be much less than 1, a condition easily met by this large dipole. MININEC prefers the largest minimum segment length to diameter ratio: 1.25:1. This condition is easily met if the segmentation density is about 40 per half wavelength or less.</p>
|
||||
<p>Even within program limitations, however, the modeler encounters some interesting program-to-program variations that are worth noting. They may not be operationally significant in terms of model reliability. Still, they will increase our awareness of program tendencies and trends, thus enabling the modeler to view a certain set of progressions as either expected or unusual.</p>
|
||||
<p>To see what happens with fat dipoles, I systematically modeled a sequence of resonant dipoles at 14.0 MHz. Since I was interested in the numerical progressions (rather than operationally-relevant limitations), I defined resonance as a source reactance of less than +/-0.01 Ohm. This permitted very small variations in resonant length to show up with normal graphing means. To encompass the widest range of diameters in the smallest span of runs, I used a semi-logarithmic progression of diameters: 0.0843, 0.2666, 0.8431, 2.6660, and 8.4306 inches. Remember that the point of this exercise is numeric: therefore, outputs will be recorded to more decimal laces than within a practical modeling exercise.</p>
|
||||
<h3>MININEC 3.13</h3>The MININEC graph of results for free space dipoles of zero-loss wire demonstrates an unexceptional progression of lengths through convergence from 10 to 40 segments per half wavelength. The following table shows the segment length related to a median dipole length of 400" and the resultant length-to-diameter ratios for the graph.
|
||||
<pre>Segments Length/ Ratio of Segment Length to Wire Diameter
|
||||
Segment" 0.0843 0.2666 0.8431 2.6660 8.4306
|
||||
10 40.00 474.50 150.04 47.45 15.00 4.75
|
||||
20 20.00 237.25 75.02 23.73 7.50 2.37
|
||||
30 13.33 158.17 50.01 15.82 5.00 1.58
|
||||
40 10.00 118.62 37.51 11.86 3.75 1.19</pre>
|
||||
<p>As is evident, segment lengths and wire diameters were selected based on a wavelength at 14.0 MHz, 843.0611 inches. The smallest wire diameter is close to the diameter of #12 AWG copper wire (0.0808").</p>
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||||
<center>
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<img src="conv-1.gif" width="639" height="516" border="2" vspace="5" hspace="9">
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<p>MININEC results are entirely unexceptional. As the dipole diameter increases, the rate of decrease in resonant length with increasing segmentation is greater. However, the largest single change in value occurs between segmentation densities of 10 and 20 per half wavelength. For the thinnest wire, the difference between the least and most segmented wires is a little over 0.3" in length, while for the fattest wire, the difference is a bit over 3.5" in length.</p>
|
||||
<p>The line for the 0.84306" diameter wire is virtually linear between segmentation densities of 10 and 40. Lines for thinner wires show an upward trend between densities of 10 and 20, while lines for fatter wires show a downward trend in the same region. Nonetheless, the variation from linearity for the 100:1 range of diameters is quite small. Moreover, the curve for the fattest wire, even though it exceeds the limitation of MININEC for diameter to segment length, shows no radical departure from the general trends.</p>
|
||||
<p>For this and NEC tests, similar runs were made using wires with some material loss (aluminum). No detectable difference in the trends was noted, so no further reference to them is needed here.</p>
|
||||
<p>The version of MININEC used (3.13) is uncorrected for the 0.5% frequency shift relative to NEC-2 and NEC-4. Frequency correction would have changed the absolute values of resonant dipole length, but not the trends recorded on the graph.</p>
|
||||
<p>So far, our investigation has made a colorful graph, but otherwise has been seemingly devoid of interest. It acquires interest only as we compare it with NEC.</p>
|
||||
<h3>NEC-4</h3>The corresponding graph for NEC-4 adhered as closely as possible to the same standards as the one for MININEC. However, segmentation was increased by 1 to ensure that the source placement would be centered. This altered the table of segment lengths and the ratios of segment length-to-diameter in the following way:
|
||||
<pre>Segments Length/ Ratio of Segment Length to Wire Diameter
|
||||
Segment" 0.0843 0.2666 0.8431 2.6660 8.4306
|
||||
11 36.36 431.29 136.38 43.13 13.64 4.31
|
||||
21 19.05 225.96 71.46 22.60 7.15 2.26
|
||||
31 12.90 153.01 48.39 15.30 4.84 1.53
|
||||
41 9.76 115.77 36.61 11.58 3.66 1.16</pre>
|
||||
<p>The corresponding graph of NEC-4 runs with a free space dipole of lossless wire at 14.0 MHz yields some interest results, if we look closely.</p>
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<center>
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||||
<img src="conv-2.gif" width="639" height="517" border="2" vspace="5" hspace="9">
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</center>
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<p>For all but the fattest wire, the curves are very well behaved. There is only 0.2" difference between the shortest and longest resonant dipoles for the thinnest wire and less than 0.8" difference for a wire over 2.5" in diameter. These figures are more tightly grouped than the corresponding figures for MININEC.</p>
|
||||
<p>However, if we examine the curve for the fattest wire, its behavior should arouse some curiosity. The curve is at every point the opposite of the curves for the other wire diameters. This behavior is not a function of having passed a certain program limit, since only the highest level of segmentation density surpasses the limit we set for MININEC. Moreover, the rate of change for the fattest wire is nearly three times the rate for the next size lower.</p>
|
||||
<p>Somewhere between the two largest diameters explored in this general test, the NEC-4 curves changed direction. The nature of the change called for more detailed modeling of intermediate values. So I checked wire diamters between 3.0" and 7.5" in diameter. Some key results for the x.5" values are shown below.</p>
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||||
<center>
|
||||
<img src="conv-3.gif" width="640" height="520" border="2" vspace="5" hspace="9">
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||||
</center>
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||||
<p>The graph of intermediate values of wire diameter shows how the curvature changes. The curves show that for any wire diameter, the downward trend typifying thin wire dipoles is only temporary. With increasing segmentation such that the wire diameter grows closer to the segment length. there is a relationship that yields the lowest resonant dipole length. This value is in the vicinity of 0.3 for the ratio of diameter to segment length. For both higher and lower values of the ratio, the resonant length tends to increase.</p>
|
||||
<p>The results of this sequence of models can be replicated at any frequency by scaling both the length and the diameter of the wire along with the frequency. Runs made at 28 MHz with wires of half the diameters resonated within limits with exactly half the length of those used in the 14 MHz test. The ratio of segment length to diameter remained the same. The behavior of the curves is endemic to NEC-4.</p>
|
||||
<p>The result has some implications for convergence testing with relatively fat wires. The fatter the wire, the less applicable the convergence test. First, increasing the number of segments per half wavelength more quickly approaches the implicit length-to-diameter limit of the program. Second, the rate of rise in resonant length for the fattest wires suggests that convergence will not be obtained in some cases.</p>
|
||||
<p>Despite these results, nothing peculiar arises with respect to either reported gain (2.12-2.14 dBi free space gain throughout) or source impedance (total range: 71.82 to 73.16 Ohms resistive). Hence, although the behavior of the NEC-4 curves is quite interesting, little of operational significance emerges from it beyond the realm of convergence testing.</p>
|
||||
<h3>NEC-2</h3>The curves for NEC-2 are singularly uninteresting for all diameters except the fattest (8.43"). In fact, they overlay the NEC-4 curves better than most gloves do hands. Hence, for all values up to about 2.5" diameter wires, the NEC-4 curves may also be called the NEC-2 curves.
|
||||
<p>However, for the fattest wire, there is a notable difference in the behavior, as shown in the following graph:</p>
|
||||
<center>
|
||||
<img src="conv-4.gif" width="636" height="519" border="2" vspace="5" hspace="9">
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||||
</center>
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||||
<p>The NEC-4 curve is identical to the one on the general graph, but expanded by the graphing system. The NEC-2 curve, however, resembles most the NEC-4 curve for a wire of 5.5" diameter. In short, with respect to dipoles, NEC- 2 is somewhat better behaved when it comes to fat wires in isolation, possibly by a factor of 1.5. The shortest resonant dipole length appears to occur when the diameter is about 0.4 to 0.5 the segment length.</p>
|
||||
<h3>Conclusion</h3>No significant conclusions emerge from this inquiry other than those to be found in the graphs. MININEC, NEC-2, and NEC-4 each respond differently to increases in segmentation density when wires of very large diameter (relative to frequency) are involved. Understanding these differences will at most reduce the number of surprises we encounter while modeling, and thus let us devote more time to the design exercise and less to wondering if we have done something wrong. This exercise in systematic modeling has at least satisfied a curiosity.<br>
|
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<p><i>Updated 3-11-98. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.</i><br>
|
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<title>Some Pitfalls of Careless dBd-ing</title>
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<h1><img src="../images/antbott.gif" align="left" width="150" height="77"><img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10">Some Pitfalls of Careless dBd-ing</h1>
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<center>
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<h3>L. B. Cebik, W4RNL</h3>
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<br>
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<p>In an earlier note on <a href="dbi.html">why I use dBi--mostly</a>, written over 2 years ago, I distinguished several possible meaning for dBd, each of which was distinct.</p>
|
||||
<p><b>dBd-I (Ideal)</b>: Since a free space lossless infinitely thin-wire dipole has a gain of 2.15 dBi (Isotropic), this interpretation of dBd simply subtracts 2.15 from the gain in dBi and presents a gain number. It has no application except in free space.</p>
|
||||
<p><b>dBd-RM (Real Model)</b>: A dipole constructed of the same material as an antenna used for comparison and placed in a model at the same height over the same ground type may make a meaningful comparison. Many antennas with directional patterns (Yagis, for example) do not experience the same gain fluctuations as a dipole does at varying heights below 2 wl, so the comparison must be used with caution. By judicious selection of heights without revealing those numbers, one can make a given antenna look up to 0.5 dB better than itself.</p>
|
||||
<p><b>dBd-RR (Real Range)</b>: A range test will use a relevantly similar dipole as a comparator for horizontally polarized gain antennas under carefully controlled test circumstances and procedures. Since the range test cannot use an isotropic radiator as the baseline comparator, translation of range tests into dBi is only dome with caution and often may be dispensed with altogether.</p>
|
||||
<p>One of the difficulties of dealing with live claims of antenna (especially Yagi) gain given in dBd is that the sources rarely tell us which--if either--sensible meaning of dBd is being used. So we are left to our own devices in evaluating these claims. One major exception has been the independent comparative studies of N0AX and K7LXC (<b><i>HF Tribander Performance</i></b>, now in its 2nd expanded edition), which has used a thoroughly discussed and consistent methodology throughout. Even if one should disagree with any of the results obtained, one has at least a firm foundation for resolving outstanding issues.</p>
|
||||
<h3>Trying to Have Reasonable Expectations</h3>Having a set of expectations for what is sensible by way of gain claims, whatever the baseline for the claimed gain, is a challenge. There are some guideposts that can assist us.
|
||||
<p>1. Jim Lawson, W2PV, established in his classic, Yagi Antenna Design, that gain is a function of boom length and that for any given number of elements, there is a maximum gain length, after which gain tends to level of fall off. The maximum gain figures obtainable are accompanied by a quite narrow operational bandwidth over which they obtain and also by mediocre front-to-back (or front-to-rear) figures. More realistic gain expectations run at least 1 dB below maximums when accompanied by a satisfactorily broad operating bandwidth and a reasonable front-to-back ratio--usually expressed in terms of a 20 dB standard.</p>
|
||||
<p>However, if we are not careful, we can misuse Lawson's work by putting into out minds a single figure for a given boom length and forgetting the bandwidth aspect of the situation.</p>
|
||||
<p>2. Programs like YA (the K6STI variant of his full featured YO Yagi Optimizing program) can develop a good sense of what is sensible with Yagi design, using the N6BV optimized designs plus some others of local origin. The key is to use the graphical outputs to supplement number sets in order to understand the performance of Yagis across a desired bandwidth.</p>
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||||
<center>
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<img src="dbd-1.gif" width="318" height="349" border="2" vspace="5" hspace="9">
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||||
<p><b>Fig. 1</b> shows the gain and front-to-rear performance of a 3-element Yagi on a 0.22 wl boom (about 8') for the 10-meter band. Note that the gain climbs steadily across the band from below 7.2 dBi to nearly 7.5 dBi. I this design, the front-to-rear ratio creates a plateau, with a rapid fall-off at either end of the band covered.</p>
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<img src="dbd-2.gif" width="318" height="349" border="2" vspace="5" hspace="9">
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||||
<p>In <b>Fig. 2</b>, we have essentially a scaled version of the same antenna (0.22 wl boom, about 16') for the 20-meter band. The gain progression yields quite similar numbers, and the front-to-rear plateau is simply displaced in the band slightly, relative to the 10-meter curve.</p>
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<p>If we lengthen the boom to about 0.33 wl (about 24'), we can obtain additional gain, as shown in <b>Fig. 3</b>. As with most 3-element deigns, the gain increases across the band from about 7.95 dBi to 8.4 dBi. In this design, the front-to-rear ratio peaks at a very high value, but at the upper end of the band it drops to about 18 dB.</p>
|
||||
<p>If we compare antenna gains in terms of dBd-I--since these are free space models--then the 0.22 wl beam provides a gain range of 5.0 to 5.3 dBd-I, while the longer boom model runs from 5.8 to 6.2 dBd-I. Note that these numbers apply to aluminum elements that are full length. On 20 meters the maximum reflector length is about 34.5', while on 10, the same element is over 17' long.</p>
|
||||
<p>In general, these are quite good numbers considering the composite specification requirements for gain, front-to-rear ratio, and operating bandwidth. (It should be clear that I am ignoring matching considerations in this discussion.)</p>
|
||||
<p>Triband Yagis of boom lengths similar to those used in the examples can approach the monoband figures, but only through the use of added elements--which may take a number of forms. Out-of-band elements may contribute to gain on a given band if their positions provide some "forward stagger" effect. Negative effects of an out-of-band element can be (sometimes) overcome by the careful placement of a compensating in-band element. In evaluating tribanders, we should look at the boom length as a fraction of a wavelength for each band covered and develop gain standards accordingly.</p>
|
||||
<h3>Using Our Expectations</h3>I recently ran into some interesting gain claims for a pair of triband Yagis, each with 3 elements. The gain numbers looked like the following:
|
||||
<pre>Antenna A B
|
||||
Gain: 10 m 4.5 dBd 5.5 dBd
|
||||
Gain: 15 m 3.9 dBd 4.5 dBd
|
||||
Gain: 20 m 3.2 dBd 4.0 dBd
|
||||
Boom length 6.0' 9.8'
|
||||
Longest element 16.8' 12.3'</pre>
|
||||
<p>Nowhere did I find any basis for these numbers, so my only recourse was to assess the claims against what I have learned about Yagis from modeling several hundred of them and building a number of the models in to functioning antennas.</p>
|
||||
<p>Let's look at the higher claims for antenna B first. The 10-meter gain claim exceeds that obtained for the 0.22 wl boom monobander, even at its peak. However, the boomlength of B is 0.27 wl on 10 meters, so the gain claim has some initial plausibility. However, the elements are only 3/4s full size. Shortening elements of any dipole-based antenna array, such as the Yagi, will result in some slight gain reduction per element, which is cumulative. These numbers do not specify how the elements are electrically lengthened to full size--or even if the entire element is functional on 10 meters.</p>
|
||||
<p>On 15 and 20 meters, the elements diminish to a maximum of one-half and one-third full size. The boom length reduces to 0.22 wl and 0.14 wl for 15 and 20, respectively. The gain of a 2-element Yagi (driver and reflector) using full size elements will be about 6.2 dBi or 4.0 dBd-I in free space for a spacing of 0.12 to 0.15 wl. That gain will vary across the band, and since it lacks a director, the gain will fall with increasing frequency. Yet antenna B, with element only 1/3 full size and no specification of the means of electrical lengthening claims the same gain.</p>
|
||||
<p>The claims of antenna A are more modest. On 10 meters, the claimed gain is about the peak gain of a decent 2-element monoband beam using the same boom length--6 feet. This antenna uses elements that are full length on 10 meters, but once more does not in these numbers specify how much of the element is active on each band.</p>
|
||||
<p>On 15 and 20, the elements shrink to 3/4 and 1/2 full size, but once more, without specification of electrical lengthening methods or the amount active on each band. The boom length shrink to 0.135 wl and 0.085 wl on 15 and 10, respectively.</p>
|
||||
<h3>What's a Poor Consumer to Conclude?</h3>Note that I have not claimed anywhere that these antennas do not achieve their claimed figures. If dBd-I is the operative notion of gain involved and if applied in free space, then it is possible that the designs might achieve these numbers as a peak figure. That they achieve such gains as a band average is dubious, because shortened elements and shortened booms tend to reduce operating bandwidth (regardless of SWR bandwidth) very significantly. Moreover, element placement for a given monoband design is a function of placement on the boom in terms of fractions of a wavelength, and using a fixed physical dimension placement tends to result in lesser performance of the bands for which placement is not optimal.
|
||||
<p>Of course, if dBd does not mean dBd-I, then this entire exercise is meaningless. However, so too are the gain numbers claimed, since they have no reference. Even should someone to claim, "This is what I measured on the range," (that is, used dBd-RR), we would have to have a complete description of the test methodology and the dipole used as a comparator before we could begin to assess the numbers.</p>
|
||||
<p>If the numbers refer to dBd-RM, then--of course--one wants to see the models used and to assess them for oneself. That would require the revelation of far more technical detail than is usually made available to potential buyers. We may note again in these numbers the absence of data regarding the active length of each element on each band and the method of electrically lengthening elements to full size.</p>
|
||||
<p>Hence, for the case study used here, one must regretfully conclude that in the absence of much more extensive data, the numbers are meaningless. Of course, one set of meaningless numbers compared to another set of meaningless numbers yields a meaningless comparison. From the claimed figures we learn nothing about the respective antennas--except the length of their longest elements and their boom lengths. Unspecified used of dBd for gain claims too often leads to just this result.</p>
|
||||
<p>However, even had the numbers been given in dBi, one still would have had to know a great deal more before those numbers would have been in any way informative. Spot numbers--even based on published models or tests--are potentially misleading. Curves across a desired operational bandwidth are far more informative.</p>
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<p><i>Updated 6-3-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.</i></p>
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<p><a href="../radio.html"><img src="../images/rtnhome.gif" align="bottom" width="40" height="40"> Return to Main Index</a><br></p>
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<p class="topics-footer">Topics: <a href='../topics.html#modeling'>Modeling</a></p><br>
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<title>Why I use dBi - Mostly</title>
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<h1><img src="../images/antbott.gif" align="left" width="150" height="77"><img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10">Why I use dBi - Mostly</h1>
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<h3>L. B. Cebik, W4RNL</h3>
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<p>Although current commercial practice is to specify antenna gain in dBd, I tend in my modeling work to use dBi. It is reasonable to ask why, if for no other reason than to understand better the other entries in this collection of notes. So I shall explain why. My object is not to get anyone to change their preferred ways, but only to make a little clearer my preference for specifying gain in dBi.</p>
|
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<center>
|
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<h3>dBi</h3>
|
||||
</center>Every measure in decibels, or dB, is ultimately a relative power measurement (with some defined relative voltage and current measures having been derived from the basic power measure). Decibels are defined this way:
|
||||
<center>
|
||||
Relative power in dB = 10 log (base 10) P1 / P2,
|
||||
</center>
|
||||
<p>where P1 and P2 are two power levels measured in the same units (e.g., watts).</p>
|
||||
<p>Since we may pick any two powers for P1 and P2, power gain or loss is strictly relative.</p>
|
||||
<p>However, we have found it useful to select--for specific purposes--certain baseline power levels. One such level is whatever power there might be in the radiation far field of an isotropic radiator. An isotropic radiator is a lossless dimensionless point in free space that radiates equally well in all directions. Although some say this is a absolutely theoretic concept only, Brian Beezley, K6STI, has established that a pretty good approximation of an isotropic radiator can actually be constructed.</p>
|
||||
<p>Using this radiator as the baseline and taking measurements at the same far field distance from the antenna, the power received from the antenna will have a certain relative level in comparison to what would have been received from the isotropic radiator. What that level is depends on the characteristics of the test antenna and the direction in which we choose to take the readings, using a full 3-dimensional sphere as the possible directions for readings. In some directions we may get more power; in others we may receive less.</p>
|
||||
<p>One of the chief advantages of the isotropic radiator is that its field never changes, so that it functions as an agreed upon constant against which every antenna may be measured in every direction.</p>
|
||||
<p>Every antenna measurement referenced to a P2 that is the far field power from an isotropic radiator has a positive or negative gain in dBi.</p>
|
||||
<center>
|
||||
<h3>Gain</h3>
|
||||
</center>When we casually refer to antenna gain, we do not normally mean the gain in any haphazard direction from the test antenna. Nor do we mean all the possible gain numbers we might gather from a systematic tour around the surface of our far field globe surrounding the antenna. Gain in every direction is important, for it defines the antenna pattern and tells us where the far field is strongest and weakest and in the middle--and by how much.
|
||||
<p>However, when we casually mention gain, we are usually interested in the direction(s) of maximum gain from a given test antenna. Then we rotate the antenna to present that antenna direction to the receiving station. For satellites, we may rotate in 3 dimensions, but for HF, 2-dimensional rotation usually suffices (unless we must somehow compensate for a bit of tricky terrain and have the wherewithal to do so).</p>
|
||||
<p>We can specify maximum antenna gain in terms of dBi. Then we can compare maximum antenna gains from 2 or more antennas by citing their gains in dBi and merely comparing numbers.</p>
|
||||
<p>This practice is perfectly reasonable so long as we do not make it a fetish; that is, so long as we do not use this number exclusively in our gain considerations. Horizontal beamwidth is also important and is usually defined in terms of the number of degrees between half-power or -3 dB points where the direction of maximum gain is the center. Vertical beamwidth is also important in estimating the success of a potential path. We also want to know, in conjunction with vertical beamwidth, the elevation angle of maximum radiation. Together, these numbers give a more complete picture of antenna performance in a desired direction than raw gain alone.</p>
|
||||
<p>I have modeled an array with a 21 dBi gain figure. However, the horizontal beamwidth is only about 17 or 18 degrees wide, making it unsuited for general amateur operation. However, we often assume that competing antennas have the same beamwidth and that all we need to know in making our selection is the maximum gain. Good practice calls for making no such assumption. Rather, before we focus on maximum gain, we should establish that all other factors are equal.</p>
|
||||
<center>
|
||||
<h3>dBd: a warm but fuzzy concept</h3>
|
||||
</center>The concept of dBd was formed to capture the gain of an antenna relative to a dipole. A dipole is considered the standard basic horizontal antenna, and comparisons to it seemed to some folks to be more meaningful than comparisons to the isotropic radiator.
|
||||
<p>Unfortunately, the concept of dBd has become a cluster of concepts. Here are some of them. The notation is my own, since few folks are anxious to distinguish the individuals in the cluster.</p>
|
||||
<p><b>1. dBd-I</b>: dBd ideal compares the gain of an antenna to an ideal dipole in free space. An ideal dipole uses infinitely thin lossless wire and is resonant at the frequency of interest. In this application, the ideal dipole has a gain of about 2.15 dBi, that is, 2.15 dB over an isotropic radiator. All measurements are thus arithmetically transportable between dBi and dBd-I by adding or subtracting 2.15, as appropriate.</p>
|
||||
<p>dBd-I is of limited utility, since my backyard dipole may have a gain of 7.15 dBi and 5 dBd. Some folks become confused by the idea that a dipole has gain over a dipole. We then have to explain that the real wire dipole has gain over the perfect dipole in free space. That rarely helps a lot. And it does not tell us until we do some arithmetic how much gain some other antenna has over a real dipole.</p>
|
||||
<p><b>2. dBd-RM</b>: dBd can be expressed as the gain over a real dipole modeled at the same height as the test antenna. For studies that are strictly modeling investigations, this measure is sometimes useful. However, it requires that we further specify the construction of the dipole in terms of element diameter and element material. Using the same material, dipole gain will vary with element diameter. It will also vary inversely with the loss of the material used for the dipole.</p>
|
||||
<p>Both these constraints apply within the further rule of keeping the dipole resonant. If we make measurements across a ham band, we shall find that the dipole gain varies with frequency unless we re-resonate it for each readout frequency. Actually, we are usually more careless than this and take one resonant reading and apply it across the band without checking. And we tend to use fairly loose standards of resonance rather than converging the results. We may more precisely say that an antenna is resonant when the reduction of feedpoint reactance results in no further changes in gain to the number of significant digits that apply to the test.</p>
|
||||
<p>As one more qualification, we should note that dipoles and other antennas may have different elevation angles of maximum radiation over the same type of ground. When we cite dBd-RM, we must also say whether we are giving the figure for the dipole at its angle of maximum radiation or at the angle chosen for the test antenna. To avoid confusion, it is usually better to give details about the differing elevation patterns.</p>
|
||||
<p><b>3. dBd-RR</b>: dBd can be expressed as the gain over a real dipole set in the same position as the test antenna, where both antennas are oriented for maximum gain relative to the far field receiving site of the test range. For fairness, one should specify the construction of the dipole to ensure that the materials are comparable to those of the test antenna.</p>
|
||||
<p>However, there are a number of variables that occur within this way of handling dBd. First, range conditions vary considerably from one site to another. Second, some testers take the average of a number of readings in various directions, while others take readings along a single line defined as the best test line. Third, different ranges may use different test heights. The importance of this factor stems from the fact that many antennas that might be tested have different elevation angles of maximum radiation than a dipole, and this variance may introduce differences in readings as we change test antennas and as we move from range to range with different test antenna heights.</p>
|
||||
<p>Good testing and modeling protocols would specify all of the relevant factors applying to the comparisons involved. We sometimes do find these specifications. Unfortunately, we often don't. Without the specifications, comparisons in dBd-R (either M or R) are quite difficult to make. If we could only bring all antennas to a single test range with a single (large) set of dipoles and standardized conditions, we could likely establish the gain of each antenna over its standard dipole and then have truly precise comparisons among antennas. Someone has noted to me that the odds of the earth being struck by a meteor like the one which ended the reign of the dinosaurs are higher than the odds of the emergence of a universal test range. I really wish I could have disagreed with this individual.</p>
|
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<p>For additional <a href="dbd.html">pitfalls of careless dBd-ing</a>, see the next item on the Index.</p>
|
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<center>
|
||||
<h3>Why I tend to stick to dBi</h3>
|
||||
</center>My antenna work includes the building of test models of antennas that are feasible to construct, but is devoted predominantly to modeling all sorts of antennas for all sorts of purposes. This factor alone suggests the use of a single standard for all comparisons, such as dBi. However, there are a number of reasons I tend not to use dBd except in special circumstances.
|
||||
<p>1. The relevant comparisons are not with a dipole. Very often, antenna comparisons are among antennas that do not include dipoles. In such cases, simply comparing gain figures in dBi tells us all we need to know and can know about the relative maximum gains of the antennas. For example, in comparing the gains of self-contained 1 wl wire-loop antennas, the best designs for a given purpose are the ones that are best within the group, and the group does not include a horizontal dipole.</p>
|
||||
<p>Likewise, when contemplating whether it is worthwhile to increase the size of a Yagi for 20 meters from 3 to 4 elements, the dipole is not relevant. Rather, the relevant gain comparison is between both models and real antennas of 3 and 4 element design. The gain advantage is derived as easily from dBi as from any other system of gain numbers.</p>
|
||||
<p>2. The relevant comparisons have only passing reference to maximum gain. Additional factors, such as elevation angle, beamwidth, etc., may be far more important than gain itself. For some applications, good antennas do not need gain relative to a dipole. But they may require close specification of other antenna properties. Gain becomes a secondary specification for which dBi suffices nicely.</p>
|
||||
<center>
|
||||
<h3>Range tests are another matter</h3>
|
||||
</center>If my work were primarily with real antennas, then dBi would become a problematical term. A test range approximation of an isotropic radiator is an unlikely event anytime soon. Hence, antennas on test ranges must be compared to some standard, and the dipole is the most likely simple horizontally polarized candidate. If we accept this premise, then it is unreasonable to expect range testers to then correlate their results to a scheme of modeling in which the gain is converted to a value in dBi.
|
||||
<p>However, this situation makes it imperative that range testers specify a test protocol and comparison antenna for the evaluation of the procedure against good engineering practice. In many instances, the comparison antenna will not be a dipole (although amateurs often think only in terms of Yagi tests). Verticals require specification of a vertical standard of the appropriate class. Nothing substitutes for the revelation of detailed test protocols where range testing is at stake.</p>
|
||||
<p>Conversion of the test situation to models--like any other case of modeling--is at best the most reasonable approximation we can develop. Absolute precision is unlikely in most instances. Hence, the conversion of range test results to modeling results--with the accompanying conversion of dBd-RR (with a clear specification of the standard dipole used) to dBi--is not an automatic process and is subject to varying degrees of adequacy.</p>
|
||||
<p>Modeling of detailed test protocols, on the other hand, can yield some correlation factors among different test protocols. A model may substitute one standard dipole for another, may insert or remove test range objects affecting results, may change antenna heights with ease, etc. As a simple example, if Smith tests his antenna at 60' up and Jones tests his at 85' up, the differences in test results (all other factors being equal or equalized) can be at least tentatively resolved with effective modeling.</p>
|
||||
<p>Whatever the prospects for such work in the future (for we have just begun to scratch the surface of effective modeling in antenna work), those who predominantly model will likely stick to dBi as the basic measure of maximum gain. Range testers will likely stick to dBd-RR, where the range test is a comparison to a dipole or other relevant standard.</p>
|
||||
<p>Since I am mostly a modeler, I use dBi---mostly.</p>
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||||
<p><i>Updated 6-23-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.</i></p>
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<img src="../images/colorbar.gif" align="middle" width="540" height="4">
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<p><a href="../radio.html"><img src="../images/rtnhome.gif" align="bottom" width="40" height="40"> Return to Main Index</a><br></p>
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<p class="topics-footer">Topics: <a href='../topics.html#modeling'>Modeling</a></p><br>
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<title>Multi-Diameter Dipoles: MININEC vs. NEC-4</title>
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<h1><img src="../images/antbott.gif" align="left" width="150" height="77"> Multi-Diameter Dipoles: MININEC vs. NEC-4<img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10"></h1>
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<center>
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||||
<h3>L. B. Cebik, W4RNL</h3>
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<br>
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While examining some Yagi models developed by K6STI, I encountered an anomaly. The models employed a large-diameter, short-length center section for each element to simulate boom mounting plates, a technique that has proven sound relative to real-world construction.
|
||||
<p>When modeled in MININEC, no problems with convergence were encountered with reasonable numbers of segments per half wavelength. However, when modeled with NEC-4, convergence only occurred with very large numbers of segments per half wavelength. Reducing the diameter of these center sections to that of the immediately adjacent sections eliminated the problem of convergence--that is, convergence occurred with reasonable numbers of segments per half wavelength.</p>
|
||||
<p>To explore this anomaly, I set up a small test of systematically modeling dipoles with larger center sections. The test frequency was 14 MHz. The initial material was 0.5" diameter aluminum. In increments of 2 feet each side of center, I increased the length of a larger diameter center section in progressive steps for total lengths of 4, 8, 12, etc. feet up to an including the total antenna length.</p>
|
||||
<p>Each antenna was resonated to less than 1 ohm reactance. Thus, the length of each model differs. In the graphs that follow, the far right entry labeled "36" is a place holder for the actual total length of the antenna at the increased diameter. Thus, that column alone violates the linear progression of the other enlarged center sections.</p>
|
||||
<p>Each model was tested using ratios of 2:1, 3:1, and 4:1 relative to the original dipole diameter of 0.5 inches, for center section diameters of 1, 1.5, and 2 inches. All models are free space.</p>
|
||||
<p>The models were first run in MININEC 3.13 via ELNEC 3. Segmentation was set at 34 segments overall, using 1 segment per foot of enlarged center section, with the remaining segments split between the smaller diameter end sections. This yielded segment lengths that are well within all MININEC boundaries for accurate results, as well as very reasonably close in length between the antenna wires.</p>
|
||||
<p>The following graphs shows the progression of gain figures for the MININEC runs. Interestingly, the gain of the models peak when the enlarged center section is just under half the total length of the antenna. As the larger center section is further lengthened, MININEC shows a decrease in gain. The curves for the 3 ratios are nicely congruent.</p>
|
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|
||||
<img src="dp1.gif" width="658" height="519" border="2" vspace="5" hspace="9">
|
||||
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|
||||
<p>The length of the resonant antenna also changes with the length of the larger-diameter center section. Overall antenna length actually peaks with center-section lengths slightly longer than those for maximum gain, as the following graph demonstrates. MININEC models do not reach a final shortened length associated with fatter elements until the entire antenna is at the larger diameter.</p>
|
||||
<center>
|
||||
<img src="dp2.gif" width="643" height="519" border="2" vspace="5" hspace="9">
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<p>The same antennas were run with NEC-4, initially with EZNEC Pro and later with a beta version of GNEC. Segmentation was virtually the same as with the MININEC models with a single additional segment in the center section to permit the required mid-segment feedpoint. As with the MININEC models, each antenna was resonated within +/- 1 ohm of zero reactance for models using 2:1, 3:1, and 4:1 ratios of the center segment to the end sections.</p>
|
||||
<p>The pattern of gain produced by the NEC-4 models, shown in the following graph, is quite unlike that yielded by MININEC. Maximum gain occurs with the shortest possible larger-diameter center section and progressively decreases as the center section is lengthened. The curves for NEC-4 are less smooth than for MININEC because the former, in the commercial versions noted, yield gain figures to 2 decimal places, while the latter yields figures to 3 decimal places. Hence, NEC-4 rounding yields somewhat stair- step curves. within those limits, the curves for the three different diameter ratios are congruent.</p>
|
||||
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|
||||
<img src="dp3.gif" width="646" height="521" border="2" vspace="5" hspace="9">
|
||||
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|
||||
<p>Equally congruent are the overall antenna length curves (shown in terms of lengths each side of the feedpoint in the graphs).</p>
|
||||
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|
||||
<img src="dp4.gif" width="647" height="517" border="2" vspace="5" hspace="9">
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|
||||
<p>Interestingly, despite the vastly different gain curves, the overall antenna length curves for MININEC and NEC are exceedingly comparable. MININEC yields slightly longer resonant lengths for each modeled case, a phenomenon long noted (and corrected for in some commercial versions of MININEC). Nonetheless, MININEC and NEC-4 show the longest resonant length at just about the same length of larger-diameter center section, as shown in the following graph. This graph uses the 4:1 ratio curves because they produce the sharpest length peaks and would be most sensitive to significant differences in the peak point for each modeling system with these models.</p>
|
||||
<center>
|
||||
<img src="dp5.gif" width="653" height="521" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>The question that remains is which of the two gain curves is the more reliable. The MININEC gain curves with a 2:1 diameter ratio of center section to end sections were rerun with double the number of sections. Gain figures were convergent within a maximum divergences of 0.003 dB. The comparable NEC-4 models, when segments were doubled (minus 1 to retain an odd number of segments in the wire containing the feedpoint), showed an order of magnitude less convergence with short center sections of 4 and 8 feet. Convergence within the two decimal places occurred only when the center section reached 24 feet long. This result is consistent with the difficulty of converging Yagi models employing short, large-diameter center sections for each element.</p>
|
||||
<p>Moreover, the NEC-4 curve totally envelopes the MININEC curve, as shown in the following graph for diameter ratios of 2:1. Within the limits of NEC-4 rounding, nowhere does the MININEC curve exceed the NEC-4 curve in gain value. In contrast, for shorter center sections, the reported gain of the NEC-4 model is significantly higher.</p>
|
||||
<center>
|
||||
<img src="dp6.gif" width="650" height="519" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>The anomalous results yielded by NEC-4 with shorter, large-diameter center sections of multi-diameter dipoles gains importance as these figures accumulate in multi-element antenna arrays. Since these gains are usually cumulative in most antennas designed for maximum or close to maximum gain, the reported gain may be significantly higher than reality.</p>
|
||||
<p>The convergence test and the fact that the NEC-4 curve envelopes the MININEC curve are strong indicators that NEC-4 may be simply inaccurate when antenna elements consist of multi-diameter sections such that the center section is short and significantly larger in diameter than succeeding sections of the element. The degree to which such an inaccuracy becomes significant operationally to an antenna design depends on many variables of both design and engineering goal and cannot be independently estimated. Unless independently confirmed as in fact accurate (with MININEC's curves consequently invalidated), the phenomenon will at least be disconcerting to antenna modelers.</p>
|
||||
<p>Attributing an anomaly to NEC-4 in this case does not itself certify the accuracy of the MININEC result. Even if correct, the increase of gain is of more mathematical interest than operational significance. At a diameter ratio of 4:1, the maximum gain is only about 0.06 dB relative to a dipole of the thinner size.</p>
|
||||
<p>For those who model antennas, the disparity between the two modeling programs should at least be noted and accounted for wherever it emerges.<br>
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<p><i>Updated 9-19-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.</i><br>
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<title>Two Limitations of NEC-4</title>
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<h1>Notes on Two Limitations of NEC-4</h1>
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<h3>L. B. Cebik, W4RNL</h3>
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NEC-4 is an advance on NEC-2. Among its advantages is the ability to handle linear elements of stepped diameter directly with accurate results. NEC-4 has not proven wholly unlimited in this regard, since segmentation must be very extensive in proportion to the largest step-size within an element.
|
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<center>
|
||||
<h4>Closely Spaced Parallel Wires of Different Diameters</h4>
|
||||
</center>NEC-4 has also proven to be limited in its ability to handle closely spaced wires of different diameters. Although it produces more reasonable results than NEC-2, it remains significantly off the mark. The following notes are a demonstration of that limitation.
|
||||
<h5>Dipoles</h5>The baseline for the demonstration is the dipole. Since dipoles of 0.5" and 0.0808" (#12) wire at 28.5 MHz are used in further steps, here is the data for MININEC (public domain version), NEC-2, and NEC-4 (as modeled in free space on ELNEC 3 and EZNEC Pro 2). Gain is in dBi and Feed Z is the feedpoint impedance recorded as R +/- jX in ohms. Segmentation is drawn from MININEC; add 1 segment for NEC.
|
||||
<pre>Antenna Output MININEC NEC-2 NEC-4
|
||||
0.5" dipole Gain 2.13 2.13 2.13
|
||||
16.52'; 66 seg Feed Z 72.08 + j0.29 72.88 + j3.69 72.90 + j3.75
|
||||
0.0808" dipole Gain 2.11 2.11 2.11
|
||||
16.72'; 66 seg Feed Z 72.64 + j0.21 73.06 + j3.09 73.06 + j3.13
|
||||
</pre>
|
||||
<p>The antenna models were initially resonated within MININEC, where resonance was considered to be a feedpoint impedance with under 1-ohm reactance. Both NEC-2 and NEC-4 show a slight difference from MININEC. The difference is of no practical importance, but is only of numerical significance for exercises like the present one. For open-ended elements, such as those of a dipole, NEC-4 (single precision mode) shows a regular numerically more positive reactance than NEC-2.</p>
|
||||
<h5>Equal Diameter Folded Dipoles</h5>The actual test consists of modeling a folded dipole. A folded dipole, where the long parallel wires have the same diameter, effects an impedance transformation of 4:1 for any spacing within reason. Thus, the anticipated feedpoint impedance should be in the region of 288 ohms (72 x 4). Since folded dipoles also act like fat wires and are thus shorter at resonance than single wire dipoles, the anticipated modeled feedpoint impedance was slightly lower than the theoretical calculation. The modeled folded dipoles used 0.5" diameter elements spaced 0.25' (3").
|
||||
<p>MININEC tends to chop corners and give erroneous results unless one of two procedures is followed. A. One may use as many segments as the program allows to minimize the size of the corner chopped. B. One may taper the segment lengths approaching the corner so that corner segments are small while the overall segment count is held to a practical minimum.</p>
|
||||
<p>The basic MININEC folded dipole used 66 segments longitudinally and 2 segments at the ends. NEC models added one segment to each longitudinal wire to maintain parallel segmentation. Tapered MININEC models used the internal segmentation values of the ELNEC program. Since these produced 8- segment mid-length wires, the NEC models added one segment to this section to satisfy the need for an off number of segments for center feeding. Finally, a more highly segmented model, using 120 segments per longitudinal wire was created to equalize the segment lengths with those of the 2- segment end wires. This last model was not adjusted for resonance.</p>
|
||||
<pre>Antenna Output MININEC NEC-2 NEC-4
|
||||
FD: equal seg Gain 2.22 2.22 2.22
|
||||
16.1'; 66/2 x2 Feed Z 285.7 + j0.90 285.9 + j4.10 285.8 + j3.99
|
||||
FD: tapered Gain 2.21 2.21 2.21
|
||||
16.06' Feed Z 281.0 - j0.68 284.2 + j9.87 284.0 + j8.66
|
||||
FD: equal seg Gain 2.22 2.22 2.22
|
||||
16.1'; 120/2x2 Feed Z 285.8 - j1.80 286.0 + j2.27 285.8 + j0.51
|
||||
</pre>
|
||||
<p>In practical terms, all programs do a satisfactory job of modeling a simple folded dipole when both wires have the same diameter. When sufficient segments are used in MININEC, tapering proves less accurate, assuming that the balance of results represents a consensus close to reality.</p>
|
||||
<p>Systematically, NEC-4 shows a slightly lower feedpoint impedance for these closed models than NEC-2. Nonetheless, when all wires have the same diameter and other modeling geometry guidelines are met, all modeling programs give equally usable results.</p>
|
||||
<h5>Unequal Diameter Folded Dipoles</h5>When the wires of a folded dipole differ in diameter, they effect (relative to a single-wire dipole) a different feedpoint impedance transformation ratio than do folded dipoles with equal diameter wires. The theoretical impedance transformation ratio is given by
|
||||
<center>
|
||||
<img src="fd1.gif" width="207" height="153" border="2" vspace="5" hspace="9">
|
||||
</center>where R is the impedance transformation ratio, s is the wire spacing, center-to-center, d1 is the diameter of the fed wire, and d2 is the diameter of the second wire, and where s, d1, and d2 are given in the same units.
|
||||
<p>If we use a wire 0.0808" in diameter (#12 AWG) for the fed wire and a wire 0.5" in diameter for the second wire, maintaining the 3" spacing, then the impedance transformation ratio will be approximately 7.47. A folded dipole of this construction would have a calculated feedpoint impedance of about 533 ohms. In practice, due to "fat wire" effect, we might expect a feedpoint impedance slightly lower than this.</p>
|
||||
<p>It should be noted that the impedance transformation equation does not account for the end wires. In this test, the end wires were also 0.0808" in diameter.</p>
|
||||
<p>If either version of NEC can handle parallel wires of differential diameters, then the results should coincide reasonably with those of MININEC, which takes such cases in stride. The test used models of similar construction to those used with equal diameter folded dipoles. A basic model used 66 segments per longitudinal wire and 2 segments per end wire; and a tapered-segment version of the antenna was created using internal tapering values. Here are the results:</p>
|
||||
<pre>Antenna Output MININEC NEC-2 NEC-4
|
||||
FD: equal seg Gain 2.21 0.69 1.59
|
||||
16.2'; 66/2 x2 Feed Z 530.5 + j1.47 375.2 + j25.8 462.6 + j17.4
|
||||
FD: tapered Gain 2.21 0.37 1.22
|
||||
16.2' Feed Z 526.5 + j10.8 347.2 + j38.5 423.4 + j37.5
|
||||
FD: equal seg Gain 2.21 0.56 1.53
|
||||
16.2'; 122/2x2 Feed Z 527.6 - j2.99 364.1 + j25.1 456.0 + j15.43
|
||||
</pre>
|
||||
<p>The MININEC models clearly come very close to expectations. Since the tapered model was not re-resonated, its values are lower, but the large equal-segmented model is likely the more accurate.</p>
|
||||
<p>NEC-2 models of parallel wires of different diameters, as has been well- established, produce highly erroneous values. Tapering throws the values even farther off the mark. Although somewhat better, NEC-4 values are also highly unreliable. Moreover, reducing segmentation of the NEC-4 models produced nothing reliable. An auto-segmented model at conservative minimums of 11 segments for the longitudinal wires and 1 segment each for the ends yielded a gain of 1.82 dBi and a feedpoint impedance of 443.8 + j39.6 ohms. Further reducing segmentation to the absolute minimums of 5 segments per long wire and 1 segment per short calculated a gain of 2.64 dBi and a feedpoint impedance of 371.3 + j26.07 ohms.</p>
|
||||
<h5>Conclusions and Implications</h5>Because the behavior of a folded dipole is well-established and easily predicted, the antenna forms a very good test of the present modeling question: the adequacy of the program to deal with parallel wires of unequal diameters. The conclusion is that NEC-4 remains deficient in this regard, and antenna modelers are duly cautioned.
|
||||
<p>The inadequacy of NEC-4 to model this situation adequately casts doubts on a number of possible modeling challenges. For example, modeling gamma and Tee matching sections as physical elements contributing to the radiation pattern as well as to effecting an impedance transformation is now dubious. Other cases are too numerous to mention. For situations calling for parallel wires of unequal diameter, MININEC remains the modeling program of choice, despite its other limitations.</p>
|
||||
<center>
|
||||
<h4>Wires of Different Diameters Joined at Sharp Angles</h4>
|
||||
</center>A second problem in the NEC-2 calculation engine is the unreliability of results when wires of unequal diameter join at right or acute angles. Although NEC-4 improves upon this situation, its results are not wholly reliable.
|
||||
<h5>Single Quad Loops of a Single Wire Diameter</h5>The foundation for testing the reliability of NEC-4 outputs when wires of different diameter join at right angles is the single quad loop. The test employed loop materials of 0.5" and 0.0808" diameters. When only a single diameter wire is used, all programs perform credibly, so long as models adhere to the antenna geometry criteria of the specific program. All loops were again modeled at 28.5 MHz, with copper wire in free space. All loops are square. Dimensions and segmentation are given for one side of the loop. The tapered-segment MININEC model employs the internal values of the ELNEC program.
|
||||
<pre>Antenna Output MININEC NEC-2 NEC-4
|
||||
0.0808" wire Gain 3.26 3.26
|
||||
9.146'; 31 segs Feed Z 126.9 + j 0.02 126.9 - j 0.13
|
||||
0.0808" wire Gain 3.25 3.26 3.26
|
||||
9.146'; 61 segs Feed Z 126.3 - j 7.93 127.0 - j 0.27 127.0 - j 0.69
|
||||
0.0808" wire Gain 3.26
|
||||
9.146'; tapered Feed Z 126.0 - j 3.38
|
||||
|
||||
0.5" wire Gain 3.37 3.37
|
||||
9.364'; 31 segs Feed Z 129.7 + j 0.21 129.7 - j 0.10
|
||||
0.5" wire Gain 3.36 3.36 3.26
|
||||
9.364'; 61 segs Feed Z 129.5 - j 4.07 130.0 + j 0.49 129.8 - j 0.41
|
||||
0.5" wire Gain 3.36
|
||||
9.364'; tapered Feed Z 129.1 - j 0.42
|
||||
</pre>
|
||||
<p>The initial models were created in NEC-4 and tested on NEC-2 and MININEC. A tapered-segment length model was created in MININEC for comparison with the equal-segment models. Convergence of the two MININEC models is good for practical purposes, although a slight numerical difference shows.</p>
|
||||
<p>For the NEC models, there is no significant numerical, let alone practical difference between NEC-2 and NEC-4 models. Moreover, and especially significant for this test, there is no significant difference between the values achieved at 31 segments per side and 61 segments per side. Practical convergence of results is achieved at much lower levels of segmentation.</p>
|
||||
<h5>Single Quad Loops of a Different Wire Diameters</h5>To test the ability of the programs to handle wires of different diameter joining at right angles, I modeled a single square quad loop. The top and bottom wires were 0.5" diameter, while the vertical wires were 0.0808" diameter. This might be a model of a portable quad loop using tubing for the horizontal members and wire for the vertical pieces, thus allowing the assembly to be collapsed for transportation.
|
||||
<p>The initial model was constructed in MININEC and then re-tested in NEC-2 and NEC-4, using 61 segments per side. The MININEC model required 10.15' side lengths to approach modeled resonance.</p>
|
||||
<pre>Antenna Output MININEC NEC-2 NEC-4
|
||||
10.15' sides Gain 3.61 3.57 3.60
|
||||
61 segs/side Feed Z 137.2 - j 5.71 175.4 + j 140 150.3 +j 44.3
|
||||
10.15' sides Gain 3.61
|
||||
tapered segs Feed Z 136.7 - j 2.30
|
||||
</pre>
|
||||
<p>The MININEC model converges well with its tapered alternative model. However, the NEC models diverge in values. Although the gain values are plausible, the feedpoint impedance values indicated a condition far from resonance. The divergence from MININEC is worse for NEC-2 than for NEC-4, suggesting that the NEC-2 figures are least reliable. Since there is no simple theoretical calculation with which to compare the overall results, one cannot claim that the MININEC qualifies as a standard against which to measure the other programs. However, given MININEC's abilities to handle wires of different diameters in other contexts and the general trend of NEC-4 results with such conditions to be closer than NEC-2 results to the MININEC figures, it seems likely that MININEC may yield outputs that are closest among the three to reality.</p>
|
||||
<p>The NEC-4 model with 61 segments per side can be brought closer to resonance by shortening each side to 9.94' in length. This figure might seem equally reliable with the MININEC lengths of 10.15' per side, except for one significant factor: the MININEC figures achieve convergence, while the NEC figures do not, especially with respect to feedpoint impedance. I ran the revised NEC-4 model through various segmentations ranging from 21 to 121 segments per side. In the following table, "delta R" and "delta X" indicate changes in the feedpoint impedance values from the preceding level of segmentation.</p>
|
||||
<pre>Segments/Side Gain Feedpoint Impedance Delta R Delta X
|
||||
21 3.54 133.4 - j 13.280
|
||||
31 3.54 134.5 - j 9.375 1.1 3.905
|
||||
41 3.53 135.5 _ j 5.589 1.0 3.786
|
||||
51 3.53 136.4 - j 1.943 0.9 3.646
|
||||
61 3.53 137.3 + j 1.616 0.9 3.559
|
||||
71 3.53 138.3 + j 5.119 1.0 3.503
|
||||
81 3.53 139.2 + j 8.663 0.9 3.544
|
||||
91 3.53 140.0 + j 11.880 0.8 3.217
|
||||
101 3.52 140.9 + j 15.36 0.9 3.48
|
||||
111 3.52 141.7 + j 18.57 0.8 3.21
|
||||
121 3.52 142.4 + j 21.60 0.7 3.03
|
||||
</pre>
|
||||
<p>The values for gain are well converged. However, those for feedpoint impedance are not. Compare, for example, the differences among figures for 31 and 61 segments per side for the equal-diameter wire loops, using either the 0.0808" or 0.5" models. NEC-4 varies by only 0.1 ohm resistance and under 0.5 ohm reactance across that spread. With the present multi-wire diameter loop, the same difference in segmentation yields a difference of 2.8 ohms resistance and 10.991 ohms reactance, a 200+% difference for each output figure.</p>
|
||||
<p>Moreover, the progression of values shows no signs of closure within the limits of practical modeling. Although there is a trend downward in the delta numbers, where it will occur remains unclear. Without convergence, the figures cannot be regarded as reliable.</p>
|
||||
<h5>Conclusions and Implications</h5>Because there is no independent standard at hand against which to measure the modeled results, the MININEC figures for the single quad loop cannot be certified as in fact closer to reality than those yielded by NEC-4 for antennas constructed of different-diameter wires joining at right angles. However, MININEC's achievement of reasonable convergence of results and NEC-4's inability to achieve converged results suggests that the NEC-4 results are less trustworthy than those of MININEC. NEC-2 figures are most divergent and least reliable of the three modeling calculation engines.
|
||||
<p>It is clear that, for a loop of a given size, NEC-4 will yield lower gain numbers and higher feedpoint values than MININEC. Otherwise expressed, NEC-4 will call for a loop of smaller dimensions to approach resonance.</p>
|
||||
<p>These trends also apply to other antennas using wires of different diameters joining at right and sharper angles. Models of folded X-beams show lesser gain and higher feedpoint values on NEC-4 than on MININEC.</p>
|
||||
<p>Given the limitation of NEC-4 with respect to parallel wires of different diameters, it is probable that the present limitation of NEC-4 is an extension of the same root mechanism. Therefore, it is likely that MININEC remains the modeling engine of choice for antennas employing angular junctions of different-diameter wires.<br>
|
||||
<br></p>
|
||||
<center>
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||||
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
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||||
</center><br>
|
||||
<br>
|
||||
<p><i>Updated 4-10-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.</i><br>
|
||||
<br></p>
|
||||
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|
||||
</center><br>
|
||||
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|
||||
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<h1><img src="../images/yagicad.gif" align="left" width="125" height="62" border="2" vspace="5" hspace="25">Notes on Modeling Antenna Elements <img src="../images/antbott.gif" align="right" width="150" height="77"></h1>
|
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</center>
|
||||
<center>
|
||||
<h3>L. B. Cebik, W4RNL</h3>
|
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<p>Having examined numerous antenna models from a wide variety of sources, I am struck by the diversity of ways in which antenna elements, subdivided into wires and segments, are created. The variety of ways in which wires are placed into the antenna geometry description makes it difficult for another modeler to read the wires page. Moreover, many of the models will produce correct far-field data and feedpoint information, but most will skew the antenna currents. This latter information can become quite important in analyzing why a complex antenna yields its particular set of performance outcomes.</p>
|
||||
<p>The usual reasons given for the odd collections of wires making up an antenna model are convenience and speed. Many antenna specifications are for half elements, where the other half is presumed to be a mirror image. So we begin in the middle and work outward. Dimensions are given with positive numbers, and it is faster to do the positive side and then replicate it with minus signs. We go directly from whatever sketch or data sheet we have to the screen entries. I've been there, done that, and learned the hard way that slowing down at the beginning saves me a bucket of time later on when I try to troubleshoot my model.</p>
|
||||
<p>So let me make some suggestions, scratched with chalk, not etched in stone. I'll also say why along the way.</p>
|
||||
<p>First, do the model on a piece of paper before touching the keyboard of your favorite modeling program. That way, you can organize your keyboarding before you begin the computer work. Second, adopt a convention, like working from the far left to the far right (since so many of our American conventions are left-to-right in direction). Avoid working from the middle outward, however initially convenient that seems.</p>
|
||||
<center>
|
||||
<img src="mod1.gif" width="679" height="257" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>Now consider the simple dipole 8.25' long, 3/4" in diameter, and fed in the middle, shown in Figure 1. Even following our conventions, there are a couple of ways of setting down the X, Y, Z coordinates. My own preference is to center the antenna at 0,0,Z, where Z is an unspecified antenna height. That way, if I add elements projecting equally beyond the first element limits, I can place their coordinates as the same number but with a different sign. So my one wire antenna description looks like this (in free space):</p>
|
||||
<pre>Wire End 1 x y z End 2 x y z Diameter
|
||||
1 -4.125 0 0 4.125 0 0 .75
|
||||
</pre>
|
||||
<p>You may choose to place the wire ends in the Y dimension just by reversing X and Y entries. My feedpoint is now Wire 1 at the 50 percent mark, which exactly centers it. For MININEC, use an even number of segments; for NEC use an odd number of segments.</p>
|
||||
<center>
|
||||
<img src="mod2.gif" width="645" height="408" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>Now consider an element of a beam using many shorter sections of tubing that decreases in diameter as you progress outward. Let's assume an element that from center outward has these dimensions: 22" at 1.125" diameter; 36" at 1"; 24" at 0.825"; 24" at 0.75"; 24" at 0.625"; and 40.5" at 0.5". The first step is to obtain running totals: 22"; 58"; 82"; 106"; 130"; and 170.5".</p>
|
||||
<p>I we follow our conventions, the full element will look like this on paper and in the geometry entry spread sheet:</p>
|
||||
<pre>Wire End 1 x y z End 2 x y z Diameter
|
||||
1 -170.5 0 0 -130 0 0 .5
|
||||
2 -130 0 0 -106 0 0 .625
|
||||
3 -106 0 0 -82 0 0 .75
|
||||
4 -82 0 0 -58 0 0 .825
|
||||
5 -58 0 0 -22 0 0 1
|
||||
6 -22 0 0 22 0 0 1.125
|
||||
7 22 0 0 58 0 0 1
|
||||
8 58 0 0 82 0 0 .825
|
||||
9 82 0 0 106 0 0 .75
|
||||
10 106 0 0 130 0 0 .625
|
||||
11 130 0 0 170.5 0 0 .5
|
||||
</pre>
|
||||
<p>This may seem like a long way to go, but for an accurate model, all these wires will have to be in the chart anyway. This left-to-right scheme just keeps them well-ordered. Note that wire 6 is the center section and can have the feedpoint specified at its center, with correct segmentation. For NEC, I might assign it 5 segments; for MININEC, 4. The sections with dimensions in the 20s might get 2 segments each, with the 36" section getting 3 segments, and the end sections 4 segments. This keeps segments lengths as close to equalized as this structure permits, while keeping the segments lengths well below maximum recommended length.</p>
|
||||
<p>A rule of thumb: do not wed yourself to the minimum segments per half wavelength rule. The more complex the antenna, the more segments per half wavelength needed to arrive at convergence, the condition where adding further segments does not alter output values significantly. Closed 1 wavelength loops may require 40-60 segments total to achieve convergence. If you are working with a multiband beam, be sure to raise the number of segments per wire in the chart in proportion as you raise frequency.</p>
|
||||
<p>For complex antennas with closely space elements, it is wise to align the segments as closely as possible from one element to another, especially with NEC. To keep myself in the habit, I try to do this with every antenna having parallel elements.</p>
|
||||
<center>
|
||||
<img src="mod3.gif" width="669" height="429" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>Now let's consider one final example, a shortened dipole with wire hats on each end. The hats consist of 4 radial wires and a perimeter wire. Where does the antenna start and end. Some quick modelers use the horizontal dipole ends and then separately model the wire structures outward and around. However, the wire hat assemblies are part of the antenna. An equally quick second answer is to treat the peaks where the radial wires end as the antenna beginning and ending. Both answers are wrong. The antenna begins and ends where the current goes to zero. MININEC gives a true zero reading, because it takes current nodes to be at the ends of segments. NEC takes current nodes to be at the center of segments, and so the lowest value will never be zero. However, you can get equally low values either side of a correctly chosen wire junction.</p>
|
||||
<p>For this example, the antenna begins in four places: at the center of each of the four perimeter lengths. It ends in the comparable places at the other end assembly. Hence, a fully modeled version of this antenna will have, starting on the left end, 8 perimeter wires, each starting mid-length and ending at a radial wire peak. The 4 radial wires come next, working from peak to center, which happens to be the horizontal wire end point. Then we have the horizontal wire, center fed, followed by 4 radial wires working outward from the hub, and finally the 8 perimeter wires, 2 from each peak to common centers.</p>
|
||||
<p>I tend to collect these wires by type so that I can adjust all the radials as a group, adjust perimeter wire lengths as a group, etc.</p>
|
||||
<p>Once more, you can take shortcuts, but only if a. you can decide in advance that you will never need or want to know the correct current magnitudes and phases on each wire, or b. you are willing to reconstruct the model if you should ever become interested in such matters.</p>
|
||||
<p>One more note: In each case, I ran the wire containing the feedpoint as a single wire fed in the center with either a voltage or current source. I could have ended each wire in the center and used a split feed (split voltage or split current). However, use care here. Some versions of NEC will return incorrect values of feedpoint impedance using split feed if you adopt the center-outward style of geometry construction. You may even get impossibly high negative resistances. (Note that some instances of negative feed resistances are correct values, but not in this particular instance.)</p>
|
||||
<p>I hope these notes are useful toward the goal of achieving more reliable models that play correctly on the first run.</p>
|
||||
<center>
|
||||
<img src="../images/colorbar.gif" width="591" height="3">
|
||||
</center>
|
||||
<p><a href="../radio.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Return to Amateur Radio Page</a><br></p>
|
||||
<p class="topics-footer">Topics: <a href='../topics.html#modeling'>Modeling</a></p><br>
|
||||
</body>
|
||||
</html>
|
||||
@@ -0,0 +1,35 @@
|
||||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<meta charset="UTF-8">
|
||||
<meta name="keywords" content="Modeling">
|
||||
<title>Model Planning Form</title>
|
||||
<link rel="stylesheet" href="../styles.css">
|
||||
</head>
|
||||
<body>
|
||||
<center>
|
||||
<h1><img src="../images/yagicad.gif" align="left" width="125" height="62" border="2" vspace="15" hspace="10"><img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10">Model Planning Form</h1>
|
||||
</center>
|
||||
<center>
|
||||
<h3>L. B. Cebik, W4RNL</h3>
|
||||
</center>
|
||||
<center>
|
||||
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
|
||||
</center><br>
|
||||
<br>
|
||||
<p>I have received numerous requests for the model planning form that I put together many years ago when first getting involved in antenna modeling. It is a convenient form that has proven useful over time for basic modeling activities that involve wires, loads, and sources as the primary elements. It allowed me to keep track of the ingredients that I placed in models, and also helped me troubleshoot models that did not seem to work as expected.</p>
|
||||
<p>As a service to newer modelers, I am making the forms available in two modes: as a Word document and as a PDF document. You may view the PDF version on the screen to ensure that it is something you can use. However,, I suspect that ultimately, you may develop an impreoved version that best suits you individual needs. Each form has a front and back side, although many models will require only the first page.</p>
|
||||
<p>To access the PDF version go to <a href="planning-form.pdf">planning-form.pdf</a>.</p>
|
||||
<p>To download the Word version, go to <a href="planning-form.doc">planning-form.doc</a>.</p>
|
||||
<p>Good luck in your modeling ventures.</p>
|
||||
<center>
|
||||
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
|
||||
</center>
|
||||
<p><i>Updated 10-17-2007. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.</i><br></p>
|
||||
<center>
|
||||
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
|
||||
</center>
|
||||
<p><a href="../radio.html"><img src="../images/rtnhome.gif" align="bottom" width="40" height="40"> Return to Index</a></p>
|
||||
<p class="topics-footer">Topics: <a href='../topics.html#modeling'>Modeling</a></p><br>
|
||||
</body>
|
||||
</html>
|
||||
@@ -0,0 +1,103 @@
|
||||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<meta charset="UTF-8">
|
||||
<meta name="keywords" content="Modeling">
|
||||
<title>Antenna Modeling Programs</title>
|
||||
<link rel="stylesheet" href="../styles.css">
|
||||
</head>
|
||||
<body>
|
||||
<center>
|
||||
<h1><img src="../images/yagicad.gif" align="left" width="125" height="62" border="2" vspace="5" hspace="25">Antenna Modeling Programs<img src="../images/antbott.gif" align="right" width="150" height="77"></h1>
|
||||
</center>
|
||||
<center>
|
||||
<h3>L. B. Cebik, W4RNL</h3>
|
||||
</center>
|
||||
<center>
|
||||
<img src="../images/colorbar.gif" width="591" height="3">
|
||||
</center>
|
||||
<center>
|
||||
<h3>2024 Update</h3>
|
||||
</center>
|
||||
<p>Most of the software listed here is old, or no longer exists. Where possible internet web archive copies of websites have been found and linked for sites that no longer exist. Currently the most commonly used modeling software in amateur radio circles is <a href="https://eznec.com/" target="_blank">EZNEC</a>, <a href="https://www.qsl.net/4nec2/" target="_blank">4NEC2</a>, and <a href="http://gal-ana.de/basicmm/en/" target="_blank">MMANA-GAL</a>.</p>
|
||||
<center>
|
||||
<h3>NEC-4 / NEC-5</h3>
|
||||
</center>
|
||||
<p>As of 2024 the current version of NEC is NEC-5 (EZNEC 7 supports NEC-5), which overcomes most of the shortcomings with earlier codes. It permits the modeling of underground radial systems, elements of varying diameter sections, carefully-constructed close-spaced parallel wires, as well as all the modeling capabilities of earlier versions of the code. NEC-4 and NEC-5 is a proprietary code of the Lawrence Livermore National Laboratory and the University of California, from whom a user-license must be obtained. Export restrictions may apply. You may obtain the license materials on line at the <a href="https://softwarelicensing.llnl.gov/product/nec-v50" target="_blank"><b>LLNL</b></a> site.</p>
|
||||
<center>
|
||||
<h3>Nittany Scientific NEC-Win Plus+ and NEC-Win Synth</h3>
|
||||
</center>
|
||||
<p>Cebik created and made available a number of models throughout the site using NEC-Win Plus+. Version 1.2 download: <a href="../../software/NWPlus-Setup12.zip">NWPlus-Setup12.zip</a>.</p>
|
||||
<ul>
|
||||
<li>
|
||||
Note: v1.2 (2003) predates Windows Vista, but installs and runs ok on Windows 7 - 11, except the polar plots function which returns a run time error. Later versions likely fixed this, appears the last version was v1.6 from 2008.
|
||||
</li>
|
||||
</ul>
|
||||
<p>NEC-Win Synth is used to generate typical models and provides a set of building blocks to build more complex models. Version 1 download: <a href="../../software/NWSynth.zip">NWSynth.zip</a>.</p>
|
||||
<p>Windows Help: Opening the help on Windows Vista or later may result in an "Feature not included" error. KB917607 for Windows Vista, 7, and 8 can be downloaded from <a href="https://archive.org/download/kb917607" target="_blank">archive.org/download/kb917607</a> which will enable the help file feature.</p>
|
||||
<p>The installers have been scanned with <a href="https://www.virustotal.com" target="_blank">Virustotal</a>, no security vendors and no sandboxes flagged the files as malicious.</p>
|
||||
<p>The Nitany Scientific site also has a number of example model files which can be downloaded from <a href="https://web.archive.org/web/20120722052456/http://www.nittany-scientific.com/examples/examples.htm" target="_blank">www.nittany-scientific.com/examples/examples.htm</a> (web.archive.org).</p>
|
||||
<center>
|
||||
<img src="../images/colorbar.gif" width="591" height="3">
|
||||
</center>
|
||||
<p>Much of my antenna research work is based on systematic antenna modeling in one or another version of the Numerical Electromagnetics Code (NEC). The following brief notes will provide links to known antenna modeling software providers.</p>
|
||||
<p>At present, I know of only two sources of commercial software for NEC-4:</p>
|
||||
<p><a href="https://eznec.com/" target="_blank"><b>Roy Lewallen, W7EL</b></a> produces <b>EZNEC Pro</b>, which has an option for NEC-4, if the purchaser has a confirmed license for NEC-4. EZNEC Pro and EZNEC Plus are also available for NEC-2 (see below). W7EL also makes available <b>EZNEC</b> (v. 4.0), a segment-restricted version of NEC-2. The latest W7EL NEC software packages are Windows-based and employ similar user interfaces which have earned praise in DOS versions for their user-friendliness. New versions of EZNEC contain a 3-D plot graphic that can be "sliced" for select 2-D patterns, direct entry for trap as well as for series and parallel R-L-C loads, and the average gain test. EZNEC also implements the NEC2/NEC-4 ground wave (RP1) output. Wire construction freatures are limited to GW commands, but include special facilities for creating rectangular wire grids, radial systems, circles, and helices. EZNEC Pro will import or export files in .NEC format. Special processing has increased the segment limit to 20,000.</p>
|
||||
<p><a href="https://web.archive.org/web/20120722052143/http://www.nittany-scientific.com/" target="_blank"><b>Nittany Scientific</b></a> (web.archive.org) produces a 32-bit Windows version of NEC-4 called <b>GNEC</b>. This program implements all all of the input cards of the complete NEC-4 input deck, thus permitting the use of catenary wires, helices, networks, rotational and linear structure movement, and coordinate and rotational based symmetry options. Control commands include the insulated sheath, near fields in both coordinate and axial form, the upper medium, as well as far-field and ground wave analysis. Output capabilities include 3-D, polar plots, and many rectangular (X-Y) graphs, as well a a large array of tabular reports and the Average Gain Test. A special insert using the NEC-Win Plus interface allows modeling by equation. The basic ASCII interface uses assist screen to formulate each command entry and is similar to the one used in <b>NEC-Win Pro</b>, described below under NEC-2.</p>
|
||||
<center>
|
||||
<h3>NEC-2</h3>
|
||||
</center>NEC-2 is a highly capable version of the code which is in the public domain. It is restricted to antenna elements of a single diameter (although some software providers have introduced corrections for linear elements whose diameters varies). It cannot handle buried radial systems, although above ground systems close to the earth can be handled. However, it is equipped with the Sommerfeld-Norton high accuracy ground model for accurate modeling of horizontal wires close to the earth.
|
||||
<p><a href="https://web.archive.org/web/20120722052143/http://www.nittany-scientific.com/" target="_blank"><b>Nittany Scientific</b></a> (web.archive.org) produces a Windows version of NEC-2 called <b>NECWin Plus</b>, which features a true spreadsheet geometry construction page set with design-by-equation capabilities. The program also offers stepped-diameter corrections, Gain Averaging Test, CAD (.DXF) file input, 2-D and 3-D plots and antenna views, and graphical outputs. NSI considers this to be an entry level program and offers a companion volume with exercise models called <i>Basic Antenna Modeling: A Hands-On tutorial</i>.</p>
|
||||
<p>The company also offers a research NEC-2 program: <b>NECWin Pro</b> (NWP). NWP employs a user-selected choice between a spreadsheet geometry construction page (adapted from NEC-Win Plus, or the normal ASCII model input page with help screen/windows for all antenna model input parameters. In addition, NWP provides direct entry or importation of NEC model inputs and provides a large assortment of available rectangular output graphics, along with other advanced NEC capabilities. NSI views NEC-Win Pro as a profession-level program.</p>
|
||||
<p>Recently added to NSI offerings is <b>NEC-Win Synth</b>, a program to synthsize wire-grid structures for use in any NEC (-2/-4) program. The user may select a preset shape and enter critical dimensions or synthsize a structure with the spreadsheet entry facility. NEC-Win Synth can be directly linked to NEC-Win Plus or save its output in a standard .NEC file.</p>
|
||||
<p><a href="https://eznec.com/" target="_blank"><b>EZNEC</b></a> for Windows, both in basic and professional versions, is available from Roy Lewallen. See the general description of EZNEC/ELNEC products under NEC-4 above. <b>EZNEC 4.0</b>, the basic version of the NEC-2 programs, offers 3-D plots with 2-D slicing, ground-wave output, stepped diameter correction, and numerous short-cuts to antenna geometry modification. As well, there are new facilities for entering traps and considerable annotation capabilities. Standard EZNEC is restricted to 500 segments. <b>EZNEC Plus</b> offers additional wire construction and movement capabilities, along with a 1500-segment limit. <b>EZNEC Pro M</b> offers all of the features of EZNEC Pro/4, with the exception of being limited to the use of NEC-2.</p>
|
||||
<p><a href="https://www.nec2go.com/" target="_blank"><b>NEC2GO</b></a>, a general purpose Nec-2d interface to Windows, is available from Nova Plus Software. It provides "Modeling by Equation," sweeping of variables, and support for Coax and Ladder Line feedlines to show impedance transformation and loss. Features include unlimited segments, sources, and loads, shifting and rotating wire definitions, automatic segment generation and Tapering, Auto Gain Test and Average gain, quick convergence testing, automatic creation of plots at max gain angles, LAPACK routines, all NEC ground options, and NT-based feedpoint matching networks. The program is fully Windows compliant with no DOS executables. A free Demo Version is available.</p>
|
||||
<p><a href="https://www.qsl.net/4nec2/" target="_blank"><b>4NEC2</b></a> is a no-cost experimental version of NEC-2, with continuous development of its facilities and interface by its programmer, Arie Voors. Since the program changes with regularity as Arie introduces new features, such as improvements to the user interface and an optimizer, a detailed description is not feasible here. The program can be downloaded freely from the unofficial NEC Archives (see below).</p>
|
||||
<p><a href="https://www.gsolver.com/" target="_blank"><b>Antenna Solver</b></a> is a product of Grating Solver Development Co. that uses NEC-2 as rewritten into C++ using dynamic array allocation. The user interface, graphical editing features, and data display capabilities allow analysis of antenna patterns, of near, far, and ground-wave fields, as well as currents and charge densities. A full-featured version of the program can be downloaded in the "DEMO" mode for 30-day use, after which the purchase of a password will be needed to permanently enable the program.</p>
|
||||
<p><a href="https://web.archive.org/web/20130917054923/http://www.supernec.com/" target="_blank"><b>Poynting Software</b></a> (web.archive.org) is making available version 2.5 of its hybrid <b>NEC-2/UTD</b> program "SuperNEC," which is implemented in C++. The program has a parallel execution option. It makes use of MatLab 5.2 to run the program and avails itself of MatLab's many input and output facilities, such as the use of MatLab language assemblies that users may add to or modify. A version (SuperNEC Lite) which is restricted to 300 segments and 3 GTD objects is available at a student price, and a demo is available at the web site.</p>
|
||||
<p><b>EM Software and Systems</b> (http://www.emss.co.za/wiregrid/default.htm not found in web.archive.org) produces a specialized user interface for NEC called "<b>WireGrid</b>." The program is a graphical user interface that automates the process of creating surfaces via wire meshes, while providing visual feedback on the structure, sources, networks, and field points. A demonstration version of the program can be down loaded from the EMSS web site.</p>
|
||||
<center>
|
||||
<h3><i>Expert</i> MININEC</h3>
|
||||
</center>Before recent advances in speed and memory, it was not feasible to run NEC on a PC. Rockway and Logan developed MININEC, a Basic language adaptation of NEC for PCs. More recently, they have advanced the MININEC algorithms and code to overcome many of its initial limitations. The "new" MININEC can handle sharp angles in antenna geometry directly (without segment length tapering) and handles antennas close to ground with much better accuracy. However, the MININEC Professional code (as well as the input/output interfaces) is a proprietary product.
|
||||
<p><a href="https://web.archive.org/web/20100305135558/http://www.emsci.com/" target="_blank"><b>EM Scientific</b></a> (web.archive.org) offers several levels of <b><i>Expert</i> MININEC Professional</b>, ranging from the basic level <b>MININEC for Windows</b> to <b>MININEC Broadcast Professional</b>. The product-level distinctions include the number of segments and unknowns available; advanced features of geometry, electrical, and solution description; and auxiliary calculations. These are all Windows products.</p>
|
||||
<center>
|
||||
<h3>MININEC</h3>
|
||||
</center>The public domain MININEC code (version 3.13) is available with several commercial user interfaces, as indicated in these notes. For general antenna analysis that does not press its limitations, MININEC is a highly competent code. It handles elements of changing diameter directly, and with segment-length tapering, can accurately model a wide range of antenna geometries. However, horizontal antennas must be at least 0.2 wavelengths above ground for accurate results. Moreover, specification of ground conditions affects only antenna far field results, but not feedpoint conditions.
|
||||
<p><a href="https://web.archive.org/web/20110707150104/http://www.antennamodel.com/" target="_blank"><b>Antenna Model</b></a> (web.archive.org), (from Teri Software) which first appeared in a DOS version in 1992, has returned with an advanced Windows version of MININEC based on 3.13. Wholly reprogrammed, the core has virtually unlimited segment capacity for models and uses revised (and sometimes alternate) algorithms to overcome MININEC difficulties with errors with increasing frequency, angular junctions, wire junctions less than 28 degrees, and wires spaced closer than 0.23 wavelengths. The program offers both 2-D and 3-D patterns, and a variety of supplemental calculating features, for example, inductor calculations that include leads and distributed capacitance and matching networks including gamma, Tee, and beta (or hairpin). The program also permits for each wire separate values of conductivity and permeability, and it is able to import successfully a wide range of model files in .nec format.</p>
|
||||
<p><a href="https://web.archive.org/web/20170727192112/https://www.orionmicro.com/" target="_blank"><b>Orion</b></a> (web.archive.org) of Canada offers a Windows95/98/NT 32-bit version of MININEC, <b>NEC4WIN</b>, using a spreadsheet geometry input page, pull down boxes for other antenna parameters, and a pattern plotting output that includes lobe identification and bandwidth. In addition, the user can vary the height of the antenna without invoking a complete recalculation of the matrix for faster results. Recent upgrades include 3-D patterns, and optimization routines. The VM (virtual memory) version of the program permits almost unlimited numbers of segments in a model.</p>
|
||||
<p><a href="http://gal-ana.de/basicmm/en/" target="_blank"><b>MMANA</b></a>, version 0.5E (English language), is available as freeware from VK5KC's "MMHamsoft" website. Based upon public domain MININEC, the program offers a large segment (pulse) capacity because the author, JE3HHT, Makoto Mori, has placed the program in a Windows framework using C++. The program offers advanced features such as segment length tapering, optimizing, and network calculation, but lacks some basic features, such as assigning a user-specified material conductivity or resistivity to the model wires, frequency compensation, or close-wire compensation. However, the price (no-cost) is excellent, although there is no customer support for the package.</p>
|
||||
<center>
|
||||
<h3>Other MOM and Antenna Software</h3>
|
||||
</center><a href="https://www.ac6la.com" target="_blank"><b>MultiNEC</b></a> by Dan Maguire, is an Excel application that can make multiple simulation runs of an antenna model while automatically changing one or more aspects of the model between runs. The program requires that the user have one of the commercial implementations of NEC-2, a generic NEC-2 core, a NEC-4 program, or the Antenna Model implementation of MININEC. The program is now available in a new upgrade for a very low cost. However, AC6LA has ended support for this application.
|
||||
<p><a href="https://web.archive.org/web/20091226110200/http://esl.eng.ohio-state.edu/codes/codes.php" target="_blank"><b>NEC-BSC</b></a> (web.archive.org), the NEC-Basic Scattering Code (and its "workbench") and other MoM-related software (including EM Surface Patch Code, Reflector Antenna Code, and Aircraft Code) are available (at about $300 per package) from the Ohio State ElectroScience Laboratory.</p>
|
||||
<p><a href="https://web.archive.org/web/20120103085733/http://www.ansoft.com/" target="_blank"><b>Ansoft Ensemble</b></a> (web.archive.org) offers planar EM simulation software for RF and wireless design, providing s-parameters and full wave fields using MoM methods. The software is applicable to microstrip and planar microwave structures, including antennas and transmission line applications. A limited-function student version is available as a free download.</p>
|
||||
<p><a href="https://web.archive.org/web/20090719064855/http://www.emmcap.com.ar/" target="_blank"><b>EMMCAP</b></a> (web.archive.org) is a user-oriented 3D "Curved" MoM software for the modeling of arbitrarily shaped wire structures and for the computation of their electromagnetic behavior, including radiation and scattering problems. The code is based in a Method of Moments formulation with curved segments. It is intended for solving problems in the areas of antenna analysis and design, EMC applications, transmission lines and nonradiating networks. The modeling of the structure can be performed by means of the EMMCAP specific 3D-tools. System responses can be computed in a frequency sweep and plotted in 2D and 3D graphical representations.</p>
|
||||
<p><a href="https://www.raylcross.net/asap/" target="_blank"><b>ASAP</b></a>, Antenna Scatterers Analysis Program--originally developed by J. W. McCormack and made available as free downloadable software in the FORTRAN source code and PC executables by R. L. Cross--is a method-of-moment antenna analysis program with a "more English-like" input system.</p>
|
||||
<p><a href="https://pe2bz.philpem.me.uk/Comm01/-%20-%20Ion-Photon-RF/-%20MagnetoTuluric/-%20EMLIB/MOMIC/Main" target="_blank"><b>MOMIC</b></a>, made available without cost by Professor Andrzej Karwowski of the Silesian Technical University in Gliwice, Poland. MOMIC is a Method of Moments Interactive Code for numerical modeling of arbitrary thin-wire radiating and scattering structures in free space.</p>
|
||||
<p><a href="https://web.archive.org/web/20220401011737/https://www.g4hfq.co.uk/" target="_blank"><b>Polar Plot</b></a> (web.archive.org) is a program for the Windows 95/98 environment that uses the audio capabilities of the PC and a receiver to allow the user to generate a polar plot of his antenna. The program was developed for Windows by Bob Freeth, G4HFQ.</p>
|
||||
<p><a href="https://atlc.sourceforge.net/" target="_blank"><b>Arbitrary Transmission Line Calculator</b></a> is a suite of programs in C developed for the analysis and design of electrical transmission lines and directional couplers of totally arbitrary cross section. By analysis, it is assumed one requires to find the electrical properties of a transmission line or coupler, where the physical dimensions of the device are known. By design, it is assumed one requires a transmission line or coupler to have certain electrical properties and one wishes to find how to physically realise such a structure. The software is under general public license.</p>
|
||||
<p><a href="https://web.archive.org/web/20030608133424/https://www.demon.co.uk/asl/" target="_blank"><b>ASL Antenna Software Ltd</b></a> (web.archive.org) of Great Britain offers a range of specialized antenna software.</p>
|
||||
<p><a href="https://web.archive.org/web/20120624132921/http://www.cemtach.com/" target="_blank"><b>CEMTACH</b></a> (web.archive.org) offer specialized computational EM simulation services and software.</p>
|
||||
<p>The sources listed above have web pages for further information on the relevant software. Brian Beezley, K6STI, also has until recently offered a wide range of NEC-related software, as well as a Yagi optimization program, a terrain analysis program, and DSP software. Contact the author via mail, since the most recent e-mail address ([email protected]) may no longer be active.</p>
|
||||
<p>These listings do not include a considerable array of hybrid modeling programs (with the exception of Ensemble) that make use of multiple techniques--many, but not all, MoM based--to model circuitry (usually derived from PSpice lists or outputs), transmission lines, and antennas (including flat surfaces and substrates). Some are compatible with AutoCAD outputs for direct graphic-to-model links. Virtually all of the advanced versions of these programs are proprietary and expensive compared to NEC offerings. However, for many aspects of UHF and EHF design, they be the proper programs of choice.</p>
|
||||
<center>
|
||||
<h3>Additional Resources</h3>
|
||||
</center><a href="https://aces-society.org/" target="_blank"><b>The Applied Computational Electromagnetics Society</b> (<b>ACES</b>)</a> is perhaps the professional focal point of advances in all forms of electromagnetics codes and related mathematical models. It holds an annual meeting on the west coast in March with a very full and varied program.
|
||||
<p><a href="https://web.archive.org/web/20221204114240/https://nec-archives.pa3kj.com/" target="_blank"><b>The (Unofficial) NEC Archives</b></a> (web.archive.org) are maintained by Ray Anderson, WB6TPU. Formerly, this collection of NEC-related software has been available only via FTP. However, the entire contents are now accessible via the web. They include many source codes for NEC and for pre- and post-processing of NEC, along with some sample input files. Another valuable website of <a href="https://web.archive.org/web/20060425135800/http://www.nittany-scientific.com/nec/" target="_blank"><b>NEC-2 information</b></a> (web.archive.org) was originated by Peter Richeson and is now maintained by Nittany-Scientific.</p>
|
||||
<p>There are several self-study modeling courses available. <a href="https://www.arrl.org" target="_blank"><b>ARRL</b></a> offers <i>Antenna Modeling</i> in its Continuing Education Series. The 30-lesson course uses EZNEC and NEC-Win Plus to introduce basic modeling concepts, techniques, and limitations related to NEC-2. The volume and the exercise models are available independently of the tutored educational program for self-study purposes. An alternative tutorial geared to NEC-Win Plus is <a href="../classes/aids.html"><b><i>Basic Antenna Modeling: A Hands-On Tutorial</i></b></a>.</p>
|
||||
<p>For more advanced users of NEC-2 and NEC-4, NSI is releasing <a href="../classes/aids.html"><b><i>Intermediate Antenna Modeling: A Hands-On Tutorial</i></b></a>. This self-study volume encompasses virtually the entire command sets for both cores, including details of command revisions in the transition between NEC-2 and NEC-4. The 450-page volume includes about 300 exercise models in .NEC format. Although geared to the cores used by NSI (NEC-Won Pro and GNEC), the volume is useful with almost any version of NEC-2 or NEC-4.</p>
|
||||
<p>To examine some of the differences among the NEC and MININEC offerings, see <i>QEX</i>, for Sep/Oct, 2005, and Nov/Dec, 2005. The 2-part series text and graphics provide an overview of significant user differences among programs, many of which appear in the above listing. It can be interesting to compare this overview to an earlier version that appeared in <i>QEX</i>, Mar/Apr, 1998. The differences will show the rate of change and of development in the field of antenna modeling software.</p>
|
||||
<p>There are--for many reasons--no instructional manuals for MININEC of the scope and independence of the self-study course for NEC. Software instruction manuals or "help" compendiums may be the best source of instruction. However, you may wish to get started by looking back to "A Beginner's Guide to Using Computer Antenna Modeling Programs," from <i>The ARRL Antenna Compendium</i>, Volume 3, reprinted in <i>Vertical Antenna Classics</i>.</p>
|
||||
<p>For more details on the use of commands, the limitations of various NEC and MININEC programs, and numerous work-arounds, see the Antenna Modeling series that appears monthly in <i>antenneX</i>. You can freely view past columns (at this site in the <a href="../amod/modeling.html"><b><i>Antenna Modeling</i></b></a> series).</p>
|
||||
<p>This listing is necessarily limited. However, the indicated web pages will lead you to other information on details, specifications, related developments, and a more complete understanding of the rapidly expanding field of electromagnetic modeling. However, as with all software information, development efforts quickly outrun written accounts.</p>
|
||||
<center>
|
||||
<img src="../images/colorbar.gif" width="540" height="4">
|
||||
</center>
|
||||
<p><i>Updated 03-10-2008. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.</i></p>
|
||||
<center>
|
||||
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
|
||||
</center>
|
||||
<p><a href="../radio.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Return to Main Index</a></p>
|
||||
<p class="topics-footer">Topics: <a href='../topics.html#modeling'>Modeling</a></p><br>
|
||||
</body>
|
||||
</html>
|
||||
@@ -0,0 +1,596 @@
|
||||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<meta charset="UTF-8">
|
||||
<meta name="keywords" content="Modeling, Stepped Diameter">
|
||||
<title>NEC-4 vs. NEC-2 Stepped-Diameter Correction and Auto-Segmentation</title>
|
||||
<link rel="stylesheet" href="../styles.css">
|
||||
</head>
|
||||
<body>
|
||||
<img src="../images/antbott.gif" align="left" width="150" height="77"><img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10">
|
||||
<center>
|
||||
<h1>NEC-4 vs. NEC-2 With Stepped-Diameter Correction<br>
|
||||
and Auto-Segmentation</h1>
|
||||
</center>
|
||||
<center>
|
||||
<h3>L. B. Cebik, W4RNL</h3>
|
||||
</center><br>
|
||||
<br>
|
||||
<center>
|
||||
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
|
||||
</center><br>
|
||||
<br>
|
||||
<p>NEC-4 is supposed to overcome several limitations of NEC-2, notable among which is the ability to handle with computational accuracy stepped-diameter elements. Implementations of NEC-2, such as EZNEC, employ a correction factor, substituting a single wire for the linear stepped-diameter group, the single wire diameter being calculated according to a formula. In the case of EZNEC, the technique follows that of Leeson.</p>
|
||||
<p>One might be tempted to simply transfer a NEC-2 model--designed for use with a stepped-diameter correction equivalency--directly to NEC-4 in order to check the accuracy of the equivalency output. However, NEC-4 is subject to its own limitations, and model adjustment is necessary.</p>
|
||||
<p>Initial comparative tests of models, performed on EZNEC Pro for ease of comparing NEC-2 corrected, NEC-2 uncorrected, and NEC-4 models, have turned up a number of interesting factors involved in transferring models. Tests were performed on Yagi antenna models developed by K6STI and presented on disk with the <i>ARRL Antenna Compendium</i>, Volume 4. One notable feature of K6STI's models is the use of short, fat element-center sections to account for mounting plates and other boom-related phenomena. This factor alone presents all versions of NEC with a challenge insofar as the diameter jump is great between the center and the immediately adjacent segments.</p>
|
||||
<p>To facilitate examination of the variances among models, I have set forth notes on the tables that immediate follow. The tables show gain, front-to- back ratio, and feedpoint impedance of models using various segmentations. "Auto S Min" = auto-segmentation, using recommended absolute minimal numbers of segments. "Auto S Con"" = auto-segmentation using recommended conservative minimal numbers of segments. The following entries represent manual segmentation designed to equalized segment lengths and, to the degree possible within the limits of the structure, to align the segments for greatest accuracy.</p>
|
||||
<p>Following each set of notes and tables are sample models used in this study, given in the form of NEC decks, with all units in meters.</p>
|
||||
<center>
|
||||
<h4>1. 240-20</h4>
|
||||
</center>The first model is a 2-element 40-meter Yagi for 7.1 MHz. The K6STI segmentation and antenna performance date are shown for reference. The entry called "Space" represents the distance rear to front of the elements. In this case, the reflector and driven element are separate by 234." All dimensions are in inches. K6STI's rearward performance figure is not directly comparable to front-to-back ratio, since it is actually a front- to-rear ratio that averages rear quadrant performance. For a 2-element Yagi, this figure will normally exceed a direct front-to-back ratio.
|
||||
<p><b>Notes:</b></p>
|
||||
<p>1. Because the centermost element section is very short, neither mode of auto-segmentation is adequate to produce a center segment anywhere close to the length of the adjacent segments. NEC-4 is sensitive to this factor, especially where there is considerable current on the unequal adjoining segments. When the center segment is very short (even though passing NEC-4 criteria checks), the gain is generally too optimistic. The last entry, which purposely makes the center segment significantly longer than adjacent segments, typically yields a pessimistic gain.</p>
|
||||
<p>2. The 58 segment manually segmented model approaches adequacy, as verified by the 116 segment model, which again was manually segmented to equalize segment length and alignment. The two models may be considered as having achieved convergence. What these models have in common is equalized segment lengths and segment alignment within structural limits, NEC-4 modeling factors that cannot be overstressed.</p>
|
||||
<p>3. NEC-2 models that do not employ a stepped-diameter correction are wholly inadequate to this task. Since convergence is not possible, model accuracy is in no way self-identifying.</p>
|
||||
<p>4. NEC-2 models employing stepped-diameter correction appear closest to NEC-4 converged models when using the minimum number of segments consistent with NEC conservative guidelines for element length and length-to-diameter ratio. Note that the NEC-2 corrected model that is auto-segmented by conservative standards most closely coincides with the values accepted above as reasonable for NEC-4.</p>
|
||||
<p>5. To check the sensitivity of NEC-4 and NEC-2 corrected to the large jump in element diameter close to the high current section of the antenna, an alternate model was constructed. The only change was to reduce the center section diameter from 4.7" to 2.5." Since this antenna now differs from the K6STI model, output figure comparisons must be confined within the model group. Once more, NEC-4 shows its sensitivity to segment length equalization at the center of the elements. Auto-segmentation is inadequate to achieve segment equalization for this particular model. However, NEC-2 with a stepped-diameter correction produces a model that coincides with the converged NEC-4 model only with manual segmentation to equalize segment lengths. This raises the question of whether the note in item 4 above is a rule or an accident. If an accident, then confidence in models using a stepped-diameter correction is compromised, even if the results are not as far afield as the results from NEC-2 when no stepped-diameter correction is used.</p>
|
||||
<pre>K6STI Model 240-20: 2-element Yagi; 7.1 MHz
|
||||
|
||||
Element tapered dimensions from center outward in inches:
|
||||
El. Space 4.7" 2.25" 2" 1" .75" 0.5" Total
|
||||
Refl 0 12 108 120 66 66 85 457"
|
||||
D.E. 234 12 108 120 66 66 25.5 397.5"
|
||||
|
||||
K6STI Reference (YO) 6.12 11.08 34.0 - 34.5
|
||||
|
||||
NEC-4 Segs Gain dBi F-B dB Feed Z R +/- jX
|
||||
Auto S Min 22 7.37 10.60 29.68 - 22.26
|
||||
Auto S Con 32 6.75 10.54 34.32 - 25.31
|
||||
20A-1 ctr 58 6.23 10.44 38.92 - 27.05
|
||||
20B-2 ctr 116 6.23 10.30 39.42 - 24.52
|
||||
20B-1 ctr 114 5.86 10.30 42.88 - 26.88
|
||||
|
||||
NEC-2 with stepped-diameter correction
|
||||
Auto S Min 22 6.69 10.75 33.14 - 30.60
|
||||
Auto S Con 32 6.21 10.68 37.03 - 33.82
|
||||
20A-1 ctr 58 5.85 10.66 40.31 - 36.78
|
||||
20B-2 ctr 116 7.13 10.45 34.48 + 4.097
|
||||
20B-1 ctr 114 5.58 10.62 43.02 - 38.43
|
||||
|
||||
NEC-2 without stepped-diameter correction
|
||||
Auto S Min 22 7.32 9.43 31.97 - 9.381
|
||||
Auto S Con 32 6.80 9.15 36.38 - 8.086
|
||||
20A-1 ctr 58 6.35 8.67 41.02 - 3.797
|
||||
20B-2 ctr 116 6.47 8.20 40.59 + 1.733
|
||||
20B-1 ctr 114 6.04 8.21 44.81 + 1.611
|
||||
|
||||
Revised Taper: First Segment 2.5"
|
||||
|
||||
NEC-4 Segs Gain dBi F-B dB Feed Z R +/- jX
|
||||
Auto S Min 22
|
||||
Auto S Con 32 6.33 10.38 38.00 - 25.30
|
||||
20A-1 ctr 58 5.89 10.27 42.30 - 26.35
|
||||
20B-2 ctr 116 5.84 10.12 43.34 - 24.09
|
||||
20B-1 ctr 114 5.55 10.12 46.21 - 25.79
|
||||
|
||||
NEC-2 with stepped-diameter correction
|
||||
Auto S Min 22
|
||||
Auto S Con 32 6.14 10.46 38.21 - 30.29
|
||||
20A-1 ctr 58 5.78 10.44 41.59 - 32.95
|
||||
20B-2 ctr 116 6.04 10.25 44.48 + 5.403
|
||||
20B-1 ctr 114 5.51 10.40 44.37 - 34.37
|
||||
|
||||
NEC-2 without stepped-diameter correction
|
||||
Auto S Min 22
|
||||
Auto S Con 32 6.01 9.02 43.58 - 8.877
|
||||
20A-1 ctr 58 5.52 8.56 49.62 - 3.890
|
||||
20B-2 ctr 116 5.43 8.12 51.51 + 2.456
|
||||
20B-1 ctr 114 5.14 8.12 55.08 + 2.538
|
||||
</pre>
|
||||
<pre>CM 2el Yagi 240-20: 32 segments
|
||||
CM Auto-segmented
|
||||
CE
|
||||
GW 1,2,-11.607,0.,0.,-9.4488,0.,0.,.00635
|
||||
GW 2,1,-9.4488,0.,0.,-7.7724,0.,0.,.00953
|
||||
GW 3,1,-7.7724,0.,0.,-6.096,0.,0.,.0127
|
||||
GW 4,2,-6.096,0.,0.,-3.048,0.,0.,.0254
|
||||
GW 5,2,-3.048,0.,0.,-.3048,0.,0.,.0286
|
||||
GW 6,1,-.3048,0.,0.,.3048,0.,0.,.0597
|
||||
GW 7,2,.3048,0.,0.,3.048,0.,0.,.0286
|
||||
GW 8,2,3.048,0.,0.,6.096,0.,0.,.0254
|
||||
GW 9,1,6.096,0.,0.,7.7724,0.,0.,.0127
|
||||
GW 10,1,7.7724,0.,0.,9.4488,0.,0.,.00953
|
||||
GW 11,2,9.4488,0.,0.,11.6078,0.,0.,.00635
|
||||
GW 12,1,-10.096,5.9436,0.,-9.4488,5.9436,0.,.00635
|
||||
GW 13,1,-9.4488,5.9436,0.,-7.7724,5.9436,0.,.00953
|
||||
GW 14,1,-7.7724,5.9436,0.,-6.096,5.9436,0.,.0127
|
||||
GW 15,2,-6.096,5.9436,0.,-3.048,5.9436,0.,.0254
|
||||
GW 16,2,-3.048,5.9436,0.,-.3048,5.9436,0.,.0286
|
||||
GW 17,1,-.3048,5.9436,0.,.3048,5.9436,0.,.0597
|
||||
GW 18,2,.3048,5.9436,0.,3.048,5.9436,0.,.0286
|
||||
GW 19,2,3.048,5.9436,0.,6.096,5.9436,0.,.0254
|
||||
GW 20,1,6.096,5.9436,0.,7.7724,5.9436,0.,.0127
|
||||
GW 21,1,7.7724,5.9436,0.,9.4488,5.9436,0.,.00953
|
||||
GW 22,1,9.4488,5.9436,0.,10.0965,5.9436,0.,.00635
|
||||
GE 0
|
||||
LD 5,1,0,0,2.5E+07,1.
|
||||
LD 5,2,0,0,2.5E+07,1.
|
||||
LD 5,3,0,0,2.5E+07,1.
|
||||
LD 5,4,0,0,2.5E+07,1.
|
||||
LD 5,5,0,0,2.5E+07,1.
|
||||
LD 5,6,0,0,2.5E+07,1.
|
||||
LD 5,7,0,0,2.5E+07,1.
|
||||
LD 5,8,0,0,2.5E+07,1.
|
||||
LD 5,9,0,0,2.5E+07,1.
|
||||
LD 5,10,0,0,2.5E+07,1.
|
||||
LD 5,11,0,0,2.5E+07,1.
|
||||
LD 5,12,0,0,2.5E+07,1.
|
||||
LD 5,13,0,0,2.5E+07,1.
|
||||
LD 5,14,0,0,2.5E+07,1.
|
||||
LD 5,15,0,0,2.5E+07,1.
|
||||
LD 5,16,0,0,2.5E+07,1.
|
||||
LD 5,17,0,0,2.5E+07,1.
|
||||
LD 5,18,0,0,2.5E+07,1.
|
||||
LD 5,19,0,0,2.5E+07,1.
|
||||
LD 5,20,0,0,2.5E+07,1.
|
||||
LD 5,21,0,0,2.5E+07,1.
|
||||
LD 5,22,0,0,2.5E+07,1.
|
||||
FR 0,1,0,0,7.1
|
||||
GN -1
|
||||
EX 0,17,1,0,1.414214,-1.883E-7
|
||||
RP 0,1,361,1000,90.,0.,0.,1.,0.
|
||||
EN
|
||||
</pre>
|
||||
<pre>CM 2el Yagi 240-20: 116 segments
|
||||
CM Manually segmented for equal lengths
|
||||
CE
|
||||
GW 1,6,-11.607,0.,0.,-9.4488,0.,0.,.00635
|
||||
GW 2,4,-9.4488,0.,0.,-7.7724,0.,0.,.00953
|
||||
GW 3,4,-7.7724,0.,0.,-6.096,0.,0.,.0127
|
||||
GW 4,8,-6.096,0.,0.,-3.048,0.,0.,.0254
|
||||
GW 5,8,-3.048,0.,0.,-.3048,0.,0.,.0286
|
||||
GW 6,2,-.3048,0.,0.,.3048,0.,0.,.0597
|
||||
GW 7,8,.3048,0.,0.,3.048,0.,0.,.0286
|
||||
GW 8,8,3.048,0.,0.,6.096,0.,0.,.0254
|
||||
GW 9,4,6.096,0.,0.,7.7724,0.,0.,.0127
|
||||
GW 10,4,7.7724,0.,0.,9.4488,0.,0.,.00953
|
||||
GW 11,6,9.4488,0.,0.,11.6078,0.,0.,.00635
|
||||
GW 12,2,-10.096,5.9436,0.,-9.4488,5.9436,0.,.00635
|
||||
GW 13,4,-9.4488,5.9436,0.,-7.7724,5.9436,0.,.00953
|
||||
GW 14,4,-7.7724,5.9436,0.,-6.096,5.9436,0.,.0127
|
||||
GW 15,8,-6.096,5.9436,0.,-3.048,5.9436,0.,.0254
|
||||
GW 16,8,-3.048,5.9436,0.,-.3048,5.9436,0.,.0286
|
||||
GW 17,2,-.3048,5.9436,0.,.3048,5.9436,0.,.0597
|
||||
GW 18,8,.3048,5.9436,0.,3.048,5.9436,0.,.0286
|
||||
GW 19,8,3.048,5.9436,0.,6.096,5.9436,0.,.0254
|
||||
GW 20,4,6.096,5.9436,0.,7.7724,5.9436,0.,.0127
|
||||
GW 21,4,7.7724,5.9436,0.,9.4488,5.9436,0.,.00953
|
||||
GW 22,2,9.4488,5.9436,0.,10.0965,5.9436,0.,.00635
|
||||
GE 0
|
||||
LD 5,1,0,0,2.5E+07,1.
|
||||
LD 5,2,0,0,2.5E+07,1.
|
||||
LD 5,3,0,0,2.5E+07,1.
|
||||
LD 5,4,0,0,2.5E+07,1.
|
||||
LD 5,5,0,0,2.5E+07,1.
|
||||
LD 5,6,0,0,2.5E+07,1.
|
||||
LD 5,7,0,0,2.5E+07,1.
|
||||
LD 5,8,0,0,2.5E+07,1.
|
||||
LD 5,9,0,0,2.5E+07,1.
|
||||
LD 5,10,0,0,2.5E+07,1.
|
||||
LD 5,11,0,0,2.5E+07,1.
|
||||
LD 5,12,0,0,2.5E+07,1.
|
||||
LD 5,13,0,0,2.5E+07,1.
|
||||
LD 5,14,0,0,2.5E+07,1.
|
||||
LD 5,15,0,0,2.5E+07,1.
|
||||
LD 5,16,0,0,2.5E+07,1.
|
||||
LD 5,17,0,0,2.5E+07,1.
|
||||
LD 5,18,0,0,2.5E+07,1.
|
||||
LD 5,19,0,0,2.5E+07,1.
|
||||
LD 5,20,0,0,2.5E+07,1.
|
||||
LD 5,21,0,0,2.5E+07,1.
|
||||
LD 5,22,0,0,2.5E+07,1.
|
||||
FR 0,1,0,0,7.1
|
||||
GN -1
|
||||
EX 0,17,2,0,.707107,-9.416E-8
|
||||
EX 0,17,1,0,.707107,-9.416E-8
|
||||
RP 0,1,361,1000,90.,0.,0.,1.,0.
|
||||
EN
|
||||
</pre>
|
||||
<center>
|
||||
<h4>2. 310-08</h4>
|
||||
</center>The second example is a 3-element Yagi designed for 28.4 MHz. For the most part, front-to-back ratios can be ignored, since they reflect only the depth of the pucker in the rear lobe(s) and do not give a clear picture of the rearward radiation. Indeed, no single number can do this job. The clearest non-graphical portrait of rearward radiation comes from a combination of the front-to-back ratio, the front-to-rear average ratio, and the "worst case" rearward ratio. This example is most notable for its exceptionally short element center section (4"). The alternative model simply eliminates this section and continues the 0.75" tubing across the center. Boom lengths total 90" with the element spacing shown.
|
||||
<p><b>Notes:</b></p>
|
||||
<p>1. As noted for the 2-element, 40-meter Yagi, NEC-2 without a stepped- diameter correction overestimates gain in both the original and the alternate model. However, in accord with generally received wisdom, the alternate model is closest to converged models with somewhat minimal segmentation. However, there is no convergence to self-identify the most reliable result.</p>
|
||||
<p>2. For the original design, NEC-4 models only approach convergence at 283 segments. Even that large model suffers from the large center-section to adjacent-section diameter jump insofar as the center section is longer than desired. However, breaking it into 2 segments exceeds the recommended diameter-to-length ratio.</p>
|
||||
<p>3. For the alternate model, NEC-4 results converge reasonably between the conservative auto-segmentation version and the manually segmented and equalized version. The 48" center section of each element provides a foundation for more reliable outputs with a far smaller model than needed for the original design.</p>
|
||||
<p>4. With this antenna design, NEC-2 results for stepped-diameter correction tend to approach NEC-4 convergence within the range of the smallest reliable NEC-4 model. However, even stepped-diameter correction results tend to progress through the NEC-4 convergence point, indicating an absence of a reliable convergence region and hence lesser confidence in the chosen model size without a cross-reference to NEC-4.</p>
|
||||
<pre>K6STI Model 310-08: 3-element Yagi; 28.4 MHz
|
||||
|
||||
Element tapered dimensions from center outward in inches:
|
||||
El. Space 2.5" .75" .625" .5" Total
|
||||
Refl 0 2 22 18 66.75 108.75"
|
||||
D.E. 36 2 22 18 57.625 99.625"
|
||||
Dir 90 2 22 18 53.125 95.125
|
||||
|
||||
K6STI Reference (YO) 7.21 22.91 25.1 - 24.4
|
||||
|
||||
NEC-4 Segs Gain dBi F-B dB Feed Z R +/- jX
|
||||
Auto S Min 27 10.15 38.92 12.93 - 14.32
|
||||
Auto S Con 42 9.34 25.28 15.72 - 16.78
|
||||
08A-1 ctr 73 8.88 36.54 17.32 - 17.86
|
||||
08B-1 ctr 143 8.14 35.63 20.33 - 20.41
|
||||
08C-1 ctr 213 7.68 35.21 22.57 - 22.45
|
||||
08D-1 ctr 283 7.32 35.22 24.50 - 24.49
|
||||
|
||||
NEC-2 with stepped-diameter correction
|
||||
Auto S Min 27 8.33 31.30 20.19 - 21.84
|
||||
Auto S Con 42 7.80 37.49 23.12 - 24.08
|
||||
08A-1 ctr 73 7.52 42.85 24.55 - 24.94
|
||||
08B-1 ctr 143 7.11 50.08 26.87 - 26.84
|
||||
08C-1 ctr 213 6.92 55.47 28.02 - 27.82
|
||||
08D-1 ctr 283 6.81 59.46 28.76 - 28.43
|
||||
|
||||
NEC-2 without stepped-diameter correction
|
||||
Auto S Min 27 11 22 28.91 9.46 - 8.74
|
||||
Auto S Con 42 10.81 24.99 10.34 - 8.81
|
||||
08A-1 ctr 73 10.68 21.84 10.18 - 7.63
|
||||
08B-1 ctr 143 10.59 19.39 9.91 - 6.25
|
||||
08C-1 ctr 213 10.61 18.26 9.57 - 5.34
|
||||
08D-1 ctr 283 10.65 17.57 9.30 - 4.70
|
||||
|
||||
NEC-4
|
||||
Auto S Min 21 6.96 37.69 27.29 - 27.44
|
||||
Auto S Con 35 7.26 37.34 25.16 - 24.73
|
||||
081X eq 68 7.30 33.06 24.69 - 23.23
|
||||
|
||||
NEC-2 with stepped-diameter correction
|
||||
Auto S Min 21 6.88 48.93 28.25 - 27.66
|
||||
Auto S Con 35 7.17 41.08 26.23 - 25.04
|
||||
081X eq 68 7.32 41.99 26.56 - 13.47
|
||||
|
||||
NEC-2 without stepped-diameter correction
|
||||
Auto S Min 21 7.08 29.59 25.35 - 22.42
|
||||
Auto S Con 35 7.42 25.38 22.85 - 18.83
|
||||
081X eq 68 7.51 21.93 21.42 - 15.35
|
||||
</pre>
|
||||
<pre>CM 3el Yagi 310-08 42 segments
|
||||
CM Conservative autosegmentation
|
||||
CE
|
||||
GW 1,5,-2.7622,0.,0.,-1.0668,0.,0.,.00635
|
||||
GW 2,1,-1.0668,0.,0.,-.6096,0.,0.,.00794
|
||||
GW 3,2,-.6096,0.,0.,-.0508,0.,0.,.00953
|
||||
GW 4,1,-.0508,0.,0.,.0508,0.,0.,.0318
|
||||
GW 5,2,.0508,0.,0.,.6096,0.,0.,.00953
|
||||
GW 6,1,.6096,0.,0.,1.0668,0.,0.,.00794
|
||||
GW 7,4,1.0668,0.,0.,2.76225,0.,0.,.00635
|
||||
GW 8,3,-2.5304,.9144,0.,-1.0668,.9144,0.,.00635
|
||||
GW 9,1,-1.0668,.9144,0.,-.6096,.9144,0.,.00794
|
||||
GW 10,2,-.6096,.9144,0.,-.0508,.9144,0.,.00953
|
||||
GW 11,1,-.0508,.9144,0.,.0508,.9144,0.,.0318
|
||||
GW 12,2,.0508,.9144,0.,.6096,.9144,0.,.00953
|
||||
GW 13,1,.6096,.9144,0.,1.0668,.9144,0.,.00794
|
||||
GW 14,3,1.0668,.9144,0.,2.53047,.9144,0.,.00635
|
||||
GW 15,3,-2.4161,2.286,0.,-1.0668,2.286,0.,.00635
|
||||
GW 16,1,-1.0668,2.286,0.,-.6096,2.286,0.,.00794
|
||||
GW 17,2,-.6096,2.286,0.,-.0508,2.286,0.,.00953
|
||||
GW 18,1,-.0508,2.286,0.,.0508,2.286,0.,.0318
|
||||
GW 19,2,.0508,2.286,0.,.6096,2.286,0.,.00953
|
||||
GW 20,1,.6096,2.286,0.,1.0668,2.286,0.,.00794
|
||||
GW 21,3,1.0668,2.286,0.,2.41617,2.286,0.,.00635
|
||||
GE 0
|
||||
LD 5,1,0,0,2.5E+07,1.
|
||||
LD 5,2,0,0,2.5E+07,1.
|
||||
LD 5,3,0,0,2.5E+07,1.
|
||||
LD 5,4,0,0,2.5E+07,1.
|
||||
LD 5,5,0,0,2.5E+07,1.
|
||||
LD 5,6,0,0,2.5E+07,1.
|
||||
LD 5,7,0,0,2.5E+07,1.
|
||||
LD 5,8,0,0,2.5E+07,1.
|
||||
LD 5,9,0,0,2.5E+07,1.
|
||||
LD 5,10,0,0,2.5E+07,1.
|
||||
LD 5,11,0,0,2.5E+07,1.
|
||||
LD 5,12,0,0,2.5E+07,1.
|
||||
LD 5,13,0,0,2.5E+07,1.
|
||||
LD 5,14,0,0,2.5E+07,1.
|
||||
LD 5,15,0,0,2.5E+07,1.
|
||||
LD 5,16,0,0,2.5E+07,1.
|
||||
LD 5,17,0,0,2.5E+07,1.
|
||||
LD 5,18,0,0,2.5E+07,1.
|
||||
LD 5,19,0,0,2.5E+07,1.
|
||||
LD 5,20,0,0,2.5E+07,1.
|
||||
LD 5,21,0,0,2.5E+07,1.
|
||||
FR 0,1,0,0,28.4
|
||||
GN -1
|
||||
EX 0,11,1,0,1.414214,0.
|
||||
RP 0,1,361,1000,90.,0.,0.,1.,0.
|
||||
EN
|
||||
</pre>
|
||||
<pre>CM 3el Yagi 310-081X 68 segment alternate
|
||||
CM Manually segmented for equalized segments
|
||||
CE
|
||||
GW 1,7,-2.7622,0.,0.,-1.0668,0.,0.,.00635
|
||||
GW 2,2,-1.0668,0.,0.,-.6096,0.,0.,.00794
|
||||
GW 3,6,-.6096,0.,0.,.6096,0.,0.,.00953
|
||||
GW 4,2,.6096,0.,0.,1.0668,0.,0.,.00794
|
||||
GW 5,7,1.0668,0.,0.,2.76225,0.,0.,.00635
|
||||
GW 6,6,-2.5304,.9144,0.,-1.0668,.9144,0.,.00635
|
||||
GW 7,2,-1.0668,.9144,0.,-.6096,.9144,0.,.00794
|
||||
GW 8,6,-.6096,.9144,0.,.6096,.9144,0.,.00953
|
||||
GW 9,2,.6096,.9144,0.,1.0668,.9144,0.,.00794
|
||||
GW 10,6,1.0668,.9144,0.,2.53047,.9144,0.,.00635
|
||||
GW 11,6,-2.4161,2.286,0.,-1.0668,2.286,0.,.00635
|
||||
GW 12,2,-1.0668,2.286,0.,-.6096,2.286,0.,.00794
|
||||
GW 13,6,-.6096,2.286,0.,.6096,2.286,0.,.00953
|
||||
GW 14,2,.6096,2.286,0.,1.0668,2.286,0.,.00794
|
||||
GW 15,6,1.0668,2.286,0.,2.41617,2.286,0.,.00635
|
||||
GE 0
|
||||
LD 5,1,0,0,2.5E+07,1.
|
||||
LD 5,2,0,0,2.5E+07,1.
|
||||
LD 5,3,0,0,2.5E+07,1.
|
||||
LD 5,4,0,0,2.5E+07,1.
|
||||
LD 5,5,0,0,2.5E+07,1.
|
||||
LD 5,6,0,0,2.5E+07,1.
|
||||
LD 5,7,0,0,2.5E+07,1.
|
||||
LD 5,8,0,0,2.5E+07,1.
|
||||
LD 5,9,0,0,2.5E+07,1.
|
||||
LD 5,10,0,0,2.5E+07,1.
|
||||
LD 5,11,0,0,2.5E+07,1.
|
||||
LD 5,12,0,0,2.5E+07,1.
|
||||
LD 5,13,0,0,2.5E+07,1.
|
||||
LD 5,14,0,0,2.5E+07,1.
|
||||
LD 5,15,0,0,2.5E+07,1.
|
||||
FR 0,1,0,0,28.4
|
||||
GN -1
|
||||
EX 0,8,4,0,.707107,0.
|
||||
EX 0,8,3,0,.707107,0.
|
||||
RP 0,1,361,1000,90.,0.,0.,1.,0.
|
||||
EN</pre>
|
||||
<center>
|
||||
<h4>3. 320-16</h4>
|
||||
</center>The third example is a 3-element Yagi designed for 14.175 MHz. Cautions similar to those given for the 10-meter beam apply to the front-to-back ratios. Also, like the 10-meter design, this example has a short element center section (8"). Because the properties of this antenna design when modeled replicate so closely those of the 10-meter model, no alternate version is shown.
|
||||
<p><b>Notes:</b></p>
|
||||
<p>1. NEC-2 without a stepped correction factor displaces the beam relative to frequency and overestimates gain while underestimating front-to-back ratio and feedpoint impedance. Because the number of steps per half- element is 50% greater than the steps used for the 10-meter beam, the offset is even worse.</p>
|
||||
<p>2. The center element diameter is about 3 times the adjacent section diameter. However, the number of diameter steps is large. These factors combine to set a practical limit to achieving convergence in NEC-4. Although the final doubling of segments between 16B and 16C shows an approach to convergence, the model has grown to 442 segments. The reasonableness of convergence and use of the output numbers at this level will depend upon the purposes of the modeling.</p>
|
||||
<p>3. As with the 10-meter model, the NEC-2 with stepped-diameter correction numbers approach those of a converged NEC-4 model somewhere between the conservative auto-segmented version and the smallest manually segmented and equalized version. However, again, this point is not self-identifying within NEC-2, since the model continues to vary in value with changes in the number of segments. Notable in this progression is a clear indication that too many segments defeats the stepped-diameter correction and produces results little better than NEC-2 without the stepped-diameter correction.</p>
|
||||
<pre>K6STI Model 320-16: 3-element Yagi; 14.175 MHz
|
||||
|
||||
Element tapered dimensions from center outward in inches:
|
||||
El. Space 3.75 1.25 1.0 .875 .75 .625" .5" Total
|
||||
Refl 0 4 44 24 20 42 20 69.625 223.625"
|
||||
D.E. 80 4 44 24 20 42 20 51.25 205.25"
|
||||
Dir 186 4 44 24 20 42 20 46.625 196.625"
|
||||
|
||||
K6STI Reference (YO) 7.25 23.32 26.7 - 25.3
|
||||
|
||||
NEC-4 Segs Gain dBi F-B dB Feed Z R +/- jX
|
||||
Auto S Min 39 9.84 33.04 14.66 - 15.32
|
||||
Auto S Con 57 9.08 33.24 17.44 - 17.73
|
||||
16A-1 ctr 112 8.40 31.39 20.08 - 19.58
|
||||
16B-1 ctr 221 7.83 29.04 22.54 - 21.02
|
||||
16C-2 ctr 442 7.74 27.80 22.74 - 20.73
|
||||
|
||||
NEC-2 with stepped-diameter correction
|
||||
Auto S Min 39 8.25 36.90 22.16 - 22.75
|
||||
Auto S Con 57 7.77 48.71 24.77 - 24.48
|
||||
16A-1 ctr 112 7.35 45.51 27.19 - 26.40
|
||||
16B-1 ctr 221 7.02 41.97 29.17 - 28.02
|
||||
16C-2 ctr 442 10.23 43.00 16.05 + 4.83
|
||||
|
||||
NEC-2 without stepped diamter correction
|
||||
Auto S Min 39 10 87 19.04 9.37 - 5.82
|
||||
Auto S Con 57 10.48 16.74 9.69 - 4.33
|
||||
16A-1 ctr 112 10.30 13.80 8.97 - 0.60
|
||||
16B-1 ctr 221 10.28 11.40 7.89 + 3.67
|
||||
16C-2 ctr 442 10.94 9.31 5.85 + 7.02</pre>
|
||||
<pre>CM 3el Yagi 320-16 57 segments
|
||||
CM Conservative autosegmentation
|
||||
CE
|
||||
GW 1,2,-5.68,0.,0.,-3.9116,0.,0.,.00635
|
||||
GW 2,1,-3.9116,0.,0.,-3.4036,0.,0.,.00794
|
||||
GW 3,2,-3.4036,0.,0.,-2.3368,0.,0.,.00953
|
||||
GW 4,1,-2.3368,0.,0.,-1.8288,0.,0.,.0111
|
||||
GW 5,1,-1.8288,0.,0.,-1.2192,0.,0.,.0127
|
||||
GW 6,2,-1.2192,0.,0.,-.1016,0.,0.,.0159
|
||||
GW 7,1,-.1016,0.,0.,.1016,0.,0.,.0476
|
||||
GW 8,2,.1016,0.,0.,1.2192,0.,0.,.0159
|
||||
GW 9,1,1.2192,0.,0.,1.8288,0.,0.,.0127
|
||||
GW 10,1,1.8288,0.,0.,2.3368,0.,0.,.0111
|
||||
GW 11,2,2.3368,0.,0.,3.4036,0.,0.,.00953
|
||||
GW 12,1,3.4036,0.,0.,3.9116,0.,0.,.00794
|
||||
GW 13,2,3.9116,0.,0.,5.68008,0.,0.,.00635
|
||||
GW 14,2,-5.2133,2.032,0.,-3.9116,2.032,0.,.00635
|
||||
GW 15,1,-3.9116,2.032,0.,-3.4036,2.032,0.,.00794
|
||||
GW 16,2,-3.4036,2.032,0.,-2.3368,2.032,0.,.00953
|
||||
GW 17,1,-2.3368,2.032,0.,-1.8288,2.032,0.,.0111
|
||||
GW 18,1,-1.8288,2.032,0.,-1.2192,2.032,0.,.0127
|
||||
GW 19,2,-1.2192,2.032,0.,-.1016,2.032,0.,.0159
|
||||
GW 20,1,-.1016,2.032,0.,.1016,2.032,0.,.0476
|
||||
GW 21,2,.1016,2.032,0.,1.2192,2.032,0.,.0159
|
||||
GW 22,1,1.2192,2.032,0.,1.8288,2.032,0.,.0127
|
||||
GW 23,1,1.8288,2.032,0.,2.3368,2.032,0.,.0111
|
||||
GW 24,2,2.3368,2.032,0.,3.4036,2.032,0.,.00953
|
||||
GW 25,1,3.4036,2.032,0.,3.9116,2.032,0.,.00794
|
||||
GW 26,2,3.9116,2.032,0.,5.21335,2.032,0.,.00635
|
||||
GW 27,2,-4.9942,4.7244,0.,-3.9116,4.7244,0.,.00635
|
||||
GW 28,1,-3.9116,4.7244,0.,-3.4036,4.7244,0.,.00794
|
||||
GW 29,2,-3.4036,4.7244,0.,-2.3368,4.7244,0.,.00953
|
||||
GW 30,1,-2.3368,4.7244,0.,-1.8288,4.7244,0.,.0111
|
||||
GW 31,1,-1.8288,4.7244,0.,-1.2192,4.7244,0.,.0127
|
||||
GW 32,2,-1.2192,4.7244,0.,-.1016,4.7244,0.,.0159
|
||||
GW 33,1,-.1016,4.7244,0.,.1016,4.7244,0.,.0476
|
||||
GW 34,2,.1016,4.7244,0.,1.2192,4.7244,0.,.0159
|
||||
GW 35,1,1.2192,4.7244,0.,1.8288,4.7244,0.,.0127
|
||||
GW 36,1,1.8288,4.7244,0.,2.3368,4.7244,0.,.0111
|
||||
GW 37,2,2.3368,4.7244,0.,3.4036,4.7244,0.,.00953
|
||||
GW 38,1,3.4036,4.7244,0.,3.9116,4.7244,0.,.00794
|
||||
GW 39,2,3.9116,4.7244,0.,4.99428,4.7244,0.,.00635
|
||||
GE 0
|
||||
LD 5,1,0,0,2.5E+07,1.
|
||||
LD 5,2,0,0,2.5E+07,1.
|
||||
LD 5,3,0,0,2.5E+07,1.
|
||||
LD 5,4,0,0,2.5E+07,1.
|
||||
LD 5,5,0,0,2.5E+07,1.
|
||||
LD 5,6,0,0,2.5E+07,1.
|
||||
LD 5,7,0,0,2.5E+07,1.
|
||||
LD 5,8,0,0,2.5E+07,1.
|
||||
LD 5,9,0,0,2.5E+07,1.
|
||||
LD 5,10,0,0,2.5E+07,1.
|
||||
LD 5,11,0,0,2.5E+07,1.
|
||||
LD 5,12,0,0,2.5E+07,1.
|
||||
LD 5,13,0,0,2.5E+07,1.
|
||||
LD 5,14,0,0,2.5E+07,1.
|
||||
LD 5,15,0,0,2.5E+07,1.
|
||||
LD 5,16,0,0,2.5E+07,1.
|
||||
LD 5,17,0,0,2.5E+07,1.
|
||||
LD 5,18,0,0,2.5E+07,1.
|
||||
LD 5,19,0,0,2.5E+07,1.
|
||||
LD 5,20,0,0,2.5E+07,1.
|
||||
LD 5,21,0,0,2.5E+07,1.
|
||||
LD 5,22,0,0,2.5E+07,1.
|
||||
LD 5,23,0,0,2.5E+07,1.
|
||||
LD 5,24,0,0,2.5E+07,1.
|
||||
LD 5,25,0,0,2.5E+07,1.
|
||||
LD 5,26,0,0,2.5E+07,1.
|
||||
LD 5,27,0,0,2.5E+07,1.
|
||||
LD 5,28,0,0,2.5E+07,1.
|
||||
LD 5,29,0,0,2.5E+07,1.
|
||||
LD 5,30,0,0,2.5E+07,1.
|
||||
LD 5,31,0,0,2.5E+07,1.
|
||||
LD 5,32,0,0,2.5E+07,1.
|
||||
LD 5,33,0,0,2.5E+07,1.
|
||||
LD 5,34,0,0,2.5E+07,1.
|
||||
LD 5,35,0,0,2.5E+07,1.
|
||||
LD 5,36,0,0,2.5E+07,1.
|
||||
LD 5,37,0,0,2.5E+07,1.
|
||||
LD 5,38,0,0,2.5E+07,1.
|
||||
LD 5,39,0,0,2.5E+07,1.
|
||||
FR 0,1,0,0,14.175
|
||||
GN -1
|
||||
EX 0,20,1,0,1.414214,0.
|
||||
RP 0,1,361,1000,90.,0.,0.,1.,0.
|
||||
EN</pre>
|
||||
<pre>CM 3el Yagi 320-16 442 segments
|
||||
CM Manually segmented and equalized
|
||||
CE
|
||||
GW 1,20,-5.68,0.,0.,-3.9116,0.,0.,.00635
|
||||
GW 2,8,-3.9116,0.,0.,-3.4036,0.,0.,.00794
|
||||
GW 3,12,-3.4036,0.,0.,-2.3368,0.,0.,.00953
|
||||
GW 4,8,-2.3368,0.,0.,-1.8288,0.,0.,.0111
|
||||
GW 5,8,-1.8288,0.,0.,-1.2192,0.,0.,.0127
|
||||
GW 6,16,-1.2192,0.,0.,-.1016,0.,0.,.0159
|
||||
GW 7,2,-.1016,0.,0.,.1016,0.,0.,.0476
|
||||
GW 8,16,.1016,0.,0.,1.2192,0.,0.,.0159
|
||||
GW 9,8,1.2192,0.,0.,1.8288,0.,0.,.0127
|
||||
GW 10,8,1.8288,0.,0.,2.3368,0.,0.,.0111
|
||||
GW 11,16,2.3368,0.,0.,3.4036,0.,0.,.00953
|
||||
GW 12,8,3.4036,0.,0.,3.9116,0.,0.,.00794
|
||||
GW 13,20,3.9116,0.,0.,5.68008,0.,0.,.00635
|
||||
GW 14,16,-5.2133,2.032,0.,-3.9116,2.032,0.,.00635
|
||||
GW 15,8,-3.9116,2.032,0.,-3.4036,2.032,0.,.00794
|
||||
GW 16,16,-3.4036,2.032,0.,-2.3368,2.032,0.,.00953
|
||||
GW 17,8,-2.3368,2.032,0.,-1.8288,2.032,0.,.0111
|
||||
GW 18,8,-1.8288,2.032,0.,-1.2192,2.032,0.,.0127
|
||||
GW 19,16,-1.2192,2.032,0.,-.1016,2.032,0.,.0159
|
||||
GW 20,2,-.1016,2.032,0.,.1016,2.032,0.,.0476
|
||||
GW 21,16,.1016,2.032,0.,1.2192,2.032,0.,.0159
|
||||
GW 22,8,1.2192,2.032,0.,1.8288,2.032,0.,.0127
|
||||
GW 23,8,1.8288,2.032,0.,2.3368,2.032,0.,.0111
|
||||
GW 24,16,2.3368,2.032,0.,3.4036,2.032,0.,.00953
|
||||
GW 25,8,3.4036,2.032,0.,3.9116,2.032,0.,.00794
|
||||
GW 26,16,3.9116,2.032,0.,5.21335,2.032,0.,.00635
|
||||
GW 27,16,-4.9942,4.7244,0.,-3.9116,4.7244,0.,.00635
|
||||
GW 28,8,-3.9116,4.7244,0.,-3.4036,4.7244,0.,.00794
|
||||
GW 29,16,-3.4036,4.7244,0.,-2.3368,4.7244,0.,.00953
|
||||
GW 30,8,-2.3368,4.7244,0.,-1.8288,4.7244,0.,.0111
|
||||
GW 31,8,-1.8288,4.7244,0.,-1.2192,4.7244,0.,.0127
|
||||
GW 32,16,-1.2192,4.7244,0.,-.1016,4.7244,0.,.0159
|
||||
GW 33,2,-.1016,4.7244,0.,.1016,4.7244,0.,.0476
|
||||
GW 34,16,.1016,4.7244,0.,1.2192,4.7244,0.,.0159
|
||||
GW 35,8,1.2192,4.7244,0.,1.8288,4.7244,0.,.0127
|
||||
GW 36,8,1.8288,4.7244,0.,2.3368,4.7244,0.,.0111
|
||||
GW 37,16,2.3368,4.7244,0.,3.4036,4.7244,0.,.00953
|
||||
GW 38,8,3.4036,4.7244,0.,3.9116,4.7244,0.,.00794
|
||||
GW 39,16,3.9116,4.7244,0.,4.99428,4.7244,0.,.00635
|
||||
GE 0
|
||||
LD 5,1,0,0,2.5E+07,1.
|
||||
LD 5,2,0,0,2.5E+07,1.
|
||||
LD 5,3,0,0,2.5E+07,1.
|
||||
LD 5,4,0,0,2.5E+07,1.
|
||||
LD 5,5,0,0,2.5E+07,1.
|
||||
LD 5,6,0,0,2.5E+07,1.
|
||||
LD 5,7,0,0,2.5E+07,1.
|
||||
LD 5,8,0,0,2.5E+07,1.
|
||||
LD 5,9,0,0,2.5E+07,1.
|
||||
LD 5,10,0,0,2.5E+07,1.
|
||||
LD 5,11,0,0,2.5E+07,1.
|
||||
LD 5,12,0,0,2.5E+07,1.
|
||||
LD 5,13,0,0,2.5E+07,1.
|
||||
LD 5,14,0,0,2.5E+07,1.
|
||||
LD 5,15,0,0,2.5E+07,1.
|
||||
LD 5,16,0,0,2.5E+07,1.
|
||||
LD 5,17,0,0,2.5E+07,1.
|
||||
LD 5,18,0,0,2.5E+07,1.
|
||||
LD 5,19,0,0,2.5E+07,1.
|
||||
LD 5,20,0,0,2.5E+07,1.
|
||||
LD 5,21,0,0,2.5E+07,1.
|
||||
LD 5,22,0,0,2.5E+07,1.
|
||||
LD 5,23,0,0,2.5E+07,1.
|
||||
LD 5,24,0,0,2.5E+07,1.
|
||||
LD 5,25,0,0,2.5E+07,1.
|
||||
LD 5,26,0,0,2.5E+07,1.
|
||||
LD 5,27,0,0,2.5E+07,1.
|
||||
LD 5,28,0,0,2.5E+07,1.
|
||||
LD 5,29,0,0,2.5E+07,1.
|
||||
LD 5,30,0,0,2.5E+07,1.
|
||||
LD 5,31,0,0,2.5E+07,1.
|
||||
LD 5,32,0,0,2.5E+07,1.
|
||||
LD 5,33,0,0,2.5E+07,1.
|
||||
LD 5,34,0,0,2.5E+07,1.
|
||||
LD 5,35,0,0,2.5E+07,1.
|
||||
LD 5,36,0,0,2.5E+07,1.
|
||||
LD 5,37,0,0,2.5E+07,1.
|
||||
LD 5,38,0,0,2.5E+07,1.
|
||||
LD 5,39,0,0,2.5E+07,1.
|
||||
FR 0,1,0,0,14.175
|
||||
GN -1
|
||||
EX 0,20,2,0,.707107,0.
|
||||
EX 0,20,1,0,.707107,0.
|
||||
RP 0,1,361,1000,90.,0.,0.,1.,0.
|
||||
EN</pre>
|
||||
<center>
|
||||
<h4>Conclusions:</h4>
|
||||
</center>
|
||||
<p>1. NEC-4 has limits in dealing with stepped-diameter elements, especially under the following circumstances:<br></p>
|
||||
<ul>
|
||||
<li>a. Where the step in diameters between adjacent elements is large, and<br></li>
|
||||
<li>b. Where the large step occurs in the region of maximum element current.<br></li>
|
||||
</ul>Achieving convergence under these circumstances may require quite large models relative to the number of antenna elements involved. These models grow larger for every diameter step involved in the structure of the element.
|
||||
<p>2. Inadequate segmentation in stepped-diameter elements in NEC-4 may result in unrealistically high values for forward gain and low values for feedpoint impedance. Adequacy of segmentation includes the following:<br></p>
|
||||
<ul>
|
||||
<li>a. Number of segments,<br></li>
|
||||
<li>b. Equalization of segment lengths within the element structural limits, and<br></li>
|
||||
<li>c. Alignment of segments among the elements.</li>
|
||||
</ul>
|
||||
<p>3. NEC-2 with stepped-diameter corrections can yield reasonable figures on antenna performance. However, the best segmentation to achieve those results is not self-identifying within NEC-2 due to the absence of a convergence trend. In general, the best modeling region for achieving reasonable results from NEC-2 with stepped-diameter corrections involves the following constraints:<br></p>
|
||||
<ul>
|
||||
<li>a. Use the fewest segments possible within the limits of conservative NEC guidelines; and<br></li>
|
||||
<li>b. Adjust segment lengths and alignment for equalization for the major element section lengths, but not for very short lengths.<br></li>
|
||||
</ul>The result will be a model somewhat larger in segment numbers than the conservative minimum, but smaller than a converged NEC-4 model.
|
||||
<p>4. NEC-2 without a stepped-diameter correction is highly unreliable. The larger the diameter jump between adjacent section of the element, the more unreliable the output figures. With small increments of diameter change and long constant-diameter sections, the results may be tentatively usable if the total number of segments is small. However, precision antenna analysis is not possible.</p>
|
||||
<p>Given the trends in the values of forward gain and front-to-back ratio (or front-to-rear calculations) for the test Yagis with stepped-diameter elements, it is entirely possible to generate misleading models in either NEC-2 or NEC-4. Good practice calls for extreme care in developing models and in reporting results. Not only should one present modeling results, but as well one should reveal all the relevant details of the model used to generate them. Likewise, those with modeling programs should check reported figures for themselves.</p>
|
||||
<p>Indeed, modeling is not in itself the solution to resolving issues of reported antenna performance figures. Without adequate descriptions of the models used (and the good engineering reasons for using those models), the output of NEC programs can be as misleading as any other antenna performance report. Properly used within their limitations and fairly reported, NEC models can be a source of important and useful information not otherwise easily obtained.<br>
|
||||
<br></p>
|
||||
<center>
|
||||
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
|
||||
</center><br>
|
||||
<br>
|
||||
<p><i>Updated 4-6-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.</i><br>
|
||||
<br></p>
|
||||
<center>
|
||||
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
|
||||
</center><br>
|
||||
<br>
|
||||
<p><a href="../radio.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Go to Amateur Radio Page</a></p>
|
||||
<p class="topics-footer">Topics: <a href='../topics.html#modeling'>Modeling</a>, <a href='../topics.html#stepped-diameter'>Stepped Diameter</a></p><br>
|
||||
</body>
|
||||
</html>
|
||||
@@ -0,0 +1,162 @@
|
||||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<meta charset="UTF-8">
|
||||
<meta name="keywords" content="Modeling">
|
||||
<title>Reading a NEC Deck</title>
|
||||
<link rel="stylesheet" href="../styles.css">
|
||||
</head>
|
||||
<body>
|
||||
<center>
|
||||
<h1><img src="../images/antbott.gif" align="left" width="150" height="77">So You Want to Read a NEC Deck<img src="../images/yagicad.gif" align="right" width="125" height="62" border="2" vspace="5" hspace="25"></h1>
|
||||
</center>
|
||||
<center>
|
||||
<h3>L. B. Cebik, W4RNL</h3>
|
||||
</center>
|
||||
<center>
|
||||
<img src="../images/colorbar.gif" width="591" height="3">
|
||||
</center>
|
||||
<p>Many users of ELNEC and EZNEC are unfamiliar with the basic elements of a standard .NEC input file. There may be some users of NEC-Win who are unfamiliar with the terms and layout of an EZNEC antenna description file (called a PD file for the abbreviated keystrokes used to generate it). So let's do a correlation between the two in order to show the basic terms of the NEC deck.</p>
|
||||
<p>In most implementations, NEC uses a card-deck input file whose format goes back to the early days of FORTRAN, when punch cards provided computational inputs. For brevity, each card contain a labeled sequence of information, the individual parts separated by a delimiter. Since we Americans use "." as our decimal indicator, we use commas or spaces to separate information. European formats may vary.</p>
|
||||
<p>To get us started, let's compare the antenna description file for a simple 2-element Yagi with the corresponding card deck. Then we can explain each type of card we encounter. If you wish, you can try your hand at correlating each element in the NEC deck to elements in the EZNEC antenna description file before reading beyond them.</p>
|
||||
<center>
|
||||
<img src="../images/colorbar.gif" width="591" height="3">
|
||||
</center><br>
|
||||
<br>
|
||||
<pre> EZNEC Antenna Description File
|
||||
2el Yagi 12M
|
||||
Frequency = 24.95 MHz.
|
||||
Wire Loss: Aluminum -- Resistivity = 4E-08 Ohm-m, Rel. Perm. = 1
|
||||
|
||||
--------------- WIRES ---------------
|
||||
Wire Conn.-- End 1 (x,y,z : ft) Conn.-- End 2 (x,y,z : ft) Dia(in) Segs
|
||||
1 -9.100, 0.000, 40.000 9.100, 0.000, 40.000 1.00E+00 11
|
||||
2 -8.800, -4.800, 40.000 8.800, -4.800, 40.000 1.00E+00 11
|
||||
3 -0.200, 0.000, 1.000 0.200, 0.000, 1.000 # 14 1
|
||||
|
||||
-------------- SOURCES --------------
|
||||
Source Wire Wire #/Pct From End 1 Ampl.(V, A) Phase(Deg.) Type
|
||||
Seg. Actual (Specified)
|
||||
1 1 3 / 50.00 ( 3 / 50.00) 1.000 0.000 V
|
||||
|
||||
--------------- LOADS ---------------
|
||||
Load Wire Wire #/Pct From End 1 R (Ohms) X(Ohms)
|
||||
Seg. Actual (Specified)
|
||||
1 6 2 / 50.00 ( 2 / 50.00) 1.000 100.000
|
||||
|
||||
-------- TRANSMISSION LINES ---------
|
||||
Line Wire #/% From End 1 Wire #/% From End 1 Length Z0 Vel Rev/
|
||||
Actual (Specified) Actual (Specified) Ohms Fact Norm
|
||||
1 1/50.0 ( 1/50.0) 3/50.0 ( 3/50.0) Actual dist 50.0 0.66 N
|
||||
|
||||
Ground type is Real, high-accuracy analysis
|
||||
Conductivity = .005 S/m Diel. Const. = 13
|
||||
|
||||
--------------- MEDIA ---------------
|
||||
Medium Conductivity(S/m) Dielectric Const. Ht(ft) R Coord(ft)
|
||||
|
||||
1 5.000E-03 13.00 0 (def) 0 (def)
|
||||
</pre><br>
|
||||
<br>
|
||||
<center>
|
||||
<img src="../images/colorbar.gif" width="591" height="3">
|
||||
</center><br>
|
||||
<br>
|
||||
<pre> .NEC Input File
|
||||
|
||||
CM 2el Yagi 12M
|
||||
CE
|
||||
GW 1 11 -9.1 0 40 9.1 0 40 .04165
|
||||
GW 2 11 -8.8 -4.8 40 8.8 -4.8 40 .04165
|
||||
GW 3 1 -.2 0 1 .2 0 1 2.6706E-03
|
||||
GS 0 0 .3048
|
||||
GE 1
|
||||
GN 2 0 0 0 13 .005 0 0 0 0
|
||||
EX 0 3 1 0 1 0
|
||||
LD 4 2 6 6 1 100 0
|
||||
LD 5 1 1 11 2.4938E7
|
||||
LD 5 2 1 11 2.4938E7
|
||||
LD 5 3 1 1 2.4938E7
|
||||
TL 1 6 3 1 50 18.01 0 0 0 0
|
||||
FR 0 1 0 0 24.95 0
|
||||
RP 0 1 361 1000 76 0 1 1
|
||||
EN</pre>
|
||||
<center>
|
||||
<img src="../images/colorbar.gif" width="591" height="3">
|
||||
</center>
|
||||
<p>The antenna described by these two files is shown in Figure 1. It is a simple 2-element Yagi of relatively poor performance: Gain: 11.1 dBi; front-to-back: 11.1 dB; feedpoint impedance: 42 + j4 Ohms. I have purposely altered the antenna to include an inductive load in the reflector, thus making it physically shorter than the driven element. I have also run a 50-Ohm transmission line straight down to within 1' of the ground and created a source wire there. Otherwise, our NEC deck would be pretty skimpy.</p>
|
||||
<center>
|
||||
<img src="necdeck1.gif" width="630" height="390" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>Let's look at each card in the deck and read out the information, cross checking it against the EZNEC file. In most cases, I have spread the data units out and labeled them beneath.</p>
|
||||
<pre>1. CM 2el Yagi 12M</pre>
|
||||
<p>This is a comment card for storing information about the file in ASCII text. It does not enter into the calculations. You may have any number of comment cards, although some implementations limit them. In EZNEC, you may have only one CM card, called the "title."</p>
|
||||
<pre>2. CE</pre>
|
||||
<p>This card is the "comment end" card, signaling that data for calculation follows.</p>
|
||||
<pre>3. GW 1 11 -9.1 0 40 9.1 0 40 .04165
|
||||
GW 2 11 -8.8 -4.8 40 8.8 -4.8 40 .04165
|
||||
GW 3 1 -.2 0 1 .2 0 1 2.6706E-03
|
||||
Type Tag Segs E1 X E1 Y E1 Z E2 X E2 Y E2 Z Radius</pre>
|
||||
<p>Type GW cards describe the antenna geometry. Each antenna wire, or "Tag," has a separate numbered card or line (1, 2, and 3). The Segs (segmentation) entry tells how many segments the wire is divided into (11 each for Tags 1 and 2, 1 segment for Tag 3). Then come the Cartesian coordinates for End 1 and End 2 of each straight wire. Here, as in the EZNEC file, they are given in feet. Finally, the wire size is given as a radius (1/2 the diameter given in the EZNEC file. However, the EZNEC file lists the radius in inches. The NEC deck must use the same units throughout the GW cards, so a 1" diameter become a 0.04165' radius. The wire size figure for Tag 3 is the radius of #14 wire, in feet.)</p>
|
||||
<pre>4. GS 0 0 .3048
|
||||
Type Multiplier</pre>
|
||||
<p>Although most implementations of NEC, such as NEC-Win and EZNEC, give the user a choice of common units of measure for setting up the antenna geometry, NEC itself calculates only in meters. In the last of its 4 columns, the "geometry scaling" card gives the multiplier needed to convert to meters.</p>
|
||||
<pre>5. GE 1
|
||||
Type End</pre>
|
||||
<p>The "geometry end" type card signals the end of the wire set-up and prepares the way for other data that enter into the calculations.</p>
|
||||
<pre>6. GN 2 0 0 0 13 .005 0 0 0 0
|
||||
Type G-type Die-C. Cond.</pre>
|
||||
<p>The ground parameter card specifies the type of ground calculation system and the necessary parameters to make the calculation. Here, we show a single medium, although a second medium can be set.</p>
|
||||
<p>There are 4 types of ground systems used with NEC: -1 = free space; 0 = a finite ground with a reflection coefficient approximation (the "fast" ground in EZNEC); 1 = a perfectly conducting ground; and 2 (used here) specifies a finite ground using the Sommerfeld-Norton method of calculation for greatest accuracy. (In addition, EZNEC implements the MININEC ground calculation system.)</p>
|
||||
<p>Finite ground conditions (cases 0 - 2) require two numbers to implement calculations. The first is a relative dielectric constant, usually given as an integer. Second is the conductivity in Siemens/meter (mhos/meter in older terminology). Both are generally derived from tables. The values shown represent a default presumption of medium earth conditions. Both numbers are omitted for perfect ground.</p>
|
||||
<p>As with many cards in the NEC deck, there are unlabled "0" fields. Some of these represent fields simply left blank; others represent input positions for more specialized conditions not relevant to most common ham HF antennas. (Some may be relevant to VHF and UHF antennas.)</p>
|
||||
<pre>7. EX 0 3 1 0 1 0
|
||||
Type S-type Tag Seg Voltage: Real Imaginary</pre>
|
||||
<p>The "exitation" or source information card allows for many types of exitation, of which only voltage sourcing is usually of HF ham use. Hence, the source-type is "0". The next two columns specify the placement of the source in terms of tag number and segment number in that wire. Here, the remote wire has only one segment, and the source is placed at its center. Many programs allow specification of the source at some distance from End-1 of the designated wire, and will then place the source as close to that point as segmentation permits.</p>
|
||||
<p>For most ham uses, sources are either voltage or current. The latter is useful for scanning current levels along a wire, since a voltage source of "1" yields small fractions of an amp current, making scanning more difficult. Current sources may also be necessary for some advanced applications.</p>
|
||||
<p>Nonetheless, both types of sources are voltage sources ultimately. The current source is generated by a voltage source set on a remote wire and transformed into a current source by a transmission line. The NEC deck will show the wire and line, while EZNEC stores this information internally.</p>
|
||||
<p>Voltages are given in terms of X and Y ("real" and "imaginary") coordinates derived from inputs that can be given as a voltage and its phase angle. User current magnitude and phase angle inputs are converted to appropriate voltage values at the remote source wire.</p>
|
||||
<p>In general, when converting among programs (for example, between EZNEC Pro and NEC-Win Pro), it is best to use a voltage source to avoid the possibility that one program cannot read the other's remote wire current source technique. Changing back to a current source can be done after file conversion is complete.</p>
|
||||
<pre>8. LD 4 2 6 6 1 100 0
|
||||
Type L-type Tag Start Seg End Seg R L or X C</pre>
|
||||
<p>There are two types of loads to consider: concentrated element loading quantities and distributed element material loads. This card illustrates an inductive load added to the center of the reflector. Load types 0 through 3 represent categories of R-L-C combinations that can make up a load. This card shows a type 4 load, which is specified in terms of a series resistance and reactance in Ohms.</p>
|
||||
<p>The "tag" and "segment" items locate the load at the midpoint of wire 2. Since there are start and end segment numbers, some loads may be distributed for more than a single section, but most ham antennas employ concentrated loading located within a single segment.</p>
|
||||
<p>The final two values (1 and 100) specify the resistance and reactance of the load in Ohms. Capacitive reactance, of course, would be entered as a negative number.</p>
|
||||
<pre>9. LD 5 1 1 11 2.4938E7
|
||||
LD 5 2 1 11 2.4938E7
|
||||
LD 5 3 1 1 2.4938E7
|
||||
Type L-type Tag Start Seg End Seg Conductivity</pre>
|
||||
<p>Material losses are type-5 loads. As with other loads, the wire (tag) must be identified, along with the first and last segments to which the load applies. Note that these loads apply in addition to any lumped-constant loading of types 0 through 4.</p>
|
||||
<p>To avoid confusion by newer modelers, EZNEC only refers to lumped constants as loads, preferring instead to call material loads "wire losses." EZNEC also expresses these losses as a function of resistivity and relative permitivity. However, the value of resistivity in this case, 4.0E-08 Ohms, is simply the reciprocal of the NEC deck conductivity value of 2.4938E7 mhos or Siemens. Additionally, EZNEC restricts antennas to one type of material per model, although the NEC deck permits a specification of a different conductivity value for each wire.</p>
|
||||
<pre>10. TL 1 6 3 1 50 18.01 0 0 0 0
|
||||
Type Start tag/seg End tag/seg Zo Length</pre>
|
||||
<p>Transmission lines are not physical models in NEC, but mathematical constructs. Hence, they can have any length, regardless of the actual distance between their start and end points on wires. Special techniques are used for shorted and open stubs, but the example here runs a common coax line from the antenna proper to a short segment used a. to terminate the transmission line and b. to serve as the overall source point for the antenna system.</p>
|
||||
<p>By now, the start and end wire and segment numbers are obvious. As in the EZNEC PD file, the next two columns specify the characteristic impedance of the line and its length. In EZNEC, this can be done in several ways, all of which translate into a final characteristic impedance and definite length in meters. In the PD file, the length was given as the actual distance between wires, 39', modified by the velocity factor of the line, .66. This results in an electrical length of 59.1' or 18.01 meters.</p>
|
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<pre>11. FR 0 1 0 0 24.95 0
|
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Type Stepping No. of FQs Start FQ Increment</pre>
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<p>Antennas are modeled at one or more frequencies. If a single frequency is used, as in this example, the information needed is limited. "Frequency sweeping" requires more information.</p>
|
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<p>Stepping can be non-linear (stepping = 1), but normal ham frequency sweeps are linear, changing frequency by the same amount each time. For sweeps, the user specifies the number of frequency steps, the start frequency, and the increment by which to step. For this single frequency model, the number of frequency steps is 1, and the increment is 0, while the modeled frequency is 24.95 MHz.</p>
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<pre>12. RP 0 1 361 1000 76 0 1 1
|
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Type Mode No. Theta No. Phi Special Theta Phi Th Inc Ph Inc</pre>
|
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<p>The report card specifies what output data is desired from the calculations. Mode "0" is the normal mode.</p>
|
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<p>Horizontal angular changes are measured as "phi" degrees. Elevation angular changes are measured as "theta" degrees. Although most hams are used to counting elevation from the ground up, NEC counts theta angles from the zenith down.</p>
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<p>This example specifies a report for one theta (elevation) angle, but a full circle of azimuth (phi) angles. Skipping the "Special" column for a moment, the theta angle is 76° (or 90° - 76° for a 14° elevation angle). The figure is a start figure, although only one theta angle has been specified. The azimuth or phi start angle is 0°, but will pass through 361° (to ensure a complete circle with a common value at each end of the progression). Both theta and phi are specified for increments of 1° for good resolution.</p>
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<p>The "Special" column contains 4 values that direct the calculations to produce certain types of outputs. 1000 is normally used for vertical, horizontal, and total non-normalized power gains with no averaging. Other outputs are available, and the user is usually interrogated in plain language for the desired output data and form by each program.</p>
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<p>Users of NEC will sometimes be surprised to find that a symmetrical antenna, such as a Yagi, produces a main lobe identified by as much as 2° to 3° less than the expected bearing. Apparently, NEC identifies the first instance of the maximum power gain as the main lobe. Increasing the phi increment will often return the main lobe to its expected position.</p>
|
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<pre>13. EN</pre>
|
||||
<p>EN signals the end of the .NEC file.</p>
|
||||
<p>Hopefully, this brief trip through a short NEC deck will orient you to how the input files are constructed for use with NEC. Remember that the card explanations have not covered all the ways in which one may place data on a card of a given type. Only the most common kinds of data inputs for typical ham antenna installations have been illustrated.</p>
|
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<p>Some programs, like EZNEC, do not generate a NEC deck, but instead communicates with the NEC-2 calculating engine via a number of binary files. (A NEC deck is available in EZNEC Pro with the NEC-4 calculating engine.) Some programs, like NEC-Win Plus, use alternative formatting methods--a spreadsheet file in this case, but also make available the option of saving the mode as a .NEC file. Others, like NEC-Win Pro or GNEC, make the deck an integral part of the modeling process. Getting used to the NEC deck can increase your ability to glean more from whatever program you choose as your basic modeling vehicle. Familiarity may also aid you in interpreting articles that present antenna modeling data in .NEC input file format. Patches, Green's functions, networks, and wire grids are beyond the scope of this introduction, but may be found in NOSC Technical Document 116, Volume 2, <i>Numerical Electromagnetics Code (NEC)--Method of Moments, Part III: User's Guide</i> (1981), which is the source of most of this data.</p>
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<p><i>Updated 3-30-1997, 04-21-2001. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.</i></p>
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<p><a href="../radio.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Return to Amateur Radio Page</a></p>
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<h1><img src="../images/pattern.gif" align="middle" width="85" height="85"> Getting the Most Out of Antenna Patterns <img src="../images/w4rnlwwr.gif" align="middle" width="99" height="83" border="2" vspace="5" hspace="10"></h1>
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<h3>L. B. Cebik, W4RNL</h3>
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<p>Ham journals are filled these days with antenna pattern graphics, like the pair shown in <b>Figure 1</b>.<sup>1</sup> The patterns are supposed to be highly informative about antenna performance. Unfortunately, to the new ham, they can be somewhat bewildering. Even the experienced ham may not be getting from them all the information that is compactly presented in the patterns. So let's start from scratch, seeing how these patterns represent antenna data that is useful to us, whether we plan to buy an antenna or build our own.</p>
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<b>Figure 1</b>: Free space azimuth (E-plane) and elevation (H-plane) far field patterns for the common dipole.
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<p>Although modern antenna modeling software produces data that can yield many different kinds of antenna patterns, the most common ones are called total far field patterns. They combine all calculated radiation from an antenna in every direction and produce a pattern that is related to a constant strength. In <b>Figure 1</b>, we can see that the pattern bulges and indents. Incidentally, the bulges are called lobes and the indentations are called nulls.</p>
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<p>Hypothetically, if we stand on a line proportional to the pattern line distance from the center point (where the antenna is located), we shall receive a radiated signal of constant strength, no matter where on the line we stand. Likewise, if someone moves a transmitter along the line, then the antenna we are using will receive a signal of constant strength, no matter where along the line we place the transmitter. In short, antenna patterns reflect both transmission and reception characteristics of the antenna being patterned, where the lobes indicate stronger signals and the nulls indicate weaker ones.</p>
|
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<p>Mastering the art of reading antenna patterns intelligently requires that we learn a number of ideas and conventions. Some relate to antenna theory itself. Some emerge from antenna modeling. Still others come from actually building and testing antennas on carefully constructed ranges. So our short story cannot end here. However, if we learn to sort out the key factors that are relevant to a particular antenna pattern we encounter, we can read them as easily as the words on this page.</p>
|
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<h3>Free Space: A Starting Point for E and H Planes</h3>
|
||||
<p>Let us begin in free space. Unlike the reflective surface of the earth, free space is a region in which there is nothing but the antenna. In fact, the patterns in <b>Figure 1</b> are free space patterns of a common horizontal resonant half wavelength dipole fed at the center. <b>Figure 2</b> shows a complete 3-dimensional view of the antenna pattern. The antenna is grossly exaggerated in size to clarify its position through the center of the pattern. In reality, it would be too small to be seen.</p>
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<img src="p2.gif" width="640" height="480" border="2" vspace="5" hspace="9">
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|
||||
<b>Figure 2</b>: The common dipole (greatly exaggerated in length) with its 3-dimensional far field pattern in free space.
|
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<p>The first thing to notice is that the pattern is symmetrically even all around the wire when viewed from the wire end. That symmetry shows up in <b>Figure 1B</b>. However, the radiation is not so even when viewed as a slice through the pattern in the plane of the wire. That is the view shown in <b>Figure 1A</b>.</p>
|
||||
<p>The difference between the two patterns reflects a fundamental property of antennas. They emit (and receive) radiation in two planes, conventionally called the E and H planes. The radiation in the E-plane is parallel with the wire. An antenna pattern taken parallel to the wire is also called an E-plane pattern. If we slice the 3-D pattern at any angle, but always barely include the antenna wire's total length, we shall in free space obtain the pattern of <b>Figure 1A</b>. Every plane will show the same indentations in field strength off the ends of the dipole wires.</p>
|
||||
<p>There is also radiation at right angles to the wire. By convention, if we take a slice, normally through the center of the antenna element, but at right angles to the wire, we have an H-plane pattern. This is the pattern of <b>Figure 1B</b>.</p>
|
||||
<p>However, the two patterns in the figure are not marked E- and H-plane. Instead, they carry a more conventional designation used these day: azimuth and elevation. We use these terms because most of our actual antennas are place above the earth, and the planet gives us a nearly flat reference plane to give meaning to the ideas of horizontal and vertical, and also to azimuth and elevation.</p>
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<img src="p3.gif" width="550" height="473" border="2" vspace="5" hspace="9">
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<b>Figure 3</b>: Free space E-plane and H-plane views of a 3-element Yagi.
|
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|
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<p>When we have more complex antenna arrays, the E-plane and H-plane patterns become even more rigorous. See <b>Figure 3</b>. Here we have a 3-element Yagi. The E-plane not only parallels the length of the main element, but as well passes through the plane formed by the 3 elements. The H-plane is at right angles and is normally centered on the driven element, to which is connected the signal source. The elements of this antenna form a horizontal line across the H-plane.</p>
|
||||
<p>E-plane and H-plane patterns for antennas are convenient is free space. In a region of space, we do not have any reflecting surfaces, so it does not matter in what orientation we place an antenna. We can always derive E-plane and H-plane patterns. The patterns are significant in just this way: when we place an antenna horizontally relative to the earth, the E-plane pattern will dominate the azimuth pattern we derive. When we place the antenna at right angles to the earth at any height, that is, when we make it vertical, the H-plane pattern will dominate the azimuth pattern we derive.</p>
|
||||
<p>In <b>Figure 1</b>, I could have set up the antenna vertically instead of horizontally in the software frame of reference. Had I done that, then the same two patterns would have emerged, but in reverse order. The elevation pattern would now correspond to the E-plane and the azimuth pattern would be the H-plane. In free space, that is the only difference of note. However, once we return to earth, the difference in orientation will make a big difference in how the antennas work.</p>
|
||||
<p>Just to make life a little more complicated, we should note in passing that in NEC, the most used antenna modeling core, the native orientation to antenna positions is not azimuth and elevation. NEC refers to ? (phi) and ? (theta) angles. Phi corresponds to azimuth, referenced to a zero point. However, theta is a "zenith" angle. That is, instead of counting in degrees up from the ground (or whatever is designated as the horizontal plane in free space), it counts down from directly overhead. If you see the "theta" notation, you can obtain the elevation angle just by subtracting the theta angle from 90 degrees.</p>
|
||||
<h3>Variations on a Theme</h3>Let's dwell a bit on the hypothetical Yagi in <b>Figure 3</b>. For the moment, we shall consider only the free space E-plane pattern, which is the azimuth pattern in most pattern-generating software. One of the key dimensions you must track is the progression of angles around the perimeter of the outer circle. To illustrate this point, consider <b>Figure 4</b>, <b>Figure 5</b>, and <b>Figure 6</b>. All three patterns show the same antenna model with their lengths plotted along one axis (call it the X-axis) and their distance apart plotted along a second axis (call it the Y-axis). The Z-axis would represent height, either measured from the ground or--in free space--measured above and below the plane made by the X and Y axes. We can call this last dimension the Z-axis.
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<b>Figure 4</b>: Free space azimuth (E-plane) far field pattern of the 3-element Yagi in AO 6.5.
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||||
<b>Figure 5</b>: Free space azimuth (E-plane) far field pattern of the 3-element Yagi in EZNEC 2.
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||||
<b>Figure 6</b>: Free space azimuth (E-plane) far field pattern of the 3-element Yagi in NEC-Win Pro.
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|
||||
<p>I plotted these antennas in this way to illustrate that you may see different conventions used by different software in the production of antenna patterns. The <b>Figure 4</b> pattern orients zero degrees at the top of the graph, with 90 degrees to the right. In <b>Figure 5</b>, zero degrees is to the right, with 90 degrees at the top. <b>Figure 6</b> places zero degrees at the top with 90 degrees to the left. Yet, they all present the same pattern information.</p>
|
||||
<p>Pattern-producing software may place varying amounts of supplemental data about the antenna on the pattern graphic. Very often, the pattern-maker has options on whether to include the data in the graphic or separately. <b>Figure 4</b> present basic pattern-identifying information in the corners. <b>Figure 5</b> provides an optional chart of data overlaid on an unused portion of the graph. <b>Figure 6</b> is bare in the presented version, but might have had other information added.</p>
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||||
<b>Figure 7</b>: Free space azimuth (E-plane) far field pattern of the 3-element Yagi in NEC4WIN.
|
||||
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|
||||
<p><b>Figure 7</b> represents a pattern of the same antenna with a chart of fairly complete antenna data to the side. Notice that its data, as well as the data in the other graphics, tend to show small variations. Different modeling software--even when using the same calculation core--tends to show operationally insignificant variations in data output. Maximum gain figures that vary under 0.1 dB and front-to-back ratios that vary by under 1 dB are normally insignificant.</p>
|
||||
<h3>Free Space and Signal Strength</h3>Before we come down to earth, let's consider how we determine how good an antenna may be. There are very many dimensions to this question, but the relevant one here is how we measure the antenna pattern. The patterns we have looked at contain both lobes and nulls, points showing gain maxima and minima. <b>Figure 7</b> provided a list of all the lobes of the 3-element Yagi, giving their angular direction. <b>Figure 5</b> gave us information on the main lobe (the strongest) and the side-lobe (or secondary lobe--the second strongest). Conveniently for our exercise, this lobe was directly to the rear of the main lobe.
|
||||
<p>One of the key figures of antenna merit is gain. We measure the gain of an antenna by looking at the point in the 3-D pattern that shows the highest level of radiation field strength. We compare that with a arbitrary but standard field and register in decibels (dB) how much stronger or weaker the antenna field is.</p>
|
||||
<p>In free space, the most common standard is the isotropic source, a hypothetical antenna point that radiates equally well in all directions. So the unit of maximum gain for our test antenna is measured in dBi, decibels stronger or weaker than an isotropic source that might be placed in the same position.</p>
|
||||
<p>There are alternative measures you may encounter. Of these, the most prevalent is dBd, decibels gain relative to a dipole. In free space, the standard hypothetical lossless dipole of immeasurably thin wire has a gain of 2.15 dBi. Hence, the translation from dBi to dBd and back again is simple arithmetic. Consequently, in antenna modeling--from which most antenna patterns emerge--dBi has become the de facto standard.</p>
|
||||
<p>In range testing antennas, measurement using dBd still have an important place. However, the reference is not to a hypothetical lossless thin wire dipole, but to a dipole that has real dimensions and material losses. Signals transmitted from it or received by it are carefully measured. Then test antennas are likewise measured and compared to the standard dipole. The gain of the test antenna may then be specified in dBd. However, the dipole used as the standard for the test must be completely described, since dipole characteristics can vary slightly according to the material used as well as the antenna height in terms of wavelengths or fractions of a wavelength.</p>
|
||||
<p>The measurements just noted apply mostly to horizontal antennas. Dipoles are less universally used as standards in the testing of vertical antennas.</p>
|
||||
<p>With the increasing use of antenna modeling software--especially NEC and MININEC--as vehicles of comparison of antenna designs, dBi is becoming the most common measure of maximum antenna gain in the most favored direction.</p>
|
||||
<h3>Front-to-. . .: Back? Rear?</h3>As shown in the Yagi patterns, many antennas exhibit unidirectional patterns, that is, patterns with maximum gain in only one direction. Unlike the bi-directional pattern of the common dipole in <b>Figure 1</b>, the Yagi beam (and many other antennas) has a much higher gain in one (forward) direction that in the other (reverse) direction. How much difference there is between the two directions is a measure of how well the antenna may suppress signals from the rear relative to signals from the forward direction.
|
||||
<p>There are several ways of measuring the difference. Perhaps the most common is the 180-degree front-to-back ratio, sometimes simply called the front-to-back ratio. To obtain this value, we simply subtract the gain to the rear from the gain forward along a straight line running from the point on the pattern of maximum gain through the pattern center where the antenna is and out the rear of the pattern. Using the data presented in <b>Figure 5</b>, if the forward gain is +8.11 dBi and the rear gain is -19.15 dBi, then the front-to-back ratio is 27.26 dB. (In dBd, for our free space model, the forward gain would be 5.96 dBd, while the rear gain would be -21.30 dBd, for a net front-to-back ratio of the same 27.26 dB. Note that the 0.01 difference in the numbers here and those in the figure is a function of rounding in the software; the difference is insignificant.)</p>
|
||||
<p>However, note the rear portion of the antenna pattern. The 180-degree direction represents a special portion of the pattern where signal rejection is greatest. However, gain to the rear off to the sides of the "dimple" is higher, meaning less rejection of signals. For this reason, alternatives to the 180-degree front-to-back ratio are often used.</p>
|
||||
<p>One system, sometimes called the averaged front-to-rear ratio, averages the gain for a rear quadrant of the antenna. This figure of merit gives an average front-to-rear ratio that many believe is a better measure of actual antenna performance in signal rejection. A further alternative is the worst-case front-to-rear ratio, which simply compares the forward gain with the highest gain found in the rear quadrants of the antenna.</p>
|
||||
<p>When interpreting statements about antenna performance, you can examine the antenna pattern and often determine what standard of rear performance is being used, even if an author does not tell you.</p>
|
||||
<h3>Polar Plots and Linear Graphs</h3>The antenna patterns display so far use the most common format: the polar logarithmic plot. The antenna is at the center of the graph, and far field strengths are plotted in a circle for all relevant directions. In free space, the plots for azimuth and for elevation both encompass 360 degrees. Although the outer circle can be specified at any level, most patterns use the antenna's maximum signal in the favored direction as the graph edge. Inner circles, as shown in <b>Figure 4</b> through <b>Figure 7</b>, represent lesser signal levels, measured in dB lower than the level of the outer ring.
|
||||
<p>However, note that the inner circles are not equally spaced, but represent a logarithmic progression. The higher the negative number toward the center, the more compressed the circles become. This most common log plot is often said to show with greatest clarity the high gain features of the pattern.</p>
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||||
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||||
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|
||||
<b>Figure 8</b>: Free space azimuth (E-plane) far field pattern of the 3-element Yagi using a polar plot with linear divisions.
|
||||
</center>
|
||||
<p><b>Figure 8</b> shows a common alternative: the polar linear plot. Here, the circles of decreasing gain are equally spaced, which tends to clarify the details of the low gain portions of the pattern. When looking at an antenna pattern, it is always necessary to note whether a log or linear plot is being used, especially when assessing matters like front-to-back ratio. The rear pattern lobes appear very different in the two figures, even though exactly the same data is being displayed by both.</p>
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<img src="p9.gif" width="640" height="433" border="2" vspace="5" hspace="9">
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|
||||
<b>Figure 9</b>: Free space azimuth (E-plane) far field pattern of the 3-element Yagi using a linear graph.
|
||||
</center>
|
||||
<p>A third way to present antenna pattern data is with a standard linear graph. <b>Figure 9</b> shows the same antenna plot on a graph where the X-axis is linearly divided into 360 degrees and the Y-axis represents the antenna's gain. When made large enough, linear graphs can show very fine pattern detail. However, they are to this date fairly rare in amateur literature.</p>
|
||||
<p>So where are we so far? Actually, we have come a fairly good distance. Although we are still in free space, we have distinguished the common antenna pattern azimuth and elevation orientations from E-plane and H-plane representations of the pattern. We have also compared the various gain measures (dBi, dBd), with dBi becoming perhaps the most used measure. We have also seen how to measure front-to-back ratio, with reference to features on the antenna pattern. Then, we looked at three ways to present antenna patterns, with the polar log plot being the most common.</p>
|
||||
<p>Having looked at all these options, we shall standardize the rest of our work. We shall use azimuth and elevation polar plots with log scaling, and when we refer to front-to-back ratio, we shall employ the 180-degree ratio as our general standard. We select these options not because they are always the best ones, but because they are the ones you will encounter most often in amateur radio antenna literature. Now we can come back to earth.</p>
|
||||
<h3>Down-to-Earth Reflections</h3>An antenna over real ground changes the way in which we use antenna patterns. Let's consider the elevation pattern first. A typical horizontally oriented Yagi pattern is shown in <b>Figure 10</b>, the same one as used in the free-space patterns of <b>Figures 4-7</b>. Notice that half of the free space pattern is missing, the part that would be below ground if the earth did not reflect antenna signals.
|
||||
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||||
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|
||||
<b>Figure 10</b>: Elevation pattern of a 3-element Yagi 1 wavelength over average ground.
|
||||
</center>
|
||||
<p>Second, notice that the pattern is elevated. Due to signal reflections, the elevation angle of maximum radiation (also called the Take-Off angle) is not at zero degrees. Since we are dealing with far field patterns instead of ground waves, there is essentially no signal at zero degrees, and antenna modeling patterns will not show line of sight radiation in its far field patterns.</p>
|
||||
<p>Third, notice that the forward lobe is not a line, but a lobe having a certain vertical thickness. The common way to designate this thickness is by measuring the number of degrees between points where the signal is reduced in strength by 3 dB relative to its maximum strength. This figure is called the vertical beamwidth of the antenna pattern.</p>
|
||||
<p>For horizontally polarized antennas, such as our Yagi, the pattern of lobes, the take-off angle of the lowest (and usually strongest) lobe, and the vertical beamwidth will vary with the antenna height, as measured in fractions of a wavelength. Suppose we have 2 3-element Yagis, one for 10 meters and one for 20 meters. We place the 20-meter Yagi at a height of 70 feet and the 10 meter Yagi at a height of 35 feet. Since each antenna is at 1 wavelength height, we would expect very similar elevation patterns from them--in fact, just the pattern shown if <b>Figure 10</b>.</p>
|
||||
<p>We shall take another look at polarization of the antenna in a while, since it make a considerable difference in antenna performance over real ground. But first, let's get acquainted with what happens to the azimuth pattern when we place our Yagi over real ground.</p>
|
||||
<p>An azimuth pattern at zero degrees elevation--the horizontal plane--will show nothing. In fact, most NEC-based programs will disallow your attempt to take that pattern. Instead, we take azimuth patterns at some higher angle of interest. The question now is what is interesting.</p>
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|
||||
<img src="p11.gif" width="640" height="480" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<center>
|
||||
<b>Figure 11</b>: Azimuth pattern of a 3-element Yagi 1 wavelength over average ground, at an elevation angle of 14 degrees (elevation angle of maximum radiation).
|
||||
</center>
|
||||
<p>In the absence of any other considerations, most folks who present azimuth patterns over real ground do so at the take-off angle. <b>Figure 11</b> is an illustration, using our handy Yagi. The pattern shape is quite similar to the free space azimuth pattern in <b>Figures 4-7</b>. However, there are some important differences.</p>
|
||||
<p>The free space azimuth pattern was a true horizontal pattern. The pattern over ground is a cone elevated from the horizontal by the specified elevation angle. Since the take-off angle of this antenna is 14 degrees, the azimuth pattern is a cone 14 degrees above the horizon. You can picture this best by drawing a line straight across the elevation pattern at point 14 degrees up from the horizontal on each side of the graph.</p>
|
||||
<p>The pattern shows a front-to-back line. This ratio is not necessarily the maximum front-to-back ratio for the antenna (although it often is). Rather, it is the front-to-back ratio for the chosen angle (14 degrees). Maximum front-to-back ratio (or front-to-rear) may be at some other angle. To get an idea of where it may be--or whether it might be different enough to be notable--simply look at the elevation pattern in the rearward direction. Or, specify some other elevation angles for the azimuth plot.</p>
|
||||
<center>
|
||||
<img src="p12.gif" width="640" height="480" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<center>
|
||||
<b>Figure 12</b>: Azimuth pattern of a 3-element Yagi 1 wavelength over average ground, at an elevation angle of 5 degrees.
|
||||
</center>
|
||||
<p>Although the take-off angle is a handy reference point in many cases, it may not be the most important one. Antenna builders may be more interested in particular paths to the stations they wish to work. If we work a lot of DX, then lower angles--perhaps in the 5 to 10 degree range--might interest us for some paths. In these cases, the antenna modeler and builder might show a lower angle for his or her chosen azimuth pattern. <b>Figure 12</b> shows the azimuth pattern for our 1 wavelength high Yagi at a 5 degree elevation angle. Note the reduced gain and slight change of pattern shape. In contrast, near-vertical incidence skip is of interest to a number of amateurs, and very high angle radiation may dictate what azimuth pattern they choose. Hence, it pays always to 1. compare both elevation and azimuth patterns and 2. read any accompanying text to find out why the pattern variables were chosen.</p>
|
||||
<p>Finally, note that the maximum gain in both our patterns over ground is considerably greater (when taken at the take-off angle) than the same antenna in free space. The signal reflected off the earth is not lost. Rather, it combines with the unreflected signal. At some elevation angles, the two are in phase and add up to a stronger signal--between 5 and 6 dB stronger. At other angles, they are out of phase and cancel, resulting in nulls rather than lobes. In general, for horizontal antennas, the number of lobes counting from the ground up to a point overhead (90 degrees up) is about 1 more than the number of wavelengths in height of the antenna. Remembering this fact will help you both to understand antenna patterns and to anticipate them as you read specifications in the text.</p>
|
||||
<p>As a rule of thumb, the lobes and nulls above the horizon can be calculated by a simple equation:</p>
|
||||
<center>
|
||||
<img src="pe1.gif" width="240" height="63">
|
||||
</center>
|
||||
<p>where Ae is the angle of the lobe or null, N is the lobe or null number counting from the ground up, and h is the antenna height in wavelengths or a fraction of a wavelength. For lobes, the value of N will be an odd integer (1, 3, 5, 7, etc.), while for nulls, the value of N will be even (0, 2, 4, 6, etc.). Our Yagi at a 1 wavelength height has lobes at about 14 degrees (the main lobe) and at 49 degrees. This calculation is only a rough guide, since the exact structure of the antenna and the terrain may alter the angles by small amounts.</p>
|
||||
<h3>Does the Good Earth Make a Difference?</h3>Most antenna patterns derived from antenna modeling software presume a flat, uncluttered terrain for the antenna. Because we live in spaces that may be littered with building, objects, and vegetation, and also because our terrain, both near and far, may be anything from flat to mountainous, model patterns only approximate the actual antenna performance we can achieve.
|
||||
<p>In general, the ground immediately beneath and around an antenna affects antenna efficiency and the feedpoint impedance. The far field pattern is most affected by the quality of earth several wavelengths from the antenna and beyond.</p>
|
||||
<p>The quality of the ground beneath an antenna can vary from exceptionally poor to salt-water good. Modeling software records the quality of the earth in a composite of two figures: conductivity, which is measured in Siemens per meter, and a dielectric constant, which has no unit of measure. For the most part, the larger either of these figures, the better the quality of ground. The range of possible ground conditions is very wide. Average soil has a conductivity of 0.005 S/m with a dielectric constant of 13. Salt water values are 5.0 S/m and 81. At the other end of the scale, extremely poor soil found in heavy inductrial areas may show values of 0.001 S/m and 3. Antenna handbooks usually have tables and even maps to help to determine the quality of ground in your area.</p>
|
||||
<p>The effect of terrain upon horizontally polarized antennas, such as our model Yagi, tends to be slight. To see this point in action, look at Table 1, which lists the gain and take-off angles for our model Yagi at various heights above 3 types of ground: "Very Poor" (0.001 S/m; 5), "Average" (0.005 S/m; 13), and "Very Good" (0.0303 S/m; 20). Note that the take-off angles are very stable, while the gain figure increase only a little as the ground quality increases.</p>
|
||||
<pre> Table 1
|
||||
Gain and Take-Off Angle of a 3-Element Yagi Over Various Soil Conditions
|
||||
|
||||
Ground Type
|
||||
Very Poor Average Very Good
|
||||
(C=0.001/DC=5) (C=0.005/DC=13) (C=0.0303/DC=20)
|
||||
|
||||
Antenna Height Gain (dBi)/ Gain (dBi)/ Gain (dBi)/
|
||||
(Wavelengths) TO angle TO angle TO angle
|
||||
|
||||
0.50 wl 11.7 / 24 12.3 / 25 12.8 / 26
|
||||
|
||||
0.75 wl 12.6 / 17 13.1 / 18 13.4 / 18
|
||||
|
||||
1.00 wl 13.0 / 13 13.4 / 14 13.7 / 14
|
||||
|
||||
1.25 wl 13.2 / 11 13.6 / 11 13.8 / 11
|
||||
|
||||
1.50 wl 13.4 / 9 13.7 / 9 13.9 / 9
|
||||
|
||||
1.75 wl 13.5 / 8 13.7 / 8 13.9 / 8
|
||||
|
||||
2.00 wl 13.6 / 7 13.8 / 7 14.0 / 7
|
||||
|
||||
Note: The model used for these representative values is aluminum and the
|
||||
check frequency is 14.175. As always, modeling is done over flat terrain
|
||||
and does not account for terrain variations. C is conductivity as measured
|
||||
in S/m; DC is a dielectric constant and has no units. TO angle is the
|
||||
elevation angle of maximum radiation and is in degrees above the horizon.
|
||||
|
||||
Table 1: Representative values for gain and take-off angle of a 3-element
|
||||
Yagi over various soil conditions.</pre>
|
||||
<p>We can make the same point by noting that when the E-plane of an antenna is parallel to the earth, the effects of ground quality are relatively small. However, if the E-plane is at right angles to the earth, the situation changes considerably. Of course, this situation corresponds to having a vertical antenna.</p>
|
||||
<center>
|
||||
<img src="p13.gif" width="400" height="480" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<center>
|
||||
<b>Figure 13</b>: Vertical dipole for 40 meters place 10' above ground at the antenna base.
|
||||
</center>
|
||||
<p>Using the same three soil types, we can take a simple vertical dipole and illustrate the difference. In this case, I modeled a full-length vertical dipole with the bottom 10' off the ground, as shown in <b>Figure 13</b>. The resulting patterns for the three ground qualities can be combined in a single graphic of the multiple polar plots, as shown in <b>Figure 14</b>. Note that the best ground quality produces the lowest take-off angle and the greatest signal strength, while the worst produces a weaker field strength at a higher angle.</p>
|
||||
<center>
|
||||
<img src="p14.gif" width="640" height="291" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<center>
|
||||
<b>Figure 14</b>: Elevation patterns for the 40-meter vertical dipole over three different soil types.
|
||||
</center>
|
||||
<p>At the same time, notice the absence of strong higher angle lobes in any of the three patterns in <b>Figure 14</b>. You will begin to see why many operators prefer vertical antennas for DX work, especially on the lower HF bands, where getting a horizontal antenna high enough to have a low-angle lobe of maximum radiation is often not feasible.</p>
|
||||
<p>These sample patterns should do more than acquaint you with the terminology and geometry of antenna patterns. They should be the beginning of the development of your expectations when seeing antenna plots of either horizontal or vertical antennas. Polarization: the Simple and the Complex</p>
|
||||
<p>Most modeling programs from which antenna patterns emerge can show not only the total far field of the antenna, but as well show both the vertically polarized and horizontally polarized components of that field. Linear antennas, such as the vertical dipole or the Yagi, tend to have negligible radiation cross polarized to the general orientation of the antenna. However, Many antenna types yield both types of radiation.</p>
|
||||
<center>
|
||||
<img src="p15.gif" width="550" height="516" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<center>
|
||||
<b>Figure 15</b>: Azimuth pattern of a half-square antenna at a 16-degree elevation angle over average soil showing the total field and its horizontally and vertically polarized components.
|
||||
</center>
|
||||
<p><b>Figure 15</b> shows the azimuth pattern at 19 degrees elevation of a half square, the general outlines of which have been superimposed on the plot. Although the maximum gain of the antenna's total field is a function of the vertically polarized radiation, the width of the field is considerably enlarged by the presence of horizontally polarized radiation, which shows itself in the cloverleaf pattern.</p>
|
||||
<center>
|
||||
<img src="p16.gif" width="640" height="189" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<center>
|
||||
<b>Figure 16</b>: Elevation patterns of a right-angle delta loop, taken broadside to the loop, for side-feed (for maximum vertically polarized radiation) and for bottom-center-feed.
|
||||
</center>
|
||||
<p>At HF, polarization becomes skewed in the ionosphere, and we normally think of the total field as making up the effective far field. However, for many types of loop antennas (quads, deltas, rectangles, etc.), where we feed the antenna can make a difference in the ratio of horizontally to vertically polarized radiation, and this, in turn can have an effect on the overall total field of the antenna. Consider <b>Figure 16</b>, which shows elevation patterns of the same delta loop. On the right, it is fed at the center of the horizontal wire, while on the left, it is fed 1/4 wavelength down from the triangle's apex. The patterns are significantly different, to say the least.</p>
|
||||
<center>
|
||||
<img src="p17.gif" width="640" height="300" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<center>
|
||||
<b>Figure 17</b>: Azimuth patterns for a 3-element 2-meter Yagi 30' above average soil for both horizontal and vertical orientations of the beam. The outer ring represents the same field strength in both patterns.
|
||||
</center>
|
||||
<p>Even where antennas are linear, we should expect pattern differences according to whether they are set up for horizontal or vertical polarization. Consider a small Yagi for 2 meters, elevated about 30' up. <b>Figure 17</b> shows the azimuth pattern at the take-off angle for the antenna when it is horizontal and when it is vertical. Vertically, it shows less gain and a much wider beam width than when horizontal. If we want to achieve a vertically polarized pattern whose shape resembles that of the horizontal Yagi, we have to turn to a different antenna design. Despite its higher gain, we cannot simple press the horizontal Yagi into service, because in line-of-sight, we shall likely lose more to cross-polarization losses than the extra gain will give us.</p>
|
||||
<h3>Comparisons, Both Educational and Practical</h3>
|
||||
<p>Now that we know how to read antenna patterns with reasonable accuracy, let's look at some ways in which comparing antenna patterns can assist us in understanding antennas. The following examples are only starters, chosen for their variety. Getting a comprehensive look at antennas is a lifetime's vocation.</p>
|
||||
<p><b>1. The Center-Fed Doublet</b>: One of the most common antennas is still one of the most misunderstood. Because the center-fed doublet yields a dipole-like pattern at its lowest frequency of operation, many hams believe that it provides a dipole-like azimuth pattern at all its frequencies of operation. Generating some azimuth patterns can tell us very quickly whether this belief is true or false.</p>
|
||||
<center>
|
||||
<img src="p18.gif" width="640" height="617" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<center>
|
||||
<b>Figure 18</b>: Azimuth patterns for a 135' doublet 50' above average soil when used on 80, 40, 20, and 10 meters. In each case, the doublet is oriented left-to-right in the pattern graphic.
|
||||
</center>
|
||||
<p>Let's make our doublet 135' long and use it from 80 meters through 10 meters. We shall make it of #14 copper wire and place it at 50' in the air. Ignoring ground clutter and terrain variables, we would get the patterns of <b>Figure 18</b> on 80, 40, 20, and 10 meters. Notice that the elevation angle of maximum radiation is different for each band. In fact, on 80 meters, because the take-off angle is so high, an arbitrary angle of 45 degrees was selected for the azimuth pattern.</p>
|
||||
<p>The antenna is 1/2 wavelength long at 80 meters, 1 wavelength long at 40 meters, etc. For your reference file, you can count the number of lobes and relate them to the antenna length in terms of wavelengths. Also note that as the antenna becomes longer relative to the frequency of operation, the direction of the strongest lobes moves from a broadside direction toward the ends of the antenna.</p>
|
||||
<p>Besides acquainting you with the antenna patterns on various bands, the azimuth patterns are also useful for practical antenna planning. First, decide which bands are your favorites and, as well, which directions from your station are best for making your most desired contacts. If you have a choice of directions in which to string up the doublet, you can to some measure erect the antenna for maximum signal strength on your favorite bands in your most desired directions. The azimuth patterns can be a useful planning tool.</p>
|
||||
<p><b>2. Directional Beams and Elevation Patterns</b>: In the maze of antenna materials, we often find it difficult to see how antennas are related. For example, in a number of talks I have given to beginners in ham radio, questions have arisen about how dipoles and various size Yagis may be kin to each other. The questioners are often surprised by how close the relationship is.</p>
|
||||
<center>
|
||||
<img src="p19.gif" width="639" height="278" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<center>
|
||||
<b>Figure 19</b>: Composite elevation patterns for a dipole, a 2-element Yagi, and a 3-element Yagi, each placed 1 wavelength above average soil.
|
||||
</center>
|
||||
<p>One simple demonstration I have used is to combine the elevation patterns of a dipole, a 2-element Yagi, and a 3-element Yagi, all at the same height. A representative version of this pattern combination appears in <b>Figure 19</b>. I have added labels to the portions of the curves that might get confusing.</p>
|
||||
<p>From the figure, two significant features appear. First, all three antennas have the same lobes and nulls at almost identical angles. Second, the symmetry of the dipole pattern fore and aft of the vertical center line disappears steadily as the parasitical elements direct the main lobe in one direction. Hence, both kinship and differences appear at once.</p>
|
||||
<p>Combining curves is something that an antenna modeler can do with ease. The casual reader of amateur magazines may see only individual patterns. However, by examining either the graphic or the text for further information on gain, front-to-back ratio, and other features of the antennas, one can get a pretty good view of two or more antennas in combination. In fact, one can transpose the pattern of one antenna upon the other for greater clarity. However, be sure that the transposed patterns are truly comparable before transposing them.</p>
|
||||
<p><b>3. Directional Beams and Azimuth Patterns</b>: There is a myth that pervades amateur radio: for every operating purpose whatsoever, always choose the highest gain, highest front-to-back antenna you can afford. Like all myths, this one has some truth, but not all truth.</p>
|
||||
<p>To sort out what is true and what is false in the myth, let's combine in one graphic the azimuth patterns for a good 2-element Yagi and a good 3-element Yagi. We shall place both at 1 wavelength in height so that the elevation angles for the patterns will be the same. The result appears in <b>Figure 20</b>.</p>
|
||||
<center>
|
||||
<img src="p20.gif" width="640" height="480" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<center>
|
||||
<b>Figure 20</b>: Composite azimuth patterns at 14 degrees elevation of a 2-element Yagi and a 3-element Yagi, each 1 wavelength above average soil.
|
||||
</center>
|
||||
<p>Obviously, the 3-element Yagi has superior gain and front-to-back ratio. As such, it may indeed be the better antenna for serious DXing, where we wish to maximize our signal to the distant receiving station and suppress as much as possible all the potential QRM from the sides and rear of our station. However, serious DXing is not the only important type of amateur operating activity.</p>
|
||||
<p>Many contesters and net operators do not want to suppress completely signals from the sides and rear. They wish to know that someone worth working is present, but not so loud as to interfere with the current station being worked. Hence, they tend to prefer antennas with some front-to-back ratio and some gain, but not the ultimate in each. For their type of operation, the 2-element Yagi may in fact be the preferred antenna.</p>
|
||||
<p>In this example, I have given a choice of only two antennas. However, the basic principle can be applied to a host of antenna types. A comparison of antenna patterns, when placed against a list of operating goals and the needs one has to achieve those goals, can be a valuable tool in antenna selection.</p>
|
||||
<p><b>4. Truth--Pattern Shape and Pattern Detail</b>: The shape of an antenna pattern is not the whole story, and one can easily fall into traps of hasty interpretation. To illustrate the point, let's look at <b>Figure 21</b> and fall into one kind of trap together.</p>
|
||||
<center>
|
||||
<img src="p21.gif" width="640" height="200" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<center>
|
||||
<b>Figure 21</b>: Azimuth patterns for two 2-element Yagis (A and B) along with a composite pattern graphic of the two (C), with each antenna 1 wavelength above average soil.
|
||||
</center>
|
||||
<p>Part A of the figure shows the free space azimuth pattern of a 2-element Yagi. The main lobe is, as expected, quite round with a good beam width. The rear quadrant shows a very high 180-degree front-to-back ratio. In most respect, this pattern appears to be superior to the free space pattern shown in Part B, where the 180-degree front-to-back ratio is under 20 dB.</p>
|
||||
<p>Part C of the figure springs the trap. The patterns in parts A and B are overlaid, demonstrating the far lower gain of the initial pattern. In fact, the gain for A is only 3.8 dBi, while the gain for B is nearly 6.6 dBi. In addition, the 180-degree front-to-back ratio for B is a little under 19 dB and is the worst case of the entire rear quadrant. By contrast, the 29 dB 180-degree front-to-back ratio of A covers only a small part of the rear quadrant and drops to a worst-case value of just over 16 dB.</p>
|
||||
<p>Without the added data, we might not have realized that the performance of the two antennas was so radically different. Even without the pattern overlay, the data for both the forward and rear quadrants of the antenna pattern make those differences clear. In fact, A is based on a model of a highly loaded and shortened 10 meter beam, while B is based on a model of a full-size 10-meter beam with phasing line connecting the two elements.</p>
|
||||
<p>When comparing antenna patterns, be certain that you have a complete data set before you start the work of comparison. As we have seen, free space patterns are not directly comparable, even though similar, to patterns over ground. When comparing patterns taken over ground, be certain that the heights are comparable and that the ground types are similar. Wherever antennas are of different types, examine both the azimuth and elevation patterns of each.</p>
|
||||
<p>These considerations become very important when trying to make purchase decisions among commercial beams. The manufacturers do not present their information with a common format, and therefore, comparisons are very difficult, even where patterns are offered. If a significant number of manufacturers do submit antenna models to ARRL in conjunction with its new advertising policy, then it will be much easier to comparatively examine models of competing antennas. However, even then, we shall have plenty of other evaluative work to do.</p>
|
||||
<p>Antenna patterns do not tell anything like the whole story with antennas. We have already seen the need to place the performance figures in juxtaposition with our operating goals and needs. In addition, we shall have to factor in such considerations as cost, weight, available space, installation complexity, and maintenance, not to mention the legalities which are becoming an increasing burden to antenna installation.</p>
|
||||
<h3>In the End, There is No End</h3>We have barely scratched the surface of the things we can learn from antenna patterns, when we learn to read them accurately and carefully. By examining the azimuth and elevation patterns for single antennas, we can gauge their performance in terms of gain, front-to-back specifications, lobes and nulls, beam width, and polarization composition. We can also compare antennas, both within a single type and among types, analyzing high and low angle lobes, lobe direction and shape, and numerous other properties.
|
||||
<p>In the end, the information you can gain from antenna patterns will help you make intelligent decisions about the best antenna for your station location. When combined with all of the other types of information you can and should gather, the more information you draw from antenna patterns, the more satisfying your ultimate decision is likely to be.</p>
|
||||
<h3>Notes</h3>
|
||||
<p>1. The antenna patterns used to illustrate the ideas in this article are taken from several commercial implementations of either MININEC or NEC-2, the most frequently used antenna modeling calculation cores. The most familiar implementations of these cores come from the following sources (listed in alphabetical order):</p>
|
||||
<ul>
|
||||
<li>AO (MININEC) and NEC-Wires (NEC-2): Brian Beezley, K6STI</li>
|
||||
<li>EZNEC (NEC-2) and ELNEC (MININEC): Roy Lewallen, W7EL</li>
|
||||
<li>NEC-Win (NEC-2): Nittany Scientific</li>
|
||||
<li>NEC4WIN95 (MININEC): Madjid Boukri, VE3GMI, Orion Microsystems</li>
|
||||
</ul>
|
||||
<p>Nothing in these notes should be interpreted either as an endorsement or as a criticism of any particular software.</p>
|
||||
<p>In addition to the commercial implementations noted above, there are other antenna modeling software packages available, some based on the most used cores and some based on individual or proprietary cores. Also obtainable are some specialized output packages for specific graphical purposes.</p>
|
||||
<p>Also see the <a href="nec.html">Antenna Modeling Programs</a> page for more information.</p>
|
||||
<center>
|
||||
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
|
||||
</center>
|
||||
<p><i>Updated 7-18-99, 02-06-01. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author. An earlier version of this items appeared in</i> CQ <i>(Jan. and Feb, 1999).</i></p>
|
||||
<center>
|
||||
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
|
||||
</center><a href="../radio.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Go to Main Index</a><br>
|
||||
<p class="topics-footer">Topics: <a href='../topics.html#modeling'>Modeling</a></p><br>
|
||||
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<title>NEC and Reciprocity</title>
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<h1>NEC and Reciprocity</h1>
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<h3>L. B. Cebik, W4RNL</h3>
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<p>In these notes, we shall examine a relatively simple-sounding question: Does NEC honor the reciprocity theorem as applied to antennas? We shall look at two demonstrations that we might use to satisfy ourselves that the popular wire-antenna modeling program does honor the theorem. One method of demonstation will not be accessible to those using some entry-level NEC implementations, such as EZNEC or NEC-Win Plus. Therefore, we shall add a second demonstation that, although less graphically complete, should satisfy any user that reciprocity applies to NEC models. In the process of setting up these demonstrations, I have striven to keep to an absolute minimum any software user calculations that are external to the NEC program. In fact, we shall need only one simple equation, letting NEC's calculations do the reminder of the work. Indeed, these notes are less about the foundations and validity of the reciprocity theorem and more about NEC itself.</p>
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<p><b>What is Reciprocity?</b></p>
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<p><i>The ARRL Antenna Book</i> (20th Ed., p. 2-1) contains a beginner's discursive explanation of reciprocity. "In the same fashion that a loudspeaker can act as a microphone, a radio antenna also follows the principle of reciprocity. In other words, an antenna can transmit as well as receive signals." This brief extract follows on an explanation of an antenna as a "special transducer" capable of converting RF current into propagating electromagnetic waves and converting intercepted waves into electrical current. The context is the very beginning of a chapter called "Antenna Fundamentals." Hence, we should not expect mathematical sophistication. Indeed, at this stage of the volume's exposition, the discussion is unprepared to answer many questions that arise within a radio operator's experience. For example, in 2-way HF communication, we very often find that there are differences in the received strengths of an outgoing signal and an incoming signal. From the initial description of reciprocity, we cannot tell if the differences are a function of how the antenna works in transmit and receive modes or a function of what happens to the electromagnetic waves between the transmitting and receiving sites, that is, a function of HF radio wave propagation.</p>
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<p>More mathematically inclined readers may wish to consult various college-level antenna texts. I keep a small number on my shelf as references, for example, Stutzman and Thiele, <i>Antenna Theory and Design</i> (2nd Ed., pp. 404-409), and Balanis, <i>Antenna Theory: Analysis and Design</i> (2nd Ed., pp. 127-132). I have listed the most relevant pages of each text for a reason. Balanis discusses reciprocity early in the text's development, but Stutzman and Thiele defer the treatment until late in the text. We shall have occasion to note the Stutzman and Thiele treatment later.</p>
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<p>Both treatments share a common kernel, the development of antenna reciprocity from the the Lorentz reciprocity theorem, which itself derives from Maxwell's equations. (Those comfortable with calculs may wish to compare the Stutzman and Thiele equation 9-36 with Balanis' equation 3-66. Because my goal is to minimize necessary reader math in these notes, I shall not reproduce the equation here, especially since it is so readily available elsewhere.)</p>
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<p>A better-known text among amateur radio operators is Kraus, <i>Antennas</i> (2nd Ed., pp. 410-413). One interesting aspect of the Kraus treatment is that he uses a different starting point for his development of reciprocity. He begins with the Rayleigh-Helmholtz reciprocity theorem as generalized in the 1920s by J. R. Carson. (Rayleigh's initial context of sound is not unrelated to the ARRL basic analogy between antennas and loudspeakers.) Without ado, Kraus expresses the theorem in the following terms: "If an emf is applied to the terminals of an antenna A and the current measured at the trerminals of another antenna B, then an equal current (in both amplitude amd phase) will be obtained at the terminals of antenna A if the same emf is applied to the terminals of antenna B." (p.411) Krause goes on to note some of the limiting conditions in which the theorem applies. Of course, the frequency of the applied emf (or voltage) must by the same, and the media must be "linear, passive and also isotropic." For our purposes in evaluating whether NEC honors reciprocity, the following note is critical: "An important consequence of this theorem is the fact that under these conditions the transmitting and receiving patterns of an antenna are the same."</p>
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<p>The last note that I cited from Kraus gives us something that we can test in various ways within the context of NEC software solely by examining the NEC output report. Sometimes, we shall even be able to use graphical representations of selected output data to illustrate the results.</p>
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<p><b>NEC Transmit and Receive Patterns</b></p>
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<p>We may use NEC itself to establish the transmit and receive patterns are the same. However, the entry-level software used by most modelers gives no clue to a proper answer to the question. Most entry-level software restricts the user to only one of the excitation possibilities, the direct voltage source (EX0) (or an indirect current source). For example, we might encounter a 6-element Yagi modeled in free space. The following lines define the model in ASCII format.</p>
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<pre>
|
||||
CM 6-el 2M Yagi
|
||||
CE
|
||||
GW 1 21 -.514604 0. 0. .514604 0. 0. .0024
|
||||
GW 2 21 -.5075174 .257302 0. .5075174 .257302 0. .0024
|
||||
GW 3 21 -.4746752 .3637788 0. .4746752 .3637788 0. .0024
|
||||
GW 4 21 -.461137 .6585204 0. .461137 .6585204 0. .0024
|
||||
GW 5 21 -.461137 .9469628 0. .461137 .9469628 0. .0024
|
||||
GW 6 21 -.443992 1.377137 0. .443992 1.377137 0. .0024
|
||||
GE 0
|
||||
LD 5 0 0 0 2.5E+07 1.
|
||||
FR 0 1 0 0 146. 0
|
||||
GN -1
|
||||
EX 0 2 11 0 1 0.
|
||||
RP 0 1 361 1500 90. 0. 1.00000 1.00000 0.
|
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EN
|
||||
</pre>
|
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<p>The EX command line specifies that we apply a voltage source to the center segment of wire 2. In most entry-level programs, we then request a radiation pattern (RP0). Since the antenna is in free space, we request an azimuth pattern, which is technically an E-plane pattern. The result appears in <b>Fig. 1</b>. Note that the wire entries place the element spacing values in the Y columns, while the elements extend in the +X and -X directions. The conventions of the software used here (NSI's GNEC) place 0 degrees at the top of the polar plot. The pattern is a phi pattern (where a true azimuth pattern would increase the degree values clockwise). Hence, the main lobe of the antenna points to the left at 90 degrees phi.</p>
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<center>
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<img src="recip-1.gif" width="625" height="415" border="2" vspace="5" hspace="9">
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</center>
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<p>The side panel in the figure provides the analytical data to accompany the normalized plot on a logarithmic scale. One reason that I selected this antenna was its free-space gain value of just over 10 dBi. For data-gathering purposes, the XNDA specification in the RP0 command is 1500. When N=5, the radiation pattern portion of the NEC output file produces an additional table. It lists for each value of phi and theta the antenna gain normalized to the peak gain of the antenna. The bearing of peak gain will read 0 dB, and all other gain values will be negative, indicating how much below the peak gain they are, as recording in dB. However, even a pattern like this one does not show why the antenna is or is not reciprocal, or even what reciprocity might mean.</p>
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<p>An antenna is reciprocal if its receiving pattern and its transmitting pattern are the same. We ordinarily record the transmitting pattern in dBi, or dB relative to an isotropic source. Normalized, the gain appears relative to a peak value of 0 dB. The counterpart to transmitting gain would be receiving sensitivity. More advanced versions of NEC offer a number of options for deriving receiving patterns. They involve the EX1 command for linear antennas, that is, providing the antenna with external excitation in the form of linear plane waves. We systematically rotate the excitation around the antenna in a series of steps. Then we invoke the PT command to record the relative current at a selected point--our former feedpoint. <b>Fig. 2</b> shows in simplified form with only 8 positions for the EX1 command how the development of receiving patterns differs from the development of transmit patterns.</p>
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<center>
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<img src="recip-2.gif" width="650" height="400" border="2" vspace="5" hspace="9">
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</center>
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<p>EX1 is only one of three types of excitation that are external to the antenna geometry.</p>
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<blockquote>
|
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<p>EX 1: incident plane wave, linear polarization</p>
|
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<p>EX 2: incident plane wave, right hand (thumb along the incident vector) elliptic polarization</p>
|
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<p>EX 3: incident plane wave, left hand (thumb along the incident vector) elliptic polarization</p>
|
||||
</blockquote>
|
||||
<p>Both of the elliptical polarization options are useful when simulating signal sources from helical and similar antennas. Linear polarization simulates from antennas that we normally classify over ground as either vertically or gorizontally polarized, both of which are forms of linear polarization. For reference, the following line shows the meaning of the entries within an EX1 command. Note that as we change the type of excitation from EX0 through EX5, the leanings for the integer and floating decimals will change. See the NEC-4 manual for other forms of excitation.</p>
|
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<pre>
|
||||
Com I1 I2 I3 I4 F1 F2 F3 F4 F5 F6 F7
|
||||
ID Type # Thta # Phi Not Th angle Ph angle Eta Theta Phi Axis El. field
|
||||
angles angles used to vector to vector pol. angle step step ratio V/m
|
||||
EX 1 1 8 0 90 0 90 0 45 0 0
|
||||
</pre>
|
||||
<p>The sample entry is for a linear plane wave. Hence, F6 is 0 by non-relevance. F7 also has a 0, but that value indicates a default value of 1 V/m. In some problems designed to ferret out coupling potentials among wires, you may use a specific value that closely approximates the value from the source signal at the structure being examined in model form.</p>
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<p>Most of the remaining entries define incident plane waves as a calculation loop within NEC (with some properties resembling the loop operation of frequency sweeps using the FR command). In the sample, for the sake of clarity, there is only one theta angle: 90 degrees. This angle is parallel to the plane of the antenna elements. The sample specifies 8 phi-angle (azimuth-angle) steps at 45-degree increments, thus providing samples evenly spaced in the element plane. The entry corresponds to the simplified situation shown in <b>Fig. 2</b>.</p>
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<p>The F3 entry, called Eta, under linear polarization is easy to memorize. With a value of 0, the polarization is in the +/-Z direction--vertically polarized for antennas over ground. If F3 is 90, the polarization is in the X-Y plane--horizontally polarized for antennas over ground. The sample in free space uses horizontal polarization for simplicity, but there is no restriction against checking results when cross-polarized or with the polarization set to intermediate angles. When using EX 2 or EX 3, elliptical polarization, the entry changes its meaning and defines the major ellipse axis. (Remember that true circular polarization is simply a special case of elliptical polarization having equal axes.)</p>
|
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<blockquote>
|
||||
<p>[<b>Special Note for NEC-2 Users</b>: The structure of the NEC-2 plane-wave excitation entry is slightly different than the NEC 4 entry. It has the following structure:</p>
|
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<pre>
|
||||
Com I1 I2 I3 I4 F1 F2 F3 F4 F5 F6
|
||||
ID Type # Thta # Phi Not Th angle Ph angle Eta Theta Phi Axis
|
||||
angles angles used to vector to vector pol. angle step step ratio
|
||||
EX 1 1 8 0 90 0 90 0 45 0
|
||||
</pre>
|
||||
<p>Note that the NEC-2 version lacks the F7 floating point entry for the electrical field strength, and the default value of 1 V/m always applies. Only 1 incident plane wave is allowed at a time (that is, before a succeeding execution step). If excitation types are mixed before a succeeding execution step, then the program will use only the last excitation type encountered.]</p>
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</blockquote>The second command necessary to produce a receiving pattern is PT (technically, Printing Options for Currents on Wires). The options of interest are the following ones:
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<blockquote>
|
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<p>PT 1: Currents printed in a format designed for a receiving pattern.</p>
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<p>PT 2: Currents printed in a format designed for a receiving pattern, plus a normalized value for the last segment's current.</p>
|
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<p>PT 3: Only the normalized current is printed.</p>
|
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</blockquote>
|
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<p>Our present interest lies in the PT entries followed by positive integers. The general format is as follows.</p>
|
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<pre>
|
||||
Com I1 I2 I3 I4
|
||||
ID Type Tag # 1st Seg Last Seg
|
||||
PT 2 2 1 11
|
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</pre>
|
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<p>The I2 through I4 entries are necessary only for PT 0 through PT 3. In this instance, the sample request asks both for the data on Tag 2, Segments 1 - 11, and for the normalized value of the data on segment 11. To make sense of this entry, refer to the initial model. Tag 2 represents the Yagi driver, and segment 11 is the segment connected to the feedline--a source segment in the transmitting mode and the focal segment in the receiving mode.</p>
|
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<p>From the EX1 and PT3 commands, we can construct a model that will provide us with the receiving counterpart of the transmitted radiation pattern for our 6-element Yagi. The following lines show the model in .NEC format. Note that NEC has a limitation in how large a receiving matrix may be. Therefore, the data generation has two parts, one from -90 to +90 degrees, the other from 90 to 270 degrees. <b>Fig. 1</b> tells us why we selected the division of the work, since peak gain occurs at a phi heading of 90 degrees. Since we shall request normalized data, each section of data must contain a peak gain/current point, which occurs at 90 degrees phi. The program then normalizes the data against this value. The PT3 command allows us to capture only the normalized current in dB at a selected segment, in this case, the same segment that we formerly used as the transmit source or feedpoint.</p>
|
||||
<pre>
|
||||
CM 6-el 2M Yagi
|
||||
CE
|
||||
GW 1 21 -.514604 0. 0. .514604 0. 0. .0024
|
||||
GW 2 21 -.5075174 .257302 0. .5075174 .257302 0. .0024
|
||||
GW 3 21 -.4746752 .3637788 0. .4746752 .3637788 0. .0024
|
||||
GW 4 21 -.461137 .6585204 0. .461137 .6585204 0. .0024
|
||||
GW 5 21 -.461137 .9469628 0. .461137 .9469628 0. .0024
|
||||
GW 6 21 -.443992 1.377137 0. .443992 1.377137 0. .0024
|
||||
GE 0
|
||||
LD 5 0 0 0 2.5E+07 1.
|
||||
PT 3 2 11 11
|
||||
EX 1 1 181 0 90 0 90 0 1 0 0
|
||||
XQ
|
||||
PT 3 2 11 11
|
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EX 1 1 181 0 -90 180 90 0 1 0 0
|
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XQ
|
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EN
|
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</pre>
|
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<p>The data for both the transmitting pattern and the receiving pattern can be transferred to a spreadsheet for graphing. For both sets of data, we have 361 data points (from 0 to 360 degrees phi). <b>Table 1</b> provides a glimpse of the data from 0 to 120 degrees for the 6-element Yagi in free space at 146 MHz. Three data points call for attention: 0, 180, and 360 degrees. Each of these points represents a free-space side null. Values for these nulls have two properties that are problematical for graphing. First, they may have very large negative values. Graphing such values may result is severe compression of the upper part of the graph. Second, the values are subject to large variations with very small differences in the rounded values of numbers that go into their development. For the sake of graphing, I have set these numbers to an artificially high value of -100 dB.</p>
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<center>
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<img src="recip-t1.gif" width="769" height="550" border="2" vspace="5" hspace="9">
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</center>
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<p>If we conjoined the two graphs--one for the transmitting pattern and one for the receiving pattern--we obtain a result like <b>Fig. 3</b>.</p>
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<center>
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<img src="recip-3.gif" width="774" height="516" border="2" vspace="5" hspace="9">
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</center>
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<p>Computer-generated graphs "write" the curve for one color and then overwrite it with the second color line. The result for our test case is the nearly complete disappearance of the red line beneath the green. A few red "dots" appear as verification that the line is present. However, as both the graph and the table suggest, the normalized pattern graphs are as identical as one might find in any data generation system. In short, within the limits of our ability to calculate and present the results, the patterns for transmitting gain and for receiving sensitivity are the same. From the perspective of NEC, the antenna performance is reciprocal with respect to transmitting and receiving.</p>
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<p><b>An Alternative Procedure Using only EX0 and RP0</b></p>
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<p>Early in the notes, I mentioned that the Stutzman and Thiele text reserves treatment of recprocity until late in their work, specifically the chapter devoted to antenna measurements. In this context, the identity or radiated and received patterns becomes significant insofar as it allows us to set up four equivalent test procedures for determining the pattern of a linear antenna. <b>Fig. 4</b> shows the possibilities.</p>
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<center>
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<img src="recip-4.gif" width="528" height="367" border="2" vspace="5" hspace="9">
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</center>
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<p>Let us suppose that we have a reasnably complex antenna with an equally complex radiation pattern. Our 6-element, 146-MHz Yagi will do well in this regard. In order to obtain the pattern, we shall need not only the test antenna, but as well a second antenna that we may use to transmit a standard unvarying signal or to receive a signal from the test antenna. We may place the test antenna in a fixed position and rotate the second antenna around it, as suggested by the upper two parts of <b>Fig. 4</b>. This arrangement tends to be mechanically complex, costly, and inconvenient for all but the crudest measurements, such as in a walk-around. However, periodic checks made of fixed broadcast antennas tend to use this system with checks at selected points around the compass. If we use the second antenna in the transmit mode, then we replicate the receive model that we have just concluded. For models, the techniques is equally applicable in both NEC-2 and NEC-4.</p>
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<p>The lower two options in <b>Fig. 4</b> represent procedures that a more common to HF and VHF antenna range testing by manufacturers. We may let the test antenna transmit while rotating it, and receive the signal of varying strength at the second antenna. Alternatively, we may let the test antenna receiving while rotating, using the second antenna as a transmitted signal source.</p>
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<p>For horizontally polarized antennas over ground, the second antenna is normally a dipole. A dipole that is resonant at the test frequency has known properties and performs very close to an ideal dipole, despite the use of common cxonductive materials and the shortening that accompanies a non-infinitesimal diameter. Since the early days of antenna experimentation, it has served as both a reference antenna and as a signal source or recpetion aerial.</p>
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<p>For reliable pattern data, the two antennas need to be well separated. At lower frequencies, one needs to be concerns about Rayleigh limits for the far field. In a VHF model, we can simply set the two antennas apart by a wide distance. In the model that we shall use, the separation will be 1 mile (5280' or 63360"). Since a wavelength at 146 MHz is between 80" and 81", the antennas will be over 750 wavelengths apart. In order to assure that we have enough current on the receive antenna elements to register, we may set the transmit power at an arbitrary 1000 W.</p>
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<p>To further simplify the set-up, we shall set the two antennas in a free-space environment. Our goal is to demonstrate a reciprocity between transmitted and received patterns, so we need not be concerned by introducing an intervening variable, such as the ground.</p>
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<pre>
|
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CM 6-el 2M Yagi and dipole
|
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CE
|
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GW 1,21,-.6885686,.514604,0.,-.6885686,-.514604,0.,.0023813
|
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GW 2,21,-.4312666,.5075174,0.,-.4312666,-.5075174,0.,.0023813
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GW 3,21,-.3247898,.4746752,0.,-.3247898,-.4746752,0.,.0023813
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GW 4,21,-.0300482,.461137,0.,-.0300482,-.461137,0.,.0023813
|
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GW 5,21,.2583942,.461137,0.,.2583942,-.461137,0.,.0023813
|
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GW 6,21,.6885684,.443992,0.,.6885684,-.443992,0.,.0023813
|
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GW 7,21,1609.344,-.48641,0.,1609.344,.48641,0.,.0023813
|
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GE 0
|
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LD 5 0 0 0 2.5E+07 1.
|
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FR 0,1,0,0,146.
|
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GN -1
|
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EX 0,7,11,0,1.,0.
|
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RP 0,1,361,1000,90.,0.,0.,1.,0.
|
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EN
|
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</pre>
|
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<p>The model that we require, in .NEC format, looks very much like the initial model for the the original 6-eleent Yagi, with only a few changes. First, we have added the dipole that is 1 mile away from the Yagi. Second, we have provided the dipole with the source (Wire 7, Segment 11). To reverse the transmit and receive functions, we need only place the source on Wire 2, Segment 11.</p>
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<p>For the sake of the doemnstation, we shall need some data about the Yagi in free space. <b>Fig. 5</b> provides a free-sapace radiation pattern and performance data from an EZNEC model. The only differences between the pattern shown and <b>Fig. 1</b> are that fact that the new pattern derives from EZNEC software, the main lobe extends along the X-axis, and the EZNEC graphic convention is to place 0 degrees phi horizontally to the right.</p>
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<center>
|
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<img src="recip-5.gif" width="500" height="450" border="2" vspace="5" hspace="9">
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</center>
|
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<p>Thge figure includes some data that we shall later use, including the maximum forward gain in dBi, the 180-degree front-to-back ratio, the front-to-sidelone ratio, and phi angles for the half-power points. (The sidelobes for this model are actually the rear quartering lobes, but they will serve our needs quite well.) We shall use all of this data to establish a coincidence between tra smit and receive patterns using only the standard entry-level RP0 request for a radiation pattern.</p>
|
||||
<p>Although I have shown the model in .NEC format, it will run on EZNEC, which simplifies the process of rotating the 6 wires that form the Yagi. In EZNEC, we shall be rotating the antenna in 10-degree increments from 0 degrees phi to 180 degrees phi. In addfition, EZNEC has a provision for setting the power level of the transmitting antenna, a facility that relieves us of the need to calculate the correct voltage to achieve that power level. We shall make two sets of model runs, one with the Yagi transmitting and one with the dipole transmitting. <b>Fig. 6</b> shows the outline of the model set-up, although only a few Yagi positions appear for clarity. The figure also includes the free-space patterns of the two antennas, derived when each in in a transmit mode.</p>
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<center>
|
||||
<img src="recip-6.gif" width="580" height="400" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>Except as a check to see that we have in fact rotated the Yagi by 10 degrees for each run of the model, we shall not initially examine the output data. The radiation pattern will show essentially the same values wherever we point it when we use it in the transmit mode. Instead, we shall use some data that is readily available even in entry-level software, although too few modelers ever even look at it. We shall look at the current magnitude and phase angle on a certain wire and segment. The relevant segment is the one that would have the source in the transmit mode, but which does not have a source in the receive mode. Many modeler would place a load on this segment, one that corresponds to the segment's impedance when in the transmit mode. Because our initial tests will seek only a clear indication of the pattern shape, we may overlook the load, but we shall add one eventually.</p>
|
||||
<p>The required current magnitrude and phase data appear in the NEC output report. Entry-level software, such as EZNEC and NEC-Win Plus, provide this data in special tables extracted from the output file. NEC itself uses peak values of voltage and current. EZNEC is somewhat unique in converting these values to RMS values. Hence, the numbers in the EZNEC current table will be related to the values in the NEC output table by a constant factor (1.414), which will not affect our ultimate evaluation of the pattern shape. One limitation of the current table is that for values that require engineering notation (for example, 1.2E-5), the table limits the entry to two significant digits. We shall keep that fact in mind when we perform a few simple external calculations on the data that we obtain.</p>
|
||||
<center>
|
||||
<img src="recip-t2.gif" width="321" height="497" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p><b>Table 2</b> provides the data that we gather from our experiment. For each row in the table, we rotate the Yagi by 10 degrees counterclockwise (in the phi direction). The middle columns record the current on the second antenna "feedpoint" segment when we provide the Yagi feedpoint with a voltage source equivalent to a supply power level of 1 kW. The right-hand columns record the current on the Yagi "feedpoint" segment when we provide the second antenna feedpoint with a voltage source equivalent to a supply power level of 1 kW. We only need to gather data between 0 and 180 degrees since the pattern is symmetrical. In certain other cases, we may wish to extend the survey for a full 360 degrees.</p>
|
||||
<p>Although the phase angles for the two situations tightly coincide, the current magnitude entries do not. However, we would find an invariant adjustment factor between the two sets of current magnitudes. The difference results from the fact that each feedpoint requires a different source voltage to obtain the requisite 1-kW power level. The Yagi impedance is about 50+j9 Ohms, but the second antenna, a resonant dipole, has a feedpoint impedance of 72+j1 Ohms. This difference will make no difference to our evaluation of the patterns as we swap positions for the transmitted and received signals.</p>
|
||||
<p>We might try to create a semblance of a polar plot using the data in the table, although it would have likely not be a pretty affair. Instead, we may evaluate the patterns against the radiation plot for the Yagi that appears in <b>Fig. 4</b>. The critical data in that plot use gain values in dB, for example, for the 180-degree front-to-back ratio and for the front-to-sidelobe ratio. We only have current magnitudes with which to work. However, we may obtain usable values in dB by reference to the common equation:</p>
|
||||
<center>
|
||||
<img src="recip-e1.gif" width="219" height="54">
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<p>Our only question will be what values to use for I1 and for I2. For I1, lets use the current for zero degrees. To obtain a value for the 180-degree front-to-back ratio, we use the current for 180 degrees. In passing, we may not the the pattern in <b>Fig. 5</b> shows a higher gain at 180 degrees than on either side of that heading, and the <b>Table 2</b> record of data shows the same small increase in terms of the current magnitude. Compare the values for 170 and 180 degrees.</p>
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<center>
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<img src="recip-t3.gif" width="257" height="385" border="2" vspace="5" hspace="9">
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<p><b>Table 3</b> shows the calculated front-to-back ratios from erach data set along with the NEC data for the radiation pattern. Since the current value for 180 degrees uses only 2 significant digits, the values coincide closely with the NEC report. Moreover, the values for the two test situations are very close to each other.</p>
|
||||
<p>With caution, we may apply the same technique to obtain a front-to-sidelobe value from the test data in <b>Table 2</b>. If we check <b>Fig. 4</b>, we find that the peak sidelobe gain occurs at 126 degrees. Our data only includes values for 120 and 130 degrees. However, these values are the dame in both sets of columns and the pattern does not show much change across the 10-degree span. Hence, we may plug the tabular datas as I2 values into our simple equation and obtain the next set of calculated data in <b>Table 3</b>. Remembering that the current data is only good to 2 significant digits, the result coincide remarkable well.</p>
|
||||
<p>Without resorting to any sort of plotting exercise, we may perform one further test. The data for <b>Fig. 4</b> show that the half-power beamwidth limit is 26.3 degrees from the heading of the main forward lobe. We have data only for 20 degrees and 30 degrees. If we use the 20-degree values for I2, we should obtain a value less than 3 dB. The result using the data for 30 degrees should be greater than 3 dB. <b>Table 3</b> confirms this anticipated result. More significantly for this test, the values derived from the reversal of transmit and receive antennas tighly coincides.</p>
|
||||
<p>The sum of these tests is that NEC produces within very close limits equivalent patterns in the test situation when the test Yagi transmits and when it receives. Even though we may be limited within entry-level software in the commands to which we have access, we can still confirm reciprocity of transmit and receive pattern shapes using the tools available.</p>
|
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<p>We have not tried to determine the forward gain of the Yagi in the test situation. To obtain this data, we shall require a modified test situation. <b>Fig. 7</b> shows its general outlines.</p>
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<center>
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<img src="recip-7.gif" width="520" height="325" border="2" vspace="5" hspace="9">
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</center>
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<p>At the top, we see our familiar test situation, except that this further test will require no rotation. We point the Yagi direcly at the second antenna. The lower portion of the figure shows that we have replaced the Yagi with a resonant dipole. For this test, we shall let the test antenna serve as a transmitter. We shall fit the second antenna with a 72-Ohm load resistor at its feedpoint segment. Now let's take current readings at the second antenna's feedpoint in both situations. When the Yagi transmits 1kW, the current is 1.57E-3 A at -13.98 degrees. When we replace the Yagi with the dipole, we obtain 6.2E-4 A at -10.24 degrees. Since we are working with such a limited number of significant digits we may ignore the slight difference in phase angle and use the two current values as I1 and I2 in our conversion equation. We obtain a value of about 8.1 dBd(r), that is gain over a dipole in a modeled range situation. Since we know that the dipole (with a significant diameter and made from real materials) has a free-space gain of 2.1 dBi, we may add this value to the calculated values to obtain a free-space gain of 10.2 dBi for the Yagi. The value reported by NEC for the transmit pattern in <b>Fig. 4</b> is 10.23 dBi.</p>
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||||
<p>We would have obtained very similar results had we omitted the load resistor in the receiving antenna (that is, a gain of 8.1 dBd(r)). Whichever way we set up the problem, we need to be consistent with the remote antenna's load resistor. With this result, we may declare--at least for the moment--that the case is closed.</p>
|
||||
<p><b>Conclusion</b></p>
|
||||
<p>We have examined a certain question, namely, whether or not NEC calcuations honor reciprocity between transmit and receive patterns. We used two basic techniques of modeling to arrive at an answer. The first technique required access to all NEC commands so that we could produce normalized receiving patterns. The second technique used only commands that are available within the most rudimentary entry-level software. In both cases, we obtained results that confirm reciprocity within a free-space environment, that is, an environment that does not introduce intervening variables.</p>
|
||||
<p>Although the demonstrations should be sufficient to establish a confidence in NEC's adherence to reciprocity in its calculations, we have not exhausted all the the tests that we might perform. There are more complex tests (or demonstrations) involving the use of ground and numerous other variables that we might throw into the model set-up. Those cases each hold an interest. However, for the moment and within the scope of these notes, we have shown some easily replicated modeling experiments that demonstrate reciprocity within NEC.</p>
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<p><i>Updated 06-14-2007. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.</i></p>
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<h1><img src="../images/antbott.gif" align="left" width="150" height="77"> Close-Spaced Wires: MININEC vs. NEC-4 <img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10"></h1>
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<h3>L. B. Cebik, W4RNL</h3>
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In another note, I established that there is a strong possibility of a systematic error in NEC-4 with respect to linear antenna elements composed of wires having significantly different diameters, especially when the center section is larger than the end sections of the element and when the larger center section is short compared to the total element length. This potential error is in addition to an earlier discovery of limitations of NEC-4 in accurately modeling closed geometry antenna elements, such as folded dipoles and quad loops, when the wires have different diameters.
|
||||
<p>Certain problems encountered with modeling Tee matches and open sleeve coupled elements led me to explore more systematically the possibility of a further systematic error. Apparent anomalous results occurred when antenna wires in NEC-4 were placed in close proximity, despite following recommended guidelines of aligning the segments of the wires to the degree possible.</p>
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<p>Therefore, I performed a simple modeling test of modeling a 1" diameter aluminum dipole for 14 MHz. I then created 3 different models of resonant 21 MHz dipoles, all aluminum, but having diameters of 0.5, 1.0, and 1.5 inches.</p>
|
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<p>In separate tests, I placed each of these 21 MHz dipoles in proximity to the 14 MHz dipole at distances of 2 through 12 inches in 2" increments. The 2" spacing was deemed the least permissible that would prevent the wire surfaces from touching. For each test, the 14 MHz fed dipole was reresonated and the gain figure recorded. As in past tests, resonance is defined as a feedpoint reactance of under 1 ohm. Since the test was designed to see the effect of the shorter wire on the longer, the original lengths of the 21 MHz antennas were preserved for each size throughout the test runs.</p>
|
||||
<p>The tests were performed on both MININEC 3.13 within ELNEC 3.0 and on NEC-4 within EZNEC Pro. Likewise, the lengths of the 21 MHz elements differed from a half-inch for the smallest diameter element to about 1" for the largest.</p>
|
||||
<p>The 14 MHz antenna used 34 segments in MININEC and 35 segments in NEC-4. The 21 MHz element was assigned 22 segments in MININEC and 23 in NEC-4. This segmentation aligned the segments quite reasonably. Since this segmentation already exceeds common practice in linear antenna design, convergence testing was not systematically undertaken, although the same performance curves appear with both fewer and more segments per half- wavelength.</p>
|
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<p>All gain figures were recorded as free space gain in dBi. With respect to closely spaced elements, there are two gain figures of note: the in-plane gain and the out-of-plane gain. The former is the maximum gain of the dipole and extra wire with the wires in line with each other. The latter is the gain in a direction broadside to a plane through the two wires. Out-of-plane gain will ordinarily be less than in-plane gain, although in- plane gain will show a front-to-back ratio approximately double the difference of the two gain figures.</p>
|
||||
<p>The tests were first run with MININEC. The following graph shows the in- plane gain for each diameter of extra wire as the distance between elements is decreased from 12 to 2 inches. Most notable in the graph is the flattening of the curves as the spacing reaches 2 inches, despite a reasonably linear progression to that point.</p>
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<img src="sp1.gif" width="642" height="520" border="2" vspace="5" hspace="9">
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<p>Some of the reason for the flattening appears in the follow graph, which records the out-of-plane gains for the wire pairs over the same range of spacings. As the distance reaches 2 inches, the gain begins a steep increase. To all appearances, the two wires begin at this close proximity to act as a single fat wire. Whatever the true accuracy of the MININEC results, they do at least accord with normal expectations for closely spaced wires.</p>
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<img src="sp2.gif" width="648" height="518" border="2" vspace="5" hspace="9">
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<p>The MININEC results acquire a further degree of confidence when one examines the range of variation. The total in-plane gain variation is less than 0.06 dB, while the out-of-plane gain variation is less than 0.02 dB.</p>
|
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<p>The gain figures encountered with NEC-4 show a quite different pattern. For example, the in-plane figures, shown in the following graph, show an overall increase through the same range of distances separating the two wires. The range of variation between 12 and 6 inch spacing is about 0.04 dB, but over the entire span of separations, the range increases to more than 1 dB.</p>
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<img src="sp3.gif" width="642" height="519" border="2" vspace="5" hspace="9">
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<p>Equally notable is the fact that NEC-4 shows the highest gain when the two wires have the same diameter. How exact this equality is cannot be determined by this test, since the secondary wire diameters are widely separated.</p>
|
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<p>A similar curve accompanies the figures for out-of-plane gain. There is a larger spread of gains in the 12 to 6 inch range (0.06 dB), but the overall gain increase with closing separation is greater than 1 dB.</p>
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<img src="sp4.gif" width="657" height="521" border="2" vspace="5" hspace="9">
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<p>At least for case at hand, which uses a secondary wire about 2/3rds the lengths of the fed wire, there appears to be a critical distance at which anomalous results begin to emerge. The following two graphs compare the in-plane and out-of-plane gains for MININEC and NEC-4 when the elements have the same diameter.</p>
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<img src="sp5.gif" width="644" height="520" border="2" vspace="5" hspace="9">
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<img src="sp6.gif" width="655" height="520" border="2" vspace="5" hspace="9">
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<p>Careful examination of the graphs shows that the curves overlap for spacing of 12 inches and 10 inches. However, between the 10" and 8" marks, the curves begin to diverge ever more radically.</p>
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<p>It is also interesting to contrast MININEC and NEC with respect to the required length of the 14 MHz element for resonance with the 21 MHz wire in close proximity. As the following graph shows, once we allow for the slight length variation of the 2 systems, the MININEC curve is much steeper than the NEC-4 curve at the closest spacings. However, the curve is in fact smoother than the NEC-4 curve, as the break in the NEC-4 curve at 6" is real and not a function of rounding.</p>
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<img src="sp7.gif" width="625" height="492" border="2" vspace="5" hspace="9">
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<p>Moreover, there are also interesting differences in the feedpoint resistance curves. As noted, the 14 MHz elements were resonated to less than 1 ohm reactance. In the graph below, the MININEC feed resistance curve shows a small dip at the 8" spacing and then a smooth progression upward. In contrast, the NEC-4 curve shows a rapid progression downward past the 6" point. These same phenomena occurred with scaled VHF antenna models.</p>
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<img src="sp8.gif" width="589" height="460" border="2" vspace="5" hspace="9">
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<p>These tests are only the beginning of a systematic exploration of the differential in gain and other figures from the MININEC and NEC-4 modeling systems. Here are a few further developments of these tests.</p>
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<p><b>Scaling</b>: Scaling all the dimensions of the situation by a factor of 10 upward--including frequency, lengths, and wire diameters--produces curves that tightly fit those produced so far. This applies to both the MININEC and NEC-4 curves. The resonant 140 MHz 0.1" diameter aluminum wire spaced from 1.2 to 0.2 inches offsets are so slight, relative to the resonant 14 MHz 1.0" diameter aluminum wire spaced from 12 to 2 inches, that they would not appear in any form of graphing.</p>
|
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<p><b>Wire Length Ratios</b>: The 20-meter antenna with a 15 meter wire forms a length ratio of 3:2. A series of NEC-4 runs was made to compare this ratio of wire lengths to wires with a 2:1 ratio and with a 4:3 ratio, focusing on wires of the same diameter (1" aluminum). The results appear in the following graph.</p>
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<img src="sp9.gif" width="639" height="517" border="2" vspace="5" hspace="9">
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<p>Interestingly, the departure of the gain from a typical MININEC curve is greatest when the fed wire is about 50% longer than the closely spaced unfed wire, at least when the wires have the same diameter. Once more, the widely separated selection of test ratios does not lend precision to this conclusion. Since wires having a 1:1 diameter ratio appear to have a greater departure from typical MININEC curves than other wire diameter ratios, it would appear that by chance, my initial tests have fallen into at least the ball park of greatest deviation.</p>
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<p><b>Close Spacing and Multi-Element Arrays</b>: The effects of a close-spaced wire on a dipole model are only indicators, but not predictors of the effect of a close-spaced wire on a parasitical beam model. Indeed, the disparity of gain and other performance figures between MININEC and NEC-4 might well be either quite profound or quite trivial.</p>
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<p>I quickly created a 3-element Yagi model to check the potential for divergent readouts. An extra wire was placed ahead of the driven element at the spacing indicated in the tables. The results were as follows:</p>
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<pre> MININEC NEC-4
|
||||
Space Gain F-B Z Gain F-B Z
|
||||
No wire 8.03 24.97 26.9+j2.1 8.08 27.94 26.6+j4.8
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2:1 Ratio
|
||||
4" 8.02 24.86 26.9+j1.1 8.68 27.81 23.4+j3.4
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7" 8.03 24.87 27.0+j1.3 8.26 27.84 25.7+j3.9
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10" 8.03 24.88 27.0+j1.4 8.14 27.85 26.4+j4.1
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13" 8.03 24.88 27.0+j1.5 8.10 27.86 26.6+j4.2
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16" 8.03 24.89 27.0+j1.5 8.09 27.88 26.7+j4.2
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3:2 Ratio
|
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4" 7.88 24.77 28.0+j0.0 9.35 27.68 20.3+j1.8
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7" 7.96 24.79 27.6+j0.4 8.61 27.76 24.1+j2.6
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10" 8.00 24.82 27.5+j0.6 8.33 27.81 25.6+j3.0
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13" 8.01 24.84 27.4+j0.7 8.21 27.86 26.4+j3.2
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16" 8.02 24.87 27.3+j0.7 8.15 27.91 26.7+j3.3
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4:3 Ratio
|
||||
4" 8.20 24.74 26.2-j1.0 6.81 27.93 37.7+j3.3
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7" 8.12 24.78 27.0-j0.5 7.34 27.91 33.1+j3.6
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10" 8.08 24.82 27.4-j0.3 7.67 27.93 30.6+j3.4
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13" 8.06 24.87 27.5-j0.2 7.85 27.98 29.2+j3.1
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16" 8.05 24.91 27.6-j0.1 7.94 28.04 28.5+j3.0</pre>
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<p>The tables hold some surprises. First, the NEC-4 gain values diverge more radically than the MININEC numbers, especially for the 2:1 ratio of driven element to extra wire. Second, for the 3:2 and 4:3 ratios, MININEC and NEC-4 gain numbers diverge in opposite directions. Nonetheless, the NEC-4 figures are still farther from the "no-wire" baseline than those of MININEC. Third, unlike the simple dipole examples, the gain of some models may decrease in the presence of the extra wire.</p>
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<p>Before you draw any conclusions, let me reveal that the above table is erroneous. It is based on a defective model that is nevertheless all too common in amateur modeling practice. All 4 elements, the 3 20-meter elements plus the added wire, whatever its length, were assigned 10 segments in MININEC and 11 segments in NEC-4. The segments do not align, which is especially important in NEC, but not insignificant in MININEC with some models. Moreover, neither model converges well with models having twice as many elements. These practices cast doubt on the reliability of the results.</p>
|
||||
<p>So I reset the models, using 34 segments per 20 meter element (35 in NEC), and a proportionate number for the shorter extra elements. Convergence with models of twice the segmentation was excellent, with a gain difference of about 0.01 dB. Running these models resulted in a change of extra- element spacing to begin at closest with 3" rather than 4." Despite the closer spacing, the following results developed.</p>
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||||
<pre> MININEC NEC-4
|
||||
Space Gain F-B Z Gain F-B Z
|
||||
No wire 8.01 26.66 28.4+j5.4 8.12 26.86 26.3+j6.6
|
||||
2:1 Ratio
|
||||
3" 8.01 26.64 28.9+j4.1 8.40 26.72 25.0+j5.2
|
||||
6" 8.01 26.65 28.7+j4.5 8.15 26.74 26.4+j5.8
|
||||
9" 8.01 26.66 28.7+j4.7 8.12 26.75 26.5+j6.0
|
||||
12" 8.01 26.67 28.6+j4.8 8.12 26.77 26.5+j6.0
|
||||
15" 8.01 24.68 28.6+j4.8 8.12 26.78 26.5+j5.2
|
||||
3:2 Ratio
|
||||
3" 8.00 26.52 29.3+j3.7 8.33 26.62 26.0+j4.1
|
||||
6" 8.00 26.57 29.2+j3.7 8.14 26.66 27.0+j4.9
|
||||
9" 8.00 26.61 29.1+j3.6 8.12 26.69 27.0+j5.2
|
||||
12" 8.00 26.65 29.1+j3.3 8.12 26.73 26.9+j5.3
|
||||
15" 8.00 26.70 29.1+j2.6 8.12 26.76 26.9+j5.3
|
||||
4:3 Ratio
|
||||
3" 8.01 26.73 30.0+j1.6 7.40 26.69 33.3+j3.9
|
||||
6" 8.01 26.80 29.8+j2.6 8.03 26.66 28.3+j4.4
|
||||
9" 8.01 26.87 29.7+j2.9 8.10 26.70 27.7+j4.5
|
||||
12" 8.01 26.95 29.6+j3.1 8.11 26.76 27.5+j4.6
|
||||
15" 8.01 27.02 29.6+j3.1 8.12 26.82 27.4+j4.7</pre>
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||||
<p>A comparison of the tables shows two very significant facts. First, when models are developed carefully, rather than casually, any tendencies for any program to deliver potentially erroneous results is lessened. All figures for each length of extra element are far more tightly grouped.</p>
|
||||
<p>Second, despite the tighter grouping, the same types of curves develop as with the casual model. To two decimal places, MININEC results are totally stable, although the third decimal place shows the mathematical progressions that appeared in the earlier model. Likewise, NEC-4 progressions show increasing gain with closer spacing for the two shorter lengths of extra elements and reduced gain with closer spacing for the longest extra element. In general, the instability with the figures occurs when spacing are closer than 6 to 9 inches at 14 MHz. Maximum deviations from the norm run from 0.2 dB to 0.5 dB for the example used. While less than with the casual model, the amounts of deviation from the normal can be significant, especially when compared to the extremely stable MININEC figures.</p>
|
||||
<p><b>Conclusion</b>: Each of these directions of research will require many more runs of wire combinations at many different frequencies before precise conclusions and systemmatic formulations of the MININEC/NEC-4 differentials can be drawn. I presume such work exists within appropriate research institutions and has simply not yet reached the community of modeling program users. At least, none has yet crossed my admittedly limited path.</p>
|
||||
<p>Nonetheless, the simple test performed here is sufficient to suggest strongly that users of NEC-4 model closely spaced wires with great caution. If NEC-4 proves to be the anomalous case, then it may not be possible to routinely model closely spaced antenna structures with any presumption of accuracy with respect to resulting gain figures.</p>
|
||||
<p>On the other hand, if MININEC proves to be more accurate in such cases, then perhaps it is time that an enterprising programmer undertook an effort to reprogram MININEC to a. release it from its 256-segment limitation and b. to enable the matrices to execute far more rapidly than in the current version.</p>
|
||||
<p>(It would be useful to be able to compare these results with the Rockway- Logan revised MININEC, but the copy I purchased is apparently flawed so that some key modules will not work after 1 or 2 runs and must be reinstalled, even then with no assurance of working results. Moreover, the interface lacks the degree of user convenience associated with such diversely styled programs as AO and ELNEC, thus lengthening the time required for setting up even simple antenna models. However, the new MININEC calculating engine within an AO, ELNEC, or NEC-Win interface would be interesting to test thoroughly.)</p>
|
||||
<p>As with all such tests, reasonableness of the appearance of results is not a sufficient validation of a modeling system. Nonetheless, it appears safe to note that closely spaced wires modeled in NEC-4 should always be approached with more caution than confidence.<br>
|
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<br></p>
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<p><i>Updated 9-24-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.</i><br>
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<title>The Tee-Match</title>
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<h1><img src="../images/yagicad.gif" align="left" width="125" height="62" border="2" vspace="5" hspace="10"><img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10">The Tee-Match:<br>
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NEC Illusions and MININEC Realities</h1>
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</center>
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<p><br></p>
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<center>
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<h3>L. B. Cebik, W4RNL</h3>
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Prior investigations of the Tee-Match left the impression that perhaps fat Tee bars may be more effective that thin Tee bars by yielding slightly, if not significantly, greater antenna gain in large Yagi antennas. The present modeling investigation, which shifted the modeling engine from NEC to MININEC, strongly suggests that there is no significant difference in performance in antennas using a Tee match with bars ranging from 0.5 to 1.5 times the driven element diameter.
|
||||
<h3>The Original T-Match Problem</h3>Many months ago, I attempted to apply NEC-4 to the modeling of a Tee-match system. The original system modeled was based on a 5-element 48'-boom Yagi design by W3LPL. The modeling was done at a height of 195' over medium earth. The Tee match elements are shown in the figure.
|
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|
||||
<img src="tee2.gif" width="400" height="168" border="2" vspace="5" hspace="9">
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|
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<p>Of all the variables investigated, the relative diameters of the Tee-match bar to the main driven element had the greatest effect on the reported antenna gain.</p>
|
||||
<pre>Antenna without Tee-match:
|
||||
Gain: 16.1 dBi @ 5 degrees
|
||||
Beamwidth: 52 degrees (does not change)
|
||||
F-B: 23.0 dB
|
||||
Feedpoint Z: 36.3 + 16.1 ohms
|
||||
|
||||
Antenna with 0.5" diameter 48" Tee match rod, spaced 6":
|
||||
Gain: 15.31 dBi
|
||||
F-B: 23.13
|
||||
Feedpoint Z: 262 + 87.9 ohms
|
||||
|
||||
Antenna with 0.5" diameter 48" Tee match rod, spaced 7.5":
|
||||
Gain: 15.5 dBi
|
||||
F-B: 22.8 dB
|
||||
Feedpoint Z: 215.7 + 87.55 ohms
|
||||
|
||||
Antenna with 2.0" diameter 48" Tee match rod, spaced 7.5":
|
||||
Gain: 16.2 dBi
|
||||
F-B: 23.0 dB
|
||||
Feedpoint Z: 196.2 + 29.9 ohms</pre>
|
||||
<p>The variability of results, including the increases in gain with increasing diameters of Tee-match rod, raised many questions about the adequacy of the model and limitations of even NEC-4 to correctly model the T-match situation. As subsequent investigation established, at 14 MHz, spacings of elements under about 9" (with variation for changes in element diameters) yield unreliable results in NEC-4. (Matters are worse in NEC-2.). Therefore, the notes were withdrawn from circulation.</p>
|
||||
<p>However, many questions remained. One was a nagging feeling that perhaps the ratio of the diameter of the Tee rod to the main driven element might have some effect on antenna gain, although perhaps not to the extent suggested by the NEC-4 models. The second question concerned how to model the Tee match adequately on MININEC.</p>
|
||||
<h3>Modeling in NEC and MININEC</h3>The original model of the W3LPL 5-element Yagi with a Tee-match is not suitable for MININEC. First, the antenna is too complexly structured, as the wire table shows:
|
||||
<pre>5-element Yagi with Tee match (2" diameter Tee rod): Freq. = 14.2 MHz.
|
||||
Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
|
||||
--------------- WIRES ---------------
|
||||
Wire Conn.--- End 1 (x,y,z :in) Conn.--- End 2 (x,y,z :in) Dia(in) Segs
|
||||
|
||||
1 0.000,-217.00,2340.00 W2E1 0.000,-150.00,2340.00 7.50E-01 12
|
||||
2 W1E2 0.000,-150.00,2340.00 W3E1 0.000,-117.00,2340.00 8.75E-01 9
|
||||
3 W2E2 0.000,-117.00,2340.00 W4E1 0.000,-84.000,2340.00 1.00E+00 9
|
||||
4 W3E2 0.000,-84.000,2340.00 W5E1 0.000,-33.750,2340.00 1.12E+00 9
|
||||
5 W4E2 0.000,-33.750,2340.00 W6E1 0.000, 33.750,2340.00 1.25E+00 12
|
||||
6 W5E2 0.000, 33.750,2340.00 W7E1 0.000, 84.000,2340.00 1.12E+00 9
|
||||
7 W6E2 0.000, 84.000,2340.00 W8E1 0.000,117.000,2340.00 1.00E+00 9
|
||||
8 W7E2 0.000,117.000,2340.00 W9E1 0.000,150.000,2340.00 8.75E-01 9
|
||||
9 W8E2 0.000,150.000,2340.00 0.000,217.000,2340.00 7.50E-01 12
|
||||
10 86.000,-214.00,2340.00 W11E1 86.000,-150.00,2340.00 7.50E-01 12
|
||||
11 W10E2 86.000,-150.00,2340.00 W12E1 86.000,-117.00,2340.00 8.75E-01 9
|
||||
12 W11E2 86.000,-117.00,2340.00 W13E1 86.000,-84.000,2340.00 1.00E+00 9
|
||||
13 W12E2 86.000,-84.000,2340.00 W14E1 86.000,-48.000,2340.00 1.12E+00 9
|
||||
14 W48E1 86.000,-48.000,2340.00 W15E1 86.000,-33.750,2340.00 1.12E+00 3
|
||||
15 W14E2 86.000,-33.750,2340.00 W16E1 86.000, 33.750,2340.00 1.25E+00 15
|
||||
16 W15E2 86.000, 33.750,2340.00 W17E1 86.000, 48.000,2340.00 1.12E+00 3
|
||||
17 W50E2 86.000, 48.000,2340.00 W18E1 86.000, 84.000,2340.00 1.12E+00 9
|
||||
18 W17E2 86.000, 84.000,2340.00 W19E1 86.000,117.000,2340.00 1.00E+00 9
|
||||
19 W18E2 86.000,117.000,2340.00 W20E1 86.000,150.000,2340.00 8.75E-01 9
|
||||
20 W19E2 86.000,150.000,2340.00 86.000,214.000,2340.00 7.50E-01 12
|
||||
21 171.000,-199.38,2340.00 W22E1 171.000,-135.88,2340.00 7.50E-01 12
|
||||
22 W21E2 171.000,-135.88,2340.00 W23E1 171.000,-102.88,2340.00 8.75E-01 9
|
||||
23 W22E2 171.000,-102.88,2340.00 W24E1 171.000,-69.875,2340.00 1.00E+00 9
|
||||
24 W23E2 171.000,-69.875,2340.00 W25E1 171.000,-22.000,2340.00 1.12E+00 9
|
||||
25 W24E2 171.000,-22.000,2340.00 W26E1 171.000, 22.000,2340.00 1.25E+00 9
|
||||
26 W25E2 171.000, 22.000,2340.00 W27E1 171.000, 69.875,2340.00 1.12E+00 9
|
||||
27 W26E2 171.000, 69.875,2340.00 W28E1 171.000,102.875,2340.00 1.00E+00 9
|
||||
28 W27E2 171.000,102.875,2340.00 W29E1 171.000,135.875,2340.00 8.75E-01 9
|
||||
29 W28E2 171.000,135.875,2340.00 171.000,199.375,2340.00 7.50E-01 12
|
||||
30 349.000,-196.25,2340.00 W31E1 349.000,-119.25,2340.00 7.50E-01 15
|
||||
31 W30E2 349.000,-119.25,2340.00 W32E1 349.000,-86.250,2340.00 8.75E-01 9
|
||||
32 W31E2 349.000,-86.250,2340.00 W33E1 349.000,-53.250,2340.00 1.00E+00 9
|
||||
33 W32E2 349.000,-53.250,2340.00 W34E1 349.000,-22.000,2340.00 1.12E+00 9
|
||||
34 W33E2 349.000,-22.000,2340.00 W35E1 349.000, 22.000,2340.00 1.25E+00 9
|
||||
35 W34E2 349.000, 22.000,2340.00 W36E1 349.000, 53.250,2340.00 1.12E+00 9
|
||||
36 W35E2 349.000, 53.250,2340.00 W37E1 349.000, 86.250,2340.00 1.00E+00 9
|
||||
37 W36E2 349.000, 86.250,2340.00 W38E1 349.000,119.250,2340.00 8.75E-01 9
|
||||
38 W37E2 349.000,119.250,2340.00 349.000,196.250,2340.00 7.50E-01 15
|
||||
39 570.000,-183.75,2340.00 W40E1 570.000,-131.75,2340.00 7.50E-01 12
|
||||
40 W39E2 570.000,-131.75,2340.00 W41E1 570.000,-98.750,2340.00 8.75E-01 9
|
||||
41 W40E2 570.000,-98.750,2340.00 W42E1 570.000,-65.750,2340.00 1.00E+00 9
|
||||
42 W41E2 570.000,-65.750,2340.00 W43E1 570.000,-22.000,2340.00 1.12E+00 9
|
||||
43 W42E2 570.000,-22.000,2340.00 W44E1 570.000, 22.000,2340.00 1.25E+00 9
|
||||
44 W43E2 570.000, 22.000,2340.00 W45E1 570.000, 65.750,2340.00 1.12E+00 9
|
||||
45 W44E2 570.000, 65.750,2340.00 W46E1 570.000, 98.750,2340.00 1.00E+00 9
|
||||
46 W45E2 570.000, 98.750,2340.00 W47E1 570.000,131.750,2340.00 8.75E-01 9
|
||||
47 W46E2 570.000,131.750,2340.00 570.000,183.750,2340.00 7.50E-01 12
|
||||
48 W13E2 86.000,-48.000,2340.00 W49E1 86.000,-48.000,2332.50 1.25E-01 2
|
||||
49 W48E2 86.000,-48.000,2332.50 W50E1 86.000, 48.000,2332.50 2.00E+00 21
|
||||
50 W49E2 86.000, 48.000,2332.50 W16E2 86.000, 48.000,2340.00 1.25E-01 2</pre>
|
||||
<center>
|
||||
<img src="tee1.gif" width="300" height="232" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>The antenna has 481 segments, organized to align corresponding segments on the elements while preserving the specified lengths of each diameter of material. All modeling was done using a 48" rod and varying only the length of the driven element end sections to restore the desired 200-ohm feedpoint impedance.</p>
|
||||
<p>MININEC is limited to 256 segment antennas. Moreover, it was anticipated that the length of the Tee-bar and the parallel section of antenna element would have to be varied, in order to achieve the desired 200-ohm feedpoint impedance. With the W3LPL model, re-segmentation would become burdensome.</p>
|
||||
<p>I chose a different model, based on a design (520-40 in YA) by K6STI, using constant diameter (1") elements. The 5-element, 40'-boom model employed 30 segments per element. This permitted adjustments to both the main element and the Tee bar with only local re-segmentation for some models to keep segments about the same length throughout the sequence of models.</p>
|
||||
<p>In addition, MININEC 3.13 has its own limitations. I have established that within normal spacings of a couple of inches and up at 14 MHz, MININEC exhibits none of the problem characteristics of NEC with respect to close- spaced wires. However, MININEC has difficulties with corners: it cuts them off, thus providing results of limited reliability. These difficulties can be overcome by a. using enough segments in the model to make the corner cut-off insignificant, or b. by tapering element lengths so that corner segments are small and of equal length.</p>
|
||||
<p>I chose the former procedure, since any change of Tee bar length or driven element length would require re-tapering the entire model. A final segmentation of 30 segments per complete element, however, made the segments adjoining the Tee-bar-to-Driven-Element connectors about twice as long as the connectors themselves. This limited the intrinsic accuracy of the reported lengths, relative to what might be found in adjusting a real Tee-match. However, the internal consistencies in the modeling sequence ensured that the results would be equally self-consistent.</p>
|
||||
<p>A further modeling issue surrounds the different implementations of MININEC. AO, by K6STI, provides a correction factor by which AO's MININEC model results coincide with those from NEC-2 without change in modeling dimensions. ELNEC, by W7EL, does not contain this factor, but it does provide a parallel-wire corrector that provides better results with close- spaced wires. Since close-spaced elements form the subject of the study, ELNEC was the program of choice. However, this forced slight changes in the model dimensions relative to a corresponding model used for NEC and AO. Nonetheless, these changes do not affect the consistency of the results reported by MININEC.</p>
|
||||
<p>The final model, shown for only one of the Tee-match situations, is shown in the following wire table. For this model, dimensions are in feet, except for wire diameter, which is in inches.</p>
|
||||
<center>
|
||||
<img src="tee3.gif" width="305" height="279" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<pre>5-element Yagi with Tee match (1" diameter Tee rod): Freq. = 14.175 MHz.
|
||||
Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
|
||||
--------------- WIRES ---------------
|
||||
Wire Conn.--- End 1 (x,y,z : ft) Conn.--- End 2 (x,y,z : ft) Dia(in) Segs
|
||||
|
||||
1 -17.600, 0.000, 0.000 17.600, 0.000, 0.000 1.00E+00 30
|
||||
2 -16.900, 6.000, 0.000 W3E1 -3.500, 6.000, 0.000 1.00E+00 12
|
||||
3 W8E1 -3.500, 6.000, 0.000 W4E1 3.500, 6.000, 0.000 1.00E+00 6
|
||||
4 W10E2 3.500, 6.000, 0.000 16.900, 6.000, 0.000 1.00E+00 12
|
||||
5 -15.900, 12.000, 0.000 15.900, 12.000, 0.000 1.00E+00 30
|
||||
6 -16.100, 23.580, 0.000 16.100, 23.580, 0.000 1.00E+00 30
|
||||
7 -15.250, 39.500, 0.000 15.250, 39.500, 0.000 1.00E+00 30
|
||||
8 W2E2 -3.500, 6.000, 0.000 W9E1 -3.500, 6.000, 0.500 1.00E+00 1
|
||||
9 W8E2 -3.500, 6.000, 0.500 W10E1 3.500, 6.000, 0.500 1.00E+00 7
|
||||
10 W9E2 3.500, 6.000, 0.500 W3E2 3.500, 6.000, 0.000 1.00E+00 1</pre>
|
||||
<p>This 159-segment model proved well-suited to MININEC's capabilities. A representative free space azimuth pattern is shown for reference.</p>
|
||||
<center>
|
||||
<img src="tee4.gif" width="635" height="331" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>I have given these modeling details for the inspection of other modelers. Like antennas themselves, antenna models must be open to critical inspection if the reported results are to be trusted.</p>
|
||||
<h3>The Results: Fat and Thin Tees are of Equal Value</h3>The only changes among models in the following sequence are alterations of the driven element length, the Tee bar length and diameter, and the segmentation of the driven element to maintain a constant segment length to the degree possible. Therefore, a tabular presentation of the data seems most efficient. All models are in free space. Length dimensions are in feet. Except for the reference model, all models are distinguished by the diameter of the Tee bar.
|
||||
<pre>Model D.E. Tee Gain F-B Feed Z
|
||||
Length Length dBi dB R+/-jX
|
||||
Reference 33.20' ---- 9.827 22.15 25.5 - j0.96
|
||||
T-0.5 34.10' 8.40' 9.855 21.71 209.7 + j0.85
|
||||
T-0.75 33.90' 7.50' 9.789 21.81 210.7 + j1.36
|
||||
T-1.0 33.80' 7.00' 9.817 21.86 209.7 + j2.49
|
||||
T-1.25 33.80' 6.80' 9.832 21.86 198.6 - j1.27
|
||||
T-1.50 33.70' 6.50' 9.853 21.92 205.2 + j1.41</pre>
|
||||
<p>In compiling these results, the reference antenna had its driven element divided into three wires, corresponding to those used in models having the Tee bar. The results are insignificantly different from a model that used a continuous driven element.</p>
|
||||
<p>The gain reports are given to 3 decimal places to demonstrate how truly insignificant the differences are among the models. Re-segmenting Tee bar and the driven element at borderline cases (around 7') creates a higher degree of change in reported gain than changing the Tee bar diameter--at the extremes no more than 0.066 dB in the above table. Compare this to the full dB of difference in the NEC models. Likewise, front-to-back ratio changes by a maximum of 0.44 dB among the models.</p>
|
||||
<p>The Tee bar length undergoes a different set of changes than with the W3LPL model (used for the original NEC studies), which had a pre-match feedpoint impedance in the vicinity of 40 ohms. Driven element lengths correctly show the requisite lengthening to provide the necessary inductive reactance for the Tee-match system.</p>
|
||||
<p>Increasing the segmentation does alter all of the figures shown. The progression from 10 to 20 to 30 segments per element shows no abatement in the changes, which suggests that final convergence of the models has not been achieved and is unlikely to be achieved within MININEC's limits. However, operationally, the gain varies by less than 0.05 dB and the front- to-back ratio varies by less than 0.6 dB across this range of segmentation for any particular model. Only the feedpoint impedance changes by amounts calling for adjustment of the model. Therefore, the models shown are considered to be reliable indicators of gain and front-to-back ratio for the range of Tee bar diameters covered.</p>
|
||||
<p>There is some small indication that further increases in the diameter of the Tee bar may indeed increase gain, but only in very small amounts. If the Tee bar is raised to twice the diameter of the main driven element, the gain reports as 9.882, which forms a progression of sorts on the high side of the chart. However, for an amount that is truly undetectable in operation, one acquires an ungainly mechanical construction problem.</p>
|
||||
<p>At the other end of the scale, reducing the Tee-bar to 1/4 the diameter of the main element appears to approach an area where the lengths of both the bar and of the main element become critical, which translates into highly finicky adjustment. It is possible that the modeling may be trickier than the actual antenna. However, the following general proposition applies: the greater the diameter of the Tee bar, the broader and easier the adjustment.</p>
|
||||
<h3>Conclusion</h3>NEC-4 models of the Tee-match system, when applied to a high gain antenna like the 5-element Yagi, are quite erroneous in their gain reports. Despite its limitations, MININEC gives every appearance of producing more reliable modeling results for this close-spaced structure.
|
||||
<p>For the range of ratios of Tee bar to driven element (0.5 to 1.5), MININEC gives no indication that any particular ratio is better or worse than any other. Variations in the reported figures are insignificantly different in all respects, especially given the limitations of the models and the program.</p>
|
||||
<p>The net result is this: within reason (+/- 50% of the main element diameter), any size Tee bar may be used with any size element with no change in antenna performance.<br>
|
||||
<br></p>
|
||||
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|
||||
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|
||||
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|
||||
<p><i>Updated 1-7-98. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.</i><br>
|
||||
<br></p>
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|
||||
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<title>Modeling Trap Antennas</title>
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<h1><img src="../images/antbott.gif" align="left" width="150" height="77">Modeling Trap Antennas<img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10"></h1>
|
||||
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|
||||
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|
||||
<h3>L. B. Cebik, W4RNL</h3>
|
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<br>
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<br>
|
||||
A number of excellent multi-element antennas exist, and many use traps. Those without traps can be modeled in a direct manner, even if the exercise is tedious with stepped-diameter elements. However, modeling element with traps still eludes some folks.
|
||||
<center>
|
||||
<h4>Modeling Traps in NEC</h4>
|
||||
</center>The procedure for modeling an element with traps is actually quite straightforward. Consider a dipole cut for 20 meters with a 15 meter trap in each leg. Figure 1 illustrates the situation. The element diameter has been made constant to simplify that aspect of the modeling so that we may concentrate on the trap.
|
||||
<center>
|
||||
<img src="trap1.gif" width="637" height="272" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>A trap consists of an inductance and a capacitance, normally resonated just at or below the lowest frequency of the higher antenna frequency range. The limiting factor in a trap is the resistive loss of the coil, since the losses in capacitors at HF are very small. A trap effectively consists of a series combination of resistance and inductive reactance in parallel with capacitive reactance. See Figure 2a.</p>
|
||||
<center>
|
||||
<img src="trap2.gif" width="466" height="507" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>Unfortunately, we cannot directly model the situation in Figure 2 as a lumped constant load. NEC loads permit series R-L-C combinations, parallel R-L-C combinations, or series R-X combinations. It is necessary therefore, to convert the complex series-parallel circuit into an equivalent parallel R-L-C circuit, as illustrated in Figure 2b. However, since this procedure requires the transformation of component values into reactances, the conversion is frequency specific. Therefore, modeling a trap requires separate calculations and models for each frequency band of interest.</p>
|
||||
<p>To do an actual calculation, we require some one of the following combinations of data:</p>
|
||||
<p>a. The inductance and Q of the coil, the capacitance, and the frequency of interest;</p>
|
||||
<p>b. The inductive and capacitive reactances, the resistance, and the frequency of interest; or</p>
|
||||
<p>c. The inductive and capacitive reactances, the coil Q, and the frequency of interest.</p>
|
||||
<p>Using measurements made by Roger Cox, WB0DGF, of commercial traps, we can consider a 15-meter trap that consists of a 3.3 uH coil with a Q in the range of 235. For resonance at 21 MHz, the coil requires a capacitance of about 17.4 pF.</p>
|
||||
<center>
|
||||
<img src="trape1.gif" width="281" height="77" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>With the given Q, the series resistance of the coil requires that we find the reactance of the coil at 21 MHz. By the standard formula, the reactance is about 436 ohms.</p>
|
||||
<center>
|
||||
<img src="trape2.gif" width="250" height="56" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>Dividing the reactance by Q, we get a resistance of about 1.9 ohms.</p>
|
||||
<p>To convert the series R-L into a parallel R-L combination, we use the standard conversion equations:</p>
|
||||
<center>
|
||||
<img src="trape3.gif" width="424" height="83" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>The equations give these values: XL = 436 ohms; R = 100,000 ohms. The corresponding value of L comes from the reverse of equation (2):</p>
|
||||
<center>
|
||||
<img src="trape4.gif" width="219" height="79" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>The parallel inductance value will be 3.3 uH. We now have our parallel R- L-C trap load for operation at 15 meters.</p>
|
||||
<p>At 20 meters, we may also calculate the requisite values of parallel R and L. The 3.3 uH inductance has a reactance of about 292 ohms. Dividing this reactance by the Q, which we assume to remain fairly constant, the series resistance is 1.25 ohms. The parallel equivalents are these: XL = 292 ohms; R = 67,300 ohms. The inductance of this parallel combination is 3.3 uH. The capacitance remains at 17.4 pF.</p>
|
||||
<p>To model the trap dipole at 21.2 MHz and 14.1 MHz (as sample frequencies), we can create a model using a 1" diameter aluminum element with the following wire limits of the X coordinate (where both the Y and Z coordinates remain "0" for a free space model):</p>
|
||||
<pre> Wire End 1 End 2 Segments
|
||||
1 -13.67 -11.3 8
|
||||
2 -11.3 -10.8 1
|
||||
3 -10.8 10.8 41
|
||||
4 10.8 11.3 1
|
||||
5 11.3 13.67 8</pre>
|
||||
<p>We place a parallel R-L-C load in elements 2 and 4. These short wires, no longer than a single segment of adjacent wire, permit independent adjustment of the antenna length for the two bands in question. For 21.1 MHz, the R-L-C values are expressed in the form most used by implementations of NEC: 1E05, 3.3E-06, 17.4E-12. For 14.1 MHz, the R-L-C values are 6.73E4, 3.3E- 06, 17.4E-12. The overall antenna element length absorbs the length of the trap. Slight differences in diameter for the short trap lengths at the current levels in the region of the traps are not significant variables, relative to real installations: ground clutter will create larger variations than trap diameters. A possible exception are dual-trap assemblies, which may be directly modeled as a larger wire diameter between traps. Use of shorted stubs as inductors also make no difference since, in principle, these radiate even less than solenoid inductors.</p>
|
||||
<p>For comparison purposes, model dipoles were constructed of the same 1" diameter aluminum tubing, but without traps. The 14 MHz dipole was 33.3' long at resonance, while the 21.2 MHz dipole was resonant when 22' long. Both dipoles showed a free space gain of 2.13 dBi with a feedpoint impedance of 72 ohms.</p>
|
||||
<p>The 21.2 MHz trap-loaded dipole showed a free space gain of 2.06 dBi, a mere 0.07 dB less than the trapless dipole. The feedpoint impedance was 73.9 ohms. The trap showed an impedance of 5175 - j22155 ohms, effectively terminating the antenna. Current levels beyond the traps were not significant, never rising above 2.5% of the source current.</p>
|
||||
<p>In contrast, the 14.1 MHz trap-loaded dipole (trap resonant at 21.0 MHz) showed a free space gain of 1.87 dBi, 0.26 dB less than its trapless counterpart, with a feedpoint impedance of 66.2 ohms. The reduction in gain is partly due to the shortening of the overall dipole length.</p>
|
||||
<p>However, the parallel R-L-C equivalent of the trap also plays a role in the gain reduction. We may derive a value for the trap's Q by reversing our calculations and deriving a set of series values for R and XL. The net parallel reactance of the trap at 14.1 MHz is given by the equation:</p>
|
||||
<center>
|
||||
<img src="trape5.gif" width="254" height="91" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>Using the resultant value of parallel reactance, 532 ohms, and the 63.7 kohms parallel resistance, we may calculate equivalent series values of resistance and reactance from standard equations:</p>
|
||||
<center>
|
||||
<img src="trape6.gif" width="416" height="92" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>The calculated series values are these: R = 4.2 ohms; XL = 532 ohms. (These values are automatically calculated by NEC and appear as part of its output data.) Dividing XL by R, we derive a Q of approximately 126 at 14.1 MHz. Note that this value varies from the expectation of those who wish to discount the capacitor and reduce the trap to a simple series combination of resistance and inductive reactance. NEC data suggests that the losses in the trap at 14.1 MHz are approximately double the losses at 21.2 MHz.</p>
|
||||
<p>An equally shortened 14.1 MHz dipole with a center loading coil requires an inductive reactance of 174 ohms to be resonant. A lossless center coil yields a dipole free space gain of 2.00 dBi. Only by adding a series resistance of 1.2 ohms can the free space gain of the dipole with 15-meter traps (1.87 dBi) be replicated. The Q of the equivalent center loading coil thus becomes about 145.</p>
|
||||
<p>The lower the frequency below the resonant frequency of the trap, the higher the Q of a given trap. At some very low frequency, lower than 1/10th the resonant trap frequency, the trap Q very closely approaches the initial Q of the coil (assuming that the initial Q is valid at that distant a frequency, which is dubious). Q of the trap assembly is lowest at resonant frequency. Hence, a 10-meter trap may show a higher Q at 20 meters than at 15 meters.</p>
|
||||
<center>
|
||||
<h4>The Effects of Traps on Beams</h4>
|
||||
</center>
|
||||
<p>Experience has shown that the losses in gain of center loaded elements are additive, at least in 2-element Yagis. If this experience holds true of the 14.1 MHz elements with 15-meter traps, then one might expect about 0.5 dB loss of forward gain relative to a full size Yagi of the same design but unloaded.</p>
|
||||
<p>To test this hypothesis, I scaled a 10-meter beam with a 50-ohm feedpoint impedance for 14.1 MHz. The new full-size beam spaced the elements by 12.12', again using 1" aluminum tubing for modeling simplicity, as shown in Figure 3. With a driven element 32.2' long and a reflector 34.94' long, the beam achieved its maximum front-to-back ratio (10.68 dB), a figure almost exactly that of its 10-meter counterpart. The resonant feedpoint impedance was 50.7 ohms. The forward gain under these condition was 6.13 dBi.</p>
|
||||
<center>
|
||||
<img src="trap3.gif" width="515" height="459" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>If a beam using two trapped elements could be constructed with a comparable maximum front-to-back ratio and a comparable feedpoint impedance, then the gain difference between it and the full size beam would be a good measure of gain reduction due to the shortening and other losses imposed the traps. In fact, such a beam was modeled, using the same element spacing. The driven element was 27.06' long, and the reflector was 27.7' long. The 15-meter traps were left in their original positions. It is possible that positioning the traps as they might be in a 2-band trap beam could alter the 20-meters values slightly, but the alteration was judged unlikely to be significant.</p>
|
||||
<p>The maximum front-to-back ratio of the 14.1 MHz beam with 15-meter traps was 10.68 dB, while the feedpoint impedance was 50.5 ohms. Under these control parameters, the forward gain was 5.64 dBi. (Note: for all the 2- element beams modeled here, higher forward gains are certainly possible, but at reduced front-to-back ratios.) The gain difference between the full size Yagi and the version with 15-meter traps is 0.49 dB.</p>
|
||||
<center>
|
||||
<img src="trap4.gif" width="666" height="634" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>Models of tri-band beams with 3 or more elements and/or more than 2 traps per element will follow the same procedure used here for these simplified models. Data for each trap will be needed for calculations of appropriate parallel R-L-C values. Also need will be a precise element diameter schedule, along with the exact location of the traps. Although time-consuming, such modeling projects should be quite straightforward.</p>
|
||||
<center>
|
||||
<h4>Conclusion</h4>
|
||||
</center>
|
||||
<p>If the technique of modeling traps is sound, then their presence does occasion some loss in forward gain relative to trapless antennas of comparable design, at least for frequencies lower than the resonant trap frequency. How significant this loss may be is a judgment requiring the examination of factors in addition to those included in the modeling exercise. Models also suggest that at frequencies for which the traps represent resonant terminations, gain will be very similar to that of trapless versions of the antenna.</p>
|
||||
<p>Whatever the gain situation, the exercise does demonstrate that traps can be modeled effectively as parallel R-L-C loads for each frequency of interest.<br>
|
||||
<br></p>
|
||||
<center>
|
||||
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
|
||||
</center><br>
|
||||
<br>
|
||||
<p>In order to ease the calculator work, I have thrown together the following GW BASIC program to calculate the properties of traps at various frequencies, based on an initial input of measured or estimated trap resonant frequency and either a. coil inductance and Q or b. coil reactance and resistance, whichever pair is known or more easily estimated. The user may refine the program as desired.</p>
|
||||
<pre>10 'trap.bas: L. B. Cebik, W4RNL April 1, 1997
|
||||
20 CLS:PRINT "Estimating Trap Properties"
|
||||
30 PRINT "L. B. Cebik, W4RNL":PRINT
|
||||
40 PRINT "To estimate the properties of a trap at various frequencies, you
|
||||
will need to know or be able to estimate the following information:"
|
||||
50 PRINT " a. The resonant frequency of the trap (normally, just below or
|
||||
at the lowest frequency of the frequency band for which it is a
|
||||
trap); and either"
|
||||
60 PRINT " b. The inductance and Q of the trap coil, or"
|
||||
70 PRINT " c. The inductive reactance and resistance of the coil.":PRINT
|
||||
100 PRINT:INPUT "Resonant frequency of trap in MHz ";FR
|
||||
110 PRINT "Coil Data: Select the letter of the data pair you know or can
|
||||
estimate.":PRINT "A. Inductance and Q; B. Inductive Reactance and
|
||||
Resistance"
|
||||
120 A$=INKEY$:IF A$="A" OR A$="a" THEN 130 ELSE IF A$="B" OR A$="b" THEN
|
||||
160 ELSE 120
|
||||
130 PRINT:INPUT "Inductance in microhenries ";L
|
||||
140 INPUT "Inductor Q ";Q
|
||||
150 XL=(6.28*FR)*L:R=XL/Q:GOTO 190
|
||||
160 PRINT:INPUT "Inductive reactance in ohms ";XL
|
||||
170 INPUT "Coil resistance in ohms ";R
|
||||
180 L=XL/(6.28*FR):Q=XL/R:GOTO 190
|
||||
190 C=25330/(L*(FR^2)):CB=C/1E+12
|
||||
200 CLS:PRINT "Estimating Trap Properties"
|
||||
210 PRINT "L. B. Cebik, W4RNL":PRINT
|
||||
220 PRINT "Basic Trap Properties at Trap Resonance"
|
||||
230 PRINT "Resonant Frequency ";FR;" MHz"
|
||||
240 PRINT "Coil Q ";Q
|
||||
250 PRINT "Coil inductance ";L;" microH"
|
||||
260 PRINT "Coil reactance ";XL;" ohms"
|
||||
270 PRINT "Capacitor ";C;" pF":PRINT
|
||||
300 PRINT "Output Data: Select the letter of the data type your would
|
||||
like.":PRINT "A. 3 selected frequencies; B. Several frequencies in one
|
||||
band"
|
||||
310 A$=INKEY$:IF A$="A" OR A$="a" THEN 320 ELSE IF A$="B" OR A$="b" THEN
|
||||
500 ELSE 310
|
||||
320 INPUT "Frequency #1 in MHz ";F1
|
||||
330 INPUT "Frequency #2 in MHz ";F2
|
||||
340 INPUT "Frequency #3 in MHz ";F3
|
||||
400
|
||||
XL1=6.28*(F1*L):R1=XL1/Q:N1=R1^2+XL1^2:R1P=N1/R1:XL1P=N1/XL1:FC1=F1*1000000
|
||||
!:XC1=1/(6.28*(FC1*CB)):D1=XL1-XC1:IF D1=0 THEN D1=.000001
|
||||
410
|
||||
XN1=-(XL1*XC1)/D1:DP1=R1P^2+XN1^2:RS1=(R1P*(XN1^2))/DP1:XLS1=((R1P^2)*XN1)/
|
||||
DP1:Q1=ABS(XLS1/RS1)
|
||||
420
|
||||
XL2=6.28*(F2*L):R2=XL2/Q:N2=R2^2+XL2^2:R2P=N2/R2:XL2P=N2/XL2:FC2=F2*1000000
|
||||
!:XC2=1/(6.28*(FC2*CB)):D2=XL2-XC2:IF D2=0 THEN D2=.000001
|
||||
430
|
||||
XN2=-(XL2*XC2)/D2:DP2=R2P^2+XN2^2:RS2=(R2P*(XN2^2))/DP2:XLS2=((R2P^2)*XN2)/
|
||||
DP2:Q2=ABS(XLS2/RS2)
|
||||
440
|
||||
XL3=6.28*(F3*L):R3=XL3/Q:N3=R3^2+XL3^2:R3P=N3/R3:XL3P=N3/XL3:FC3=F3*1000000
|
||||
!:XC3=1/(6.28*(FC3*CB)):D3=XL3-XC3:IF D3=0 THEN D3=.000001
|
||||
450
|
||||
XN3=-(XL3*XC3)/D3:DP3=R3P^2+XN3^2:RS3=(R3P*(XN3^2))/DP3:XLS3=((R3P^2)*XN3)/
|
||||
DP3:Q3=ABS(XLS3/RS3)
|
||||
460 PRINT:PRINT"Frequency","Reactance","Resistance","Q","Para. Res."
|
||||
470 PRINT F1,XLS1,RS1,Q1,R1P
|
||||
480 PRINT F2,XLS2,RS2,Q2,R2P
|
||||
490 PRINT F3,XLS3,RS3,Q3,R3P
|
||||
495 GOTO 640
|
||||
500 CLS:PRINT "Estimating Trap Properties"
|
||||
510 PRINT "L. B. Cebik, W4RNL":PRINT
|
||||
520 PRINT "Basic Trap Properties at Trap Resonance"
|
||||
530 PRINT "Resonant Frequency ";FR;" MHz"
|
||||
540 PRINT "Coil Q ";Q
|
||||
550 PRINT "Coil inductance ";L;" microH"
|
||||
560 PRINT "Coil reactance ";XL;" ohms"
|
||||
570 PRINT "Capacitor ";C;" pF":PRINT
|
||||
580 INPUT "Lowest frequency for band scan in MHz ";FL
|
||||
585 PRINT:PRINT"Frequency","Reactance","Resistance","Q","Para. Res."
|
||||
590 FOR J=FL TO (FL+.5) STEP .1
|
||||
600
|
||||
F1=J:XL1=6.28*(F1*L):R1=XL1/Q:N1=R1^2+XL1^2:R1P=N1/R1:XL1P=N1/XL1:FC1=F1*10
|
||||
00000!:XC1=1/(6.28*(FC1*CB)):D1=XL1-XC1:IF D1=0 THEN D1=.000001
|
||||
610
|
||||
XN1=-(XL1*XC1)/D1:DP1=R1P^2+XN1^2:RS1=(R1P*(XN1^2))/DP1:XLS1=((R1P^2)*XN1)/
|
||||
DP1:Q1=ABS(XLS1/RS1)
|
||||
620 PRINT F1, XLS1, RS1, Q1,R1P
|
||||
630 NEXT
|
||||
640 PRINT:PRINT "Press (a) for a new trap; (f) for a new frequency run; or
|
||||
(q) to quit"
|
||||
650 A$=INKEY$:IF A$="A" OR A$="a" THEN 10 ELSE IF A$="F" OR A$="f" THEN 200
|
||||
ELSE IF A$="Q" OR A$="q" THEN 19000 ELSE 650
|
||||
19000 PRINT:PRINT "To return to Main Menu, press (m)."
|
||||
19001 REM c:\basic\autoend.bas
|
||||
19005 M$=INKEY$:IF M$="m" OR M$="M" THEN RUN "C:\basic\menu.bas" ELSE 19005
|
||||
</pre><br>
|
||||
<br>
|
||||
<center>
|
||||
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
|
||||
</center><br>
|
||||
<br>
|
||||
<p><i>Updated 4-2-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.</i><br>
|
||||
<br></p>
|
||||
<center>
|
||||
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
|
||||
</center><br>
|
||||
<br>
|
||||
<a href="../radio.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Go to Amateur Radio Page</a><br>
|
||||
<p class="topics-footer">Topics: <a href='../topics.html#modeling'>Modeling</a>, <a href='../topics.html#traps'>Traps</a></p><br>
|
||||
</body>
|
||||
</html>
|
||||
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