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<meta name="keywords" content="Phased Array, HF Upper, HB9CV / ZL Special">
<title>HB9CV Phased Array</title>
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<h1><img src="../images/yagicad.gif" align="left" width="125" height="62" border="2" vspace="1" hspace="25"><img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="1" hspace="10"><br>
<br>
The HB9CV Phased Array and Gain Comparisons</h1>
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<h3>L. B. Cebik, W4RNL</h3>
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The HB9CV version of the 2-element phased array appeared in 1961. In Europe, some writers refer to almost any 2-element horizontal phased array as an HB9CV, while the English-speaking world tends to refer to the ZL- Special to mark the genre of antenna. The HB9CV version of the antenna and many variants are widely used in Europe, with Christmas tree stacks for 20- 15-10 meters. Users swear by them, claiming near to, and sometimes better than, 3-element Yagi performance.
<p>These facts set up a small cluster of interesting questions. What is the HB9CV phased array, and how does it differ from the "ordinary" ZL-Special? The antenna has been so successfully built by so many European hams that it deserves more attention by US hams.</p>
<p>But before we look at the HB9CV, let's first look at what a claim for 3- element performance by a 2-element antenna might mean. Then we can make some intelligent evaluations of the performance claims.</p>
<center>
<h3>3-Element Yagis</h3>
</center>We can roughly divide well-designed monoband 3-element Yagis into two classes: high-performance, narrow band models and moderate performance, wide-band models.
<p>A high-performance, narrow band 3-element Yagi aims for the highest levels of gain and front-to-back ratio (in some form of a design balance) at the expense of a wide operating bandwidth--normally defined in terms of a 2:1 SWR ratio. The narrower bandwidth does not necessarily mean that the antenna will not operate with a 2:1 SWR ratio across any of the upper HF bands (or the first MHz of 10 meters). The following model antenna shows a gain of 8.1 dBi free space gain and a front-to-back ratio of over 27 dB at 28.5 MHz with better than 900 kHz of operating bandwidth. This performance is typical of what is possible with moderate boom-length 3-element Yagis.</p>
<pre> 3-Element Yagi: High Gain
Element Length in Feet Spacing from Driven Element in Feet
Reflector 17.19 5.2
Driven Element 16.41 ---
Director 15.44 6.0</pre>
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<img src="hb1.gif" width="435" height="328" border="2" vspace="5" hspace="9">
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<img src="hb2.gif" width="438" height="327" border="2" vspace="5" hspace="9">
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<img src="hb3.gif" width="431" height="323" border="2" vspace="5" hspace="9">
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<p>For wide bands, say from 10 meters on up, some 3-element monoband Yagi designers sacrifice some gain and front-to-back ratio for operating bandwidth. The following model shows an operating bandwidth that exceeds all of the 10-meter band (with a direct 50-ohm feed impedance). The design frequency of 28.5 MHz shows a gain of 7.0 dBi free space with a front-to- back ratio of about 21 dB. The gain is stable across the band, varying by about 0.25 dB, while the equally stable front-to-back ratio varies by only a little over 2 dB. A scaled version of the antenna covers all of 6 meters with ease.</p>
<pre> 3-Element Yagi: Wide Band
Element Length in Feet Spacing from Driven Element in Feet
Reflector 17.83 6.2
Driven Element 16.50 ---
Director 14.67 5.0</pre>
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<img src="hb4.gif" width="436" height="332" border="2" vspace="5" hspace="9">
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<img src="hb5.gif" width="440" height="330" border="2" vspace="5" hspace="9">
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<img src="hb6.gif" width="439" height="335" border="2" vspace="5" hspace="9">
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<p>We can get more than 8.1 dBi free space gain from a narrow-band 3-element Yagi either by using a longer boom or by resizing and spacing elements--or both. In the process, we generally sacrifice front-to-back ratio. However, if we need a standard for 3-element monoband Yagis, the 8.1 dBi free space gain figure will do nicely, especially if we keep in mind the other properties of the antenna that make it desirable. The wide-band Yagi becomes, by comparison, somewhat of a special purpose antenna.</p>
<center>
<h3>2-Element Yagis</h3>
</center>Well-designed 2-element Yagis that seek the best blend of gain and front- to-back ratio tend to be spaced about 1/8 wavelength as a compromise between those figures and an adequate operating band width. Under these conditions, we can expect to show at the design target frequency (28.5 MHz) about 6.25 dBi free space gain and between 11 and 12 dB front-to-back ratio. The 30-35-ohm feedpoint impedance is amenable to beta, gamma, or Tee matches.
<pre> 2-Element Yagi: Typical Design
Element Length in Feet Spacing from Driven Element in Feet
Reflector 17.50 4.3
Driven Element 16.00 ---</pre>
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<img src="hb7.gif" width="435" height="330" border="2" vspace="5" hspace="9">
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<img src="hb8.gif" width="435" height="330" border="2" vspace="5" hspace="9">
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<img src="hb9.gif" width="431" height="329" border="2" vspace="5" hspace="9">
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<p>Unlike the stable 3-element Yagis, 2-element models show much greater variations of gain across the band. Gain varies by over 0.7 dB across the first MHz of 10-meters with this model, which is typical of the genre. The gain for this particular antenna peaks outside the 10-meter band at 27.3 MHz, with a figure of 7.04 dBi free space gain (with a front-to-back ratio of only 6.0 dB and a feedpoint impedance of about 16 ohms).</p>
<p>The 2-element Yagi is thus capable of better than 7 dBi free space gain--if we are willing to sacrifice other desirable antenna properties. More efficient at producing raw gain are 2-element Yagis using a director closely spaced to the driven element. With a spacing of 2.5', one such model shows (at 28.5 MHz) 6.73 dBi free space gain with a front-to-back ratio of over 22 dB and a feed point impedance of about 18 ohms. However, such beams have very narrow operating bandwidths. The subject model at 28 MHz shows only 5.9 dBi free space gain and a 2.7 SWR relative to the target frequency impedance. At 29 MHz, the gain reaches a peak of 7.38 dBi (free space), but the front-to-back ratio has dropped to 8 dB and the SWR is above 6:1 relative to the target frequency feedpoint impedance.</p>
<pre> 2-Element Yagi: Driven Element + Director
Element Length in Feet Spacing from Driven Element in Feet
Driven Element 17.10 ---
Director 16.00 2.5</pre>
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<img src="hb10.gif" width="432" height="328" border="2" vspace="5" hspace="9">
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<img src="hb11.gif" width="431" height="328" border="2" vspace="5" hspace="9">
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<img src="hb12.gif" width="428" height="325" border="2" vspace="5" hspace="9">
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<p>There are uses for such 2-element Yagis, if front-to-back ratio is of no concern and if feedpoint and matching losses can be accommodated or overcome. It is clear that, in terms of raw gain, it is possible to exceed the wide-band 3-element Yagi, although figures are still short of well- designed high performance 3-element Yagis.</p>
<center>
<h3>The ZL-Special 2-Element Phased Array</h3>
</center>The 2-element phased array has been around in ham circles since the 1950s. Originally thought to be a 135-degree impedance phase-shifted array, we have come to understand the antenna as a -45-degree current shifted array with a reversed rear element (created by half-twisting the phasing line). Actually, depending on a number of variables--such as element size, spacing, natural feedpoint impedance, etc.--the magnitude and phase of the current required on the rear element relative to the forward element for desired operation can vary quite widely from about 0.75 to 1.1 and from about 20 to 65 degrees.
<p>The classic ZL and G manner of constructing such arrays is to use two dipoles--either equal in length or with the forward element shorter--spaced about 0.125 wavelengths apart with a length of standard parallel feedline between the two (with the half-twist, of course). For a phasing line, single-wire dipoles have usually used 70-ohm parallel line (almost impossible to come by today in power handling versions), while folded dipole models tend to use 300-ohm parallel line.</p>
<p>Phased arrays are usually designed to optimize front-to-back ratio as a mark of perfect phasing. The mathematics of the requisite current phasing were shown in "Modeling and Understanding Small Beams: <a href="../mu/mu5a.html">Part 5: The ZL Special</a>," <i>Communications Quarterly</i>, (Winter, 1997), pages 72-90. One interesting result was that standard Yagi dimensioning that shortens forward elements and lengthens rear elements must be set aside. At least one model required a rear element shorter than its forward partner to achieve so-called perfect phasing.</p>
<p>The number of design options using standard parallel transmission lines as the phasing element are not very many. Such designs tend to perform with respect to gain about on a par with well-designed 2-element Yagis with average forward gains of about 6.3 dBi free space. One would tend to prefer such an array only if the high front-to-back ratio (which can approach 50 dB at a target frequency) is needed. However, the rear null is quite frequency specific, and most such antennas will drop to a front-to- back ratio of under 20 dB within a half MHz of the target design frequency on 10 meters.</p>
<center>
<h3>The HB9CV</h3>
</center>The HB9CV version of the 2-element horizontal phased array seeks greater gain as well as freedom from the restrictions of existing parallel feedlines as phasing elements. The technique involves a careful selection of element lengths and an interesting combined phasing and matching system.
<p>The following data is taken from 10th edition of Y21BK, Karl Rothammmel's <i>Antennenbuch</i> (Berlin: 1984) (graciously provided to me by Siegfried Rambaum, KB2YVC/DE8FGO). There are two versions of the antenna, one for balanced lines; the other for unbalanced lines. What the two antennas have in common is the basic dimensions of the elements. The forward element is 0.46 wavelengths long, while the rear element is 0.50 wavelengths long, with a spacing of 0.125 wavelengths. Y21BK reports that elements should be 0.47 and 0.51 wavelengths for antennas made from wire. For tubing (copper or aluminum), the recommended diameter is about 0.0025 wavelength.</p>
<p>Before examining the phasing and matching system, we can discover some interesting data about the potential of the antenna from the element recommendations. For 28.5 MHz, the dimensions call for 1" tubing spaced 51.77" (4.31') apart. The forward element is 190.5" (15.875') long, while the rear element is 210.31" (17.526') long.</p>
<p>Plugging these dimensions into a NEC or MININEC model and using separate sources for the front and rear elements, we can determine a number of things. First is the current magnitude and phase for the reversed rear element, relative to the forward element, to achieve maximum gain. A maximum free space gain of 7.32 dBi was achieved with a rear current magnitude of 0.90 of the forward element at a relative phase angle of -18 degrees (equivalent to 162 degrees standard rear element phasing). At this gain, the front-to-back ratio is 7.2 dB. These figures are quite similar to those of a similarly sized Yagi set for maximum gain.</p>
<p>Second, we can also determine the rear element relative current magnitude and phase to achieve maximum front-to-back ratio. With the model, a front- to-back figure of over 50 dB was achieved. However, as with all 2-element horizontal phased arrays, this figure represents the ratio in a direct line with the maximum forward gain lobe. It amounts to a deep dimple in the overall rearward lobe, which has a worst-case figure of about 20 dB down from the forward gain lobe. The requisite rear element relative current magnitude was 0.92 at a relative phase of -44 degrees (equivalent to 136 degrees standard rear element phasing). Antenna gain for this situation was about 6.37 dBi free space, or about 0.9 dB down from maximum gain.</p>
<p>Performance tapers gradually as the phase angle increases above -44 degrees and more rapidly as the current departs from the target magnitude. With lower relative current magnitudes and higher current phase numbers it is possible to achieve figures similar to those one might obtain with a constant 0.9 current magnitude and phase figures between -18 and -44 degrees.</p>
<p>The figure below outlines the complete HB9CV antenna, including the two versions of the matching network. The sketches are not to scale in order to permit the addition of the necessary dimensional annotations.</p>
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<img src="hb13.gif" width="621" height="344" border="2" vspace="5" hspace="9">
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<p>The dimensions in the sketches are for a feedpoint impedance for the balanced system of 150 ohms and for the unbalanced system of 75 ohms. Adjustment is essentially a matter of lengthening or shortening the length of the Tee or Gamma section (or the element length) until the proper feedpoint impedance is achieved.</p>
<p>Modeling a complete HB9CV system is not a simple task, because the antenna parts press the limits of both MININEC and NEC (2 or 4). The number of right angles in the system calls for complex wire length segment tapering or extremely small segment lengths, both of which exceed the maximum allowable number of segments within public domain MININEC. NEC produces inaccurate results with angular junctions of wires having dissimilar diameters or with closely spaced parallel wires of dissimilar diameters.</p>
<p>One potential solution is the use of a modeled transmission line between the forward and rear element matching "bars," a potential open only to NEC. The balanced system yielded quite plausible models when the Tee bars and connectors were increased to 1" diameter to match the main elements.</p>
<p>To reduce the effects of closely spaced element, which can introduce errors, the Tee bar was set at a 4" distance from the main element, both front and rear. Using check models with no feedline between the front and rear elements and with 2 sources (one on each of the Tee bars), NEC models showed a systematic variance of about 0.13 to 0.15 dB difference in gain and a difference of up to 1 dB in front-to-back ratio (between 20 and 30 dB ratios) from equivalent MININEC models, each fed with identical current magnitudes and phase angles. For the present exercises, these differences were considered not significant.</p>
<p>However, it is possible to construct models that give wholly unrealistic results. The HB9CV design is limited by the maximum gain and maximum front-to-back figures inherent in the element size and spacing relationships when dual sources are optimized for both magnitude and phase angle. Every matching system can only match: it cannot increase either maximum gain or maximum front-to-back ratio beyond the limits. Models that suggest higher gains are suspect, and turn out to commit one or more violations of NEC limitations. I have produced models showing up to 8.2 dBi free space gain with almost 28 dB front-to-back ratios: as appealing as these numbers are, they will not stand tests of convergence and independent source substitution.</p>
<p>Using most of common line impedances from 50 to 450 ohms along with sundry velocity factors, HB9CV models with Tee matching ranged in gain from 6.2 to 6.54 dBi free space. Front-to-back ratios ranged from 19.5 to 26.1 dB at the design center frequency, with lower values generally corresponding to higher gain figures.</p>
<p>The most stable nonsymmetrical model was a gamma-match system that used 1" elements throughout, even for the gamma bars and connectors, with a spacing of 4" between the element and gamma bars. The connecting transmission line was 75 ohm, 0.66 VF line. This model produced a very stable model between 28 and 29 MHz with a center point source impedance of 53 ohms. However, the gain was only about 6.2 dBi, with a front-to-back ratio of 20 dB (+/-3 dB across the frequency span). The gain is only that of a normal 2-element Yagi, while the front-to-back ratio is about an S-unit better. This model falls well within the range of models using a Tee-match system.</p>
<p>These models, of course, have limitations, since the Tee-bars and gamma-bars are not as specified within the HB9CV instruction set. However, nothing in a matching system, when physically modeled within the limits of any of the NEC programs, alters gain by more than 0.1 dB and front-to-back by more than about 0.5 dB. (See notes on the Tee match elsewhere in this collection.) The correspondence between the Tee-bar models with and without a connecting phasing line (using dual sources in the latter case) suggests that within broad limits, the models correctly report performances that one may obtain from the HB9CV.</p>
<p>A gain in the range of 6.4 to 6.5 dBi free space is an improvement over the standard 2-element Yagi. Front-to-back ratios between 20 and 26 dB represent improvement factors of 1.5 to 2.0 over the standard 2-element Yagi. Indeed, operators will likely interpret the QRM-killing ability of the HB9CV over the 2-element Yagi as additional gain, given improvements in signal-to-noise ratio.</p>
<p>An additional advantage of the HB9CV is the flexibility of its matching design. Using almost any phasing line design, the Tee or gamma can be adjusted with respect to length and spacing from the main element to achieve a desired match, either with or without a transformer or balun. The antenna models showed good stability over a minimum of 750 kHz on 10 meters, and most covered more than the first MHz with under 2:1 SWR and very reasonable gain and front-to-back ratios at the operating band ends.</p>
<p>The following graphs show the free space gain, front-to-back ratio, and Matched SWR curves for two models: one a relatively high-gain model with a 300-ohm phase line, the other a relatively high SWR model with a 150-ohm phase line. The rates of change for both gain and front-to-back are less steep than those of standard 2-element Yagis. The feedpoint impedances are not 50-ohms, so matching was employed. The medium-gain, high-F-B model used a 1/4 wl 75-ohm match section, while the high-gain, medium F-B model used 3.3' of 75-ohm (VF=0.66) line to achieve a 50-ohm match. (The use of other than 1/4 wl sections of 75-ohm lines as matching sections to 50-ohm lines for reactive impedances in the 70-90 ohm range is a subject needing more widespread understanding, since it is a cheap and effective matching technique.)</p>
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<img src="hb14.gif" width="439" height="334" border="2" vspace="5" hspace="9">
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<img src="hb15.gif" width="434" height="332" border="2" vspace="5" hspace="9">
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<img src="hb16.gif" width="434" height="330" border="2" vspace="5" hspace="9">
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<p>The graphs show that it is relatively easy to develop a fine-performing HB9CV without too much concern for the exact phasing line impedance--and to match it to a 50-ohm feedline.</p>
<p>Despite these laudable properties, extensive modeling and model testing shows that the claims of gains above 7 dBi free space are supported only by faulty models to this point in the testing process. With a front-to-back (or front-to-rear) ratio of about 20 dB as a cut-off point for minimal rearward performance, gains have only approached 6.6 dBi maximum in all models tested. However, within the "normal" range of HB9CV figures, characteristics are stable across a wide operating bandwidth.</p>
<p>In the end, the HB9CV uses element phasing to excellent effect in yielding the most productive combinations of gain and front-to-back ratio achievable from the basic geometry, combinations that cannot be achieved from parasitical operation alone. Moreover, it does so within a basic boom length of 1/8th wavelength. When well designed, it offers stable operating characteristics over a considerable bandwidth. Nonetheless, it remains an antenna subject to the physical limitations of its basic geometry.</p>
<center>
<h3>An Alternative Phasing System</h3>
</center>It is possible to increase the design target frequency gain to in excess of 7.0 dBi free space and to increase the front-to-back ratio to better than 20 dB in a 2-element horizontal phased array--and to achieve at the same time a relatively wide (1 MHz at 10 meters) operating bandwidth with a direct 50-ohm feed.
<p>One overlooked factor that the ZL-Special and the HB9CV have in common is the use of elements approximately 0.5 wl long. When the elements are fed by any phasing method that achieves high gain or maximum front-to-back ratio, the rear element shows an impedance of R - jX, while the forward element shows an impedance of R + jX. This condition sets limitations on direct phase-line interconnection of the two elements or--as with the HB9CV--requires special matching circuitry.</p>
<p>If both elements could be made to show inductive reactance at system resonance, then the element impedances could be tailored to simpler phase- line interconnection. The resistive component can be altered by varying the element length, while the reactance can be set by placing series capacitance at the element feedpoint.</p>
<p>In order to achieve this goal, both elements must be lengthened. Elements in the 0.7 region suffice to provide a direct 50-ohm feed using a phasing line between 75 and 150 ohms (with a velocity factor of 1.0). For the test model using 1" diameter elements, the forward element was 23.4' long (0.678 wl), while the rear element was 24.2' long (0.701 wl) with a spacing of 4.31' (0.125 wl). A 150-ohm open wire transmission line connects the two elements. The figure shows the antenna schematically.</p>
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<img src="hb17.gif" width="620" height="271" border="2" vspace="5" hspace="9">
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<p>Because the elements are longer than 0.5 wl, they exhibit inherently more gain, which also translates into greater gain of the phased system. When the elements are separately fed, the array shows a maximum free space gain of 7.7 dBi when the rear element shows a current magnitude of 1.07 of the forward element at a relative phase angle of -18 degrees. (This figure is under 0.5 dB down from the narrow-band 3-element Yagi gain figure used as our standard.) The front-to-back ratio in this condition is only about 7.6 dB. Maximum front-to-back is better than 50 dB (with a free space forward gain of 6.8 dBi) when the rear element current is 1.27 of the forward element current with a phase angle of -44 degrees.</p>
<p>The actual array is designed for reasonable wide-band 50-ohm operation with a compromise between gain and front-to-back ratio. The following graphs display the anticipated performance across the first MHz of 10 meters.</p>
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<img src="hb18.gif" width="429" height="324" border="2" vspace="5" hspace="9">
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<img src="hb19.gif" width="428" height="326" border="2" vspace="5" hspace="9">
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<img src="hb20.gif" width="432" height="326" border="2" vspace="5" hspace="9">
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<p>A 150-ohm phasing line can be constructed from almost any wire from #14 to #10. #12 AWG copper wire requires 0.14" center-to-center spacing or 0.06" edge-to-edge spacing. Placing a piece of #14 AWG wire between 2 lengths of #12 wire achieves the correct spacing. Tape the wires and withdraw the center wire, replacing the center wire with a small insulated spacer at each tape point. The result is a 150-ohm parallel line. Keep the line taut to prevent shorts. Using #12 AWG enamel wire will not likely adversely affect the velocity factor by much. However, for 100-Ohm and 150-Ohm lines, it may be simpler to construct lines using series connected 50-Ohm and 75-Ohm coaxial cables. The shielding permits the builder to place the lines inside a metal boom used to support the elements with no interaction. However, one must account for the velocity factor of the chosen line to ensure that the physical length will reach the elements and the electrical length will meet the phasing requirements.</p>
<p>The series capacitors can be standard value lumped components. However, one can also use lengths of smaller tubing, insulated by a tube (or rolled sheet) of Teflon or other material for a tight but movable fit. Because of the number of variables involved in the tubing and insulating materials available, you will have to experiment to check the capacitance per inch of overlapping tubing to determine the correct amount for each elements.</p>
<p>One advantage of lumped components is that they can be brought out at right angles to the element. In this manner, if you are concerned that your phasing line has a velocity factor less than 1.0, you can use a slightly shorter length. However, slight changes in element spacing are less problematical than most experimenters are usually led to believe. Hence, you can adjust spacing and phase line length in small amounts for the best compromise.</p>
<p>The following figure shows the free space azimuth pattern of the suggested alternative phased array at 28, 28.5, and 29 MHz.</p>
<center>
<img src="hb21.gif" width="640" height="480" border="2" vspace="5" hspace="9">
</center>
<center>
<h3>Conclusion</h3>
</center>The alternative phased array is a design exercise to see if one can do with 2 elements what others do with 3. Although the HB9CV array surpasses the performance of a 2-element Yagi, it fails to match the performance of even a wide-band lower-gain 3-element Yagi. In contrast, the alternative design meets or exceeds the goal in most respects--even to having a 50-ohm feedpoint impedance. However, because hams tend to be conservative and prefer common half wavelength elements, I doubt that anyone will actually build the design.
<p>Hence, the alternative is largely a design exercise. The exercise demonstrates that understanding all aspects of each element, plus what occurs along a transmission line current transformer, provides a wealth of design opportunity for improving antenna performance. It is not enough to rely on a few broad antenna ideas. The goal should be to grow familiar with every possible aspect of both element and array condition and performance.</p>
<p>Has the limit been reached for maximizing gain while retaining a good front-to-back ratio and a workable feedpoint impedance in a 2-element array? I doubt it. The alternative design is simply a step in a certain direction. It exists because I asked why I should restrict myself to half- wavelength elements when longer elements offered some interesting advantages. The next design will come when I discover the right question to ask about another antenna.</p>
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<p><i>Updated 2-10-98, 09-18-99. &COPY; 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 Amateur Radio Page</a></p>
<p class="topics-footer">Topics: <a href='../topics.html#hb9cv-zl-special'>HB9CV / ZL Special</a>, <a href='../topics.html#hf-upper'>HF Upper</a>, <a href='../topics.html#phased-array'>Phased Array</a></p><br>
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<title>Two-Element Horizontal Phased Arrays Index</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"> Some Notes on Two-Element Horizontal Phased Arrays</h1>
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<center>
<h3>L. B. Cebik, W4RNL</h3>
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<br>
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<p>The directional 2-element phased array achieved notoriety in the 1950s with builder claims that one or another variation on the basic design outperformed 3- and even 4-element Yagis. Although we now know that the appearance of high performance owed much to Yagi deficiencies of the period, horizontal phased arrays have retained much of their mid-century aura of magic. Since magic and an understanding of antennas are mutually exclusive, perhaps we should begin again.</p>
<p>The notes in this series will begin with some basic modeling data that tends to set limits to the performance expectations that we may logically have of 2-element phased arrays. In the second part, we shall explore the degree to which the geometry of the parasitic array can capture the potential of phased element performance. Part 3 will examine one of the two classic methods of array phasing: the ZL-Special with its single phase line. In Part 4, we shall look at two different ways of phasing a pair of elements using element-matching techniques, one by R. Baumgartner, HB9CV, the other by Eric Gustafson, N7CL. Throughout. we shall try to integrate specific design strategies into an overall picture of the performance of which 2-element phased arrays are capable.</p>
<p>This series of items has appeared in <i>The National Contest Journal</i> in 2001-2002. All items will appear at the site after their appearance in <i>NCJ</i></p>
<p><a href="ph1.html"><b>1. The Limits of Performance</b></a> (Nov/Dec, 2001)</p>
<p><a href="ph2.html"><b>2. The Limits of Geometric Phasing</b></a> (Jan/Feb, 2002)</p>
<p><a href="ph3.html"><b>3. The Limits of a Single Phase Line: The ZL-Special</b></a> (Mar/Apr, 2002)</p>
<p><a href="ph4.html"><b>4. Removing the Limits of a Single Phase Line by Element Matching</b></a> (May/Jun, 2002)</p>
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<p><i>Updated 05-10-2002. &COPY; 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><br></p>
<p class="topics-footer">Topics: <a href='../topics.html#hf-upper'>HF Upper</a>, <a href='../topics.html#phased-array'>Phased Array</a></p><br>
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<title>Two-Element Horizontal Phased Arrays Part 1</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"> Some Notes on Two-Element Horizontal Phased Arrays<br>
Part 1: The Limits of Performance</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>
<p>The directional 2-element phased array achieved notoriety in the 1950s with builder claims that one or another variation on the basic design outperformed 3- and even 4-element Yagis. Although we now know that the appearance of high performance owed much to Yagi deficiencies of the period, horizontal phased arrays have retained much of their mid-century aura of magic. Since magic and an understanding of antennas are mutually exclusive, perhaps we should begin again.</p>
<p>The notes in this series will begin with some basic modeling data that tends to set limits to the performance expectations that we may logically have of 2-element phased arrays. In the second part, we shall explore the degree to which the geometry of the parasitic array can capture the potential of phased element performance. Part 3 will examine one of the two classic methods of array phasing: the ZL-Special with its single phase line. In Part 4, we shall look at two different ways of phasing a pair of elements using element-matching techniques, one by R. Baumgartner, HB9CV, the other by Eric Gustafson, N7CL. Throughout. we shall try to integrate specific design strategies into an overall picture of the performance of which 2-element phased arrays are capable.</p>
<h3>A Few Preliminaries</h3>The idea of a 2-element phased array contains an ambiguity. At the most general level, the notion can refer to the relative phasing of the elements in any 2-element array. Under this heading, we may include arrays with a single driven element as well as two driven elements. The perspective offered by this most general idea of a phased array will be useful in seeing where some antennas fit into a larger picture.
<p>Alternatively, the concept of a 2-element phased array often refers specifically to an "all-driven" antenna, that is, to an array in which both elements receive power directly from the source. The key question that immediately arises within this view of phased arrays is how we may get energy to the individual elements in the correct magnitude and phase to effect a desired set of performance characteristics. The most common means is via a "phasing line" composed of a length or lengths of transmission line. Indeed, this means of conveying energy from the array source to the individual elements has been the source of numerous misconceptions about how phased arrays operate.</p>
<p>The phasing-line system of energy transfer, of course, is quite unnecessary. As Brian Egan, ZL1LE, demonstrated with a 15-meter phased array in the 1990s, one may create a phasing network of lumped components and then use separate lines to each element so long as they preserve the relative values of current magnitude and phase created by the network.</p>
<p>The key to understanding 2-element horizontal phased arrays is the fact--stressed by Roy Lewallen, W7EL, in many writings--that the relative current magnitude and phase between the two elements determines the operating characteristics of the antenna. In the early days of phased-array popularity, most builders thought in terms of the impedance transformation along a transmission line linking the elements. However, the impedance along a mismatched line does not track with the current magnitude and phase transformations along the line. Impedance values repeat on a lossless line twice for each wavelength of line. However, current magnitude and phased values appear only once per wavelength.</p>
<p>From this misunderstanding others emerged. Although the most popular line lengths interconnecting elements were in the vicinity of 1/8 wavelength, most folks thought in terms of a 135-degree phase shift. However, with or without a half twist in the short line, the current can only make an approximate 45-degree phase shift. (The number is a crude marker, since we have already noted that the current phase may change more or less than 45-degree in a line that is 45-degree long.) If a straight line yields a 45-degree phase shift in current, then a line with a half twist yields a -45-degree phase shift. Antenna patterns may be identical to those produced by feeding the elements 135 degrees out of phase, but the current behavior and the consequences for evaluating means of obtaining the correct phasing of the elements will depend upon the -45-degree perspective. Because we shall be looking at close-spaced element systems, we shall adopt this orientation throughout these notes.</p>
<p>A further constraint upon our understanding of 2-element horizontal arrays has been the magic associated with 1/8 wavelength spacing. In fact, no particular spacing between elements holds any theoretically superior place in the scheme of 2-element arrays. We shall discover that in some respects, almost any spacing will do, although specific spacings between elements can result in arrays that are easier to implement.</p>
<h3>A Modeling Project</h3>In a number of past articles, I have presented a partial portrait of phased array performance potentials, for example, in the series in NCJ on log-cell Yagis. In the remainder of this first set of notes, I want to expand our appreciation of phased array performance parameters, although space will not allow an absolutely complete account.
<center>
<img src="ph1-1.gif" width="514" height="320" border="2" vspace="5" hspace="9">
</center>
<center>
Fig.1-1 The basic parts and structural variables of a 2-element horizontal phased array.
</center>
<p><b>Fig. 1-1</b> presents the basic parts of a 2-element phased array as we shall model it in NEC-4. We shall assign to each element a current source, specifying both the magnitude and phase angle. By convention, the designated forward element will have a current magnitude of 1.0 and a phase angle of 0.0 degrees. The designated rear element will then be assigned the values of current magnitude and phase that yield a desired performance limit. Since we are working with directional arrays with a single main forward lobe, the forward element will always be the element in the direction of that lobe. Assigning separate values of current magnitude and phase angle to each element is an analog of what we accomplish with a phasing network. Such networks cannot yield performance that exceeds the limits of separate sources for each element, no matter the ingenuity of the system.</p>
<p>For the notes in this section, we shall reduce the total number of variables to a manageable number. We shall vary the spacing between elements systematically. We shall also examine some variations in element length, using both equal-length and unequal-length elements in the study. However, these results will change if we alter the diameter of the elements. For convenience, we shall employ 10-meter (28.5-MHz) elements made from 0.5" diameter aluminum. These elements give us a reasonably realistic model that scales easily to other amateur bands. With a fixed element diameter, we shall not explore variations that result from selecting other diameter materials.</p>
<p>When exploring sources with a relative phase angle between 0 and -90-degree, we must simulate the line half twist by setting up the model elements in opposite directions. That is, if the forward elements extends from a - value to a + value, then the rear element extends from a + value to a minus value. Adhering to this modeling scheme keeps the instantaneous current directions correct.</p>
<p>The basic element for our exploration is a resonant dipole of the specified material. In a NEC-4 model, such a dipole is 197.6" long or about 0.4771 wavelength long at 28.5 MHz. (The half-inch diameter element is 0.001207 wavelength across.) The subject dipole has a resonant impedance of 72.1 + j 0.5 Ohms. Now we are finally ready to examine a 2-element phased array.</p>
<h3>Maximum Front-to-Back Ratio Configurations</h3>The basic model consisted of two self-resonant dipoles of the type just described set at various distances apart. The spacing ranged from 0.05 wavelength to 0.2 wavelength in 0.025 wavelength increments. This range covers--with some interesting but practically useless excess--the element spacing used in virtually all recorded directional phased array construction.
<p>In addition to using equal-length self-resonant elements, I also made up pairs that are 10% shorter and 10% longer than the basic model. The short elements are 177.84" long (0.4294 wavelength), while the long elements are 217.36" long (0.5249 wavelength). As we shall see, resonance is not a requisite for a phased pair of elements. (We shall look at unequal-length elements soon.)</p>
<p>The first exercise attempted to arrive at the rear element relative current magnitude and phase angle necessary top achieve a maximum 180-degree front to back ratio. Although the pursuit of a perfect null can go on indefinitely, it proved fairly easy to obtain a rear null greater than 60 dB lower than the forward lobe maximum value. Since the maximum null is a very narrow-bandwidth phenomenon, -60 dB seemed deep enough to show general trends when we set 2-element phased arrays for a maximum front-to-back ratio.</p>
<center>
<img src="ph1-2.gif" width="376" height="338" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 1-2 Comparative free-space azimuth patterns of a 2-element horizontal phased array configured for maximum 180-degree front-to-back ratio with close-spaced and wide-spaced elements.
</center>
<p><b>Fig. 1-2</b> shows typical patterns for the narrowest element spacing and the widest element spacing used. Although only one set of patterns appear in the figure, the general properties apply to all three of the subject models. As element spacing increases beyond 0.1 wavelength, gain drops off. More notable are the rear lobes. The deep null occurs within a rearward lobe, leaving angle side lobes. The lobes are weakest at the most narrow spacing levels and increase with wide spacing. To some degree, then, aiming at the maximum 180-degree front-to-back ratio may be operationally misdirected, although it serves to set operational limits for the 2-element array.</p>
<pre> Equal-Length 2-Element Phased Array Performance
Maximum 180-Degree Front-to-Back Configuration
Model SHT-E Element Length (Front and Rear): 0.2147 wl
Frequency: 28.5 MHz Diameter: 0.001207 wavelength (0.5")
Space Gain Front-to-Back Z1 (Rear) Z2 (Foprward) Rear I Rear I
wl dBi Ratio dB R +/- jX Ohms R +/- jX Ohms Magnitude Phase
0.05 6.41 65.58 3.9 - j110.3 3.2 - j 78.8 1.024 -17.4
0.075 6.42 66.13 7.9 - j117.1 7.5 - j 71.8 1.035 -26.4
0.1 6.36 73.68 11.9 - j120.7 14.7 - j 64.0 1.045 -35.6
0.125 6.25 61.40 15.7 - j122.8 24.4 - j 57.6 1.051 -44.9
0.15 6.11 65.41 19.1 - j123.8 35.7 - j 53.7 1.056 -54.3
0.175 5.92 68.86 22.3 - j124.3 47.7 - j 53.0 1.057 -63.8
0.2 5.69 65.46 25.7 - j124.2 59.1 - j 55.8 1.057 -73.2
Model RES-E Element Length (Front and Rear): 0.2386 wl
Frequency: 28.5 MHz Diameter: 0.001207 wavelength (0.5")
Space Gain Front-to-Back Z1 (Rear) Z2 (Forward) Rear I Rear I
wl dBi Ratio dB R +/- jX Ohms R +/- jX Ohms Magnitude Phase
0.05 6.50 63.70 10.7 - j 35.5 -1.6 + j 7.0 1.033 -17.0
0.075 6.50 88.97 15.9 - j 37.5 4.6 + j 24.2 1.049 -26.0
0.1 6.44 60.36 20.7 - j 38.4 15.3 + j 39.4 1.063 -35.2
0.125 6.33 64.42 25.1 - j 38.8 29.8 + j 51.2 1.074 -44.7
0.15 6.18 66.73 29.1 - j 38.6 46.8 + j 58.2 1.080 -54.3
0.175 5.99 61.47 32.8 - j 38.2 64.6 + j 60.1 1.083 -64.0
0.2 5.76 63.34 36.0 - j 37.6 81.3 + j 56.7 1.080 -73.6
Model LNG-E Element Length (Front and Rear): 0.2624 wl
Frequency: 28.5 MHz Diameter: 0.001207 wavelength (0.5")
Space Gain Front-to-Back Z1 (Rear) Z2 (Forward) Rear I Rear I
wl dBi Ratio dB R +/- jX Ohms R +/- jX Ohms Magitude Phase
0.05 6.59 66.90 18.9 + j 39.0 - 7.3 + j 95 5 1.045 -16.6
0.075 6.59 74.73 25.9 + j 41.8 1.0 + j125.3 1.067 -25.5
0.1 6.52 63.87 32.0 + j 43.8 16.4 + j150.6 1.087 -34.9
0.125 6.41 65.07 37.4 + j 45.5 37.7 + j169.4 1.101 -44.5
0.15 6.26 66.57 42.3 + j 47.0 62.8 + j180.7 1.110 -54.4
0.175 6.08 72.84 46.7 + j 48.6 88.8 + j183.6 1.113 -64.3
0.2 5.85 67.24 50.7 + j 50.0 113.3 + j178.5 1.110 -74.3
Note: All gain values are for free-space. Rear current (I) magnitude and phase
values are relative to forward element values of 1.0 and 0.0 degrees. Model RES-
E uses elements of equal length to an independent resonant dipole at the test
frequency. Models SHT-E and LNG-E uses elements that are 10% shorter and 10%
longer, respectively.
Table 1. Performance and operating conditions of 3 equal-length element 2-
element phased arrays in a maximum 180-degree front-to-back ratio configuration.</pre>
<p><b>Table 1</b> provides full data for the short, resonant, and long element pairs. As we might expect, the maximum gain for any spacing is partly dependent upon the element lengths. consistent among the three test models is the occurrence of maximum gain at the closest spacing levels: 0.05 and 0.075 wavelength. Thereafter, gain decreases steadily. The front-to-back values are simply for the record to verify that the model obtained the requisite depth of rear null.</p>
<p>At a spacing of 0.125 wavelength, a popular element separation for 2-element Yagis and phased arrays, the forward gain of the maximum-null phased arrays do not differ significantly from the gain of a well-designed Yagi. In the maximum front-to-back configuration, then, the phased array's claim to fame is only its rearward null and not its gain.</p>
<center>
<img src="ph1-3.gif" width="722" height="544" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 1-3 The rear element relative current magnitude and phase angle for short, resonant, and long element lengths in arrays having equal- length forward and rear elements, and set for maximum front-to-back ratio. "I-M" means rear element relative current magnitude. "I-P" means rear element relative current phase. "Sht" refers to model SHT-E; "Res" refers to model RES-E; and "Lng" refers to model LNG-E. See Table 1 for model specifications.
</center>
<p>Of primary interest to us are the rear element relative values of current magnitude and phase angle necessary to yield the deep null. <b>Fig. 3</b> graphically portrays the tabulated data of <b>Table 1</b>. Of immediate notice is that the change in element lengths between models has almost no effect on the requisite phase angles. The graphs of the three lines overlap and proceed in a virtually linear curve from about -17 degrees at 0.05 wavelength spacing to about -73 degrees at 0.2 wavelength spacing. Equally notable is the fact that we may obtain a rearward null for any spacing in this range.</p>
<p>What does change with the length of the elements is the relative current magnitude required on the rear element. The longer the element pair, the higher the required value of relative rear element current to achieve. The differentials for 10% changes in element length are between 2% and 3%.</p>
<p>Not all element spacings will be easy to implement with standard means of element phasing. The tabulated data shows negative resistance values in some entries for very close-spaced elements. These values are correct and simply mean that the mutual coupling between elements is providing more energy to the affected element than the source itself.</p>
<h3>A Test of Equal vs. Unequal Element Lengths</h3>There are three possible element arrangements for a 2-element horizontal phased array. As we have just examined, both elements may be equal in length. However, <b>Fig. 1-4</b> shows two more configurations. The forward elements may be shorter than the rear element, and the forward element may be longer than the rear element. Our familiarity with the requirements for parasitic beams makes one of the arrangements natural and the other almost unthinkable.
<center>
<img src="ph1-4.gif" width="364" height="328" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 1-4 Three options for element length relationships between the forward and rear elements of a 2-element phased array.
</center>
<p>Nevertheless, both types of unequal-length element arrays are fully functional in a phased array. all that we need to do is provide the two elements with the correct relative current magnitudes and phase angles. <b>Table 2</b> provides the complete modeling data on the test runs. The equal-length model is the same as used for the earlier runs. Each of the unequal-length arrays has one element that is the same as our original self-resonant dipole and a second element that is 5% longer: 207.48" or 0.5010 wavelength. As the table shows, there is no significant difference in the maximum forward free-space gain. Once more, at the closest element spacing modeled, a negative resistive component on the forward element is possible.</p>
<pre> Unequal-Length 2-Element Phased Array Performance
Maximum 180-Degree Front-to-Back Configuration
Model RES-UF Element Length: Front: 0.2505 wl; Rear: 0.2386 wl
Frequency: 28.5 MHz Diameter: 0.001207 wl (0.5")
Space Gain Front-to-Back Z1 (Rear) Z2 (Forward) Rear I Rear I
wl dBi Ratio dB R +/- jX Ohms R +/- jX Ohms Magnitude Phase
0.05 6.52 62.19 12.1 - j 38.7 -3.6 + j 53.5 1.114 -16.9
0.075 6.52 69.26 17.3 - j 39.5 3.5 + j 75.7 1.139 -25.9
0.1 6.45 63.68 22.0 - j 39.7 16.4 + j 95.2 1.160 -35.3
0.125 6.34 65.22 26.2 - j 39.5 34.0 + j109.8 1.175 -44.9
0.15 6.20 63.14 30.1 - j 39.0 54.6 + j118.6 1.185 -54.6
0.175 6.02 67.19 33.5 - j 38.4 76.1 + j120.6 1.186 -64.4
0.2 5.79 68.90 36.6 - j 37.6 96.3 + j116.4 1.184 -74.2
Model RES-UR Element Length: Front: 0.2386 wl; Rear: 0.2505 wl
Frequency: 28.5 MHz Diameter: 0.001207 wl (0.5")
Space Gain Front-to-Back Z1 (Rear) Z2 (Forward) Rear I Rear I
wl dBi Ratio dB R +/- jX Ohms R +/- jX Ohms Magnitude Phase
0.05 6.52 63.77 13.3 + j 4.5 -2.4 + j 3.7 0.962 -16.9
0.075 6.52 61.79 19.3 + j 3.7 3.7 + j 22.1 0.974 -25.9
0.1 6.45 67.19 24.8 + j 3.6 14.5 + j 38.0 0.985 -35.1
0.125 6.35 62.79 29.7 + j 3.7 29.2 + j 50.1 0.992 -44.5
0.15 6.20 65.18 34.2 + j 4.2 46.2 + j 57.4 0.997 -54.1
0.175 6.01 65.28 38.4 + j 4.9 64.0 + j 59.3 0.998 -63.7
0.2 5.78 63.36 42.1 + j 5.9 80.8 + j 56.3 0.998 -73.3
For comparative data on Model RES-E, see Table 1.
Note: All gain values are for free-space. Rear current (I) magnitude and phase
values are relative to forward element values of 1.0 and 0.0 degrees. Model
RES-E uses elements of equal length to an independent resonant dipole at the test
frequency. Models RES-UF and RES-UR uses elements that are 5% longer than those
in RES-E at the forward and at the rear elements, respectively.
Table 2. Performance and operating conditions of 2 unequal-length element
2-element phased arrays in a maximum 180-degree front-to-back ratio configuration.</pre>
<p><b>Fig. 1-5</b> shows the relative current magnitude on the rear element, along with the relative phase angle. As with the three equal-element-length arrays, the phase angles required to achieve a 180-degree front-to-back ratio in excess of 60 dB overlap with considerable precision. The differences are almost solely in the realm of the required relative current magnitude for the rear element. In this figure and in <b>Fig. 1-3</b>, you will note a slight decrease in the rear element current magnitude at the maximum spacing used (0.2 wavelength). The reversal of direction in current magnitude is consistent for all models in the series, both the ones used here and others in my collection.</p>
<center>
<img src="ph1-5.gif" width="723" height="545" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 1-5 The rear element relative current magnitude and phase angle for various element-length relationships in 2-element horizontal phased arrays that are set for maximum front-to-back ratio. "Equal" refers to model RES-E; "F=Lng" refers to model RES-UF; and "R=Lng" refers to model RES-UR, according to whether the elements are equal in length, the forward element is 5% longer, or the rear element is 5% longer. See Table 2 for the specifications of models RES-UF and RES-UR.
</center>
<p>These models cannot guarantee that any particular element arrangement will provide an adequate basis for a practical array. However, when experimenting with phased arrays and various phasing schemes, it pays not to overlook the potential of a longer forward element.</p>
<h3>Maximum Gain Configurations</h3>The maximum front-to-back ratio configuration of a phased array represents one limit of performance, one marked by moderate gain and a deep rearward null. We may also set the relative current magnitudes and phase angles to achieve maximum forward gain, letting the front-to-back ratio become whatever it will be. In general, the conditions for maximum forward gain in a 2-element horizontal phased array do not favor high front-to-back ratios. <b>Fig. 1-6</b> shows a typical maximum gain pattern, with a front-to-back ratio well below 10 dB.
<center>
<img src="ph1-6.gif" width="376" height="338" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 1-6 A typical free-space azimuth pattern for a 2-element phased array set for maximum forward gain.
</center>
<p>For the 5 models that we previously examined, <b>Table 3</b> provides the necessary data. Maximum gain does not occur at the very closest spacing tested, but appears in the 0.75 to 0.1 wavelength region of element spacing. Front-to-back ratios show a steady decrease with increasing element spacing. The maximum gain phenomenon has a wider bandwidth than the maximum front-to-back null. Therefore, each registered data set comprises a centered set of values in the middle of the range or phase angles and the range of current magnitudes that yield the highest gain. Over this region, the front-to-back ratio may change by as much as 2 dB, and the table shows only the center value.</p>
<pre> Equal-Length and Unequal-Length 2-Element Phased Array Performance
Maximum Gain Configuration
Model SHT-E Element Length (Front and Rear): 0.2147 wl
Frequency: 28.5 MHz Diameter: 0.001207 wl (0.5")
Space Gain Front-to-Back Z1 (Rear) Z2 (Forward) Rear I Rear I
wl dBi Ratio dB R +/- jX Ohms R +/- jX Ohms Magnitude Phase
0.05 7.10 8.57 1.8 - j102.1 1.5 - j 87.4 1.010 - 8.0
0.075 7.23 7.57 3.5 - j104.5 3.2 - j 85.1 1.015 -11.0
0.1 7.24 7.42 5.4 - j105.0 6.2 - j 80.1 1.020 -14.8
0.125 7.21 7.01 7.0 - j103.8 10.5 - j 75.5 1.020 -18.0
0.15 7.15 6.67 8.8 - j101.9 15.5 - j 70.4 1.025 -21.3
0.175 7.06 6.33 10.6 - j 99.7 21.4 - j 66.5 1.025 -24.5
0.2 6.96 5.95 12.6 - j 97.2 27.7 - j 63.4 1.030 -27.5
Model RES-E Element Length (Front and Rear): 0.2386 wl
Frequency: 28.5 MHz Diameter: 0.001207 wl (0.5")
Space Gain Front-to-Back Z1 (Rear) Z2 (Forward) Rear I Rear I
wl dBi Ratio dB R +/- jX Ohms R +/- jX Ohms Magnitude Phase
0.05 7.19 8.17 4.9 - j 24.6 -0.7 - j 5.7 1.015 - 7.5
0.075 7.31 7.72 7.0 - j 21.8 2.0 + j 5.1 1.020 -11.0
0.1 7.31 7.38 9.5 - j 18.1 6.2 + j 15.9 1.030 -14.5
0.125 7.28 7.08 11.8 - j 14.2 12.3 + j 25.5 1.038 -18.0
0.15 7.21 6.75 13.7 - j 10.2 20.3 + j 33.7 1.035 -21.5
0.175 7.13 6.46 16.1 - j 6.3 28.9 + j 40.6 1.040 -25.0
0.2 7.02 5.97 18.3 - j 1.7 37.9 + j 45.1 1.040 -27.8
Model LNG-E Element Length (Front and Rear): 0.2624 wl
Frequency: 28.5 MHz Diameter: 0.001207 wl (0.5")
Space Gain Front-to-Back Z1 (Rear) Z2 (Forward) Rear I Rear I
wl dBi Ratio dB R +/- jX Ohms R +/- jX Ohms Magnitude Phase
0.05 7.28 8.48 9.3 + j 52.5 - 3.8 + j 78 0 1.025 - 7.5
0.075 7.39 7.71 11.8 + j 62.1 0.3 + j 98.1 1.030 -10.8
0.1 7.39 7.47 14.5 + j 69.9 7.0 + j116.4 1.035 -14.5
0.125 7.35 7.11 17.5 + j 77.5 15.6 + j132.1 1.045 -18.0
0.15 7.29 6.77 20.3 + j 84.5 26.6 + j145.2 1.050 -21.5
0.175 7.20 6.43 23.4 + j 91.1 39.2 + j155.7 1.055 -25.0
0.2 7.10 6.03 26.1 + j 97.6 53.0 + j162.6 1.050 -28.3
Model RES-UF Element Length: Front: 0.2505 wl; Rear: 0.2386 wl
Frequency: 28.5 MHz Diameter: 0.001207 wl (0.5")
Space Gain Front-to-Back Z1 (Rear) Z2 (Forward) Rear I Rear I
wl dBi Ratio dB R +/- jX Ohms R +/- jX Ohms Magnitude Phase
0.05 7.21 8.19 5.2 - j 28.3 -1.1 + j 38.7 1.085 - 7.5
0.075 7.33 7.74 7.6 - j 24.2 1.7 + j 53.1 1.100 -11.0
0.1 7.33 7.36 9.7 - j 19.8 7.1 + j 66.5 1.110 -14.5
0.125 7.30 7.04 11.9 - j 15.3 14.3 + j 78.6 1.120 -18.0
0.15 7.23 6.70 13.7 - j 11.0 23.7 + j 88.6 1.120 -21.5
0.175 7.15 6.40 16.0 - j 6.7 34.1 + j 96.9 1.125 -25.0
0.2 7.04 6.02 18.5 - j 2.4 45.1 + j102.8 1.130 -28.3
Model RES-UR Element Length: Front: 0.2386 wl; Rear: 0.2505 wl
Frequency: 28.5 MHz Diameter: 0.001207 wl (0.5")
Space Gain Front-to-Back Z1 (Rear) Z2 (Forward) Rear I Rear I
wl dBi Ratio dB R +/- jX Ohms R +/- jX Ohms Magnitude Phase
0.05 7.21 8.60 6.6 + j 16.5 -1.4 - j 8.8 0.950 - 7.8
0.075 7.33 7.80 8.8 + j 21.8 1.5 + j 2.8 0.950 -11.0
0.1 7.33 7.44 11.5 + j 27.0 5.9 + j 14.2 0.955 -14.5
0.125 7.30 7.13 14.1 + j 32.2 12.0 + j 24.4 0.960 -18.0
0.15 7.23 6.82 16.9 + j 37.3 19.6 + j 33.3 0.965 -21.5
0.175 7.15 6.36 19.0 + j 42.6 28.5 + j 39.7 0.960 -24.5
0.2 7.04 6.01 21.7 + j 47.6 37.9 + j 44.7 0.960 -27.8
Note: All gain values are for free-space. Rear current (I) magnitude and phase
values are relative to forward element values of 1.0 and 0.0 degrees. Model
RES-E uses elements of equal length to an independent resonant dipole at the test
frequency. Models SHT-E and LNG-E uses elements that are 10% shorter and 10%
longer, respectively. Models RES-UF and RES-UR uses elements that are 5% longer
than those in RES-E at the forward and at the rear elements, respectively.
Table 3. Performance and operating conditions of 5 2-element phased arrays in
a maximum-gain configuration.</pre>
<p><b>Fig. 1-7</b> graphs the current magnitude and phase angle data for the 3 equal-element-length models. Once more the phase angle curves form an overlapping trio. Irregularities in the current magnitude curves arise from the simple averaging and centering procedure used to produce the curves. However, the general trend is both clear and consistent with the maximum front-to-back curves: the longer the elements, the higher the required relative current magnitude level on the rear element to achieve the desired performance curve.</p>
<center>
<img src="ph1-7.gif" width="725" height="545" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 1-7 The rear element relative current magnitude and phase angle for short, resonant, and long element lengths in arrays having equal- length forward and rear elements, and are set for maximum forward gain. "I-M" means rear element relative current magnitude. "I-P" means rear element relative current phase. "Sht" refers to model SHT-E; "Res" refers to model RES-E; and "Lng" refers to model LNG-E. See Table 3 for model specifications.
</center>
<p>The maximum gain curves represent the highest gain level that we may achieve with 2 elements of the sizes in the models. In general, the highest gain levels coincide with those for a quite short boom 3-element Yagi or a 2-element quad, both of which are designed for adequate 10-meter band coverage. The Yagi boom length would be about 8' for this gain level, with 12' boom 3-element Yagis capable of 8 dBi free-space gain across the first MHz of 10 meters. However, the phased-array data, taken at a single frequency, do not necessarily hold over an equivalent operating bandwidth.</p>
<h3>Conclusions and Compromise</h3>The exercise that we have presented is at most a demonstration of phased array properties and not a proof of them. What it shows is two sets of limits between which most horizontal phased arrays operate. In general, designers either consciously select or discover through experimentation phasing arrangements that yield acceptable performance with respect to gain, front-to-back ratio, and operating bandwidth.
<pre> Performance Shifts With Changes in Relative Current Magnitude and Phase Angle
Model RES-E at 3 Element Spacings
Element Spacing: 0.05 wavelength
1. Rear Element Relative Current Phase Angle: -17.0 degrees
Rear I Gain Front-to-Back Z1 (Rear) Z2 (Forward)
Magnitude dBi Ratio dB R +/- jX Ohms R +/- jX Ohms
0.933 6.34 15.23 3.7 - j 38.9 5.9 + j 6.1
0.983 6.47 21.48 7.4 - j 37.0 2.2 + j 6.6
1.033 6.50 63.70 10.7 - j 35.3 -1.6 + j 7.0
1.183 6.42 21.95 13.7 - j 33.8 -5.3 + j 7.5
1.133 6.28 16.30 16.4 - j 32.4 -9.0 + j 7.9
2. Rear Element Relative Current Magnitude: 1.033
Rear I Gain Front-to-Back Z1 (Rear) Z2 (Forward)
Phase Angle dBi Ratio dB R +/- jX Ohms R +/- jX Ohms
-13.0 6.88 17.45 8.5 - j 30.7 -2.0 + j 1.6
-15.0 6.69 23.97 9.6 - j 33.1 -1.8 + j 4.3
-17.0 6.50 63.70 10.7 - j 35.3 -1.6 + j 7.0
-19.0 6.30 25.07 11.9 - j 37.6 -1.2 + j 9.7
-21.0 6.11 19.47 13.2 - j 39.8 -0.7 + j 12.4
Element Spacing: 0.125 wavelength
1. Rear Element Relative Current Phase Angle: -44.7 degrees
Rear I Gain Front-to-Back Z1 (Rear) Z2 (Forward)
Magnitude dBi Ratio dB R +/- jX Ohms R +/- jX Ohms
0.974 6.31 23.22 20.3 - j 42.5 33.8 + j 46.2
1.024 6.33 29.53 22.8 - j 40.5 31.8 + j 48.7
1.074 6.33 64.42 25.1 - j 38.8 29.8 + j 51.2
1.124 6.31 29.77 27.2 - j 37.1 27.9 + j 53.7
1.174 6.28 24.03 29.1 - j 35.7 25.9 + j 56.2
2. Rear Element Relative Current Magnitude: 1.074
Rear I Gain Front-to-Back Z1 (Rear) Z2 (Forward)
Phase Angle dBi Ratio dB R +/- jX Ohms R +/- jX Ohms
-40.7 6.52 25.75 22.7 - j 35.4 26.2 + j 48.1
-42.7 6.42 31.85 23.9 - j 37.1 28.0 + j 49.7
-44.7 6.33 64.42 25.1 - j 38.8 29.8 + j 51.2
-46.7 6.23 32.45 26.4 - j 40.4 31.7 + j 52.7
-48.7 6.14 26.50 27.8 - j 41.9 33.7 + j 54.0
Element Spacing: 0.2 wavelength
1. Rear Element Relative Current Phase Angle: -73.6 degrees
Rear I Gain Front-to-Back Z1 (Rear) Z2 (Forward)
Magnitude dBi Ratio dB R +/- jX Ohms R +/- jX Ohms
0.980 5.76 26.01 32.5 - j 41.3 80.3 + j 51.3
1.030 5.76 32.36 34.3 - j 39.4 80.8 + j 54.0
1.080 5.76 63.34 36.0 - j 37.6 81.3 + j 56.7
1.130 5.76 32.38 37.5 - j 36.0 81.8 + j 59.3
1.180 5.75 26.68 38.9 - j 34.5 82.3 + j 62.0
2. Rear Element Relative Current Magnitude: 1.080
Rear I Gain Front-to-Back Z1 (Rear) Z2 (Forward)
Phase Angle dBi Ratio dB R +/- jX Ohms R +/- jX Ohms
-69.6 5.92 28.63 33.6 - j 35.1 77.3 + j 57.3
-71.6 5.84 34.61 34.8 - j 36.4 79.3 + j 57.0
-73.6 5.76 63.34 36.0 - j 37.6 81.3 + j 56.7
-75.6 5.69 35.05 37.3 - j 38.8 83.3 + j 56.3
-77.6 5.61 28.98 38.7 - j 39.9 85.3 + j 55.8
Note: Total rear element relative current magnitude shift: +/- 10%; total rear
element relative current phase angle shift: +/- 2 degrees
Table 4. Performance shifts in model RES-E at 0.05, 0.125, and 0.2 wavelength
element spacing with a constant rear element relative phase angle and a variable
relative current magnitude and with a constant rear element current magnitude and
a variable relative current phase angle.</pre>
<p><b>Table 4</b> gives us a partial view of what happens to the performance characteristics of a 2-element array as we drift away from the conditions that yield maximum front-to-back ratio. Varying the rear element relative current magnitude alone (with a fixed relative current phase angle) by about +/- 10% shows a gradual decline in gain and a more rapid decrease in front-to-back ratio whether the current magnitude goes too high or too low. However, as we fix the current magnitude on the rear element and vary the phase angle, we obtain a different progression. The front-to-back ratio decreases on both sides of the optimal values. However, the change in phase angle shows a single low-to-high progression in the +/-2 degree variation in the example.</p>
<p>The table shows clearly that the operating bandwidth for a set of conditions varies directly with the spacing between elements. The cost of obtaining the wider operating bandwidth is, of course, a decrease in the forward gain. However, the rate of gain decrease itself increases with spacings above about 0.125 wavelength. Indeed, one of the sensible reasons for selecting an element spacing in the 0.1 to 0.15 wavelength region is that we acquire reasonable operating bandwidth while maintaining higher gain levels.</p>
<center>
<img src="ph1-8.gif" width="376" height="338" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 1-8 Typical "desirable" free-space azimuth pattern for a 2-element horizontal phased array set for acceptable amateur operation.
</center>
<p>Designers of phased arrays rarely survey the potentials for practical beams by extending the systematic model variation exemplified by <b>Table 4</b>. There are too many variables involved in the design work for one to fix upon a set of relative current magnitudes and phase angles and then design means for obtaining them. Instead, they tend to discover configurations that meet our usual amateur standards for what counts as a "good" beam. <b>Fig. 1-8</b> shows a typical and desirable phased array pattern for an array using equal length (self-resonant) elements and spaced 0.125 wavelength. Gain does not appear on the pattern, but the triple rear lobe everywhere exceeds -20 dB relative to the forward lobe.</p>
<pre> Performance Shifts With Changes in Relative Current Magnitude and Phase Angle
Model RES-E at 0.125 wavelength Element Spacing Stepped Between Front-to-Back
and Gain Settings
Setting Rear I Rear I Gain Front-to-Back Z1 (Rear) Z2 (Forward)
No. Mag. Phase dBi Ratio dB R +/- jX Ohms R +/- jX Ohms
1 1.074 -44.7 6.33 64.42 25.1 - j 38.8 29.8 + j 51.2
2 1.065 -38.0 6.64 21.05 20.8 - j 33.3 24.2 + j 45.5
3 1.056 -31.4 6.94 14.53 17.1 - j 27.4 19.5 + j 39.3
4 1.047 -24.7 7.17 10.32 14.1 - j 21.0 15.4 + j 32.6
5 1.038 -18.0 7.28 7.08 11.8 - j 14.2 12.3 + j 25.5
Table 5. Performance shifts as the relative rear element current magnitude and
phase angles are shifted in proportional steps between maximum front-to-back
ratio and maximum gain settings.</pre>
<p>There is no single set of values for relative current magnitude and relative phase angle that will yield patterns of this sort. <b>Table 5</b> lists data for a set of compromise values developed simply by taking proportional parts of the differentials between the magnitude and phase angle values for the two extreme or limiting cases. <b>Fig. 1-9</b> graphs the free-space gain and front-to-back ratio. The setting numbers correspond to the combinations shown in the table.</p>
<center>
<img src="ph1-9.gif" width="723" height="543" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 1-9 Free-space gain and front-to-back ratio of 2-element horizontal phased arrays at compromise settings of rear element relative current magnitude and phase angles between the limits of maximum forward gain settings and maximum front-to-back ratio settings. See Table 5 for details of the compromise settings.
</center>
<p>As noted earlier, the very high 180-degree front-to-back ratio decreases quickly, so that a phase angle of -38 degrees on the rear element with a 1% decrease in current magnitude results in a front-to-back ratio just over 20 dB. However, in this increment, gain only rises by about 0.1 dB, with the steeper gain increase curve appearing between settings 2 and 3. As a result, one must accept a front-to-back ratio of less than 20 dB to achieve gain levels higher than 6.5 dBi.</p>
<p>The strategy used for these models can well be altered with possibly different results. We have sampled only two of many strategies in the effort to find a satisfactory set of operating conditions, and we have not explored the question of operating bandwidth--the frequency range over which the performance characteristics sustain themselves at acceptable levels. One reason for this void in our discussion is that the means by which we effect the current magnitudes and phase angles on each element play a significant role in setting the operating bandwidth. The exploration of such means is yet to come. We can only note at this stage that the number of variables involved in phased array design is high enough to preclude anything like a complete treatment.</p>
<p>So far, we have only scratched the surface of horizontal array understanding. The exercise has set performance limits. The data in <b>Tables 1 and 2</b>, however, are more than interesting numbers: they provide insight into the conditions that yield individual element impedances in paired combinations. The pattern of impedances will take on considerable importance in Parts 3 and 4 of this series.</p>
<p>As well, we have identified some of the factors affecting operating bandwidth, such as element spacing and where we set the rear element relative current magnitude and phase angle between the maximum gain and the maximum front-to-back values. Of course, we have not mentioned a third significant factor that affects operating bandwidth, namely, the diameter of the elements that we use. However, element diameter as a fraction of a wavelength will play a role in operating bandwidth, especially as one examines wire and tubular implementations of 2-element phased arrays.</p>
<p>So far, we have not explored how close we may come to a nearly perfect array with the ordinary design means available to us. One of those ordinary means that we usually overlook is antenna geometry. We shall explore the nature and limitations of that design route in the next episode.</p>
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<p><i>Updated 01-12-2002. &COPY; L. B. Cebik, W4RNL. This item originally appeared in</i> The National Contest Journal <i>(Nov./Dec., 2001). 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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<title>Two-Element Horizontal Phased Arrays Part 2</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"> Some Notes on Two-Element Horizontal Phased Arrays<br>
Part 2: The Limits of Geometric Phasing</h1>
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<h3>L. B. Cebik, W4RNL</h3>
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<p>In Part 1, we noted that there are two ways of looking at the idea of a phased array. One perspective views the phased array as a combination of elements, all of which are fed. The other perspective is more general: it examines the relative current magnitude and phase angle of element combinations, regardless of which one or more of them may be fed. From this latter perspective, a 2-element parasitic array is phased in the sense that the unfed element will display a relative current magnitude and phase angle.</p>
<p>The parasitic array, of course, has a more common name: the Yagi-Uda beam. The Yagi (for short) may have as many parasitic elements as a designer can put to good use. Our interest will be in the smallest of such arrays: 2-element models. <b>Fig. 2-1</b> shows the options that we have for creating 2-element Yagis. We may either use a director or forward parasitic elements with a driven element, or we may use a reflector or rear parasitic element with a driven element.</p>
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<img src="ph2-1.gif" width="371" height="278" border="2" vspace="5" hspace="9">
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Fig. 2-1. Options for the element arrangement of a 2-element Yagi.
</center>
<p>The names "director" and "reflector" are simply conventional tags by which we identify a given parasitic element. The names do not themselves indicate how a parasitic array operates. Indeed, among those new to antennas, we find numerous misconceptions concerning reflectors, including the idea that they function similarly to the mirrored surface behind the light source in a flashlight. Directors, by the same analogy, appear to function in the manner of optical lenses by focusing the beam of RF.</p>
<p>Let's approach 2-element Yagis from a different point-of-view. The close proximity of the 2 elements provides significant inter-element coupling such that the unfed element will show at its center a relative current magnitude and phase angle. By adjusting the element diameters, spacing, and lengths, we may alter the unfed element relative current magnitude and phase angle. However, this process is limited by the basic geometry of the array. It is composed of parallel linear elements. Hence, the three variables of length, diameter and spacing can only go so far in yielding on the unfed element a relative current magnitude and phase angle that corresponds with those identified in Part 1 as able to produce a desired radiation pattern.</p>
<p>In this episode, we shall look more closely at the basic properties of 2-element Yagis in both the reflector-driver and the driver-director configuration. Our efforts will be to understand what limitations that geometry alone, as a set of design variables, places on the performance of 2-element arrays, especially compared to independently feeding both elements. When we are done, we should be able to correlate typical Yagi patterns with the relative phasing conditions for the two elements. At the end, we shall look at some alternative 2-element geometries designed to improve those conditions.</p>
<h3>The Reflector-Driver and Driver-Director 2-Element Arrays</h3>The earliest detailed study of 2-element Yagis using method-of-moments modeling software is the work of Jerry Hall, K1TD, whose results appear in the 15th and 16th editions of <i>The ARRL Antenna Book</i> (pp. 11-2 through 11-8). I shall replicate his work in part, using the modeling constraints applied in Part 1. The test frequency will be 28.5 MHz. The array elements will use 0.5" (0.001207 wl) diameter elements. Throughout our simplified examination of 2-element Yagis, I shall aim for two simultaneous goals: maximum front-to-back ratio and driver resonance. A driver will be considered resonant when the source reactance is +/-1 Ohm or less. Using these twin goals will not yield the absolute maximum 180-degree front-to-back ratio possible with two elements, but it will be close. As well, the results will permit easier graphing of the source impedances of corresponding reflector-driver and driver-director arrays.
<p>We shall also limit our samples to the same increments of element spacing that we used in Part 1: from 0.05 wl to 0.2 wl in 0.025-wl increments. Where our interest will depart from the earlier study is in the recording of the relative current magnitude and phase angle on the parasitic element when the driver has a current magnitude of 1.0 and a phase angle of 0.0 degrees.</p>
<pre> 2-Element Reflector-Driver Performance
Set for Maximum 180-Degree Front-to-Back Ratio and Resonance
Element Reflector Driver Gain Front-to-Back Feedpoint Z
Spacing wl Length wl Length wl dBi Ratio dB R +/- jX Ohms
0.05 0.2505 0.2387 6.24 11.36 8.1 + j 0.1
0.075 0.2507 0.2356 6.36 11.40 15.4 - j 0.2
0.1 0.2511 0.2334 6.32 11.33 24.3 - j 0.1
0.125 0.2514 0.2310 6.25 11.18 33.8 + j 0.0
0.15 0.2513 0.2312 6.18 10.96 42.9 - j 0.1
0.175 0.2513 0.2310 6.06 10.69 52.1 + j 0.0
0.2 0.2511 0.2312 5.91 10.36 60.2 - j 0.0
Note: All elements 0.5" (0.001207 wl) aluminum
Table 1. 2-element reflector-driver Yagi performance when set for maximum 180-degree
front-to-back ratio and driver resonance.</pre>
<p><b>Table 1</b> provides the basic performance data for the models of a reflector-driver parasitic array meeting the conditions we have just specified. In addition to the usual performance data (free-space gain in dBi, 180-degree front-to-back ratio in dB, and the source impedance in Ohms), the table provides element lengths as a function of a wavelength at the test frequency. Unlike the models in Part 1, which used a relatively arbitrary but consistent dimensions for each model, the parasitic array must have different element lengths at each increment of spacing to achieve the maximum front-to-back ratio at a resonant driver impedance.</p>
<p>The dimensions themselves hold some interest. As you scan the table, note that the reflector length required to meet the twin modeling objectives reaches a peak length at a spacing of 0.125 wl and then decreases. In contrast, the required driver length decreases until the element spacing is 0.175 wl and then increases.</p>
<center>
<img src="ph2-2.gif" width="724" height="543" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 2-2. Gain and 180-degree front-to-back ratio of reflector-driver 2-element Yagis set for maximum front-to-back ratio and resonance at the design frequency (28.5 MHz) at element spacings from 0.05 wl to 0.2 wl.
</center>
<p><b>Fig. 2-2</b> graphs the gain and front-to-back ratio data as a convenient way to examine the trends. Within the limitations of the increments of element spacing used here, the gain and the front-to-back ratio reach their peak values with an element spacing of 0.075 wl. As we shall see, there are two good reasons why we rarely, if ever, design 2-element reflector-driver Yagis with this particular spacing. One of those reason is the low source impedance: just above 15 Ohms. The other reason is the narrowness of the operating bandwidth at this spacing, a facet of 2-element Yagi design that we shall examine more thoroughly in a moment.</p>
<p>The low level of the front-to-back ratio of the reflector-driver design has struck many antenna enthusiasts and has occasioned two responses. One is the design of 3-element and larger Yagis. The second is the design of arrays that feed both elements. The front-to-back ratio with an element spacing of 0.125 wl is about 11.18 dB. We can increase this level to about 11.50 dB largely by shortening the driver and thereby changing the mutual coupling between the elements. However, in the process, the gain begins to decrease, and the source impedance reaches a value of about 30 - j 52 Ohms. Hence, draining the reflector-driver design of the last modicum of front-to-back ratio tends to result in relatively impractical source impedance values.</p>
<pre> Actual vs. Ideal Rear Element Relative Current Magnitude and Phase Angle
2-Element Reflector-Driver Yagis
Actual Ideal
Element Relative Relative Relative Relative Gain
Spacing wl I Mag. I Phase I Mag. I Phase dBi
0.05 0.833 165.1 0.963 163.1 6.51
0.75 0.774 158.1 0.953 154.1 6.51
0.1 0.719 150.7 0.944 144.9 6.44
0.125 0.670 143.1 0.938 135.6 6.33
0.15 0.636 136.5 0.938 126.1 6.18
0.175 0.603 129.3 0.936 116.6 6.00
0.2 0.576 122.4 0.937 107.1 5.77
Note: all phase angles adjusted for positive values. For negative angle values
corresponding to those in Part 1, subtract 180 from the listed value. All "ideal
models" set to a 180-degree front-to-back ratio greater than 60 dB.
Table 2. Actual vs. ideal rear element relative current magnitude and phase
angle values for maximum 180-degree front-to-back ratios for 2-element reflector-
driver Yagis in Table 1.</pre>
<pre> Bandwidth Characteristics for 2-Element Reflector-Driver Yagis
At 0.1, 0.125, and 0.15 WL Element Spacing
Element Spacing: 0.1 wl
Frequency Gain Front-to-Back Feedpoint Z SWR Relative
MHz dBi Ratio dB R +/- j X Ohms to 24.3 Ohms
28.0 6.84 9.53 16.3 - j 23.1 3.20
28.25 6.58 10.94 20.2 - j 11.3 1.71
28.5 6.32 11.33 24.3 - j 0.1 1.01
28.75 6.07 11.01 28.4 + j 10.4 1.53
29.0 5.86 10.41 20.5 + j 20.5 2.16
Element Spacing: 0.125 wl
Frequency Gain Front-to-Back Feedpoint Z SWR Relative
MHz dBi Ratio dB R +/- j X Ohms to 33.8 Ohms
28.0 6.72 9.92 24.7 - j 21.4 2.19
28.25 6.48 10.91 29.3 - j 10.3 1.43
28.5 6.25 11.18 33.8 + j 0.0 1.00
28.75 6.04 10.94 38.1 + j 9.8 1.35
29.0 5.85 10.45 42.3 + j 19.2 1.73
Element Spacing: 0.15 wl
Frequency Gain Front-to-Back Feedpoint Z SWR Relative
MHz dBi Ratio dB R +/- j X Ohms to 33.8 Ohms
28.0 6.61 9.89 33.3 - j 20.0 1.78
28.25 6.39 10.71 38.1 - j 9.7 1.31
28.5 6.18 10.96 42.9 - j 0.1 1.00
28.75 5.98 10.80 47.4 + j 9.0 1.25
29.0 5.80 10.41 51.7 + j 17.7 1.52
Table 3. Bandwidth characteristics for 2-element reflector-driver Yagis at 0.1,
0.125, and 0.15 wl element spacing.</pre>
<p><b>Table 2</b> reveals the reason for the low levels of front-to-back ratio associated with reflector-driver Yagi designs. The table lists the modeled rear-element relative current magnitude and phase angle values, along with the values needed for the same set of elements to achieve more than 60 dB front-to-back ratio. (The ideal front-to-back ratio models show the same deep 180-degree null as those in Part 1, along with the rearward side lobes that result in worst-cast front-to-back ratios between 17 and 22 dB.) The gain of the models using two sources appear in the right-most column. The ideal phase angles have been converted from the negative angles typical of models in Part 1 to values that correspond to those yielded by models of Yagis. To convert either value to more suited to phasing networks, simply subtract 180 degrees from the listed value.</p>
<p>In concert with the curves that we saw in <b>Fig. 2-2</b>, the relative current magnitude and the phase angle of the optimized Yagi both depart more radically from the ideal numbers with the widening of the spacing between elements. Coincidence is closest at the narrowest spacings. However, the narrower the spacing between elements, the more exact the coincidence must be to yield the ideal maximum front-to-back value of more than 60 dB. Hence, the closeness of the values at a spacing of 0.05 wl is still not close enough to yield the highest front-to-back ratio. As well, the ideal model shows its highest gain at the narrowest spacing, although the Yagi does reach maximum gain until the spacing is 0.075 wl. Interestingly, the ideal models have a higher gain potential only until the spacing reaches 0.15 wl, after which the Yagi shows slightly higher gain.</p>
<pre> 2-Element Driver-Director Performance
Set for Maximum 180-Degree Front-to-Back Ratio and Resonance
Element Driver Director Gain Front-to-Back Feedpoint Z
Spacing wl Length wl Length wl dBi Ratio dB R +/- jX Ohms
0.05 0.2498 0.2378 6.48 26.03 11.0 - j 0.0
0.075 0.2486 0.2335 6.52 23.60 21.1 + j 0.2
0.1 0.2465 0.2298 6.44 14.85 29.7 + j 0.2
0.125 0.2443 0.2263 6.22 10.66 36.6 + j 0.1
0.15 0.2423 0.2234 5.98 7.94 41.2 + j 0.2
0.175 0.2407 0.2202 5.62 5.96 45.9 + j 0.1
0.2 0.2395 0.2170 5.23 4.45 50.0 + j 0.2
Note: All elements 0.5" (0.001207 wl) aluminum
Table 4. 2-element driver-director Yagi performance when set for maximum 180-
degree front-to-back ratio and driver resonance.</pre>
<p>If we shift to driver-director models of parasitic arrays, we do not get the same picture of results. <b>Table 4</b> lists the element lengths and the basic performance figures for the driver-director configuration. Unlike the reflector-driver dimensions, the driver-director element lengths continuously decrease with increased spacing between elements.</p>
<center>
<img src="ph2-3.gif" width="723" height="544" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 2-3. Gain and 180-degree front-to-back ratio of driver-director 2-element Yagis set for maximum front-to-back ratio and resonance at the design frequency (28.5 MHz) at element spacings from 0.05 wl to 0.2 wl.
</center>
<p>The table also confirms the general proposition that a driver-director array develops a significant gain and front-to-back superiority over the reflector-driver array when the spacing is fairly narrow--under 0.1 wl. <b>Fig. 2-3</b> tracks the gain and front-to-back ratio values. Above 0.1 wl element spacing, the front-to-back ratio drops rapidly to the reflector model values and below. The gain values start their drop above 0.75-wl spacing. Since the 21-Ohms impedance of the 0.075-wl model is manageable with a matching network, this element spacing region is among the most popular for driver-director arrays.</p>
<p>The flatted curve between 0.05-wl and 0.075-wl element spacing hides a surprise for those not familiar with Jerry Hall's study. The slope of the curve beyond the 0.075-wl mark suggests that in the lowest region of spacing, there is a peak in the front-to-back value. In fact, at a spacing of 0.0625 wl, the front-to-back ratio can reach nearly 47 dB with a free-space gain of 6.52 dBi and a source impedance of about 16.5 + j 7.9 Ohms. Such an array also comes closest to meeting the ideal conditions for maximum front-to-back ratio, with a relative magnitude of 0.964 and a phase angle (adjusted) of 158.6 degrees (or -21.4 degrees). For single-frequency use, such an array might well fill a need.</p>
<pre> Actual vs. Ideal Rear Element Relative Current Magnitude and Phase Angle
2-Element Driver-Director Yagis
Actual Ideal
Element Relative Relative Relative Relative Gain
Spacing wl I Mag. I Phase I Mag. I Phase dBi
0.05 0.934 162.8 0.961 163.1 6.51
0.75 1.006 149.5 0.951 154.1 6.51
0.1 1.140 149.7 0.948 144.9 6.43
0.125 1.333 146.1 0.943 135.5 6.31
0.15 1.555 145.6 0.939 126.1 6.16
0.175 1.845 145.8 0.926 116.7 5.96
0.2 2.188 147.3 0.910 107.3 5.72
Note: all phase angles adjusted for positive values. For negative angle values
corresponding to those in Part 1, subtract 180 from the listed value. In
addition, actual angles are taken from the director and appear as negative angles
relative to the driver to the rear. The relative current magnitude values have
been adjusted to reflect the values on the rear element if the forward element
is set at 1.0. All "ideal models" set to a 180-degree front-to-back ratio
greater than 60 dB.
Table 5. Actual vs. ideal rear element relative current magnitude and phase
angle values for maximum 180-degree front-to-back ratios for 2-element driver-
director Yagis in Table 3.</pre>
<pre> Bandwidth Characteristics for 2-Element Driver-Director Yagis
At 0.075, 0.1, and 0.125 WL Element Spacing
Element Spacing: 0.075 wl
Frequency Gain Front-to-Back Feedpoint Z SWR Relative
MHz dBi Ratio dB R +/- j X Ohms to 21.1 Ohms
28.0 5.59 12.31 33.0 - j 21.6 2.47
28.25 6.03 16.75 27.0 - j 11.6 1.72
28.5 6.52 23.60 21.1 + j 0.2 1.01
28.75 7.00 15.47 15.7 + j 13.9 2.22
29.0 7.30 8.87 11.6 + j 29.2 5.66
Element Spacing: 0.1 wl
Frequency Gain Front-to-Back Feedpoint Z SWR Relative
MHz dBi Ratio dB R +/- j X Ohms to 29.7 Ohms
28.0 5.64 11.39 39.2 - j 19.5 1.87
28.25 6.03 13.54 34.7 - j 10.3 1.43
28.5 6.44 14.85 29.7 + j 0.2 1.01
28.75 6.84 12.96 24.6 + j 12.4 1.63
29.0 7.15 9.28 20.1 + j 26.4 2.98
Element Spacing: 0.125 wl
Frequency Gain Front-to-Back Feedpoint Z SWR Relative
MHz dBi Ratio dB R +/- j X Ohms to 36.6 Ohms
28.0 5.55 9.35 43.2 - j 18.7 1.64
28.25 5.87 10.24 40.2 - j 9.8 1.31
28.5 6.22 10.66 36.6 - j 0.1 1.00
28.75 6.56 10.05 32.7 + j 11.1 1.40
29.0 6.84 8.36 28.8 + j 23.7 2.11
Table 6. Bandwidth characteristics for 2-element driver-director Yagis at 0.075,
0.1, and 0.125 wl element spacing.</pre>
<p><b>Table 5</b> provides data comparing the modeled relative current magnitude and phase angle for the unfed element. The data has been adjusted to coincide in form with other data that we have examined. The negative phase angles of the director have been made positive, as if the forward element had a value of 0.0 degrees. As well, the current magnitude has been adjusted as if the director had a value of 1.0. This set of adjustments allows the ideal data to correspond with all other dual-source models we have so far examined, where all forward elements are set to a magnitude of 1.0 and a phase angle of 0.0 degrees, and the rear element values are presented for comparison. In concert with the curves of <b>Fig. 2-3</b>, <b>Table 5</b> makes evident the rapid departure from ideal phasing conditions for maximum front-to-back ratio above 0.075-wl element spacing. Equally evident, in comparison with the data for the reflector-driver Yagi, is the relative uselessness of the driver-director array as a directional beam able about 0.1-wl element spacing.</p>
<center>
<img src="ph2-4.gif" width="724" height="544" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 2-4. Resonance impedance of reflector-driver and driver-director 2-element Yagis at element spacings from 0.05 wl to 0.2 wl.
</center>
<p>Despite the radical differences in gain and front-to-back behavior between reflector-driver and driver-director Yagis, the resonant impedances of the two arrays do not differ greatly for any given element spacing. <b>Fig. 2-4</b> tracks the source resistance of the two array designs as optimized for each element spacing increments. An interesting property of reflector-driver designs is that the impedance curve is nearly linear, in contrast to the curve for the driver-director array.</p>
<center>
<img src="ph2-5.gif" width="725" height="544" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 2-5. SWR curves of reflector-driver 2-element Yagis set for maximum front-to-back ratio and resonance at the design frequency (28.5 MHz) at element spacings from 0.1 wl to 0.15 wl.
</center>
<p>In our exploration of the two types of parasitic arrays, we overlooked <b>Table 3</b> and <b>Table 6</b>. These tables present modeled performance figures for each array at 3 increments of element spacing from 28.0 to 29.0 MHz. For each array, the most common element spacings are listed: 0.1 through 0.15 wl for the reflector-driver array and 0.75 through 0.125 wl for the driver-director Yagi. As expected, operating bandwidth increases with increased element spacing. The reflector-driver Yagi, shown in <b>Fig. 2-5</b>, can be adjusted to cover the entire 1-MHz bandwidth by selecting a design frequency of about 28.35 rather than the 28.5-MHz figure used in this study. At a slightly wider element spacing of 0.15 wl, the 2-element reflector-driver design can be designed to cover all of the 10-meter band. At each level of element spacing, the gain and the front-to-back values tend to show the same sort of curve broadening with each increase in spacing, although the peak values decrease along the way.</p>
<center>
<img src="ph2-6.gif" width="722" height="543" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 2-6. SWR curves of driver-director 2-element Yagis set for maximum front- to-back ratio and resonance at the design frequency (28.5 MHz) at element spacings from 0.075 wl to 0.125 wl.
</center>
<p>The driver-director Yagi SWR curves, shown in <b>Fig. 2-6</b>, are naturally steeper, given the narrower element spacings involved. The most notable feature of the SWR graph is it reversal from the one for the reflector-driver array: here, more rapid increases occur above the design frequency rather than below it. Likewise, gain increases with rising frequency (rather than with decreasing frequency in the case of the reflector-driver array). The source impedance of the driver-director array shows an increasing reactance with frequency in accord with the relative shortening of the element. However, the resistive component of the impedance decreases with rising frequency (in contrast to the resistance curve of the reflector-driver Yagi). At the spacing increments generally used in driver-director designs, narrow bandwidth is a condition of maximizing performance.</p>
<p>Understanding basic 2-element Yagi-Uda performance is a necessary condition of understanding the urge to design phased arrays in which both elements are fed. In principle, the dual source phased array is capable of higher gain and better front-to-back performance than all but the most closely spaced parasitic arrays. The reason is simple: the wider the spacing of a parasitic array, the further the elements get from relatively ideal conditions of element current magnitude and phase angle.</p>
<h3>Alternative Geometries</h3>Although we have omitted many details of 2-element Yagi behavior (relative to the more complete data in some areas on interest that appear in Jerry Hall's study), we would be remiss if we did not acknowledge design efforts to overcome some of the phasing failings of 2-element parasitic arrays using linear parallel elements. Let's look in detail at only one of those efforts to use an alternative geometry: the Moxon rectangle. <b>Fig. 2-7</b> shows the basic outline of this antenna that owes its origin largely due to the initial efforts of G6XN.
<center>
<img src="ph2-7.gif" width="316" height="219" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 2-7. An alternative geometry array with parallel and end coupling: the Moxon rectangle.
</center>
<p>The Moxon rectangle owes its operating characteristics to not one, but two forms of inter-element coupling. Between the parallel portions of the elements, we encounter the same sort of mutual coupling that is almost the sole source of coupling within a standard Yagi design. However, by bending the elements toward each other, we obtain an added form of coupling, often called capacitive coupling between the element ends. The result is a broader beamwidth and an increase in the front-to-back ratio. By judicious control of the element diameter, the gap between element tails, and the other dimensions of the array, we may obtain a broad-band reflector-driver array.</p>
<center>
<img src="ph2-8.gif" width="725" height="545" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 2-8. Gain and 180-degree front-to-back ratio of a Moxon rectangle from 28.0 to 29.0 MHz (design frequency: 28.35 MHz).
</center>
<p><b>Fig. 2-8</b> shows the free-space gain and front-to-back curve for a typical Moxon rectangle designed for 28.35 MHz using 0.5" aluminum elements. The design frequency is necessary, since reflector-driver arrays decrease their front-to-back ratio and increase their SWR more slowly above the design frequency than below it. The resulting array covers the first MHz of 10 meters. The gain decreases nearly linearly across the passband, while the front-to-back ratio peaks just below the 28.4-MHz mark on the graph. <b>Fig. 2-9</b> shows the 50-Ohm SWR curve for the design.</p>
<center>
<img src="ph2-9.gif" width="723" height="544" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 2-9. 50-Ohm SWR curve of a Moxon rectangle from 28.0 to 29.0 MHz (design frequency: 28.35 MHz).
</center>
<p>Since Moxon rectangle designs using a variety of element materials and design frequencies are now common in antenna literature, we may turn our attention to <b>Table 7</b>. This table summarizes the performance data shown in the graph. In addition, it provides values for the rear element relative current magnitude and phase angle. At the design frequency, the parallel portions of the elements are about 0.133 wl apart. At that spacing, an ideal phase angle would be about 132.5 degrees (or -47.5 degrees). The rear element relative current magnitude would be close to 0.94. Compare these values to the ones in the table for 28.2 (0.967 and 134.1 degrees) and 28.4 MHz (0.943 and 128.0 degrees). Little wonder that the Moxon rectangle achieves a maximum front-to-back ratio of well over 30 dB at its design frequency.</p>
<pre> Bandwidth Characteristics for 2-Element Moxon Rectangle
Frequency Gain Front-Back Feedpoint Z 50-Ohm Refl. Refl.
MHz dBi Ratio dB R +/- j X Ohms SWR I Mag. I Phase
28.0 6.36 17.79 39.2 - j 15.7 1.53 0.980 140.1
28.2 6.16 25.95 46.3 - j 8.3 1.21 0.967 134.1
28.4 5.95 34.12 53.2 - j 2.2 1.08 0.943 128.0
28.6 5.75 22.21 59.3 + j 2.9 1.20 0.911 122.5
28.8 5.57 17.81 64.6 + j 7.3 1.33 0.874 117.6
29.0 5.40 15.20 69.2 + j 11.4 1.46 0.835 113.2
Note: Aluminum element diameter: 0.5" (0.001207 wl)
Table 7. Bandwidth characteristics for 2-element Moxon rectangle, with modeled
rear element relative current magnitudes and phase angles.</pre>
<p>The cost for this improved front-to-back figure is a decrease in gain, partly resulting from the increased beamwidth relative to a standard Yagi design. Since the bent portions of the elements still have significant current levels near the array corners, their contribution to gain becomes a contribution to beamwidth. Hence, the Moxon rectangle has an average free-space gain of about 6.0 dBi, somewhat below the levels of the optimized Yagis and of the idealized phased arrays that we examined in Part 1.</p>
<center>
<img src="ph2-10.gif" width="448" height="342" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 2-10. Some alternative 2-element parasitic array geometries.
</center>
<p>The Moxon rectangle is not the only attempt to alter geometry to improve performance over parallel-element Yagis. <b>Fig. 2-10</b> shows some of the other arrangements tried with greater or lesser success. The VK2ABQ square was a forerunner of the Moxon rectangle. The diamond lends itself to inexpensive construction with a single non-conductive support for wire element ends. The hex and folded-X have been popular from time to time as near-ultimate compact but full size designs. An interesting study, but beyond the scope of these notes, would be to investigate the relative current magnitude and phase on the unfed element in each design, noting that the most common implementation of the folded X-beam is as a driver-director array. The others are all reflector-driver arrays.</p>
<h3>Conclusions</h3>Our goal has been to track the performance potential of parasitic arrays with only a single fed element with an eye toward understanding the limitations of using geometry alone to set the relative current magnitude and phase angle conditions between the elements. Both reflector-driver and driver-director Yagis show very serious limitations in this regard, except for very closely spaced driver-director models that are impractical for most (but not all) amateur applications. Alternative geometries, such as the Moxon rectangle, are able to overcome the problem of achieving high front-to-back ratio values by using multiple element coupling methods. However, they cannot achieve the higher gain levels (by about 0.5 dB or so) attained in principle by some ideal and compromise phased array designs.
<p>The key to 2-element Yagi design shortcomings is also the key to 2-element horizontal phased array success. Can we find a practical way to implement a 2-element phased array with both elements fed to arrive at desired gain, front-to-back ratio, and bandwidth values? In the next episode, we shall begin our exploration by reviewing the ZL-Special and its variants, all of which make use of what seems in principle to be the simplest phasing mechanism possible: a single phasing line that connects the two elements. More complex systems, such as the HB9CV and the N7CL systems do exist, but basic principles of phasing are often best explored by keeping the number of design variables to a minimum. The more complex systems will have their turn in Part 4.</p>
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<p><i>Updated 01-12-2002. &COPY; L. B. Cebik, W4RNL. This item originally appeared in</i> The National Contest Journal <i>(Jan/Feb, 2002). 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/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"> Some Notes on Two-Element Horizontal Phased Arrays<br>
Part 3: The Limits of a Single Phase Line: The ZL-Special</h1>
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<h3>L. B. Cebik, W4RNL</h3>
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<p>When George Pritchard (ZL3MH, later ZL2OQ) introduced the amateur community to the 2-element phased array, it seemed to offer magic in the form of performance up to 7 dBd (9+ dBi free-space equivalent) and up to 40 dB front-to-back ratio. Unfortunately, the comparators of the day were relatively primitive 2- and 3-element Yagis that rarely performed up to their theoretical possibility. Nonetheless, the antenna type acquired the name "ZL-Special" and has been the subject of performance debate ever since. For a reasonably complete bibliography of ZL-Special articles in English, see my "Modeling and Understanding Small Beams: <a href="../mu/mu5a.html">Part 5: The ZL Special</a>," <i>Communications Quarterly</i>, (Winter, 1997), 72-90.</p>
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Fig. 3-1. Outline sketches of several classic ZL-Special designs.
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<p><b>Fig. 1</b> shows several of the variations on the ZL-Special theme. Some of them work; others do not--or at least not very well. Virtually all early work on horizontal phased arrays presumed that we needed only attend to the impedance transformation along a transmission line. Hence, with 1/8 WL spacing and a similar transmission line, a half twist would yield a 135&deg; phase shift with the accompanying high gain forward lobe and a deep rear null. <b>Fig. 1</b> shows both linear and folded elements, along with the most popular phase line characteristic impedances. The trombone attempted to overcome the velocity factor of the common TV twinlead line (about 0.8) by making wide-spaced folded elements that were physically 1/8 WL at their outer edges but electrically 1/8 WL apart relative to the phase line. Although the trombone works quite well, the structure is completely unnecessary: simple folded dipoles would work as well.</p>
<p>Not until Roy Lewallen, W7EL, pointed out the fundamental error in amateur conceptions of the ZL-Special did we begin to re-analyze the 2-element horizontal phased array with some precision. (See Lewallen, "<a href="https://www.eznec.com/Amateur/Articles/Field_Day_Special.pdf" target="_blank">Try the 'FD Special' Antenna</a>," <i>QST</i> (June, 1984), 21-24.) What controls the performance of the ZL-Special phase line is not so much the impedance transformation, but the current transformation (in terms of both current magnitude and phase angle). The current and the impedance do not change at the same rate except when the line is exactly matched to the element that forms its load. Hence, we had to take a wholly new approach to the single-line phased array. In these notes, we shall follow this lead.</p>
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<h3>ZL-Special Basics</h3>
</center><b>Fig. 2</b> shows the deceptively simple elements of a ZL-Special. The two elements bear "forward" and "rear" element labels, where the forward element indicates two things. First, the main forward lobe is in the direction of the forward lobe. Second, the standard ZL-Special feedpoint is at the junction of the phase line and the forward element.
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Fig. 3-2. The basic elements of a ZL-Special 2-element horizontal phased array.
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<p>Most radio amateurs do not fully appreciate how many variables are at work in this seemingly simple arrangement. First, the individual elements exhibit center-point impedances that are functions of the mutual coupling between them. The mutual coupling depends upon the element diameters, lengths, and spacing between them. Second, the feedline meets a parallel current division at the forward junction, which requires that all other variables result in the same voltage at the junction. The requisite voltage is a function of the source impedance of the forward element and the "share" of current received by that element.</p>
<p>Third, the rear element impedance at its center sets both a current magnitude and phase angle and a voltage magnitude and phase angle, both of which undergo transformation down the selected length of phase line. From Terman, <i>Radio Engineers' Handbook</i> (McGraw-Hill: 1943), p. 185, we have equations for the current and the voltage at any point down a transmission line from a load or antenna element. The following equations are for lossless lines, which is satisfactory for the short phasing lines used in 2-element horizontal phased arrays and which also coincides with the calculations within the TL facility of NEC-2 and NEC-4:</p>
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<p>The meaning of the terms is as follows:</p>
<ul>
<li>Er is the voltage at the load or antenna end of the line,</li>
<li>Es is the voltage at the source end of the line,</li>
<li>Ir is the current at the load or antenna end of the line,</li>
<li>Is is the current at the source end of the line,</li>
<li>Zo is the characteristic impedance of the line, and</li>
<li>(2PI (l/WL)) is an expression for the electrical length of the line of the line in degrees for the frequency of interest.</li>
</ul>
<p>Because both the voltage and the current have an associated phase angle and resolve into real and imaginary components, the use of these equations in calculations is more complex that the initial appearance of them. Some of the math involved appears in the earlier note <i>Communications Quarterly</i> article. However, such calculations are available within NEC in the TL facility and are also available in the <a href="../radio.html#HAMCALC">HAMCALC</a> suite of GW Basic utility programs from VE3ERP.</p>
<p>Critical to our understanding of is the fact that the resultant values of voltage and current (magnitude and phase) at the forward end of the phase line are interactive, as the basic equations make evident. Achieving a current level that balances with the portion of source current used by the forward element at a common voltage such that the rear element then has a current magnitude and phase angle to yield a desirable pattern requires juggling all of the variables into a usable collection.</p>
<p>Even if we arrive at a usable collection of values, we have several other variables to consider. First, the calculated characteristic impedance of the phase line must be one that we can acquire or build. Second, the requisite physical length of the phase line (accounting for the line's velocity factor) for the current transformation must be at least the space between the elements. As well, it should not be too much longer than that spacing in light of practical considerations for supporting the line. Since the line will be open--whether we use coax or parallel line for the task--we must isolate it from disturbances that a metallic boom might create. Designing a ZL-Special, then, requires either careful analysis or some very lucky guesses.</p>
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<h3>A Design Example</h3>
</center>Let's analyze a single design for 28.5 MHz to see if we can make the picture clearer. We shall begin with 2 elements. Both will be our standard 0.5" (0.001207 WL) aluminum elements. The forward element will be 0.465 WL long, while the rear element is 0.506 WL long. The spacing will be 0.125 WL. However, from Part 1 of this series, we should now understand that the selected spacing is somewhat arbitrary, since for any element spacing, we may find element lengths that result in a desired phased array pattern.
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Fig. 3-3. Design steps for a ZL-Special used for array analysis.
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<p><b>Fig. 3</b> shows the 4 steps in our analysis, and the results appear in <b>Table 1</b>. If we arrange the elements individually in a NEC model and feed them independently with current sources, then the feed values in the table's step 1 under the relative current columns will result in the relative voltage and the individual element impedances. The models follow the system used in Part 1 of reversing the direction of the rear element relative to the forward element so that any phase line that we add can be in normal orientation. Notable is the similarity of the element impedances, a useful condition (but not the only such condition) for successful ZL- Special design. The tables in Part 1 show in a general way what conditions must exist for us to achieve such similar impedances: the relative longer length of the rear element when both elements are longer than a self-resonant dipole at the frequency of interest is a promising combination at the 1/8-WL spacing. As <b>Fig. 4</b> shows, we have not striven for the highest gain or front-to-back value, but simply for highly usable values.</p>
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Fig. 3-4. Free-space azimuth pattern of the sample ZL-Special at 28.5 MHz.
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<p>The second step in our analysis creates a model with a transmission line attached to the rear element, but with its forward end brought to a source wire independent of the forward element. The selected line--from calculations, is RG-83, 35-Ohms coax with a velocity factor of 0.66. The required length is 0.13 WL physically or 0.197 WL electrically. This length of the chosen line yields the correct relative rear element current magnitude and phase angle. At the same time, it yields the required forward-end voltage magnitude and phase angle to match the value for the forward element. Note that the required forward line end current is 0.664 (relative to a forward element value of 1.0) with a phase angle of 44.25&deg;.</p>
<p>Step 3 in the analysis requires that we connect the forward end of the phase line and the forward element center to create a single feedpoint for the array. Under these conditions, supplying the feedpoint with a current of 1.0 at 0.0&deg; phase angle, we obtain the relative element current levels and phase angles shown. The forward element phase angle is a function of the reactance at its center. However, the net phase angle difference between elements is still - 44.18&deg;. At this stage, we have a complete array that we can frequency sweep from 28.0 to 29.0 MHz. <b>Fig. 5</b> shows the results. The gain shows a nearly linear curve upward, with a total change of about 0.9 dB. The front-to-back ratio remains above 20 dB from the lower band edge to above 28.8 MHz and is at all points superior to the front-to-back ratio of a common reflector- driver Yagi by 5 dB minimum. However, as Table 1 shows, the source impedance is just above 20 Ohms.</p>
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Fig.3-5. Gain and 180&deg; front-to-back ratio of the sample ZL-Special from 28.0 to 29.0 MHz.
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<p>The final step in our design is to add a matching system to raise the impedance to something compatible with common 50-Ohms coaxial cable. The low source impedance reactance suggest a matching section. A 0.13-WL section of the same 35-Ohms cable (RG-83) used for the phase line functions as a near-1/4-WL section to achieve the goal. With this section in place, we achieve the 50-Ohms SWR curve shown in <b>Fig. 6</b>. One might select other lengths for the matching line to better center the SWR curve, but the values shown would be in most cases quite satisfactory. For reference, <b>Fig. 7</b> shows the array patterns at 28.1 and 28.9 MHz to confirm that the patterns are usable and to show the evolution of the rear lobes as we increase frequency.</p>
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Fig. 3-6. 50-Ohm SWR curve of the sample ZL-Special from 28.0 to 29.0 MHz.
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Fig. 3-7. Free-space azimuth patterns of the sample ZL-Special at 28.1 and 28.9 MHz.
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<p>The design explored here has attempted to show the required alignment of the many variables involved in ZL-Special design. It is not the only design that will work, but it shares many characteristic with successful ZL-Specials. Most significant is the required low characteristic impedance of the phase line, calling for a coaxial cable. Such lines are vulnerable to external disruption from near-metallic contact, so a non-conductive boom is desirable without resorting to complex phase line support construction.</p>
<pre> Sample ZL-Special Analysis Data
The following data come from NEC-2/NEC-4 models of a 2-element horizontal phased array for
28.5 MHz using 0.5" aluminum elements. The rear element is 0.506 WL long, while the forward
element is 0.465 WL long. The modeling environment is free space. In all cases, the free-space
gain is 6.34 dBi, and the 180&deg; front-to-back ratio is 30.15 dB.
Step 1. Independent elements, independent sources:
Element Rel. I Rel. I Rel. V Rel. V Impedance
magnitude phase angle magnitude phase angle R +/- J X Ohms
Rear 0.8935 -44.18&deg; 26.24 -23.58&deg; 27.49 + j 10.34
Forward 1.0 0.0&deg; 33.53 31.94&deg; 28.46 + j 17.76
Step 2. Independent elements, independent sources, phase line installed:
Element Rel. I Rel. I Rel. V Rel. V Impedance
Magnitude phase angle Magnitude phase angle R +/- J X Ohms
Rear 0.8935 -44.15&deg; --- --- 27.49 + j 10.34
Phaseline 0.664 44.25 33.56 32.02&deg; 49.74 - j 8.98
Forward 1.0 0.0&deg; 33.51 31.96&deg; 28.43 + j 17.73
Step 3. Phase line connected to forward element, single source
Element Rel. I Rel. I Rel. V Rel. V Impedance
Magnitude phase angle Magnitude phase angle R +/- J X Ohms
Rear 0.5734 -60.80&deg; --- ---
Forward 0.6418 -16.62&deg; --- ---
Feedpoint 1.0 0.0&deg; 21.53 15.34&deg; 20.76 + j 5.70
Step 4. Matching section added:
Element Rel. I Rel. I Rel. V Rel. V Impedance
Magnitude phase angle Magnitude phase angle R +/- J X Ohms
Rear 0.9774 -133.7&deg; --- ---
Forward 1.0939 -89.48&deg; --- ---
Feedpoint 1.0 0.0&deg; 60.67 6.14&deg; 60.32 + j 6.49
Table 1. Sample ZL-Special analysis data from NEC models in the 4 steps of antenna analysis
demonstrated in the text.</pre>
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<h3>Folded-Dipole ZL-Specials</h3>
</center>The use of folded dipoles as ZL-Special elements arose to overcome to problems: cost and the need for low-impedance phasing lines. Early versions of such designs taped the elements to bamboo horizontal supports. In general, most of these designs simply set two TV- twinlead elements 1/8 WL apart with a section of TV twinlead as the phasing line. Element lengths were a matter of trial and error experimentation.
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Fig. 3-8. Basic outline of a W7EL Field-Day Special for 28.5 MHz.
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<p>W7EL's "Field-Day Special" rests on a different approach--an attempt to calculate the mutual impedance consequences of the elements, with the selection of element length, spacing, and line length designed to achieve the required current magnitude and phase angle transformation. <b>Fig. 8</b> shows the outline of a 10-meter version of the antenna that I have built. The line lengths indicated are for modeled versions using #18 wire at a 1" spacing (about 450 Ohms impedance as a transmission line and for #20 wire spaced 0.375" (about 300 Ohms as a transmission line. The longer length for the thinner wire, when taken individually and as a spaced 2-wire pair) is natural. The following notes are based on the 1"-spaced model. In both cases, using vinyl-covered wire shortens the physical element by 1-2% to account for the velocity factor of the insulation in antenna use.</p>
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3-9. Free-space azimuth patterns of the Field-Day Special at 28.1, 28.5, and 28.9 MHz.
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<p>Although the element spacing is 4.27' (0.1237 WL), the phase line is 4.9' (0.1420 WL) long, despite the 0.8 velocity factor of high-quality twinlead. Indeed, calculations suggest that a higher front-to-back ratio results from the use of 340-Ohms line. However, as <b>Fig. 9</b> shows in the free-space azimuth patterns across the first MHz of 10 meters, performance with a 300- Ohms line achieves similar levels to the first design that we explored. As well, with a 300-Ohms line, slightly better performance is possible by lengthening the forward element slightly, although the difference is unlikely to be noted in practical operation.</p>
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Fig. 3-10. Gain and 180&deg; front-to-back ratio of the Field-Day Special from 28.0 to 29.0 MHz.
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<p><b>Fig. 10</b> shows the gain and 180&deg; front-to-back curves for the model across the 28.0 to 29.0 MHz span. Typical of ZL-Special designs of any sort, the gain rises almost linearly, while the front-to-back ratio shows a broad peak centered a bit below the center of the design passband. <b>Fig. 11</b> provides figures on the resistance and reactance within the design passband. The resistance range is only about 7.5 Ohms. The reactance changes by a total of 56 Ohms. As Fig. 8 indicated, a pair of series capacitors, each with a reactance of -110 Ohms (about 50 pf at 28.5 MHz) would provide a very reasonable SWR curve across the passband.</p>
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Fig. 3-11. Source resistance and reactance of the Field-Day Special from 28.0 to 29.0 MHz.
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<p>The need for a compact portable antenna inspired the original design of the Field-Day Special. However, for our purposes, it serves additional functions. One is to illustrate that equal- length elements (each about 0.468 WL long) result in wide-band performance that is not significantly different from the use of unequal length elements in the first example. A second function is to show that folded dipole elements have no advantage or disadvantage relative to single elements in performance--although there may be differences in the physical convenience of one or another element type. Third, the elements have widely divergent impedances: forward Z 124 + j 84 Ohms; rear 80 - j 256 Ohms. Nevertheless, the right length of the right impedance phase line effects the correct current division at the feedpoint junction so that we arrive ar the correct current magnitude and phase angle on the rear element to achieve proper or acceptable phased performance.</p>
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<h3>A Dual-Line ZL-Special</h3>
</center>Before we leave the ZL-Special, let's examine a further variation on the general theme of phasing with a single transmission line section between the element. There is no rule that says that one must feed the system precisely at the junction with the forward element, even if tradition has imbedded this view in our minds. <b>Fig. 12</b> shows the general outline of a variant of our first ZL-Special study model.
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Fig. 3-12. Basic outline of the dual-line ZL-Special for 28.5 MHz.
</center>
<p>The design uses the same element lengths as our initial model. The forward element is 0.465 WL long and the rear element is 0.506 WL long. Both are 0.5" (0.001207 WL) diameter aluminum. The original design used a single phase line length of 0.13 WL of 35-Ohms 0.66 velocity factor line. Suppose that one cannot obtain the required RG-83, but has some RG-8X with a 50-Ohms impedance and a velocity factor of 0.78. The higher-impedance line at any length will not achieve in a single line the desired phasing for reasonable ZL-Special performance.</p>
<p>However, we may effect transformations of current magnitude and phase angle on both the forward and the rear elements by bringing lengths of transmission line from each element to a middle point. The length of line from the rear element is 0.13 WL. Although this length is physically similar to our original design, electrically, it is only 0.167 WL electrically, since the velocity factor of our new line is higher. A 0.015-WL line from the forward element is 0.192 WL electrically or about 0.52'. At the junction, given a source current of 1.0 at 0.0&deg;, we arrive at a relative current split of this dimensions: forward 0.950 at 4.35&deg; and rearward 0.458 at -2.1&deg;. The resulting current ratio of rear to forward elements is 0.811 at -44.8&deg;, close to the values for the original design.</p>
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Fig. 3-13. Free-space azimuth pattern of the dual-line ZL-Special at 28.1, 28.5, and 28.9 MHz.
</center>
<p><b>Fig. 13</b> shows the azimuth patterns across the 28-29 MHz span of the design passband. Only the front-to-back ratio suffers a bit relative to the more ideally phased original example, as shown in the gain and front-to-back curves in <b>Fig. 14</b>. A bit of element length adjustment might well have improved the numbers a bit, but would have altered the demonstration.</p>
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Fig. 3-14. Gain and 180&deg; front-to-back ratio of the dual-line ZL-Special from 28.0 to 29.0 MHz.
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<p>The natural impedance at 28.5 MHz for the new phase line arrangement is about 23.5 + j 13.1 Ohms. The low reactance suggests that a modified 1/4-WL line section might effect a match. 0.167 WL (electrical) of 35 to 37 Ohms line provides the broad 50-Ohms SWR curve shown in <b>Fig. 15</b>. The line might consist of either RG-83, or in the absence of such line, a parallel section of RG-59. In each case, the line velocity factor will determine the physical length.</p>
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Fig. 3-15. 50-Ohm SWR curve of the dual-line ZL-Special from 28.0 to 29.0 MHz.
</center>
<p>The design shown here is similar in principle to the one used to improve front-to-back performance of a 10-meter hilltopper 2-element Yagi. (See "Two Hilltoppers for 10 Meters," <i>The ARRL Antenna Compendium</i>, Vol. 6, pp. 1-9.) Like the single-line ZL-Special, the antenna requires a non-conductive boom to ensure that the phase-line remains clear of unwanted interactions.</p>
<center>
<h3>Tentative Conclusions</h3>
</center>We have examined the numerous variables that go into the design of a ZL-Special. The somewhat simplistic view of 2-element horizontal phased array design taken in the early years of ZL-Special building has given way to a more complete appreciation of the number of interactive variables involved, including the antenna dimensions and consequential mutual coupling. As well, the phasing work became more complex in terms of the current magnitude and phase angle transitions down a length of line having a given characteristic impedance so as simultaneously to provide each element with the correct relative current magnitude and phase angle and to effect a current division as the line junction or feedpoint that would result in those values.
<p>Many possible ZL-Special designs prove to be unfeasible. The requisite characteristic impedance of the phasing line may not exist and cannot be constructed. The required line length may be shorter than the distance between the elements, or it may be excessively long.</p>
<p>The key to successful ZL-Special design is to find a set of element lengths and a spacing that meets two conditions. First, the relative current magnitude and phase angle on the individual elements must provide a satisfactory pattern in terms of gain and front-to-back ratio. Second, the impedances of the elements under the first condition must permit the design of a phasing line (or pair of lines) that employs an available or achievable characteristic impedance and that allows the requisite current division and transformation. As we saw in Part 1, there is in principle not restriction upon element spacing within the range of 0.05 to 0.2 WL, although element spacing in the 0.1 to 0.13 WL range tends to yield the most easily achieved gain and operating bandwidth levels.</p>
<p>There is, in principle, no restriction upon the element lengths relative to the length of a resonant dipole at the design frequency. As well, there is no restriction upon the relative lengths of the elements: the forward element may be in principle shorter than, equal to, or longer than the rear element. Some combinations may be more favorable than others, although to date, there is no complete survey of all combinations.</p>
<p>Perhaps the major disadvantage of the ZL-Special phasing system lies in the need to use folded dipole elements with high-impedance phase lines or to use with single tubular elements a low-impedance line. Many, if not most, builders wish to use a metallic boom and hence to have a phase line that is not susceptible to unwanted interactions. The quest for a stable phasing system has led to some interesting variants of phasing schemes for the 2-element horizontal array. The early HB9CV system--still in use today--and the recent N7CL system are two approaches to the same end. If the elements and the desired phase line do not match, let's add matching networks. As we shall see in the next episode, a slight increase in electrical complexity can lead to significant simplifications in the physical design of 2-element horizontal phased arrays.</p>
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<p><i>Updated 03-14-2002. &COPY; L. B. Cebik, W4RNL. This item originally appeared in</i> The National Contest Journal <i>(Mar/Apr, 2002). 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="ph4.html"><img src="../images/fwdrd.gif" align="bottom" width="36" height="33"> Go to Part 4</a></p>
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<p class="topics-footer">Topics: <a href='../topics.html#hb9cv-zl-special'>HB9CV / ZL Special</a>, <a href='../topics.html#hf-upper'>HF Upper</a>, <a href='../topics.html#phased-array'>Phased Array</a></p><br>
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<title>Two-Element Horizontal Phased Arrays Part 4</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"> Some Notes on Two-Element Horizontal Phased Arrays<br>
Part 4: Removing the Limits of a Single Phase Line<br>
by Element Matching</h1>
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<h3>L. B. Cebik, W4RNL</h3>
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<p>The chief limitation of the ZL-Special form of a 2-element horizontal phased array has been mechanical: how to use single tubular elements with phase lines that are not susceptible to interaction with a metallic boom supporting the elements. Successful tubular-element ZL-Specials require low-impedance phase lines, while higher-impedance phase lines are more suited to folded-dipole elements.</p>
<p>Solutions to this problem have been available since R. Baumgartner, HB9CV, developed the array bearing his call in 1954. Interestingly, the HB9CV array has been exceptionally popular on the continent of Europe, but has met mostly silence in the English-speaking realm of amateur radio. Indeed, Rothammels <i>Antennenbuch</i> (now produced by DARC) devotes several sections to HB9CVs for various frequency ranges, and 1984 saw the production of a book devoted to the antenna (Fuchs-Collins, <i>HB9CV: Richtantenne mit allen Variationen</i> [Frech-Verlag, 1984]). This later book still insisted on favorably comparing the phased 2-element array to a 4-element Yagi.</p>
<p>Since the HB9CV's appearance, several other systems of overcoming the shortcomings of the ZL-Special have appeared. We shall sample only two of them: the recent N7CL phased array and a system of capacitively matching elements to the phase line. All three systems have a common thread. If the natural impedance of the rear element does not match well with a higher impedance phase line, we may alter the impedance of the element through the use of a matching system. The techniques that we shall examine vary chiefly in the means used to effect the match.</p>
<p>All of the variables that we examined in the case of the ZL-Special remain in effect. Element diameter and length, and the relative lengths of the two elements, determine the required relative current magnitudes and phase angles on the individual elements for a desired level of performance within the limits set in Part 1. However, instead of selecting the physical dimensions that will match the phase line we opt to use, we shall select dimensions that are appropriate for the application of a matching network to create the desired impedance on the rear element. We shall not ignore the forward element, since its dimensions must not only provide the desired rear element impedance when combined with that element, but as well, its impedance must allow the desired current division at the feedline junction and yield a feedpoint impedance that we can match to our most common feedlines.</p>
<center>
<h4>The HB9CV</h4>
</center>The original HB9CV design, shown at the top of <b>Fig. 4-1</b>, attempted to permit the use of 300-Ohm (or other parallel line available in the 1950s) with single tubular elements by the use of Tee or double gamma-match sections. A later version, shown in the lower part of the figure, varied the feedline system for use with 75-Ohm coaxial cable. By setting the gamma match in opposite directions on the two elements, the coax shield could connect to the element centers and to the boom. In fact, later versions of the HB9CV employed the boom as in of a pair of lines, with a small diameter line forming the partner. Since the smaller wire in a parallel line with different diameter wires general determines the line impedance, a single line could run from the rear element connection to the forward element connection and serve both as half the phase line and as the gamma section. Although the feedpoint is shown at the forward element of the illustrated versions of the HB9CV, various feedpoints between that point and the mid-point between elements are used.
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Fig. 4-1. General outlines of 2 versions of the HB9CV array.
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<p>HB9CV specified certain dimensions for the antenna. The rear element should be 0.5 wavelength long, and the forward element should be 0.46 wavelength long, if the element diameter is between 0.004 and 0.007 wavelength in diameter. At ten meters, 0.004 wavelength is well over 1.5", which is larger than most builders would use. Therefore, adjustments are natural to HB9CV design. As well, HB9CV also specified the lengths and spacing of the gamma sections for both the Tee and gamma versions. Once more, these dimensions will vary with the actual materials used in construction.</p>
<p>Although not fully appreciated by some antenna modelers, the HB9CV antenna is somewhat difficult to model physically. Since the gamma sections will have a different diameter than the elements, we encounter angular junctions of dissimilar diameter wires in NEC-2 and NEC-4 models, and this situation tends to yield inaccurate results. MININEC models do not suffer this problem, but require very high segmentation densities, since the wires of the antenna structure create so many sharp angles. As well, the gamma match section are closely spaced to the elements and may need a version of MININEC having a close-wire correction factor. I have created models of the HB9CV with unreasonably high gain reports (&gt;8.1 dBi free-space gain) by violating some of the limitations of the modeling system.</p>
<p>However, the HB9CV antenna can be modeled in principle within NEC-2 or NEC-4 by using a constant diameter wire size for both the elements and the gamma sections, adequate segmentation, and a TL phase line. In these notes, I shall examine the modeled results of both Tee and gamma versions of the HB9CV that use 1" diameter materials throughout. The forward element is 0.46 wavelength long, while the rear element is 0.508 wavelength long, with an element spacing of 0.125 wavelength. The gamma sections are spaced 0.0096 wavelength from the main element with lengths adjusted as follows: The Tees are 0.125 wavelength long, while the one-sided gammas are 0.053 wavelength long. The results do not report directly on the performance of the original designs or any specific variation of them, but they do indicate a set of reasonable expectations for performance.</p>
<p>These modeled dimensions vary from the original design chiefly in the spacing and length of the Tee and gamma sections. The revised model spacing is to avoid potential NEC inaccuracies of closely spaced wires of different lengths. However, the sections are only crucial to performance in setting the impedance of the elements, as seen by the phase line, at a desired level. As long as the element obtain the required relative current magnitudes and phase angles for a desired performance level, one may use any gamma diameter and length that will produce it.</p>
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Fig. 4-2. Gain and 180-degree front-to-back ratio of the sample HB9CV arrays from 28.0 to 29.0 MHz.
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<p><b>Fig. 4-2</b> shows the modeled free-space gain and front-to-back performance of the Tee and gamma models. The Tee uses a 300-Ohm phase line, while the gamma uses a 75-Ohms line. As with all of the models in this series, these models do not necessarily indicate the peak performance of which an array is capable. They only serve to illustrate the principles of the array designs. Hence, the relatively low gain figures for the gamma-HB9CV might well increase with further optimization.</p>
<p>More interesting than the precise numbers for the reported gain is the difference in the gain curves for the two types of HB9CVs. The gamma version shows the nearly linear increase in gain with frequency to which we have grown accustomed from our ZL-Special efforts. However, the balanced Tee-HB9CV shows an almost perfectly flat gain across the first MHz of 10 meters. Independent element versions of the modeled design show the rear element, with its matching section, to have an impedance of about 250 Ohms with almost no reactance, a good match for the phase line. The single-sided gamma version does not show the same closeness of match with its 75-Ohms line. Indeed, measurements on an HB9CV 2-meter antenna that uses a single-wire for the phase line and gamma sections indicates a line in the 200-Ohm range for a direct 50-Ohm coax feed.</p>
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Fig. 4-3. SWR curves of the sample HB9CV arrays from 28.0 to 29.0 MHz.
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<p>The cost of the Tee-version's relatively even performance across the first MHz of 10 meters is the feedpoint impedance. As shown in <b>Fig. 4-3</b>, the HB9CV has an SWR curve referenced to 100 Ohms. A 2:1 matching network or device is required for standard coax feed. In contrast, the gamma version shows a well-behaved 50-Ohm SWR curve. <b>Fig. 4-4</b> samples the free-space azimuth patterns of the Tee-version of the HB9CV at 28.0, 28.5, and 29.0 MHz to indicate the evolution of the pattern across the operating passband.</p>
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<img src="ph4-4.gif" width="376" height="570" border="2" vspace="5" hspace="9">
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Fig. 4-4. Free-space azimuth patterns of the Tee-version of the HB9CV array at 28.0, 28.5, and 29.0 MHz.
</center>
<p>In the 1950s, the 1/8 wavelength spacing of elements and the use of element lengths similar to those of 2-element Yagis held a mystique among phased array designers. From our work with both ideal phased arrays in Part 1 and optimized Yagis in Part 2, we now understand the appeal of the 1/8 wavelength spacing. It represents a reasonable balance between operating bandwidth and gain. Beyond the 1/8 wavelength mark, gain tends to decrease ever more rapidly for elements near the 1/2 wavelength or self-resonant length. Below a spacing of 1/8 wavelength, the operating bandwidth decreases ever more rapidly.</p>
<p>However, for the proper phasing of an array to produce good performance--relative to having only 2 elements--there is no magic spacing. So long as we achieve the correct confluence of all of the variables in a phased 2-element horizontal array, we may use any spacing between 0.05 and 0.2 wavelength. The gamma and Tee matching system to bring the rear element into reasonable alignment with the impedance of a chosen phase line and the forward element to an impedance that yields the proper current division and feedpoint impedance might well be adaptable to other element lengths and spacings. However, the success builders have had with the original HB9CV designs has tended to suppress both experimentation and calculation that would yield new variants.</p>
<center>
<h4>The N7CL Beta-Matching System</h4>
</center>In the search for less complex mechanical designs of 2-element horizontal phased arrays, Eric Gustafson, N7CL, has developed within the past few years a different approach to the same end. N7CL wanted to do away with virtually all of the visible superstructure of the HB9CV while achieving similar performance capabilities. To this end, he turned to the shorted-stub form of the beta or hairpin stub, although he used coaxial cable sections for his stubs.
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<img src="ph4-5.gif" width="382" height="257" border="2" vspace="5" hspace="9">
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Fig. 4-5. General outlines of the N7CL phased array.
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<p><b>Fig. 4-5</b> shows the schematic outline of the N7CL phased array. It consists of 2 elements, a phase line, and two stubs. For the Phase line, N7CL selected a 100-Ohm line created from side-by-side (series) sections of standard coaxial cable. The shielding provided by the cable braids permit the line to ride inside the metal mast supporting the elements with no ill effects.</p>
<p>However, single tubular elements do not match well to 100-Ohms phase lines. The key to effecting a match is to change the element impedance from its natural value to something very close to 100 Ohms. A beta match will do the job, but under the condition that the element impedance exhibits a sufficient capacitive reactance to form the series reactance to go with the shunt or parallel inductive reactance of the stub in classic L-network terms.</p>
<p>We cannot simply apply a beta match to any element and expect good results. We must begin with an acceptable 2-element design using separate feedpoints. Since the rear element must show a capacitive reactance, it must be shorter than a self-resonant half wavelength, if we are to believe the indications of the tables in Part 1. We shall want a net reactance on the feedline-phase line junction that is also capacitive, which indicates a forward element that is shorter still.</p>
<p>For this 10-meter design example, using 0.5" aluminum elements, I selected a forward element length of 0.4446 wavelength and a rear element of 0.0.4772 wavelength. The element spacing is 0.1112 wavelength. With this combination and a rear element relative current magnitude of 0.8762 at -38.53 degrees, we obtain a performance potential of 6.39 dBi free-space gain and 23.88 dB front-to-back ratio. One might further vary these values for higher performance, but for the design example, I declared them satisfactory.</p>
<p>The forward element impedance is 20.9 - j 32.7 Ohms. The rear element impedance is 16.4 - j 39.7 Ohms. I selected a 100-Ohm phase line. To raise the impedance of the rear element to about 100 Ohms, I added a shorted stub, the shunt component of a beta or L-network. The required value from network calculations was about j 44 Ohms. Since the length of a shorted stub will vary with both the desired reactance and the characteristic impedance of the line used, I arbitrarily created a 50-Ohms stub with an electrical length of 0.1116 wavelength.</p>
<p>I then created a phase line with the specifications of 100 Ohms and a velocity factor of 0.78 to simulate RG-8X or similar cable. The physical length is 0.1314 wavelength to ensure that there is enough cable to reach from the center of the boom tube to the elements at each end. The line has an electrical length of 0.1684 wavelength, the length necessary to transform the current magnitude and phase for the desire conditions on each element. With the rear stub and the 100-Ohms phase line added to the model, we obtain the desired performance indicated from the initial model with independently fed elements. However, the feedpoint impedance at the junction of the forward element and the phase line is 21.33 - j 22.45 Ohms.</p>
<p>The capacitive reactance and low resistance at the feedpoint are ripe for a second beta match, this time a 50-Ohm shorted stub with an electrical length of about 0.126 Ohms. The result is a feedpoint impedance of 43.8 - j 7.0 Ohms at the design frequency.</p>
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<img src="ph4-6.gif" width="722" height="543" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 4-6. Gain and 180-degree front-to-back ratio of the N7CL phased array from 28.0 to 29.0 MHz.
</center>
<p><b>Fig. 4-6</b> shows the free-space gain and front-to-back curves for this sample design across the first MHz of 10 meters. Because the rear-element beta match reverses the impedance progression with changing frequency relative to an element with no matching system, the gain curve shows a reverse direction relative to other phased arrays with which we have worked. The front-to-back curve peaks at about 28.3 MHz. Both progressions of values can be altered with further design refinements.</p>
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<img src="ph4-7.gif" width="722" height="544" border="2" vspace="5" hspace="9">
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<center>
Fig. 4-7. SWR curve of the N7CL phased array from 28.0 to 29.0 MHz.
</center>
<p>In the design example, the elements were not sufficiently optimized to yield both an SWR under 2:1 across the passband and a minimum value close to 1:1, as shown in <b>Fig. 4-7</b>. The feat may be more difficult than might appear at first sight, since any adjustment to the length of the forward element to move the SWR curve will also affect the natural--and hence, the transformed--impedance of the rear element. Moreover, the element spacing--just over 0.11 wavelength--also works to narrow the operating passband of the array. <b>Fig. 4-8</b> shows sample free-space azimuth patterns at both the band edges and mid-band.</p>
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<img src="ph4-8.gif" width="376" height="570" border="2" vspace="5" hspace="9">
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<center>
Fig. 4-8. Free-space azimuth patterns of the N7CL phased array at 28.0, 28.5, and 29.0 MHz.
</center>
<p>The N7CL phasing system is currently in use in 30-meter and 40- meter arrays under the Cal-Av label. I am grateful to Eric for permission to describe his patented matching system, although he is in no way responsible for the slant given to the explanation or for my simple design example. As I have noted, design examples do not necessarily equal production designs in performance.</p>
<center>
<h4>Capacitive Element Loading</h4>
</center>
<p>A few years ago (1998-99), I took a different tack in trying to overcome the problem of designing a phased array that could use a higher impedance or twin-coax phasing line. (See <a href="hb.html">"The HB9CV Phased Array and Gain Comparisons"</a>.) As we increase the length of a dipole, the impedance increases. If we lengthen the dipole sufficiently, the impedance approaches 100 Ohms resistive, but with a considerable inductive reactive component. We may compensate for this reactance by inserting capacitors at the element feedpoint in series with the element.</p>
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<img src="ph4-9.gif" width="430" height="256" border="2" vspace="5" hspace="9">
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<center>
Fig. 4-9. General outlines of the capacitive-element-matching phased array.
</center>
<p>When we deal with 2 elements, the problem becomes only slightly more complex due to the interaction of the elements. The result will be elements considerably longer than a self-resonant dipole. The final design result was the array pictured in <b>Fig. 4-9</b>. The forward element is 0.602 wavelength long, while the rear element is 0.622 wavelength long. Because the gain of a dipole tends to increases modestly with increases in length, I used a relatively wide spacing of 0.145 wavelength to achieve satisfactory performance. The elements are 1" diameter aluminum.</p>
<p>We need not bring each element to zero reactance in order to have a satisfactory array. The rear element uses a total capacitance of 25.4 pF (two 50-pF capacitors in series on each side of the feed junction). The forward element uses 15 pF (two 30-pF capacitors). When modeled as independent element separately fed, the rear element impedance is 82.9 - j 11.4 Ohms, while the forward element is 102.6 + j 35.7 Ohms. We may now add a 100-Ohms phase line using the same 0.78 velocity factor twin 50-Ohms coax construction used in the preceding example. The physical length for the design example is 0.145 wavelength, although in practice, some extra line may be useful for making connections. A 0.150 wavelength line will not significantly change performance due to the initial good match between the line and the rear element. The feedpoint junction requires no additional matching network, because the forward-element capacitors were adjusted to provide a low 50-Ohms SWR.</p>
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<img src="ph4-10.gif" width="723" height="544" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 4-10. Gain and 180-degree front-to-back ratio of the capacitive-element- matching phased array from 28.0 to 29.0 MHz.
</center>
<p><b>Fig. 4-10</b> shows the free-space gain and front-to-back ratio potential performance across the 28.0 to 29.0 MHz spread. The system is not at all finicky, as revealed by the values obtained simply by replacing the 100-Ohm line with a 150-Ohm, as might be obtained by employing 75-Ohm coax lengths as shielded twinlead. However, the system is relatively optimized for the 100-Ohm line. The 150-Ohm line shows superior band-edge front-to-back performance, although the 100-Ohm line version shows a higher peak value. Since the matching capacitors only compensate for the element inductive reactance and do not transform the impedance, the gain curve shows its normal upward trend with frequency.</p>
<center>
<img src="ph4-11.gif" width="723" height="544" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 4-11. SWR curve of the capacitive-element-matching phased array from 28.0 to 29.0 MHz.
</center>
<p>In <b>Fig. 4-11</b>, we find the SWR curves for both the 100-Ohm and the 150-Ohm line versions. Both are satisfactory. However, we might classify the 100-Ohm line version as somewhat "tamer." <b>Fig. 4-12</b> provides the standard 28.0, 28.5, and 29.0 MHz free-space azimuth patterns for performance reference. The array with capacitively loaded elements is an experiment and not a finished product. The elements are long by most array standards--about 20% longer than those of a standard array. However, the reward for heavier elements is a somewhat simplified structure for matching the rear element impedance to the phase line and the array feedpoint impedance to standard coaxial cable feedlines.</p>
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<img src="ph4-12.gif" width="376" height="570" border="2" vspace="5" hspace="9">
</center>
<center>
Fig.4-12. Free-space azimuth patterns of the capacitive-element-matching phased array at 28.0, 28.5, and 29.0 MHz.
</center>
<center>
<h4>Conclusions</h4>
</center>The three systems we have explored in this part of the series illustrate ways in which we may achieve 2-element phased arrays using normal beam constructions with a metallic boom supporting the elements. In each case, the designer has matched the element impedances to a desired phase line, using a varied assortment of techniques. Once more, our goal has not been to produce paradigm production designs, but only design examples sufficient to illustrate the principles involved. If we have gained some appreciation of the techniques of matching the rear element to the phase line and changing everything else to align the other variables involved in a 2-element horizontal phased array, then we have gotten out of them everything intended.
<p>Indeed, some may wish to emphasize the performance differences among the examples, but this would be a mistake. Many designs can undergo further optimization. What should strike us is the basic similarity in performance among the ZL-Special and the matched-element designs. One cannot be absolute on the basis of a sampling, but it is likely that the performance range among the models explored so far represents the main arena for 2-element horizontal phased array performance.</p>
<p>Free-space makes an ideal environment for comparing the potential performance of antennas of essentially the same type. However, over the years, some folks have questioned whether or not there might be a difference between the performance of phased horizontal arrays and of parasitic arrays over ground. The only free-space evidence a potential difference in performance would be a significant dissimilarity between the elevation or H-plane patterns of Yagis and phased arrays. None exists.</p>
<pre> Comparative Performance Figures of Sample 2-Element Arrays
All Arrays 1 Wavelength Above Good Ground at 28.5 MHz
1. Reflector-Driver Yagi
Dimensions:
Reflector Driver Element Element
Length wl Length wl Spacing wl Diameter wl
0.5028 0.4620 0.1250 0.001207 (0.5")
Performance:
Gain TO Angle Second Lobe Angle Main-Second Front-Back
dBi degrees Gain dBi degrees Lobe Ratio dB Ratio dB
11.61 14 9.35 46 -2.26 12.52
2. Driver-Director Yagi
Dimensions:
Driver Director Element Element
Length wl Length wl Spacing wl Diameter wl
0.4972 0.4670 0.0750 0.001207 (0.5")
Performance:
Gain TO Angle Second Lobe Angle Main-Second Front-Back
dBi degrees Gain dBi degrees Lobe Ratio dB Ratio dB
11.83 14 9.49 46 -2.34 19.58
3. ZL-Special
Dimensions:
Rear El. Forward El. Element Element Phaseline--Note 1
Length wl Length wl Spacing wl Diameter wl Length Zo VF
0.5060 0.4650 0.1250 0.001207 (0.5") 0.1300 35 0.66
Performance:
Gain TO Angle Second Lobe Angle Main-Second Front-Back
dBi degrees Gain dBi degrees Lobe Ratio dB Ratio dB
11.68 14 9.51 47 -2.17 31.62
2. N7CL Phased-Array with Rear-Element-Matching
Dimensions:
Rear El. Forward El. Element Element Phaseline--Note 2
Length wl Length wl Spacing wl Diameter wl Length Zo VF
0.4972 0.4670 0.0750 0.001207 (0.5") 0.1314 100 0.78
Performance:
Gain TO Angle Second Lobe Angle Main-Second Front-Back
dBi degrees Gain dBi degrees Lobe Ratio dB Ratio dB
11.74 14 9.49 46 -2.25 31.44
Note 1: ZL-Special uses a feedpoint impedance matching section.
Note 2: N7CL array uses shorted stubs for rear-element matching and for
feedpoint matching.
Table 1. Comparative performance figures of sample 2-element arrays with all
arrays 1 wavelength above good ground at 28.5 MHz.</pre>
<p>However, we may use a more direct demonstration by modeling sample parasitic and phased arrays over real ground. <b>Table 1</b> lists the critical performance parameters of two Yagis, a reflector-driver array with an element spacing of 0.125 wavelength and a driver-director array with a 0.075 wavelength element spacing. These arrays come from part 2 of the series. The sample phased arrays are the 35-Ohms phase line model from Part 3 and the N7CL array from our work in this section. All arrays are 1 wavelength above ground. At 1 wavelength, a parasitic array elevation pattern shows both a lower main lobe at about 14 degrees elevation along with a secondary lobe above. The differential in the secondary lobe is a good indicator of performance similarity or difference.</p>
<center>
<img src="ph4-13.gif" width="376" height="380" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 4-13. Elevation patterns of two types of parasitic arrays 1 wavelength above good ground.
</center>
<center>
<img src="ph4-14.gif" width="376" height="380" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 4-14. Elevation patterns of two types of phased arrays 1 wavelength above good ground.
</center>As the figures in the table show--backed up by the elevation patterns in <b>Fig. 4-13</b> and <b>Fig. 4-13</b>--the differentials are too small to support a claim of performance differential. The differentials that do exist lie in the realm of gain and front-to-back ratio. The 2-element horizontal phased array is capable of slightly higher gain than a 2-element Yagi of similar operating bandwidth. The gain advantage runs between 0.2 to 0.7 dB. However, with a reasonable front-to-back ratio, the gain of a 2-element horizontal phased array never reaches the level of a well-designed 2-element quad or a short-boom 3 element Yagi.
<p>If the gain advantage of the horizontal phased array is marginal relative to parasitic arrays of similar operating bandwidth, the front-to-back advantage is significant and operationally noticeable. A reflector-driver Yagi with coverage of the first MHz of 10 meters will have a peak front-to-back ratio of about 12 dB. A similarly sized phased array with equal or greater gain is capable--when optimally designed--of nearly 20 dB across the full passband, with peak values in the 30 dB region. Whether one wishes the additional quietness from the rear of the phased array or wants to be able to hear what may be happening in directional to which the beam is not aimed depends on the type and style of operation. In short, the desirability of one type of array over another is a user judgment.</p>
<p>These comparative notes relate only to full-size models of both parasitic and phased arrays. Shortened, loaded elements yield lesser gain in virtually all circumstances, although loaded reflectors may increase the front-to-back ratio of a reflector-driver Yagi. A shorter-element phased array may be capable of the full gain that its elements permit with inherently good front-to-back ratio as well. In the end, the variables involved in antenna selection--where 2 elements form the common baseline among candidates--may outnumber the variables involved in properly phasing 2-element horizontal arrays.</p>
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<p><i>Updated 05-10-2002. &COPY; L. B. Cebik, W4RNL. This item originally appeared in</i> The National Contest Journal <i>(May/Jun, 2002). 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/yagicad.gif" align="middle" width="125" height="62" border="2" vspace="5" hspace="10">Horizontal Phased Arrays with Parasitic Directors<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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Although well-known in other parts of the world, combined horizontal phased arrays with parasitic directors are relatively obscure in the U.S. To remove some of that obscurity, I went through the process of capturing a design procedure appropriate to this type of antenna. The result is an experimental 3-element beam with the gain of a 4-element short-boom Yagi and the front-to-back ratio of a saint.
<h3>Background</h3>Consider the 2-element phased horizontal array, which is often called the ZL-Special, with HB9CV variations. Both elements are fed. A phasing line between the two elements is designed to set the relative magnitude and phase angle of the currents at the two feed points. The phase line is often brought to the forward element, but need not be that way. In many instances, achieving the correct phasing will require a central current dividing point with different length lines running to each of the two elements.
<p>2-element phased arrays can be set up for maximum gain or for maximum 180- degree front-to-back ratio. The latter set-up is the norm for phased verticals, but does not yield maximum gain. Indeed, for most horizontal 2- element arrays, maximizing the rear null results in gain that equals or is less than that of a 2-element Yagi (which has only a modest front-to-back ratio).</p>
<p>Maximizing gain results in about an extra dB of gain relative to the maximum rear null configuration. However, the front-to-back ratio goes to pot, dropping easily to under 10 dB.</p>
<p>Note that all of this is done without changing the antenna dimensions. Although Yagis require a certain geometry to achieve either maximum gain or maximum rear null, phased arrays achieve the same results by setting the relative current magnitude and phase on the two elements. If we use networks to set the individual current magnitudes and phases, we may use equal element lengths of approximately 1/2 wl.</p>
<p>The norm is to use transmission line lengths to set the relative current magnitudes and phases, and this practice sets limits to what is possible. Since we have only a few types of available commercially made transmission lines, using them restricts design variations. We may also make our own lines, but in most cases, they will have too high a characteristic impedance to handle linear dipole-style elements and are better suited for use with folded dipoles.</p>
<p>To compensate for restrictions in the feasible limits of setting current magnitudes and phases with transmission lines, we often alter the geometry of the elements to achieve a given result. For maximum rear null configurations, the rear element may actually be shorter by a small amount than the forward element in some cases.</p>
<p>However, practical design rarely chooses either the maximum gain (too little front-to-back ratio) or the maximum rear null (too little gain) configurations. Intermediate values are the general rule and result in gains up to about 1/2 dB greater than with a 2-element Yagi of equal spacing while keeping the front-to-back ratio in the 18-20 dB ballpark. Such phased arrays tend to have the appearance of a 2-element Yagi with a low impedance connecting cable between the two elements.</p>
<p>For further work on the fundamentals of 2-element horizontal phased arrays, see "Modeling and Understanding Small Beams: <a href="../mu/mu5a.html">Part 5: The ZL Special</a>," <i>Communications Quarterly</i> (Winter, 1997), pp. 72-90</p>
<h3>Adding a Director</h3>The design we shall explore is not new to the world, although it may be new to many folks. The configuration of the antenna is shown in <b>Figure 1</b>.
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<p>The sketch makes the antenna appear to be a 2-element phased array with a director ahead. Appearances do not deceive. This experimental antenna for 24.95 MHz uses a 14' boom (roughly comparable to 12' at 10 meters or 24' at 20 meters). This is considered a long boom for a 3-element Yagi but a short boom for a 4-element Yagi. Dimensions appear in the figure. Models of the antenna use 3/4" diameter aluminum. The phasing line is a 6.6' length of RG-8 (velocity factor 0.66) or equivalent. Connections are reversed, since the required current phasing is that of a -45-degree line, not that of a +135-degree line. (Although impedance goes through two cycles per 360 degrees of transmission line, voltage and current go through but 1 cycle in the same length. A short half-twist line thus cannot effect a 135-degree current transition directly, but accomplishes the equivalent by a reversal of both voltage and current phase, but must always count backwards from zero in accounting for the current magnitude and phase in the line.)</p>
<p>Using coax as the phase line calls for special precautions due to the reversal. Proximity to metal booms can disrupt the characteristic impedance of the line due to external couplings. Hence, spacing the line from the boom is necessary. (Early ZL-Special builders often forgot this and taped the phased line to the metal boom, resulting in disappointing performance.)</p>
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<p>The antenna performance is quite remarkable and quite even across narrow bands like 12 meters. As <b>Figure 2</b> notes, the maximum free-space gain is over 8.6 dBi, with a 180-degree front-to-back ratio approaching 34 dB.</p>
<p>Feeding the antenna is a bit of a challenge, since the feedpoint impedance is about 15.5 + j23.0 Ohms. However, we can use a little appreciated version of the beta match. The beta match is simply an L-network, where the series reactance is part of the antenna feedpoint impedance in series with the resistive component. If the reactance is correct, we can simply add a shunt reactance of the opposite type across the terminals to effect an impedance transformation to 50 Ohms. See <b>Figure 3</b>.</p>
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<p>Since the series reactance of the antenna feedpoint is inductive, the shunt reactance must be capacitive. The required reactance value is about 35 Ohms, which translates into a capacitance of about 180 pF for 12 meters. Since there will be construction variables in every antenna, a variable capacitor should be used to establish the exact value required for a good coax match. Replace the variable with an equivalent fixed capacitor of the nearest value. Be certain that it has substantial internal and external lead size to handle the high currents at the feedpoint. Because of the low antenna source impedance, ensure that all connections are very tight electrically. Weather seal the capacitor and its connections. Use a choke balun between the matching section and the main coax cable. The director essentially controls both the gain and the front-to-back ratio of the array. (In Yagi design of greater than 2 elements, the reflector largely controls the driver impedance, with the director having the greater effect upon both gain and front-to-back ratio.) We can easily glimpse this fact by stripping away the director and checking the performance of the 2 phased elements.</p>
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<p>As <b>Figure 4</b> shows, the correct design of the 2-element phased array portion of the total antenna is to set it for maximum gain, in this case, a native free-space value approaching 7.2 dBi. The front-to-ratio is about 10 dB, mediocre at best.</p>
<p>Adding the director yields an additional gain of about 1.4 dB. Moreover, the front-to-back ratio improves by over 20 dB. Had the original phased 2- element section been set for maximum rear null, the final performance figures would not have been obtained.</p>
<h3>Comparative Performance</h3>How does the phased array with director stack up against other antennas with similar boom lengths. To check this, I went into my files and chose the best 3-element and 4-element designs with similar boom lengths.
<p>The 3-element design uses a boom length less than a foot shorter than our array. However, its gain is limited to about 8.1 to 8.15 dBi in free space if it is to sustain a front-to-back ratio above 20 dB. The feedpoint impedance is just about 25 Ohms when resonant.</p>
<p>The 4-element Yagi uses a boom less than a foot longer than our array. Its gain approaches that of the array, being about 0.2 dB less. The front-to- back ratio is in the same ball park. The feedpoint impedance is midway between our array and the 3-element Yagi. However, this performance is purchased at the cost of an added element.</p>
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<p><b>Figure 5</b> tells the same story graphically. Phased arrays with parasitical directors can yield exceptional performance relative to wholly parasitical antenna designs with the same boom length and number of elements.</p>
<p>Not all designs calling themselves phased arrays with directors are true 3- element designs. Some multiband designs use "log" cells for drivers on multiple bands or multiple parts of bands. The crossed lines work, but not as either contributors to gain or to rear nulling.</p>
<h3>Conclusion: Just the Beginning</h3>For monoband beam use, the combination of a phased 2-element array replacing the normal reflector and driven element of a Yagi can add up to 0.5 dB added gain--at least in three element versions--for a given boom length over conventional Yagis. It also is capable of excellent front-to- back performance.
<p>However, these brief notes only hint of work to be done. The phased array portion of the antenna has not been optimized for the source impedance. Whether the performance of this design can be sustained at a higher and more desirable source impedance is not known to me at this time. Whether the added gain of the 3-element array carries over into 4 and 5 element versions is also not known to me at this time.</p>
<p>This very preliminary work was done without reference to any commercial antenna. Unfortunately, I do not have on file any detailed design plans of antennas claiming to use or actually using these principles. In the end, these unknowns suggest that the phased array plus director(s) is a design worth further investigation as time permits.<br>
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<p><i>8-27-98. &COPY; 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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<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">Don't Be Phased By Phasing</h1>
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<h3>L. B. Cebik, W4RNL</h3>
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Many antenna builders cringe at the mention of a certain word: phasing. Unless you are using a simple antenna, like a resonant 1/2 wavelength wire (commonly called a dipole), your antenna consists of phased elements. If it is a Yagi, it is phased. If it is a 135' doublet used on 10 meters, it is phased. If it is a 4-element system of collinear extended double Zepps spaced 5/8 wavelengths vertically with all elements fed, it is phased. (I have modeled this little system for about 22 dBi forward gain and a beam width of under 17 degrees--or better than most flashlights in directivity.)
<p><b>What Phasing Is</b>: It may be useful to understand a little better what phasing is all about. Any time we have more than a half- wavelength of wire (or more than a quarter wavelength with verticals), we have phasing. Phasing is simply a readout of the current on a designated secondary part of the antenna or antenna system relative to the designated primary part. We are not interested in those currents for their own sake, but for what they do to the resulting radiation pattern of the antenna. The patterns that result are a function of the current magnitudes, the current phases, the length of the primary and secondary parts, and their separation.</p>
<p><b>Geometric and Electronic Phasing Control</b>: If we understand phasing well enough, we can not only see what the interaction of these 4 phasing factors yields, but we can also control the radiation pattern by juggling the factors. Consider a 2-element Yagi: a driven element and a reflector.</p>
<p>Just the relative lengths of elements and their spacing can determine the current magnitude and phase on the reflector relative to the driven element. There are good combinations and bad combinations--those with more gain and/or front-to-back ratio and those with less. But we quickly learn that with two elements, there is a limit to both gain and front-to-back ratio.</p>
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<p>Figure 1 will show some of the limits we encounter, if we supplement it with a small table. The curve marked "normal" is a typical 2-element Yagi design. Let us for the sake of the example freeze a couple of dimensions: spacing is set at 51" and the aluminum elements are 0.75" in diameter. Moreover, in all cases, the current on the front element is given an arbitrary magnitude of 1.0 at 0.00 degrees phase.</p>
<pre>Antenna DE L. Ref. L. Gain F-B Feed Z Ref. Current
inches inches FS dBi dB R+/-jX Mag/Phase
Normal 191.0 210.0 6.06 11.0 36+j2 0.64/140.5
Max Gain 191.8 200.0 7.02 5.6 19-j6 0.82/164.1
Max F-B 38.1 204.4 6.22 14.6 0.8-j1100 0.12/145.8
Phased 191.0 210.0 6.35 52.0 ------- 0.93/136.4</pre>
<p>First, let's explore what some simple changes of geometry can do for and to our antenna. We can alter the lengths of the two elements to achieve the maximum gain from the elements, but at a cost of most of the front-to-back ratio and with a feedpoint impedance that is quite low. To achieve a nearly 5 dB greater front-to-back ratio, we must radically alter the length of the driven element until the feedpoint impedance become wholly unusable. In short, there are limits to what we can achieve simply by altering the physical geometry of the antenna.</p>
<p>Suppose we could control the current magnitude and phase on the rear element without changing the original dimensions of our modest "normal" antenna. One thing we discover is that we cannot squeeze out significantly more gain, but we can improve the front-to-back ratio--at least for a small frequency range. Using the original elements, we find that we can dramatically increase the front-to-back ratio by controlling the current magnitude and phase to the rear element. (The very sharp null in the rear holds good for only a very narrow frequency range.)</p>
<p>One way to achieve the required phasing for a maximum front-to-back ratio is to construct a ZL Special, a 2-element phased array. It uses a precisely calculated set of element lengths, spacings, and an equally precisely calculated length of transmission line between them. The current splits at the feedpoint, part going to the forward element, and part being transformed along the phasing line so that, at the rear element, the current has the magnitude and phase to maximize front-to-back ratio at the target frequency. An alternative is the HB9CV, which aims for a combination of gain (approaching 7 dB) and reasonable front-to-back ratio (about 20 dB) with a specially formulated phase line and matching system. In principle, the HB9CV is a variation of the ZL Special, and both antennas employ the same basic principles.</p>
<p>Of all 2-element configurations that I have encountered, the Moxon rectangle comes closest to achieving the rear element phasing necessary for maximum front-to-back ratio with purely geometric means--that is, without the use of phasing networks or phasing lines. Moxon rectangles are explored in other notes in this collection. Essentially, bending the elements inward toward each other at the ends--in precise lengths and end spacings--alters the element coupling from the standard Yagi straight element design. The cost is a little gain, but the benefit is a highly enhanced front-to-back (and front-to-rear) ratio. The result is also amenable to direct 50-ohm feed and has a very wide operating bandwidth.</p>
<p>Let's look again at the difference between geometric and electronic control of the current on a second element, this time using 1/4 wavelength verticals. We shall set two of verticals exactly 1/4 wavelength apart. First, we shall make both antenna elements the same length and feed only one. That yields the "spaced" pattern in Figure 2. It is a nice pattern, but we can improve the front-to-back ratio. Next, we shall increase the rear (reflector) element length and shorten the driven element back to resonance so that the two elements have about a 4% length difference. The performance peaks out on the curve called "parasitic" in Figure 2. In short, altering geometry can do only so much to establish the conditions for maximum front-to-back ratio. (For many operating situations, the improvement in front-to-back ratio may be sufficient; for others, it will need improvement.)</p>
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<p>The curve marked "phased" is the pattern of two elements of the same length 1/4 wavelength apart when both are fed in a certain way. The forward element has a current of 1 and a phase angle of zero; the rear element has a current of 1.03 and phase angle of 96 degrees. What the pattern shows is over 42 dB of front-to-back ratio.</p>
<p>The patterns also show other important things. First, the maximum gain set-up differs from the maximum front-to-back set-up. The "spaced" array of two identical elements with only one fed yields the most gain. Both attempts to improve front-to-back ratio show less gain. Second, we always have to evaluate whether the gain or the front-to-back ratio will do us the most good for our operating needs.</p>
<p><b>More Elements</b>: To improve gain, we shall need more elements, that is, more 1/2 wavelength sections for antenna. Yagis with 3 or more elements alter the relative current phase and magnitude on all unfed elements by the proper spacing and sizing of directors in addition to a reflector. We can also create collinear arrays, that is, antennas with the elements end-to-end. The patterns will add or subtract according to their placement. Think of an extended double Zepp (a 1 1/4 wavelength wire, center-fed) as two half- wavelength wires separated by a quarter wavelength. This spacing lets the dipole patterns add up and narrow for more gain and a narrower beamwidth. The center section establishes the pattern of current distribution along the wire to permit the addition of patterns from the two half wavelength sections.</p>
<p><b>Phasing Methods</b>: There are only a few basic methods of altering the current magnitude and phasing of the secondary antenna parts.</p>
<p><b>1. Element length and spacing</b>: We have seen with both the Yagi and vertical examples how element length and spacing alter current distribution. If we need or want a current distribution that geometry will not give us, then we must use other means.</p>
<p><b>2. Transmission lines as phasing transformers</b>: Every transmission line is a transformer of voltage, current, and impedance along its length. For antenna work (and contrary to what we think about when considering the feedline to the shack), it is the current phase and magnitude that is most important. How this transformation occurs is a function of the characteristic impedance of the feedline (and its velocity factor). The ZL Special transformation is a very precise thing if one wants more than mediocre results. Not just any line will do, nor will just any length of line (relative to the antenna element lengths and spacing) do. For certain simple cases, like phasing 2 verticals 90 degrees, lengths of line can do the job, but those cases are somewhat limited.</p>
<p>Many collinear arrays make use of phasing lines between element ends. Most are simple cases of reversing the end-to-end phasing. The 1/2 wavelength wire that runs between the two drooping ends of a half-square antenna is such a line. It does not radiate (much), but presents the "far end" vertical with the same magnitude of current as the fed end, but 180 degrees out of phase. The vertical patterns then add to give the peanut- shaped pattern useful to low band DXers. More complex arrays may need precise electrical lengths of phasing lines to effect a specific change of current phase to an adjacent wire, as in collinear EDZs.</p>
<p><b>3. "Brute force"</b>: For precisely tuned phased arrays, nothing beats L- networks (along with PIs and Tees) for establishing the exact phase change needed to make an array work. Every such network changes the phase of the entire voltage-current magnitude set relative to the input (although the voltage and current retain their initial phasing relative to each other). Hence, we can achieve any desired relative current settings. If we then use multiples of a half wavelength of transmission line from the network to the element, we can set each element where we want to set it. Sounds simple, doesn't it.</p>
<p>In some ways it is, but. . .let's not forget that the network also creates an impedance transformation. When we take these matters into account, the calculations can get a little more complex. We have to make certain that the element gets the correct current level and phase under a matched condition. Phasing 3, 4, and more wire systems is an exercise for someone who loves his calculator.</p>
<p><b>Vertical Phasing</b>: So far we have been thinking in 2-dimensional terms. Now lets add a third--the vertical. We can stack antennas vertically for more gain. The principle is to place the two patterns in a proper phase relationship so that the forward patterns add--a vertical version of collinear pattern adding. The principle works with almost any type of antenna. Vertically spaced EDZs are common. Most vertically spaced arrays feed each antenna in phase--that is, each driven element has the same current magnitude and phase. A number of notes in this collection sample a fair array of different phasing situations.</p>
<p>In another note in this series, we have shown with models that the proper spacing for maximum gain increases for a pair of Yagis increases as the gain of the original Yagis increases. While 5/8 wavelength spacing works well for 3-element Yagis of good gain, we need a lot more space between 5- or 6-element Yagis to get the maximum gain possible from the pair. To make matters a bit hairier, the front-to-back maxima do not occur in the same spacing places as gain maxima. However, the antennas can be redesigned slightly to bring the maximum stacked gain and the maximum stacked front-to-back ratio into alignment.</p>
<p>This small note is not a how-to-do-it manual. We would need a book for that, and handbooks already abound. Instead, the point is only to ensure that we understand that phasing is a significant concept even when there are no phasing networks or phasing lines in sight. If we have convinced you that phasing is everything in antenna work, then you may not be phased by all the references to phasing in what you read about antennas. Phasing can never be phased out of antenna work.<br>
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<p><i>Updated 02-04-98. &COPY; L. B. Cebik, W4RNL. A briefer version of this item appeared in</i> QRP Quarterly<i>, January, 1998. 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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