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+<head>
+  <meta charset="UTF-8">
+  <meta name="keywords" content="LPDA, HF Multi Band">
+  <title>4-30 MHz LPDA Design Concepts</title>
+  <link rel="stylesheet" href="../styles.css">
+</head>
+<body>
+  <center>
+    <h1>4-30 MHz LPDA Design Concepts</h1>
+  </center>
+  <center>
+    <h3>L. B. Cebik, W4RNL</h3>
+  </center><br>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  <p>Government, military, and some commercial enterprises have employed wide-range LPDAs for coverage of the HF region from about 4 to 30 MHz. The appeal of using a single antenna for the entire frequency range is multi-faceted. A single antenna permits frequency scanning and rapid changes of frequency without the need for antenna retuning or switching. The directional pattern of the LPDA offers gain in the desired direction at all frequencies, as well as QRM and QRN reduction from other directions.</p>
+  <p><b>A Review of single LPDA Design Potential</b></p>
+  <p>However, the single LPDA designed to cover the entire HF spectrum from about 4 to 30 MHz suffers some serious limitations. In a pair of articles in <i>QEX</i> ("Notes on Standard Design HF LPDAs," May-August, 2000), I explored some of the problems and pitfalls of designing LPDAs with a wide passband--something of the order of a 10:1 frequency range. It may be useful to review some of the outcomes of the study.</p>
+  <center>
+    <img src="330-1.gif" width="500" height="560" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig 1</b> provides outlines of three different LPDAs, each the best of its boom length used in the earlier study. The following table provides some of the basic data about each antenna model.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+      Boom        No. of      Phase Stub? Element
+      Length      Elements    Line                    Treatment
+      feet                    Impedance
+1.     65'        20          200         No          Tau-tapered diameter
+2.    100'        23          200         Yes         Tau-tapered diameter
+3.    164'        26          150         Yes         Tau-tapered diameter
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>The reference to Tau-tapering of the element diameter refers to increasing the diameter of each element--referenced to the most forward elements--by the inverse of the value of Tau used to establish the basic design. In general, element diameters ranged from 0.5" for the forward element to about 6.5" for the rear-most element. This practice maintains a relatively constant length-to-diameter ratio for the design.</p>
+  <p>The shortest LPDA in the lot was specifically designed for 4-30 MHz and has a 132.1' rear element. The longer boom designs set the low frequency cut-off at 3 MHz and have a 167.3' rear element.</p>
+  <p>The following graphs explore the performance potential of the resulting LPDAs in 0.25 MHz increments. To make the graphs readable, I have divided each parameter into 2 charts, one covering 3.5-17 MHz, the other covering 17.25-30 MHz. Vertical axis scales have been matched so that the two graphs for each parameter will join seamlessly.</p>
+  <center>
+    <img src="330-2.gif" width="647" height="528" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    <img src="330-3.gif" width="647" height="528" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 2</b> and <b>Fig. 3</b> provide the gain potential of the LPDA designs. The shortest- boom model is obviously gain deficient until it reaches 5 MHz or higher. As well, it exhibits an obvious weakness at about 7.75 MHz. Above 10 MHz, the average free-space gain fluctuates around the 6 dBi mark.</p>
+  <p>The 100' boom model has no obvious weaknesses in gain across the spectrum, but the added 35' of boom and 3 additional elements only raises the average gain to about 6.3 dBi (free-space). However, the 100' boom length is already a major mechanical challenge for support and rotation.</p>
+  <p>The longest model averages just above 7 dBi free-space gain, with one odd peak at 8.5 MHz. To achieve this gain, we need at least 26 elements and a boom of nearly 165'.</p>
+  <center>
+    <img src="330-4.gif" width="646" height="528" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    <img src="330-5.gif" width="648" height="529" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 4</b> and <b>Fig. 5</b> present the potential 180-degree front-to-back ratio performance potential of the big LPDAs. Only the longest LPDA model sustains a front-to-back ratio of better than 20 dB. The mid-size model achieves that level of performance above about 8 MHz, while the shortest model slowly approaches the 20-dB level in the 12-14 MHz range. Below 5 MHz, the front-to-back ratio of the 65' model drops below 10 dB.</p>
+  <center>
+    <img src="330-6.gif" width="648" height="529" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    <img src="330-7.gif" width="647" height="530" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The VSWR curves of <b>Fig. 6</b> and <b>Fig. 7</b> use different reference impedances. Each reference value was chosen to provide the flattest possible SWR curve. Of the three wide-range LPDA models, only the longest maintains an SWR of less than 2:1 across the design range (with a 75-Ohm reference). The mid-size model, using a 95-Ohm reference, shows significant peaks above 2:1 in the upper frequency region--where SWR in the HF region becomes a more important factor in terms of line losses. The shortest model, using an 85-Ohm reference, shows similar upper HF peaks as well as some narrow peaks at the low end of the spectrum.</p>
+  <p>Not evident in these graphs is the very high variability in the behavior of the antenna patterns. The shorter the boom length, the wider the frequency range over which we encounter pattern distortion. The forward lobe may be shaped like a garden spade or even develop a minor double lobe. Rear patterns tend to broaden so that the 180-degree front-to-back ratio is no longer a reasonable guide to rear lobe behavior. Rear side lobes down by only 15 dB are common. These expanded rear lobes are marks of incipient harmonic activity in lobes to the rear of those most active at a given frequency. Hence, the problems increase with frequency.</p>
+  <p>If we take these models as typical of LPDA performance for the boom lengths indicated--and well-engineered exceptions certainly are possible--we are faced with a dilemma. The shortest boom is most easily maintained at operating height but has marginal performance at best. However, to attain performance roughly on a par with a 2-element quad--but across the wide passband--we need boom lengths that present very major mechanical challenges. The challenges do not merely include erecting the array, but also involve wind, snow, and ice load factors.</p>
+  <p>The single LPDA for the entire HF range concept arose over 20 years ago. At that time, the basic idea was a single antenna for a single receiver or transceiver, with a single feedline coming to the equipment's single antenna connection. In the intervening years, a number of technical advances have appeared that seem not yet to have affect HF LPDA use for complete spectrum coverage. Perhaps it is time to rethink the LPDA for 4-30 MHz.</p>
+  <p><b>Not 1, But 3</b></p>
+  <p>In the intervening years, a number of techniques for antenna selection or "polling" have appeared, and the technology is widely applied to cell and related services wherever higher gain and narrower beamwidth antennas are required. Such techniques might easily be applied to wide-range HF service as well.</p>
+  <p>In addition, for most applications requiring the coverage or scanning of the entire HF range, neither resources nor real estate are a major problem. Hence, one might well erect multiple towers, each one holding an LPDA optimized to the degree possible for a portion of the total frequency range. The feedlines can be brought to a central location for polling and then routed to the equipment.</p>
+  <p>The entire 4-30 MHz range is nearly 3 octaves in bandwidth. We may easily subdivide the design problem into 3 roughly 2:1 frequency-range models. 2:1 bandwidth LPDAs are significantly easier to design than a single antenna with nearly a 10:1 frequency range. To make the design challenge more difficult but the mechanical and maintenance problem less daunting, let's set a 50-56 foot limit to the boom in each case.</p>
+  <p>It might be tempting to suggest placing all three antennas on a single rotating tower. Such a system might well be made to work in some cases. However, it presents another dilemma. Mechanically, the antenna for the lowest portion of the range wants to rest at the lowest of the 3 levels, where mechanical support is greatest. However, electronically, it needs to be at the highest level for transmitting and receiving effectiveness in terms of lower elevation angles of radiation.</p>
+  <p>For the moment, we can set aside the problem of support systems and look in a more focused way at the electrical design of the individual LPDAs. For convenience, we shall divide the spectrum into 3 sections. The Low Range will run from 4 to 7 MHz. The Middle Range will cover 7 to 14 MHz. The High Range will complete the picture with 14 to 30 MHz coverage. The ratio of highest to lowest frequencies for each antenna increase with frequency, since we have limited the boom length. It is easier to reach beyond the 2:1 target ratio at the upper HF region than it is even to reach that ratio at the low end of the spectrum.</p>
+  <p>As well, the system of LPDAs in this design exercise has considerable overlap, as shown in the following table:</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Range       Boundary    Low Freq.         High Freq.        Overlap as a
+            Frequency   Limit for         Limit for         Percentage of
+                        &lt;2:1 vswr         &lt;2:1 vswr         boundary frequency
+low         7           3.75 MHz          7.70 MHz          12%
+middle      14          6.85              15.4              16%
+high        --          13.1              30+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>The overlapping coverage of the arrays points to a further advantage of a triple LPDA antenna farm for covering the HF spectrum: if one antenna suffers damage, the other two remain in operation. As well, some of the gap in coverage is filled by the remaining antennas.</p>
+  <p>The three antennas forming the array for this exercise have the following basic properties.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Range       No. El.,    Element     Tau         Sigma       Phase       Stub?
+            Boom Len.   Size/Type                           Line Zo
+Low         13          Tau-taper   0.9245      0.0250      200 Ohms    Yes
+            53.0'       2.5-6.4"
+Middle      16          1.0"        0.9300      0.0400      150         Yes
+            56.17'      alum.
+High        22          0.5"        0.9500      0.056       100         No
+            55.83'      alum.
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>In all three designs, the value of Tau was kept high to maintain a relatively high element density for better low-end performance. As well, the highest frequency of use was set well above the highest frequency to be used to sustain gain at the upper spectrum end. However, each antenna in the set presented unique design challenges, so each deserves an individual examination.</p>
+  <p><b>The Low-Range LPDA</b></p>
+  <center>
+    <img src="330-8.gif" width="192" height="387" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 8</b> provides an outline of the low-range antenna designed to cover 4 to 7 MHz. Clearly apparent is the relatively close spacing of the elements that results from the selection of a low Sigma value. Indeed, the value of Sigma is below that recommended in design calculations. Hence, the design was developed by a good bit of trial-and-error modeling. The values of Tau and Sigma, suited to the design length of the boom, also dictated the narrower frequency coverage for this array (1.75:1).</p>
+  <p>The low-range model has some interesting features. First, it is the only model of the set to require Tau-tapered elements to achieve the design goals. The elements range from 2.5 to 6.4 inches in diameter, as shown in the following partial model table.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+13 el 53' 3.8-7.5 MHz                Frequency = 4.35  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)  Dia(in) Segs
+
+1            0.000,-64.729,  0.000         0.000, 64.729,  0.000 6.41E+00  29
+2            6.559,-60.750,  0.000         6.559, 60.750,  0.000 5.93E+00  27
+3           12.622,-56.435,  0.000        12.622, 56.435,  0.000 5.48E+00  25
+4           18.228,-52.173,  0.000        18.228, 52.173,  0.000 5.07E+00  23
+5           23.410,-48.233,  0.000        23.410, 48.233,  0.000 4.69E+00  21
+6           28.201,-44.591,  0.000        28.201, 44.591,  0.000 4.33E+00  19
+7           32.630,-41.223,  0.000        32.630, 41.223,  0.000 4.00E+00  17
+8           36.724,-38.110,  0.000        36.724, 38.110,  0.000 3.70E+00  17
+9           40.509,-35.417,  0.000        40.509, 35.417,  0.000 3.42E+00  15
+10          44.009,-32.667,  0.000        44.009, 32.667,  0.000 3.16E+00  13
+11          47.244,-30.167,  0.000        47.244, 30.167,  0.000 2.93E+00  13
+12          50.235,-28.750,  0.000        50.235, 28.750,  0.000 2.70E+00  11
+13          53.000,-26.583,  0.000        53.000, 26.583,  0.000 2.50E+00  11
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>The stub used in the model is 1.5' of 600-Ohm shorted line.</p>
+  <center>
+    <img src="330-9.gif" width="646" height="503" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The free-space gain of the array from 4 to 7.5 MHz appears in <b>Fig. 9</b>. Only above 7 MHz does the gain drop below 6 dBi. (Do not let the steep curve mislead you into thinking that gain varies by a wide margin. The Y-axis spreads a relatively small range--0.5 dB--over a large linear distance.) The gain in this frequency region is similar to that of the 100' wide-range model, but with half the boom length. For the remainder of the frequency span, gain will be higher. Indeed, part of the design conception was to limit lower gain performance to the smallest possible portion of the entire passband. No other combination of Tau and Sigma within the general limit of the boom length approached these gain figures for the entire 4-7 MHz range.</p>
+  <center>
+    <img src="330-10.gif" width="646" height="501" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The 180-degree front-to-back ratio shows, in <b>Fig. 10</b>, generally increasing values as the frequency increases. Although low by upper HF standards, the values are in keeping with the general gain levels shown in <b>Fig. 9</b>.</p>
+  <center>
+    <img src="330-11.gif" width="651" height="502" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 11</b> provides a 60-Ohm referenced VSWR curve for the array. It surpasses 2:1 at two points: at 6.5 and 7.25 MHz. In general, VSWR values above 2:1 but below 2.5:1 may be considered acceptable in the lowest portion of the spectrum where even coaxial cable losses are close to negligible at these levels. If equipment is sensitive to the reflected voltage taken from a line sample, one might well add one of the newer automatic antenna tuners to the line to ensure full power output.</p>
+  <p>Short-boom LPDAs for the lower HF range press LPDA design not only up to its limits, but beyond. However, by judicious experimental modeling, it is possible to design an acceptable LPDA for the lowest frequency range without limiting the remainder of the HF spectrum to the same level of performance. Even a 53' boom length will present mechanical challenges, since the elements will be very long. The longest element is nearly 130'. The design element diameter can be approximated either through the use of open-frame triangular structures or by multiple strands of widely spaced wire.</p>
+  <p><b>The Mid-Range LPDA</b></p>
+  <center>
+    <img src="330-12.gif" width="267" height="339" border="2" vspace="5" hspace="9">
+  </center>
+  <p>As shown in <b>Fig. 12</b>, the mid-range LPDA in the set is quite standard in appearance. The 16-element design using 1.0" diameter aluminum elements requires a 56.17' boom and a 150-Ohm phase-line. The following wire table provides element details.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+.93/.04 6.88-15 MHz                      Frequency = 13  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1            0.000,-36.200,  0.000         0.000, 36.200,  0.000 1.00E+00  27
+2            5.904,-34.150,  0.000         5.904, 34.150,  0.000 1.00E+00  27
+3           11.395,-31.915,  0.000        11.395, 31.915,  0.000 1.00E+00  25
+4           16.501,-29.681,  0.000        16.501, 29.681,  0.000 1.00E+00  23
+5           21.250,-27.603,  0.000        21.250, 27.603,  0.000 1.00E+00  21
+6           25.667,-25.671,  0.000        25.667, 25.671,  0.000 1.00E+00  21
+7           29.774,-23.874,  0.000        29.774, 23.874,  0.000 1.00E+00  19
+8           33.594,-22.203,  0.000        33.594, 22.203,  0.000 1.00E+00  19
+9           37.146,-20.649,  0.000        37.146, 20.649,  0.000 1.00E+00  17
+10          40.450,-19.203,  0.000        40.450, 19.203,  0.000 1.00E+00  15
+11          43.522,-17.859,  0.000        43.522, 17.859,  0.000 1.00E+00  15
+12          46.380,-16.609,  0.000        46.380, 16.609,  0.000 1.00E+00  15
+13          49.037,-15.525,  0.000        49.037, 15.525,  0.000 1.00E+00  13
+14          51.520,-14.654,  0.000        51.520, 14.654,  0.000 1.00E+00  13
+15          53.892,-14.042,  0.000        53.892, 14.042,  0.000 1.00E+00  11
+16          56.167,-13.692,  0.000        56.167, 13.692,  0.000 1.00E+00  11
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>The 72.4' longest element will likely require an equivalent diameter considerably in excess of 1 inch, while the 27' shortest element might well have an equivalent uniform diameter closer to a half inch. Tau-tapering the elements in this array had no significant effect upon the performance. However, a shorted stub consisting of 2' of 600-Ohm line proved useful.</p>
+  <p>Although the bulk of the elements adhere to the 0.93 Tau and 0.04 Sigma values, the rear-most and forward-most elements were subjected to Tau-circularization to optimize performance. A close look at <b>Fig. 12</b> will reveal that the element tips do not form a straight line, but a small ogee curve.</p>
+  <center>
+    <img src="330-13.gif" width="647" height="503" border="2" vspace="5" hspace="9">
+  </center>
+  <p>As shown in <b>Fig. 13</b>, the average free-space gain of the array is between 7.1 and 7.15 dB, about the same as the gain of a 2-element quad. Note that this performance was achieved only by the 164' full-spectrum LPDA model--about 3 times longer than our mid-range LPDA. Because the boom length has been limited, resulting in a fairly low value of Sigma, the upper end of the spectrum shows increasing fluctuations, for a total gain variance of about 0.35 dB from 7 to 14 MHz. The gain drops below 6.9 dBi only within the overlap region with the high- range LPDA.</p>
+  <center>
+    <img src="330-14.gif" width="648" height="502" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 14</b> shows the 180-degree front-to-back ratio across the passband. The ratio remains above 20 dB, with well-control rear lobes, up to 14 MHz.</p>
+  <center>
+    <img src="330-15.gif" width="648" height="502" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The 50-Ohm SWR curve in <b>Fig. 15</b> shows the mid-range LPDA to maintain under 2:1 across the pass band. The curve would be slightly better using a reference impedance of 55 Ohms.</p>
+  <p>The mid-range LPDA is in every way conventional, including the circularized Tau factor used to modify the original design that emerged from initial calculations. It provides good performance for the boom length and number of elements.</p>
+  <p><b>The High-Range LPDA</b></p>
+  <p>The high-range LPDA requires only scant comment, since it has appeared before in these pages.</p>
+  <center>
+    <img src="330-16.gif" width="366" height="279" border="2" vspace="5" hspace="9">
+  </center>
+  <p>As the outline in <b>Fig. 16</b> reveals, the design is the same 14-30 MHz design on a 55.83' boom developed in detail in the past few months. The design uses a parasitic director to enhance upper range performance more than circularizing Tau alone can do. The following wire table will review the dimensions.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+14-30 MHz .95/.056 21+dir 55.8            Frequency = 28  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1            0.000,-18.025,  0.000         0.000, 18.025,  0.000 5.00E-01  25
+2            4.015,-17.083,  0.000         4.015, 17.083,  0.000 5.00E-01  23
+3            7.829,-16.167,  0.000         7.829, 16.167,  0.000 5.00E-01  23
+4           11.452,-15.367,  0.000        11.452, 15.367,  0.000 5.00E-01  21
+5           14.894,-14.598,  0.000        14.894, 14.598,  0.000 5.00E-01  21
+6           18.164,-13.868,  0.000        18.164, 13.868,  0.000 5.00E-01  19
+7           21.271,-13.175,  0.000        21.271, 13.175,  0.000 5.00E-01  19
+8           24.222,-12.516,  0.000        24.222, 12.516,  0.000 5.00E-01  17
+9           27.025,-11.890,  0.000        27.025, 11.890,  0.000 5.00E-01  17
+10          29.689,-11.296,  0.000        29.689, 11.296,  0.000 5.00E-01  15
+11          32.219,-10.731,  0.000        32.219, 10.731,  0.000 5.00E-01  15
+12          34.623,-10.195,  0.000        34.623, 10.195,  0.000 5.00E-01  15
+13          36.907, -9.685,  0.000        36.907,  9.685,  0.000 5.00E-01  13
+14          39.076, -9.201,  0.000        39.076,  9.201,  0.000 5.00E-01  13
+15          41.137, -8.741,  0.000        41.137,  8.741,  0.000 5.00E-01  13
+16          43.095, -8.304,  0.000        43.095,  8.304,  0.000 5.00E-01  11
+17          44.955, -7.888,  0.000        44.955,  7.888,  0.000 5.00E-01  11
+18          46.722, -7.494,  0.000        46.722,  7.494,  0.000 5.00E-01  11
+19          48.400, -7.119,  0.000        48.400,  7.119,  0.000 5.00E-01   9
+20          49.995, -6.763,  0.000        49.995,  6.763,  0.000 5.00E-01   9
+21          51.510, -6.425,  0.000        51.510,  6.425,  0.000 5.00E-01   9
+22          55.833, -7.392,  0.000        55.833,  7.392,  0.000 5.00E-01  11
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>The feedpoint is on wire 21, and the phase line for this model is 100 Ohms. (The 250-Ohm phase line model uses a 14.2' element for wire 22.) The following graphs are presented to show performance below 14 MHz as wel as within the design passband.</p>
+  <center>
+    <img src="330-17.gif" width="648" height="504" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 17</b> shows the gain curve at 0.25 MHz intervals. Note that this close spacing of check point reveals two relatively weak region: at 19.75 and 26.5 MHz. One or both of these regions can be virtually eliminated by adding a shorted stub to the rear of the assembly. Neither is so serious as to reverse the antenna pattern, but both show that even with relatively high values of Tau and Sigma, harmonic operation of elements to the rear of the most active element may still occur.</p>
+  <p>The free-space gain drops off rapidly below 14 MHz, but remains above 8.2 dBi at 13.25 MHz. The parasitic director permits a free-space gain above 9.0 dBi at 28.25 MHz and higher.</p>
+  <center>
+    <img src="330-18.gif" width="648" height="506" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The 180-degree front-to-back ratio, shown in <b>Fig. 18</b>, reaches 20 dB by 13.75 MHz and remains above that value until 29.5 MHz. The exceptions are the two weak regions previously noted. The weaknesses can be removed by using a 250-Ohm phase line. Using this line will lower the gain slightly across the passband and result in a feedpoint impedance best referenced to about 110 Ohms. A 2:1 wide-band transmission-line transformer balun would provide a satisfactory match to a 50-Ohm cable.</p>
+  <center>
+    <img src="330-19.gif" width="648" height="504" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 19</b> provides the VSWR curve relative to a directly fed 50-Ohm feedline. The SWR drops to under 2:1 by 13.1 MHz. Only in the upper region of the passband--largely as a result of adding the parasitic director--does the SWR approach 2:1.</p>
+  <p>With high-range LPDA performance that is superior to the mid-range LPDA down to 13.1 MHz, the crossover point between the mid-range and the high-range LPDAs is a matter of choice at installation. The overall free-space gain of the high-range array averages about 8.8 dBi, with a superior front-to-back ratio.</p>
+  <p><b>Conclusion</b></p>
+  <p>Three 55' booms just about equal the total boom length of the 164' wide-range LPDA. However, each of the individual LPDAs with an approximate 2:1 frequency span manages patterns that are better behaved. The use of three separate arrays confines lesser performance to the frequency region where it may be necessary, with increasingly better performance as we move up in the frequency regions. As well, the use of separate arrays and electronic selection and/or polling offers at least partial system operation should one antenna be down for maintenance.</p>
+  <p>The triple LPDA array is an expensive proposition, best fit for military, governmental, or commercial applications calling for relatively complete coverage of the HF spectrum. The present design exercise has attempted to see if there might be an alternative to the use of single arrays with somewhat marginal performance in such applications. Using 3 LPDAs, each optimized to a portion of the spectrum, provides increasingly better performance within the 55' boom limitation.</p>
+  <p>It is possible, in principle, to build an unconditionally stable LPDA to cover the range from 3 to 30 MHz. The free-space gain will range from a low of 10.25 dBi to a high of about 11.35 dBi, using a Tau of 0.955 and a Sigma of 0.18. Unfortunately, this 60-element antenna will be just short of 1250' long.</p>
+  <p>Perhaps three relatively short LPDAs are not so bad after all as a substitute.</p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p><i>Updated 03-01-2002. &COPY; L. B. Cebik, W4RNL. The original item appeared in</i> AntenneX <i>for February, 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>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p><a href="../radio.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Go to Main Index</a></p>
+  <p class="topics-footer">Topics: <a href='../topics.html#hf-multi-band'>HF Multi Band</a>, <a href='../topics.html#lpda'>LPDA</a></p><br>
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+  <meta name="keywords" content="LPDA, HF Upper">
+  <title>3 More 14-30 MHz LPDA Designs</title>
+  <link rel="stylesheet" href="../styles.css">
+</head>
+<body>
+  <center>
+    <h1>3 More 14-30 MHz LPDA Designs</h1>
+  </center>
+  <center>
+    <h3>L. B. Cebik, W4RNL</h3>
+  </center><br>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  <p>In an earlier article ("Long-Boom LPDAs for 14-30 MHz"), I described the basic design of an idealized log-periodic dipole array (LPDA) for the 20-10 meter range. It had a free-space gain range of 8.7 to 9.0 dBi, with correspondingly high front-to-back figures. The 56' boom was not considered a hindrance for this "dream beam." The array used a Tau of 0.9500 and a Sigma of 0.0560 along with 22 elements to achieve its performance.</p>
+  <p>The design had some interesting features, designed to overcome some of the weaknesses of finite-length LPDAs. First, the value of Tau was circularized in the elements at each end of the array, resulting in a shortening of the very longest elements and a lengthening of the shortest elements. The result is an LPDA whose element ends describe a slight ogee curve. The "Tau-circularizing" technique tends to equalize gain at the passband ends relative to mid-band performance. However, it must be used with care so as not to unduly disturb the feedpoint impedance across the pass band.</p>
+  <p>Since the circularizing technique is most effective at the lower end of the passband, gain still tends to fall off at the upper end of the passband unless the shortest element is calculated as if the highest operating frequency was about 1.6 times its actual value. Such a high upper-end frequency limit adds a number of elements to the design, along with considerable boom length. Interestingly, early work on LPDAs in the 1960s recognized a "high frequency truncation coefficient," but failed to associate the idea with a clear notion of which elements in an LPDA are active. Early thinking led to the misconception that only the immediately adjacent elements to the one nearest resonance were active. In fact, virtually all elements forward of the most active element are themselves active and contribute to the pattern formation for a given frequency.</p>
+  <p>To effect the desired performance gain with fewer elements, the forward-most element was made parasitic and lengthened to form a director for the highest band (10 meters). The length and spacing for this element are selected to achieve the desired gain with least effect on the feedpoint impedance of the array at all other frequencies. The further away from the closest LPDA element, the higher the gain, but the lower the front-to-back ratio and the greater the disturbance to feedpoint impedance values.</p>
+  <p>These same design techniques can be applied to shorter-boom LPDAs with relatively equal success--subject only to limitations imposed by using fewer elements on a shorter boom. In this article, in addition to a quick review of the ideal LPDA for 20-10 meters, we shall examine designs using 16, 12, and 9 elements on 42, 32, and 21 foot booms respectively. The ideal design replicates 4-element monoband Yagi performance assuming a moderately long boom. The 16-element design provides close to long-boom 3-element monoband Yagi performance across the pass band--about 8 dBi free-space gain. The 12-element model gives us about 2-element quad or short-boom 3-element monoband Yagi performance--about 7 dBi across the passband. Finally, the shortest member of the family comes close to 2-element monoband reflector-driver Yagi performance--something close to 6 dBi free-space gain. When comparing the performance numbers to those of other types of arrays, remember that the LPDA provides performance both within and between the ham bands.</p>
+  <center>
+    <img src="3lpda-1.gif" width="395" height="870" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 1</b> provides some comparative outline sketches of the 4 members of this LPDA family. There is little difference in the longest and shortest elements for each set, but considerable difference in total boom length, total weight, and performance. Note also that the position of the parasitic director has been selected by hand to optimize each design within the overall objectives for each.</p>
+  <center>
+    <img src="3lpda-2.gif" width="491" height="302" border="2" vspace="5" hspace="9">
+  </center>
+  <p>In <b>Fig. 2</b>, we have the free-space azimuth patterns for the family members for the middle of the 20-meter band (14.175 MHz). The stepped gain differential is clearly apparent. The larger step downward in gain for the smallest LPDA is a function of the fact that the shorter the LPDA, the lower both Tau and Sigma go, mutually reducing gain potential for the array.</p>
+  <p>The rear lobes of an LPDA pattern in a very general way are the reciprocal of the forward lobes. The higher the forward gain, the higher the 180-degree front-to-back ratio. Once that ratio passes about 30 dB, we find variations in the rear pattern, even in the best controlled arrays. The rear may look like a single lobe, a three-lobe pattern with either the central or side lobes emphasized, or a small ripply blob. Although gain and front-to-rear performance are closely correlated, the natural variations in each over the full passband do not directly coincide.</p>
+  <center>
+    <img src="3lpda-3.gif" width="486" height="305" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 3</b> shows the corresponding free-space azimuth patterns for 28.85 MHz. Here, we do not see the even stair-stepping of forward gain due to the variable treatment of the parasitic director. The highest gain model (9556) has a widely spaced director which reduces the front-to-back ratio to barely 20 dB. In contrast, the 16-element model (9306) shows considerably better rearward performance, but less relative forward gain--due to the close spacing of the director (see Fig. 1). The smallest two LPDAs in the collection (9105 and 8705) have relatively wide-spaced directors, although 9105 manages a higher gain than perhaps it needed for balance across the entire passband. However, as we shall see, it also shows the widest gain range across 10 meters.</p>
+  <p>In designing the members of this LPDA family, I set as a goal the equalization of high-end gain with mid-band gain (about 21 MHz) with acceptable feedpoint impedances and a 180-degree front-to-back ratio of 20 dB. Only in a couple of instances does the front-to-back ratio dip slightly below the target value.</p>
+  <p>The feedpoint impedance was selected to match either a 50-Ohm or a 75-Ohm system. In some designs, the use of 75-Ohm coaxial cable or a 75-to-50 Ohm balun transformer may yield lower SWR values than a direct 50-Ohm feed. The practical concern is not so much line losses, but the sensitivity of some equipment to SWR values above 1.5:1: some gear tends to reduce power or shut down at SWR values well below the traditional limit of 2:1. In all cases, for the low impedance feed system, the phase lines were set at a characteristic impedance (Zo) of 100 Ohms.</p>
+  <p>The designs were also tested--and modified, if necessary--for a phase line Zo of 250 Ohms. As we shall see, the higher phase-line impedance reduces gain performance slightly (0.1 to 0.15 dB on average), but results in an unconditionally stable array across the passband. The mid-point feed impedance ranges from 100 to 120 Ohms, and the arrays may be fed using a 2:1 broad-band transmission line transformer, such as one of those designed by W2FMI, Jerry Sevick, and available from Amidon. In general, the higher phase-line Zo results in a smoother SWR curve across the passband and a total absence of "spikes."</p>
+  <p>All of the family members use an idealized element diameter of 0.5". In general, the dimensions shown for each family member are satisfactory for all but the longest and shortest elements (including the parasitic director) in the arrays. Elements whose lengths have been adjusted for a parasitic function or in the course of circularizing Tau should be remodeled using the exact element diameter taper to be used the version constructed. In practical terms, this means remodeling the entire array with each element using its diameter taper. However, this necessary procedure may limit those who model LPDAs in NEC-2. The Leeson-correction system for linear elements using a tapered diameter schedule will only function on elements that are within about 15% of resonant length for the frequency being tested. Elements outside that range will not be corrected, and subtle errors in the modeled performance may result. Hence, NEC-4 would be the software of choice for final design modeling for the LPDAs in our family.</p>
+  <p><b>A Review of 9556</b></p>
+  <p>9556 is the ideal 56' long LPDA which we have examined in the past. The following table gives the overall element length and cumulative spacing for the design.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+Element #        Length (feet)         Spacing from
+                                       Reflector (feet)
+ 1               36.05                 -----
+ 2               34.17                  4.02
+ 3               32.33                  7.83
+ 4               30.73                 11.45
+ 5               29.20                 14.89
+ 6               27.74                 18.16
+ 7               26.35                 21.27
+ 8               25.03                 24.22
+ 9               23.78                 27.03
+10               22.59                 29.69
+11               21.46                 32.22
+12               20.39                 34.62
+13               19.37                 36.91
+14               18.40                 39.08
+15               17.48                 41.14
+16               16.61                 43.10
+17               15.78                 44.96
+18               14.99                 46.72
+19               14.24                 48.40
+20               13.53                 50.00
+21               12.85                 51.51
+22               14.78/14.60           55.83  Director:  See text.
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>The two lengths listed for the director apply to the different values of phase-line Zo: the longer director applies to the 100-Ohm line, while the shorter applies to the 250-Ohm line. The change in length was necessitated to optimize--so far as possible--the gain and SWR curves on 10 meters.</p>
+  <center>
+    <img src="3lpda-4.gif" width="535" height="230" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 4</b> shows the SWR curves for the entire passband, taken at 0.25 MHz intervals. The interval is sufficiently small to show signs of performance instability, and none appear with either choice of phase line Zo. In fact, the design does not require the use of a shorted transmission line stub behind the longest element, although one may be added to set all of the elements at the same DC value. Something of about 450-600 Ohms characteristic impedance and a length of about a foot should do the job with minimal disturbance to the performance curves. When both Tau and Sigma together reach a certain level--obtained in this design--a stub is not necessary to control or remove impedance and performance spikes.</p>
+  <p>The anticipated performance of the array for each value of phase line Zo is listed in the following tables.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+9556143X:  22 elements (21 LPDA + 1 par):  55.83' boom: 0.5" dia.
+Tau = 0.9500; Sigma = 0.0560:  ogee'd:  TL = 100 Ohms
+
+Freq.     Gain      F-B       Feed Impedance      50-Ohm    75-Ohm
+MHz       dBi       dB        R +/- jX Ohms       VSWR      VSWR
+20
+14.0      8.85      24.84     75.6 + j 0.2        1.51      1.01
+14.175    8.85      30.28     74.2 - j 3.5        1.49      1.05
+14.35     8.81      39.01     71.9 - j 6.5        1.46      1.10
+17
+18.118    8.83      38.18     67.2 - j 7.0        1.38      1.16
+15
+21.0      8.72      42.61     64.7 + j 0.1        1.29      1.16
+21.225    8.71      41.67     66.9 - j 0.5        1.34      1.12
+21.45     8.72      41.04     67.2 - j 1.8        1.35      1.12
+12
+24.94     8.81      32.04     73.2 - j 2.2        1.47      1.04
+10
+28.0      8.92      24.94     72.3 + j16.5        1.58      1.26
+28.85     9.04      21.29     47.3 - j30.7        1.87      1.98
+29.7      9.05      19.57     50.2 + j20.9        1.51      1.69
+
+Delta Gain:  0.34 dB
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+9556143Y:  22 elements (21 LPDA + 1 par):  55.83' boom: 0.5" dia.
+Tau = 0.9500; Sigma = 0.0560:  ogee'd:  TL = 250 Ohms
+(Parasitic length revised for 250-Ohm TL:  from +/-7.392 to +/-7.3)
+
+Freq.     Gain      F-B       Feed Impedance      100-Ohm
+MHz       dBi       dB        R +/- jX Ohms       VSWR
+20
+14.0      8.68      26.48     131.1 - j 5.5       1.32
+14.175    8.68      30.95     134.1 - j 3.9       1.34
+14.35     8.69      34.01     137.6 - j 8.2       1.39
+17
+18.118    8.71      47.27     130.3 - j 9.4       1.32
+15
+21.0      8.79      36.30     130.3 - j11.9       1.33
+21.225    8.81      34.27     132.2 - j18.4       1.38
+21.45     8.80      33.29     127.4 - j26.1       1.40
+12
+24.94     8.63      32.78      98.7 - j21.6       1.24
+10
+28.0      8.76      25.63      82.1 - j39.7       1.61
+28.85     8.66      25.92     102.0 - j 7.5       1.08
+29.7      8.83      22.34      70.1 - j40.9       1.82
+
+Delta Gain:  0.20 dB
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>Since both models are stable across the entire passband, the choice of phase line Zo value is optional with the builder. Note that the average gain of the model with the higher Zo is about 0.15 dB lower than for the model using a 100-Ohm line. However, the 250-Ohm line model shows a lower variation in gain across the pass band.</p>
+  <p><b>9306: 16 Elements on a 42' Boom</b></p>
+  <p>If 9556 is unrealistic for all but a hand full of builders, 9306 might appeal to perhaps a double handful of antenna constructors. The 42' boom is somewhat less daunting, but should not be underestimated for its support complexity. As well, the 16 elements carry considerable raw weight and wind load. Nonetheless, the array comes close to providing full 3-element monoband performance from 14 to 30 MHz.</p>
+  <p>The following table provides dimensions.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+Element #        Length (feet)         Spacing from
+                                       Reflector (feet)
+ 1               35.80                 -----
+ 2               33.80                  4.43
+ 3               31.70                  8.55
+ 4               29.60                 12.38
+ 5               27.60                 15.94
+ 6               25.67                 19.25
+ 7               23.87                 22.33
+ 8               22.20                 25.20
+ 9               20.65                 27.86
+10               19.20                 30.34
+11               17.86                 32.64
+12               16.61                 34.79
+13               15.45                 36.78
+14               14.36                 38.63
+15               13.36                 40.36
+16               14.70/14.20           41.96  Director:  See text.
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>Regardless of the choice of phase line Zo, the design uses a 0.5' long shorted stub with a 600-Ohm characteristic impedance. Fig. 5 will show why the stub--optional on the big brother of this LPDA--is necessary here.</p>
+  <center>
+    <img src="3lpda-5.gif" width="575" height="230" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The SWR curves for two versions of the LPDA appear in <b>Fig. 5</b>. The 100- Ohm phase line curve uses the 75-Ohm SWR because it shows smaller excursions than the corresponding 50-Ohm line. However, either feedline would be quite usable.</p>
+  <p>The 250-Ohm phase line model is completely stable. However, the 100-Ohm line model shows a spike at about 23 MHz. The impedance spike actually peaks narrowly at 22.95 MHz with an SWR that is greater than 4:1 and a reduction in gain to under 6 dBi. The front-to-back ratio is less than 10 dB. Such a narrow spike, well outside of the amateur bands, may be acceptable for some builders, not for others, depending upon the design specifications one sets for the array.</p>
+  <p>Within the ham bands, the performance of the array in both versions can be summarized in two tables.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+9306Q16:  16 elements (15 LPDA + 1 par):  41.96' boom: 0.5" dia.
+Tau = 0.9300; Sigma = 0.0600:  ogee'd:  TL = 100 Ohms
+
+Freq.     Gain      F-B       Feed Impedance      50-Ohm    75-Ohm
+MHz       dBi       dB        R +/- jX Ohms       VSWR      VSWR
+20
+14.0      8.08      28.78     61.5 + j 3.3        1.24      1.23
+14.175    8.07      33.97     67.2 + j 5.1        1.36      1.14
+14.35     8.05      39.35     72.3 + j 1.4        1.45      1.04
+17
+18.118    8.06      33.96     74.0 - j 5.2        1.49      1.07
+15
+21.0      8.02      37.06     70.9 - j 1.0        1.42      1.06
+21.225    8.03      36.56     72.8 - j 4.3        1.47      1.07
+21.45     8.03      36.38     71.8 - j 8.6        1.47      1.13
+12
+24.94     8.00      40.49     71.5 + j 1.3        1.43      1.05
+10
+28.0      7.77      27.28     72.1 + j 0.4        1.44      1.04
+28.85     7.93      25.88     47.7 - j11.1        1.26      1.63
+29.7      8.15      20.55     56.0 + j33.3        1.88      1.79
+
+Delta Gain:  0.38 dB
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+9306P16:  16 elements (15 LPDA + 1 par):  41.96' boom: 0.5" dia.
+Tau = 0.9300; Sigma = 0.0600:  ogee'd:  TL = 250 Ohms
+(Parasitic length revised for 250-Ohm TL:  from +/-7.35 to +/-7.1)
+
+Freq.     Gain      F-B       Feed Impedance      120-Ohm
+MHz       dBi       dB        R +/- jX Ohms       VSWR
+20
+14.0      7.95      31.96     126.2 - j15.3       1.14
+14.175    7.97      34.68     126.4 - j 7.5       1.08
+14.35     7.99      38.02     133.4 - j 2.5       1.11
+17
+18.118    7.90      335980    119.7 - j 9.1       1.08
+15
+21.0      7.91      38.50     116.2 - j26.3       1.25
+21.225    7.86      39.66     112.2 - j20.9       1.21
+21.45     7.82      40.10     111.6 - j14.8       1.16
+12
+24.94     7.83      32.41     112.4 - j41.0       1.43
+10
+28.0      7.70      31.41     104.5 - j15.5       1.22
+28.85     7.85      27.78     126.6 + j 5.1       1.07
+29.7      7.81      23.33     137.3 - j82.3       1.90
+
+Delta Gain:  0.29 dB
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>The 250-Ohm phase line version of the 16-element LPDA shows a gain deficit of about 0.15 dB on average relative to the 100-Ohm phase line version. In exchange for the reduced gain, the builder obtains a completely stable array, with no weaknesses. In general, the lower the phase-line Zo, the greater the tendency to have one or more weaknesses in the overall performance curve, and these are generally signaled by a spike in the SWR curve. However, the SWR spike maximum and the greatest disturbance to performance may not occur at precisely the same frequency. However, they will be overlapping phenomena within 100 kHz or so.</p>
+  <p>The higher the values of both Tau and Sigma--resulting in a higher number of elements and a longer boom--the narrower that a spike will be. The use of the stub can reduce either the number or severity of a spike, as well as control its frequency. In this case, the spike was moved to a frequency that is generally harmless in terms of amateur operations. As the values of Tau and/or Sigma are reduced, the chief protection from spikes becomes a higher phase line Zo.</p>
+  <p><b>9105: 12 Elements on a 32' Boom</b></p>
+  <p>The next step down the ladder in our family of LPDAs is a 12-element model on a 32' boom. The dimensions of the array appear in the following table.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+Element #        Length (feet)         Spacing from
+                                       Reflector (feet)
+ 1               36.00                 -----
+ 2               34.00                  4.15
+ 3               31.30                  7.93
+ 4               28.47                 11.36
+ 5               25.90                 14.48
+ 6               23.55                 17.33
+ 7               21.42                 19.93
+ 8               19.47                 22.28
+ 9               17.70                 24.43
+10               16.10                 26.38
+11               14.63                 28.15
+12               15.17                 32.00  Director:  See text.
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>For this design, it was unnecessary to alter the length of the director to obtain acceptable results with both the 100-Ohm and 250-Ohm phase lines. The design does use a 1' 450-Ohm Zo shorted stub on the rear of the boom. However, as we shall see, this stub can reduce and/or move weaknesses that appear in the 100-Ohm phase line model, but it cannot eliminate "spikes" altogether.</p>
+  <center>
+    <img src="3lpda-6.gif" width="575" height="410" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig.6</b> shows the 50-Ohm SWR with the 100-Ohm phase line and the 110-Ohm SWR with the 250-Ohm phase line. As we reduce the number of elements and boom length--with a correspondingly reduced value of Tau--we should note larger excursions of SWR, regardless of the phase line value. The excursions are interesting, if we also track the changes of resistance and reactance along the way. Maximum values of capacitive and inductive reactance tend to occur when the resistance value is near its mean, while reactance tends to go to zero when the resistive component of the feedpoint impedance is at a high or low. Excursions of reactance are smaller with higher values of Tau and Sigma (together): hence, the SWR changes are smaller. As we shorten the boom and reduce Tau, the reactance undergoes a wider range of values.</p>
+  <p>The spike in the 50-Ohm curve in <b>Fig. 6</b> is also more extreme than the one in <b>Fig. 5</b>. It is both higher--exceeding an SWR of 10:1--and wider, covering nearly a half MHz. <b>Fig. 7</b> shows the worst-case azimuth pattern, in which the pattern technically reverses direction.</p>
+  <center>
+    <img src="3lpda-7.gif" width="375" height="280" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 8</b> shows why. Virtually all of the elements to the rear of the active one are also active, but in a harmonic mode, as indicated by the "double-hump" curves that register the current magnitude. This example is especially interesting, since in most cases, not all of the rear elements will be so active.</p>
+  <center>
+    <img src="3lpda-8.gif" width="436" height="263" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The following two tables provide the anticipated performance of the 12- element array.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+91051431:  12 elements (11 LPDA + 1 par):  32.000' boom: 0.5" dia.
+Tau = 0.9099; Sigma = 0.0550:  ogee'd:  TL = 100 Ohms
+
+Freq.     Gain      F-B       Feed Impedance      50-Ohm    75-Ohm
+MHz       dBi       dB        R +/- jX Ohms       VSWR      VSWR
+20
+14.0      7.33      32.93     94.6 - j 1.8        1.89      1.26
+14.175    7.30      27.52     84.5 + j 5.7        1.78      1.26
+14.35     7.25      24.91     71.0 - j16.0        1.55      1.25
+17
+18.118    7.19      26.48     62.7 - j 0.2        1.25      1.20
+15
+21.0      7.24      24.86     82.5 - j 5.4        1.66      1.12
+21.225    7.26      25.85     78.2 - j11.9        1.62      1.17
+21.45     7.28      27.19     71.8 - j14.3        1.54      1.22
+12
+24.94     7.19      24.57     47.7 + j 1.1        1.05      1.57
+10
+28.0      7.57      27.68     41.4 - j18.6        1.56      1.97
+28.85     7.69      24.26     35.6 + j 1.6        1.41      2.11
+29.7      8.01      19.95     70.6 + j25.9        1.73      1.43
+
+Delta Gain:  0.82 dB
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+91051431:  12 elements (11 LPDA + 1 par):  32.000' boom: 0.5" dia.
+Tau = 0.9099; Sigma = 0.0550:  ogee'd:  TL = 250 Ohms
+
+Freq.     Gain      F-B       Feed Impedance      110-Ohm
+MHz       dBi       dB        R +/- jX Ohms       VSWR
+20
+14.0      7.12      26.83     106.2 - j 0.8       1.04
+14.175    7.07      25.63     117.2 + j11.7       1.13
+14.35     7.03      24.90     134.2 + j14.2       1.26
+17
+18.118    7.02      25.95     131.3 - j15.8       1.25
+15
+21.0      7.20      27.91     107.7 - j28.8       1.30
+21.225    7.18      28.71     105.2 - j21.9       1.23
+21.45     7.15      29.10     106.2 - j16.4       1.17
+12
+24.94     7.20      27.34     138.9 + j 6.0       1.26
+10
+28.0      7.38      28.70      70.4 - j22.4       1.66
+28.85     7.52      26.51      84.3 - j 6.0       1.31
+29.7      7.89      20.33     113.4 - j63.3       1.75
+
+Delta Gain:  0.88 dB
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>Performance of the 250-Ohm phase line model is down about 0.14 dB from the 100-Ohm phase line model. However, the 250-Ohm version is stable across the entire passband.</p>
+  <p><b>8705: 9 Elements on a 21' Boom</b></p>
+  <p>The final member of the LPDA family is the shortest--only 21' in boom length (plus a little excess for element mounting fixtures). As well it has the least number of elements--9--and the lowest value of Tau--0.8688. Indeed, these values are about the least that I would recommend for satisfactory performance, if we define that term as being close to the performance of a 2-element reflector-driver monoband Yagi. Even so, we shall discover that the low values used in the design of the LPDA yield the highest fluctuations in performance.</p>
+  <p>The dimensions for the 9-element array are as follows.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+Element #        Length (feet)         Spacing from
+                                       Reflector (feet)
+ 1               36.00                 -----
+ 2               32.30                  3.89
+ 3               28.06                  7.26
+ 4               24.38                 10.19
+ 5               21.18                 12.74
+ 6               18.40                 14.96
+ 7               15.98                 16.88
+ 8               13.89                 18.55
+ 9               13.60                 21.00  Director:  See text.
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>Both designs employ a stub. In both cases, a 1.9' shorted length of 450-Ohm transmission line or its equivalent is sufficient to tame the design.</p>
+  <p>As with the 12-element model, the 9-element design requires no change in the length of the director as we move from a 100-Ohm phase line to a 250-Ohm version. However, the spike which we might anticipate in the 100-Ohm phase line model shows itself vividly in <b>Fig. 9</b>, the SWR curves for both phase lines across the entire passband. The spike is higher and wider (with respect to frequency) than any other so far encountered. SWR values higher than 2:1 extend from abut 26.25 to 27.5 MHz.</p>
+  <center>
+    <img src="3lpda-9.gif" width="583" height="385" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Although the spike in the 100-Ohm phase line model is located well outside the amateur bands, it does interfere with operation of the array on the Citizen's Band. In contrast, the 250-Ohm phase line model permits operation throughout the passband.</p>
+  <p>Amateur band performance of both models appears in the following tables.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+8705B:  8 elements (7 LPDA + 1 par):  21.000' boom: 0.5" dia.
+Tau = 0.8688; Sigma = 0.0523:  ogee'd:  TL = 100 Ohms
+
+Freq.     Gain      F-B       Feed Impedance      50-Ohm    75-Ohm
+MHz       dBi       dB        R +/- jX Ohms       VSWR      VSWR
+20
+14.0      5.63      11.20     82.3 - j27.4        1.91      1.43
+14.175    5.74      11.88     67.4 - j29.4        1.79      1.53
+14.35     5.83      12.43     55.4 - j26.0        1.65      1.65
+17
+18.118    6.03      14.13     66.3 + j25.1        1.67      1.46
+15
+21.0      6.33      15.06     61.5 + j19.2        1.49      1.41
+21.225    6.30      15.10     69.5 + j17.6        1.56      1.29
+21.45     6.26      15.18     76.1 + j11.8        1.58      1.17
+12
+24.94     6.13      18.10     67.2 + j29.5        1.79      1.53
+10
+28.0      6.03      18.21     61.4 - j19.0        1.49      1.41
+28.85     6.17      17.05     64.6 - j10.4        1.37      1.23
+29.7      6.24      17.36     61.1 - j14.7        1.39      1.35
+
+Delta Gain:  0.70 dB
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+8705C:  8 elements (7 LPDA + 1 par):  21.000' boom: 0.5" dia.
+Tau = 0.8688; Sigma = 0.0523:  ogee'd:  TL = 250 Ohms
+
+Freq.     Gain      F-B       Feed Impedance      120-Ohm
+MHz       dBi       dB        R +/- jX Ohms       VSWR
+20
+14.0      5.55      10.69      93.6 - j18.8       1.36
+14.175    5.61      11.07      91.7 - j 3.0       1.31
+14.35     5.66      11.38      94.6 + j12.5       1.30
+17
+18.118    6.09      13.58     168.3 - j48.3       1.61
+15
+21.0      6.14      15.48     150.5 - j29.6       1.37
+21.225    6.13      15.46     136.8 - j41.6       1.42
+21.45     6.12      15.44     120.8 - j45.3       1.45
+12
+24.94     6.26      17.22     159.2 - j47.0       1.55
+10
+28.0      6.27      19.07     104.5 - j13.6       1.20
+28.85     6.27      19.74     100.4 - j29.4       1.38
+29.7      6.39      22.64      80.6 - j31.2       1.66
+
+Delta Gain:  0.84 dB
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>The average gain of the two arrays across the entire passband is about the same. However, the 250-Ohm phase line version begins with lower gain on 20 meters and ends with higher gain on 10 meters. As well, relative to longer members of the array family, the 20-meter gain is in both cases below the array average--a result of decreasing the value of Tau below about 0.9. Most LPDAs with Tau values below about 0.9 and with Sigma values in the 0.04 to 0.06 range tend to show decreasing gain at the low end of the spectrum.</p>
+  <p>Nonetheless, the array provides serviceable performance a cross the design passband--about as good as a 20' long LPDA can do with elements that average 0.5" in diameter. Increasing the average element diameter can improve gain somewhat, with the most needed increase on 20 meters. Since most implementations of this or similar designs would have equivalent element diameters larger than 0.5" for the longest elements, we can expect some natural improvement to 20 meter performance as a matter of course.</p>
+  <p><b>Conclusion</b></p>
+  <p>The goal of this design exercise was to produce a family of LPDAs with relatively smooth performance across the entire design passband from 14 to 30 MHz. By the judicious use of standard LPDA modification techniques, the goal has been achieved, although before construction can begin, the designs would need to be customized to the element diameter taper schedule actually used.</p>
+  <p>Since small changes of construction may move the spike frequencies that occur on the smaller members of the family, the use of the 250-Ohm phase line--or something similar, may be the surest route to a successful building project. The average loss of 0.15 dB forward gain is unlikely to be noticed in operation. Because low-loss wide-band 2:1 transmission line transformer baluns are available, the higher feedpoint impedance natural to the high impedance phase line should present no problems. In fact, with the smaller version of the array, the higher natural feedpoint impedance may reduce SWR excursions.</p>
+  <p>Further LPDA construction details can be found in various handbooks, most notably, Chapter 10 of the latest ARRL Antenna Book. Since this is a basic design study, I shall forego construction details altogether. The object has been to show what is possible. The 4 LPDA family members do that well enough to encourage those interested to perfect the designs for particular building circumstances.</p>
+  <center>
+    <img src="../images/colorbar.gif" width="591" height="3">
+  </center>
+  <p><small>Note: The purpose of this article is to disseminate information and ideas. The author retains all design rights associated with the subject arrays, including modifications for improved performance over standard arrays of a similar type and including all reasonable variations upon them both stated or implied by the text or the designs themselves.</small></p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p><i>Updated 11-1-2001. &COPY; L. B. Cebik, W4RNL. The original item appeared in</i> AntenneX <i>for October, 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>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><a href="../radio.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Go to Main Index</a><br>
+  <p class="topics-footer">Topics: <a href='../topics.html#hf-upper'>HF Upper</a>, <a href='../topics.html#lpda'>LPDA</a></p><br>
+</body>
+</html>

content/lpda/80v1.html

@@ -0,0 +1,189 @@
+<!DOCTYPE html>
+<html lang="en">
+<head>
+  <meta charset="UTF-8">
+  <meta name="keywords" content="LPDA, Vertical, HF Lower">
+  <title>An 80-Meter LPMA Part 1. Designing the LPMA With a MININEC Ground</title>
+  <link rel="stylesheet" href="../styles.css">
+</head>
+<body>
+  <center>
+    <h1>An 80-Meter LPMA: A Design Idea and a Modeling Dilemma<br>
+    Part 1. Designing the LPMA With a MININEC Ground</h1>
+  </center>
+  <center>
+    <h3>L. B. Cebik, W4RNL</h3>
+  </center><br>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  <p>Although many amateurs are familiar with the log periodic dipole array (LPDA), fewer are familiar with the log periodic monopole array (LPMA). The LPMA has been around almost as long as its bigger brother, but not many amateur applications have emerged from the basic design. These notes will focus on a 3.5-4.0 MHz limited passband LPMA in a design exercise that will highlight some of the main electrical and physical characteristics of the antenna type. As well, we shall look at some of the stumbling blocks to the design of an LPMA that might actually be implemented with confidence.</p>
+  <p>In principle, the LPMA is a series of ground-mounted monopoles (although other arrangements have been used) with a phasing line running from the base feedpoint of one monopole to the next--complete with the line reversal as it connects to each succeeding vertical element. The elements can be designed using standard LPDA design equations and then using only one side of the dipole. As well, the LPMA is amenable to the same kinds of performance-enhancing modifications as the LPDA.</p>
+  <p>These are the design principles of the LPMA. Most LPMAs are designed by equation and then checked on software something like MININEC. Such software might be MININEC itself or a version of NEC with access to a MININEC ground. The elements are set with their bases touching ground, without the use of an actual ground plane. For many purposes, a MININEC ground is an adequate substitute--at least in preliminary design work--for a NEC-4 buried radial field of considerable size--more than 32 or so radials. However, as I have shown in the series I did on 160-meter vertical arrays, MININEC has some limitations that make its ground system inadequate for accurately modeling the performance of some antenna types. In the end, the question that will face us is whether the MININEC ground is adequate for the modeling of an LPMA, and if so, under what conditions.</p>
+  <p><b>A Single LPMA</b></p>
+  <p>The basic design used in this exercise is the 8-element version of the horizontal LPDA for 3.5 to 4.0 MHz described near the end of "80-Meter Wire LPDAs" in last month's issue of <i>AntenneX</i>. Since the elements are wholly vertical and a large ground radial field is assumed, the initial design effort can use a MININEC ground for efficiency. It is well to note that the array gain will vary with the ground quality in the Fresnel zone of the antenna well beyond the radial system. Therefore, the cited gain figures should be compared to a reference. A 1/4 wavelength resonant monopole over good ground using a MININEC ground system with NEC-4 registers a gain between 0.4 and 0.5 dBi. Although the LPMA gain will vary with the quality of the radial system and the surrounding ground quality, its advantage over a monopole with a similar radial system and surrounding ground quality will be close to the difference between the gain figures to be cited and the reference monopole.</p>
+  <p>The initial modeling of the 8-element array--86' long overall--yielded the following performance figures across 80/75 meters:</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+. . . . . .
+                           8-Element LPMA Performance Potential
+Freq.       Gain        TO Angle    F-B Ratio   Beamwidth   Feedoint Z        50-Ohm
+ MHz        dBi         degrees      dB         degrees     R +/- jX          VSWR
+3.5         4.36        22          18.34       133         50.8 - j 3.0      1.06
+3.75        4.04        22          14.94       137         54.2 + j 4.6      1.13
+4.0         4.32        22          19.53       129         45.1 - j 7.0      1.20
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+. .</pre>
+  <p>The test model specified #12 AWG copper wire, and for this reason, the model has a defect. It has no support. Therefore, except as a reference point, it is not a feasible antenna, although one might build the end elements from tower sections. However, even though the elements have been Tau-tapered to increase performance, the catenary arc of the non-conductive support cable would not likely be above all of the element tips.</p>
+  <center>
+    <img src="80v-1.gif" width="418" height="282" border="2" vspace="5" hspace="9">
+  </center>
+  <p>As a consequence of these considerations, the LPMA was further modified by the addition of two parasitic elements, each composed of tower sections. A 79' tower reflector was added to the rear of the 8 phased elements, and a 50' tower director was added ahead of the same element set. <b>Fig. 1</b> shows the general layout of the LPMA. The overall length was increased to 123' to accommodate these support towers. The following model description shows the dimensions of the design, along with the specified 100-Ohm phase line.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+. . . . . .
+80-m t=.92 s=.05 3.3-4.5                    Frequency = 3.75  MHz.
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+              --------------- WIRES ---------------
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+1            0.000,  0.000, 79.000     G   0.000,  0.000,  0.000 6.00E+00  29
+2           18.000,  0.000, 75.500     G  18.000,  0.000,  0.000    # 12   27
+3           33.494,  0.000, 69.500     G  33.494,  0.000,  0.000    # 12   25
+4           47.771,  0.000, 64.563     G  47.771,  0.000,  0.000    # 12   23
+5           60.928,  0.000, 60.000     G  60.928,  0.000,  0.000    # 12   21
+6           73.050,  0.000, 55.500     G  73.050,  0.000,  0.000    # 12   19
+7           84.221,  0.000, 51.500     G  84.221,  0.000,  0.000    # 12   17
+8           94.515,  0.000, 48.000     G  94.515,  0.000,  0.000    # 12   17
+9          104.000,  0.000, 44.500     G 104.000,  0.000,  0.000    # 12   15
+10         123.000,  0.000, 50.000     G 123.000,  0.000,  0.000 6.00E+00  17
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1          15     9 / 96.67   (  9 /100.00)      0.707       0.000       V
+                -------- TRANSMISSION LINES ---------
+Line  Wire #/% From End 1   Wire #/% From End 1    Length       Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)                Ohms Fact Norm
+1      2/98.1  (  2/100.)    3/98.0  (  3/100.)  Actual dist  100.0  1.00  R
+2      3/98.0  (  3/100.)    4/97.8  (  4/100.)  Actual dist  100.0  1.00  R
+3      4/97.8  (  4/100.)    5/97.6  (  5/100.)  Actual dist  100.0  1.00  R
+4      5/97.6  (  5/100.)    6/97.4  (  6/100.)  Actual dist  100.0  1.00  R
+5      6/97.4  (  6/100.)    7/97.1  (  7/100.)  Actual dist  100.0  1.00  R
+6      7/97.1  (  7/100.)    8/97.1  (  8/100.)  Actual dist  100.0  1.00  R
+7      8/97.1  (  8/100.)    9/96.7  (  9/100.)  Actual dist  100.0  1.00  R
+Ground type is Real, MININEC-type analysis
+Conductivity = .005 S/m    Diel. Const. = 13
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+. .</pre>
+  <p>The double-duty towers not only are capable of supporting the non-conductive cable to hold the elements in place, but as well add considerably to the performance of the LPMA. The following table can be legitimately compared to the preceding one, since the 8 phased elements were not altered.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+. . . . . .
+               8-Element LPMA Plus Parasitic Elements Performance Potential
+Freq.       Gain        TO Angle    F-B Ratio   Beamwidth   Feedoint Z        50-Ohm
+ MHz        dBi         degrees      dB         degrees     R +/- jX          VSWR
+3.5         5.04        22          20.35       115         48.8 + j 5.5      1.12
+3.75        4.99        22          18.46       113         42.4 + j 4.7      1.21
+4.0         5.28        22          20.33       106         38.4 - j21.9      1.75
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+. .</pre>
+  <p>The addition of the parasitic elements added about 0.85 dB to the average array gain across the band. However, higher gain brings with it a somewhat narrower beamwidth. The performance is very stable, as demonstrated by the 50-Ohm SWR graph in <b>Fig. 2</b>.</p>
+  <center>
+    <img src="80v-2.gif" width="640" height="210" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 3</b> overlays azimuth patterns for the 3 80-meter checkpoints to demonstrate that the array holds a fairly consistent pattern throughout the operating passband, with under 0.3 dB variation across the band.</p>
+  <center>
+    <img src="80v-3.gif" width="640" height="480" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The array design and its performance potential as compared to a simple monopole over the same ground system is somewhat self-explanatory. Therefore, let's focus on a limitation of the array as presented. It is anchored to the ground at every element and hence is fixed. If we wish to cover more than the stated -3 dB beamwidth, we must add more such arrays.</p>
+  <p><b>A Bi-LPMA</b></p>
+  <p>The parasitic reflector has a third function besides being an anchor tower and a reflector: it also serves to isolate arrays placed in opposing directions. When one array is active, the other shows no negative effects on its operation. <b>Fig. 4</b> shows the outline of the bi-LPMA with a common parasitic reflector.</p>
+  <center>
+    <img src="80v-4.gif" width="496" height="256" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Each array is identical to its mate, and both are designed to be mechanically anchored at the high end by the central tower-reflector. In the model description, simply create a directional mirror image of the single array shown. The following table shows the reported performance potential for each of the two arrays.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+. . . . . .
+              8-Element Bi-LPMA Plus Parasitic Elements Performance Potential
+Freq.       Gain        TO Angle    F-B Ratio   Beamwidth   Feedoint Z        50-Ohm
+ MHz        dBi         degrees      dB         degrees     R +/- jX          VSWR
+3.5         5.28        22          19.61       110         48.8 + j 6.2      1.14
+3.75        5.15        22          21.93       113         42.4 + j 5.1      1.22
+4.0         5.31        22          25.43       108         38.4 - j21.7      1.74
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+. .</pre>
+  <p>The operational predictions have scarcely changed any numbers, and the reported feedpoint impedance values are a measure of the degree to which the two LPMAs are isolated. The only change worthy of notice is the slight increase in average gain for the array. It has climbed another 0.15 dB and is now a full dB higher than the 8-element model without parasitic elements.</p>
+  <center>
+    <img src="80v-5.gif" width="640" height="210" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The SWR curve in <b>Fig. 5</b> shows its close kinship to the one for the single array. There are slight changes in the pattern shapes, especially to the rear, as demonstrated by the overlaid patterns in <b>Fig. 6</b>. For most situations, the differences from the single LPMA would be considered operationally insignificant.</p>
+  <center>
+    <img src="80v-6.gif" width="640" height="480" border="2" vspace="5" hspace="9">
+  </center>
+  <p>More significant for anyone contemplating the implementation of a dual LPMA is the coverage provided. <b>Fig. 7</b> overlays sample patterns to show both the covered area and the gaps in coverage at right angles to the dual LPMA.</p>
+  <center>
+    <img src="80v-7.gif" width="640" height="480" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Although the double array might be suitable for a station on a great arc between Europe and Australia, the gaps remain troublesome for anyone wishing full horizon coverage.</p>
+  <p><b>A Tri-LPMA</b></p>
+  <p>It is possible to redesign the dual array into a triple array by placing LPMAs at 120-degree angles around the central reflector tower. Since the bandwidth of the array is somewhat less than 120 degrees, it is possible that the central reflector would provide sufficient isolation to permit the individual arrays to operate without pattern distortion from elements of the inactive arrays.</p>
+  <center>
+    <img src="80v-8.gif" width="415" height="403" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 8</b> shows the general outline of the tri-LPMA system. Each array is operated independently of the other two, with only the reflector serving as a common element. The degree of isolation maintained by the system is demonstrated in the potential performance table that follows.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+. . . . . .
+             8-Element Tri-LPMA Plus Parasitic Elements Performance Potential
+Freq.       Gain        TO Angle    F-B Ratio   Beamwidth   Feedoint Z        50-Ohm
+ MHz        dBi         degrees      dB         degrees     R +/- jX          VSWR
+3.5         5.38        21          14.24       102         48.0 + j 7.7      1.18
+3.75        5.52        21          19.02       101         41.6 + j 5.7      1.25
+4.0         5.67        21          23.94        97         37.9 - j21.7      1.76
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+. .</pre>
+  <p>The triple array is perfectly usable, with another 0.3 dB increase in average gain. The increase suggests that the 3 arrays are not completely independent, and the reduction in 3.5-MHz front-to-back ratio confirms the suggestion. As well, the slight reduction in array independence and the small increase in gain also appear as a further reduction on -3 dB beamwidth.</p>
+  <center>
+    <img src="80v-9.gif" width="640" height="210" border="2" vspace="5" hspace="9">
+  </center>
+  <p>As <b>Fig. 9</b> shows, however, the changes in the feedpoint impedance across the band are relatively insignificant. The 50-Ohm SWR curve is not materially different from the two we have already seen.</p>
+  <center>
+    <img src="80v-10.gif" width="640" height="480" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The degree to which the rearward arrays effect changes in the azimuth patterns of the active LPMA becomes apparent in <b>Fig. 10</b>, where checkpoint patterns are overlaid once more. More crucial to the desire for full horizon coverage from the triple array is <b>Fig. 11</b>, which set forth the worst case coverage on 4.0 MHz, where the beamwidth is narrowest. Whether the coverage is adequate is, of course, a potential user judgment.</p>
+  <center>
+    <img src="80v-11.gif" width="640" height="480" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The desire for relatively equal signal strength across the entire horizon raises the possibility of making an array of 4 LPMAs at 90-degree angles to each other. The outline of such an array appears in <b>Fig. 12</b>.</p>
+  <center>
+    <img src="80v-12.gif" width="441" height="382" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Although such an array is tempting, especially within the paper-design phase, it will turn out to be impractical. The interaction among arrays that began to appear at 3.5 MHz in the triple array will become major interaction across the band. The modeled performance report for a square of LPMAs appears in the following table.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+. . . . . .
+            8-Element Square-LPMA Plus Parasitic Elements Performance Potential
+Freq.       Gain        TO Angle    F-B Ratio   Beamwidth   Feedoint Z        50-Ohm
+ MHz        dBi         degrees      dB         degrees     R +/- jX          VSWR
+3.5         3.59        21           7.52       171         44.4 + j11.1      1.30
+3.75        5.46        21          16.59        96         40.1 + j 6.7      1.31
+4.0         5.98        21          25.61        86         37.2 - j21.9      1.78
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+. .</pre>
+  <p>Although the SWR curve has remained relatively stable, other operating categories shows major fluctuations relative to the previously examined versions of the LPMA.</p>
+  <center>
+    <img src="80v-13.gif" width="640" height="480" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 13</b> overlays 3.5 and 4.0 MHz patterns for a quadruple LPMA. Not only has the gain and front-to-back ratio diminished at 3.5 MHz, the beamwidth at that frequency has widened extremely. At the other end of the band, we see some pattern distortion that contributes to a narrowing of the beamwidth to 86 degrees. In fact, the narrowest beamwidths occur in the region from 3.55 to 3.65 MHz, with the beamwidth shrinking to about 78 degrees.</p>
+  <p>The highly variable set of patterns in the 4-square LPMA arrangement result from the natural operation of an LPDA or and LPMA. As we change frequencies, different elements become highly active, that is, carry higher levels of current. This phenomenon applies not only to the active array, but as well to the inactive arrays to which the near field of the active array may be coupled. At the lowest frequencies, the elements closest to the reflector will be active. The effect of parasitic inactive long elements on the pattern will be quite different than the effect at higher frequencies of shorter elements spaced further from the reflector. As well, the degree of coupling will also be variable as we change frequency and involve different elements, thus changing the current magnitude and phase on the inactive parasitic side elements. On this narrow-band LPMA, the range of effects is small, although two distinct types of pattern distortion emerge. On a wider-range LPMA, the range of potential pattern distortion is considerably greater.</p>
+  <p>The square LPMA composed of 4 arrays places the side arrays well within the stronger portions of the active LPMA. Consequently the interactions are high--high enough to dis-recommend this arrangement. By way of contrast, the tri-LPMA places the two inactive arrays well to the rear and generally in the weakest portions of the active array's pattern. Consequently, a much higher degree of isolation exists. The isolation is not perfect, as shown by the rise in gain and by the reduction in the 3.5 MHz front-to-back ratio. However, the tri-LPMA remains perfectly serviceable for full horizon coverage with a gain variation of just about 4-5 dB.</p>
+  <p><b>The Adequacy of the Design and the Design Technique</b></p>
+  <p>When I began this design exercise, I had confidence in the use of a MININEC ground system for the initial work. In general, where a MININEC ground goes astray is when one or more of the elements in a vertical array at or close to ground level is not perfectly vertical. A horizontal component to any element--driven or parasitic--in a MININEC model invokes to one degree or another the errors inherent in the system with horizontal wires below about 0.2 wavelength. Since the elements of an LPMA are vertical throughout, the MININEC ground should be reliable as a guide to design.</p>
+  <p>However, in attempting to translate the final designs into NEC-4 models employing buried radials, a number of difficulties were encountered, especially in attempts to develop either simplified or composite buried radial systems. Eventually, I discovered that the most successful route to a buried radial model was also the most straightforward, if not the easiest from a modeling perspective. The result is the conclusion that the LPMA design explored here is usable as a physical antenna, but only if certain conditions are met. Since these conditions are not quite simple or easy to implement--and since the temptations to alternative ground treatment systems are many--perhaps we should devote some time to the subject in Part 2.</p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p><i>Updated 05-01-2002. &COPY; L. B. Cebik, W4RNL. The original item appeared in</i> AntenneX <i>for April, 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>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p><a href="80v2.html"><img src="../images/fwdyl.gif" align="bottom" width="36" height="33"> Go to Part 2</a></p>
+  <p><a href="../radio.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Go to Main Index</a><br></p>
+  <p class="topics-footer">Topics: <a href='../topics.html#hf-lower'>HF Lower</a>, <a href='../topics.html#lpda'>LPDA</a>, <a href='../topics.html#vertical'>Vertical</a></p><br>
+</body>
+</html>

content/lpda/80v2.html

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+<!DOCTYPE html>
+<html lang="en">
+<head>
+  <meta charset="UTF-8">
+  <meta name="keywords" content="LPDA, Vertical, HF Lower">
+  <title>An 80-Meter LPMA Part 2. The Adequacy of the LPMA Design</title>
+  <link rel="stylesheet" href="../styles.css">
+</head>
+<body>
+  <center>
+    <h1>An 80-Meter LPMA: A Design Idea and a Modeling Dilemma<br>
+    Part 2. The Adequacy of the LPMA Design</h1>
+  </center>
+  <center>
+    <h3>L. B. Cebik, W4RNL</h3>
+  </center><br>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  <p>Everything that has been said so far about the 10-element 3.5-4.0 MHz LPMA design, whether using 1, 2, or 3 arrays, is based upon models in NEC-4 using a MININEC ground. The use of NEC-4 is not essential, since the same results appear using NEC-2. Unfortunately, the requirement to use a mathematical phase line precludes modeling the array wholly in MININEC 3.13, since public domain MININEC does not have the TL facility. Physically modeling the transmission line would require an exceptional number of segments, since the number of right-angle junctions would be very high.</p>
+  <p>However, the real question that we must raise is whether the MININEC ground is adequate to provide an accurate model whose performance can be transferred to a physical antenna. On the surface, the LPMA has none of the features previously identified as invalidating the use of a MININEC ground. (A study of such invalidating factors appeared in the <i>National Contest Journal</i> series on "Some facts of Life About Modeling 160-Meter Vertical Arrays" during 2000 and 2001.) All of those array types that resulted in faulty MININEC-ground models used elements that were not completely vertical. They had to one or another degree a horizontal component to their radiated fields, and at close proximity to ground, the performance reports were erroneous.</p>
+  <p>In contrast to the faulty models, the 80/75-meter LPMA consists of entirely vertical elements. Since the phase line is a mathematical and not a modeled physical entity, it does not modify the radiation patterns except by current magnitude and phase variations of predictable sorts. Consequently, the model based on the use of a MININEC ground should be reliable.</p>
+  <p>Whatever we may expect at first sight, there is a test that we can make to determine whether or not the MININEC-ground model provides enough confidence for us to build the LPMA (assuming that we have the resources to build it). For every adequate MININEC ground model, there is a purely NEC-4 model that uses a buried ground plane/radial/grid system that achieves results that are very closely akin to those reported by the MININEC-ground model. For example, consider monopole that is 1/4 wavelength long at 2 MHz and intended for use until it is about 5/8 wavelength long at 5 MHz.</p>
+  <center>
+    <img src="80v2-1.gif" width="450" height="600" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 1</b> shows the outline of a monopole for 2-5 MHz (where its height varies from 1/4 wavelength to 5/8 wavelength). The monopole is 118' tall and 6" in diameter to simulate a tower structure. The monopole was run on NEC-4 over a MININEC ground and over a Sommerfeld-Norton ground with radials buried 0.5' beneath the ground surface using recommended modeling techniques. Radial systems of 30 and 60 125'-radials of 0.1" diameter were tested. Throughout, the ground quality was set at "good" (cond.: 0.005 S/m; D.C.: 13). Since take-off angles did not vary at any given frequency by more than 1 degree between the two ground systems, they are omitted from the following table of results. As the table shows, when compared to the MININEC-ground results, the results for the NEC-4 buried radial systems are very sensible--and vice versa.</p>
+  <pre>                                   Monopole Performance
+Freq. Gain  Source Z          Gain  Source Z                Gain  Source Z
+                                 1.  2-7 MHz 118' monopole
+a.  MININEC ground            b.  S-N Ground, 30 radials    c.  S-N Ground, 60 radials
+2     1.31    36 + j  2       0.94    41 + j 10             1.25    37 + j  8
+3     0.66   175 + j287       0.75   245 + j319             1.04   232 + j325
+4     0.44  1064 - j 85       0.70   672 - j489             0.93   658 - j493
+5     1.00   118 - j318       0.68    78 - j251             0.77    79 - j252</pre>
+  <p>The progression shows a few notable variations from a fully adequate correlation of MININEC and buried-radial models. The S-N radial systems show a consistent increase in gain and a consistent reduction of the resistive component of the feedpoint impedance with the increase in the size of the radial system. In short, the S-N buried radial model is capable of showing the decreasing ground losses with increases in the field size, in contrast to the single value returned by the MININEC-ground model. Moreover, the changes in gain with changes in frequency are not completely consistent between the MININEC ground and the S-N radial systems. For the test monopole, the gain progression is steadily downward from the low frequency to the high. The MININEC system is variable.</p>
+  <p>It appears that the MININEC ground system is based throughout on image calculations whenever the lower end of an element has a Z-axis value of zero, that is, touches the ground. Impedance with a MININEC ground is always calculated for a perfect ground. It appears that with a MININEC ground, gain and other performance figures are also calculated for a perfect ground--which uses image techniques--and then adjusted for wire and ground quality losses. In contrast, when not using a perfect ground but instead using the Sommerfeld-Norton system, NEC-4 calculates the actual ground losses entering into the antenna performance. Hence, although the MININEC ground system and calculating technique provides a ballpark estimate of values for a highly refined radial field (more than about 70 radials), its performance calculating technique falls short of perfection relative to modeling a full buried radial system. However, the MININEC values are sufficiently close to those emerging from the large radial systems to account the simplified model adequate for many purposes.</p>
+  <p>When I started work on the 80-meter LPMA, I was also working on designs for larger LPMAs, larger in terms of the number of elements (17-24), larger in terms of frequency range (2 to 7 MHz), and larger in terms of overall size (boom length: 220'). Arrays of this size almost defy efforts to provide buried ground radial, grid, or treatment systems, since the number of segments required can easily run to 10,000 or more. Consequently, the search for a simplified system to serve the entire array was a natural direction of effort.</p>
+  <center>
+    <img src="80v2-2.gif" width="640" height="480" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 2</b> shows some of the configurations explored. The results of none of the systems were anywhere close to satisfactory. No buried radial model in the sequence has approached closely the performance predictions supplied by the MININEC-ground model of an LPMA. Depending upon the buried ground system design, gain has ranged from 2 to 10 dB below values reported with a MININEC ground. In fact, the monopole model shown earlier as an example of good coincidence between MININEC-ground and buried radial results provides more gain in the 3.5-4.0 MHz region than do any of the buried-radial LPMA models that I tried.</p>
+  <p>The following table summarizes only some of the trial models. It will be useful to help isolate a few of the temptations that proved simply not to work.</p>
+  <pre>. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+             Reference Table of Gain Ranges with Types of Ground Systems
+
+No.          System Type                                               Gain Range dBi
+                                                                       1.8 MHz 7.3 MHz
+ 1    No radials, S-N ground                                            2.88    1.02
+ 2    Pair of radials, same length as elements, 2 per element
+      (called SW for "side-wires" in further entries), 1' deep         -6.20  -15.55
+ 3    Revised SW system, with 1' feed segment per element              -6.06  -15.48
+ 4    System 3 with tapered segment length elements                    -6.40  -15.84
+ 5    System 4 with 4' spaced longitudinal grid lines at 1.5'          -2.03  -17.73
+ 6    System 4 with a connecting line between SW junctions             -0.40  - 5.49
+      (Note: variations of this system with extensions beyond towers
+      yielded no better results.)
+ 7    Single buried wire connecting elements 1' below ground           -5.12  -11.98
+ 8    System 6 with a centered radial system at -1.5' of 30 140'
+      radials                                                           0.27  - 5.43
+ 9    System 6 with 2 sets of 30 radials:  140' set at 82' mark, 47'
+      set at 214' mark (most active elements at 1.8 and 7.3 MHz,
+      respectively)                                                     0.32  - 4.13
+10    System 9 radial sets connected to nearest SW junction             0.96  - 4.52
+11    SW system only, all wires elevated 1' above ground                0.58    0.53
+12    SW system only, towers touch ground, phased elements elevated 1'  1.21  - 0.35
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>The attempt to provide "side-wires" for each element is a natural temptation. The spacing of wires in the array does not permit full radial systems at the same level without a multitude of intersections. Indeed, it is difficult to provide any given element in the array with more than one radial without intersections among the radials that are not at perfect right angles to the boom line. None of these systems yielded worthy results. One temptation that seemed to improve results slightly was running a buried model wires between the intersections of the side-wires along the boom line. In fact, this line would ultimately prove more problematical as the correct solution to the problem emerged.</p>
+  <p>Combining side-wires with spot radial systems had some ameliorative affect on the array gain. However, the array gain appeared to peak in certain frequency regions and to decline rapidly in others. System 10 proved the most promising, although better results would be needed.</p>
+  <p>To achieve better results, it would be necessary to initially work with a smaller model. The 24-element LPMA that defied simplified buried radial systems was replaced with a version of the 80/75-meter LMPA in Part 1. The model used had only the 8 0.1" diameter elements and omitted the 2 parasitic support towers. For the validation work at hand, it was considered legitimate to presume that the 0.1" wires could be self-supporting. The following model description provides the essential physical and electrical details.</p>
+  <pre>. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+80-m t=.92 s=.05 3.3-4.5                    Frequency = 3.5-4.0  MHz.
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+1            0.000,  0.000, 75.500     G   0.000,  0.000,  0.000 1.00E-01  27
+2           15.494,  0.000, 69.500     G  15.494,  0.000,  0.000 1.00E-01  25
+3           29.771,  0.000, 64.563     G  29.771,  0.000,  0.000 1.00E-01  23
+4           42.928,  0.000, 60.000     G  42.928,  0.000,  0.000 1.00E-01  21
+5           55.050,  0.000, 55.500     G  55.050,  0.000,  0.000 1.00E-01  19
+6           66.221,  0.000, 51.500     G  66.221,  0.000,  0.000 1.00E-01  17
+7           76.515,  0.000, 48.000     G  76.515,  0.000,  0.000 1.00E-01  17
+8           86.000,  0.000, 44.500     G  86.000,  0.000,  0.000 1.00E-01  15
+
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1          15     8 / 96.67   (  8 /100.00)      0.707       0.000       V
+
+                -------- TRANSMISSION LINES ---------
+Line  Wire #/% From End 1   Wire #/% From End 1    Length       Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)                Ohms Fact Norm
+1      1/98.1  (  1/100.)    2/98.0  (  2/100.)  Actual dist   75.0  1.00  R
+2      2/98.0  (  2/100.)    3/97.8  (  3/100.)  Actual dist   75.0  1.00  R
+3      3/97.8  (  3/100.)    4/97.6  (  4/100.)  Actual dist   75.0  1.00  R
+4      4/97.6  (  4/100.)    5/97.4  (  5/100.)  Actual dist   75.0  1.00  R
+5      5/97.4  (  5/100.)    6/97.1  (  6/100.)  Actual dist   75.0  1.00  R
+6      6/97.1  (  6/100.)    7/97.1  (  7/100.)  Actual dist   75.0  1.00  R
+7      7/97.1  (  7/100.)    8/96.7  (  8/100.)  Actual dist   75.0  1.00  R
+
+Ground type is Real, MININEC-type analysis
+Conductivity = .005 S/m    Diel. Const. = 13
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>The performance of the array with a MININEC ground can be summarized by using 3.5, 3.75, and 4.0 MHz checkpoints. In the following table, TO angle is the elevation angle of maximum radiation. The front-to-rear ratio is the worst case ratio of gain forward to rear taken from an elevation plot. The 180-degree front-to-back ratio is taken from an azimuth plot at the TO angle. The beamwidth refers to the angle between -3 dB points on the azimuth pattern. The 75-Ohm phase line yield a reasonable match for 50-Ohm coaxial cable and the 50-Ohm SWR is given in the last column.</p>
+  <pre>. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                    8-Element 80/75 MHz LPMA with MININEC Ground
+Freq.        Gain  TO     F-R Ratio    F-B Ratio    B/W   Feed Z       50-Ohm
+MHz          dBi   deg    dB           dB           deg   R+/-jX       SWR
+3.5          4.44  22     16.11        18.97        132   50.3-j 3.5   1.07
+3.75         4.12  22     13.80        15.32        136   54.7+j 4.4   1.13
+4.0          4.39  22     16.59        19.94        128   44.7-j 6.5   1.20
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>In attempting to validate this model, it is not necessary to produce the exact figures. However, the patterns and general levels should be consistent with the values given. For example, the model shows a small gain decline mid-band, accompanied by a similar small decline in the F-R and F-B values. The mid-band region also shows a rise in the resistive component of the feedpoint impedance.</p>
+  <p>Providing this model with sundry simplified ground-treatment systems all failed to yield acceptable results. For example, placing a single 60-radial buried system beneath the array, using 140' radials and a connection to the center element of the LPMA yielded no better gain -1.84 dBi and that only at one frequency. The key move was proving 3 radial systems of differential lengths connected to the end and the middle elements. Gain rose to a peak of 1.34 dBi, but again, only at one frequency.</p>
+  <p>The key to a satisfactory radial system for the array did not arise from the differential radial lengths used in the last trial, but from the connections to elements. The more elements that had a radial system directly and independently tied to them, the better the response. Hence, the final system provided an independent radial system for each element in the array.</p>
+  <center>
+    <img src="80v2-3.gif" width="640" height="350" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 3</b> shows the outline sketch of the largest model in the final test group, with 976 wires and 2690 segments. However, it only achieves 23 radials per element. In fact, the radial systems themselves are interesting in terms of the techniques used to ensure their independence, where independence means that no wire from one system touches a wire from another system. The 8 individual radial systems are at different levels, separated by 3". This technique held the lowest level, used for the rear element, at the 2' level below ground. Other test models have shown that in the lower HF region, there is insignificant difference among models with buried radials in the 6" to 24" range below ground.</p>
+  <p>Since each radial system has a connecting wire to the element that it serves, it was necessary to ensure that no radial passed though a connecting wire. Therefore, I chose to use an odd number of radials, beginning with a set of 7 per element, as shown in <b>Fig. 4</b>.</p>
+  <center>
+    <img src="80v2-4.gif" width="640" height="400" border="2" vspace="5" hspace="9">
+  </center>
+  <p>By setting the initial radial at right angles to the boom line, all of the subsequent radials would take angles so that none would be parallel to the boom. By increasing the sequence in 8-radial steps (7-15-23-31-etc.), the same condition would exist and avoid model crashes.</p>
+  <center>
+    <img src="80v2-5.gif" width="703" height="421" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Modeling a buried radial system requires adherence to several NEC guidelines which will explain the modeling structure shown in <b>Fig. 5</b>. A segment junction--usually a wire end-- must be a Z=0, that is, at ground level. Since the connector wires to the radials would be short, and since angular junctions are best served by segment lengths that are equal, a form of segment length tapering for the radials was in order. As well, the segments on either side of the source segment should equal the length of the source segment. For a vertical element, the source (or phase line connection for an LPMA) should be on the lowest segment. To achieve this and to have the first segment above the source segment be of the same length, a separate "source wire" was constructed, with the vertical element above that point also tapered in terms of segment length.</p>
+  <p>The resulting model results in wire junctions quite different from those of the MININEC model. Therefore, a second MININEC-ground model was constructed with the elements tapered exactly as they would be in the buried-radial model. The results are extremely close to the version using standard segmentation techniques.</p>
+  <pre>. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+       8-Element 80/75 MHz LPMA with MININEC Ground (Segment Tapered Elements)
+Freq.        Gain  TO     F-R Ratio    F-B Ratio    B/W   Feed Z       50-Ohm
+MHz          dBi   deg    dB           dB           deg   R+/-jX       SWR
+3.5          4.48  22     16.10        18.98        132   49.7-j 3.7   1.08
+3.75         4.17  22     13.79        15.30        136   54.2+j 3.9   1.12
+4.0          4.44  22     16.59        19.96        128   44.2-j 6.6   1.21
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>The only differences occur in the last decimal column for any entry, indicating a very tight correlation with the original model.</p>
+  <p>The buried radial model was run using 7, 15, and 23 radials per element. These runs produced interesting results, and further runs with higher numbers of radials per element would be useful. However, the run time increases exponentially with increases in wires and segments, so tests were limited to data gathering that required less than 1.5 hours per check point. (We shall see an indirect validation technique shortly.) The results for the runs are in the following table.</p>
+  <pre>. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+             8-Element 80/75 MHz LPMA with 7 Buried Radials per Element
+Freq.        Gain  TO     F-R Ratio    F-B Ratio    B/W   Feed Z       50-Ohm
+MHz          dBi   deg    dB           dB           deg   R+/-jX       SWR
+3.5          0.87  22     13.75        15.07        135   48.5-j 1.4   1.04
+3.75         0.99  22     15.80        18.26        130   54.8-j 4.7   1.14
+4.0          1.34  23     14.91        15.95        129   45.3-j 2.5   1.12
+
+             8-Element 80/75 MHz LPMA with 15 Buried Radials per Element
+Freq.        Gain  TO     F-R Ratio    F-B Ratio    B/W   Feed Z       50-Ohm
+MHz          dBi   deg    dB           dB           deg   R+/-jX       SWR
+3.5          2.81  22     13.38        14.51        138   50.5-j 2.7   1.06
+3.75         2.98  22     13.98        15.49        135   59.2-j 4.7   1.21
+4.0          3.30  23     14.44        15.56        133   45.3-j 1.6   1.11
+
+             8-Element 80/75 MHz LPMA with 23 Buried Radials per Element
+Freq.        Gain  TO     F-R Ratio    F-B Ratio    B/W   Feed Z       50-Ohm
+MHz          dBi   deg    dB           dB           deg   R+/-jX       SWR
+3.5          3.53  23     12.99        14.03        140   51.1-j 4.2   1.09
+3.75         3.61  23     13.25        14.41        137   60.4-j 1.6   1.21
+4.0          3.85  23     14.42        15.59        133   45.8-j 1.5   1.10
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>The progression of values with increasing numbers of radials per element is promising, and the impedance values are especially attractive, since even with the lowest number of radials per element, they track the MININEC model very closely. Performance has smoothed out across the passband of the array to a level that is not only higher, but is as well more equal at every checkpoint than in any of the simplified ground treatments. The question that remains is whether there is a radial count level per element that will likely yield array results equal to or better than those predicted by the MININEC model.</p>
+  <p>By fiat, I declared the 23-radial system to be the largest that I would run with the full 8-element array. This foreclosed direct determination of an answer to the remaining quandary. However, there is an indirect route to an answer. I modeled a simple monopole for 3.75 MHz using radial systems in increments of 8 but starting with 7. <b>Fig. 6</b> shows the smallest (7 radials) and the largest (63 radials) of the sequence. Each monopole and radial system used the same structure as an individual element in the LPMA model.</p>
+  <center>
+    <img src="80v2-6.gif" width="410" height="550" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The following table summarizes the results of the test model.</p>
+  <pre>. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+              3.75 MHz Monopole Performance with Various Radial Systems
+No. of       Gain         TO Angle           Feed Impedance            50-Ohm
+Radials      dBi          degrees            R +/- jX Ohms             SWR
+ 7           -1.08        24                 54.8 + j 16.2             1.38
+15           -0.25        25                 46.5 + j 13.1             1.33
+23            0.13        25                 43.1 + j 11.9             1.34
+31            0.36        25                 41.1 + j 11.2             1.37
+39            0.51        25                 39.7 + j 10.6             1.39
+47            0.61        25                 38.7 + j 10.2             1.41
+55            0.69        25                 37.9 + j  9.8             1.43
+63            0.74        25                 37.3 + j  9.4             1.44
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>The model surpasses a MININEC-ground version of the monopole in gain at the 39-radial level and equals it in impedance at the 63-radial level.</p>
+  <p>By examining the rate of change of the monopole figures throughout its range of radial systems, we can project similar rates of change to the progression of LPMA values, using average gain values for the entire array passband. The result is a projection of values above the level of radial systems explored directly.</p>
+  <center>
+    <img src="80v2-7.gif" width="647" height="526" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 7</b> provides a graph of the monopole values, the combined LPMA direct and indirect values, and reference lines for the predicted MININEC-ground models for both antennas. The LPMA projection values should be read with caution, since a number of real antenna variables may intervene to deny the array its ultimate performance levels. Obtaining the highly complex field of radials for the LMPA is a construction challenge several orders of magnitude greater than that associated with layout radials for a single monopole.</p>
+  <p>Nevertheless, the modeling and derivation techniques do establish some useful points. First is the fact that the MININEC-ground LPMA can be realized with a buried radial system. However, that system may be more extensive and of a nature not fully appreciated before this exercise. Each element needs to be supplied with a radial system of its own, independent of the radial system serving other elements. At this point, it is not certain whether one can use an interlocking grid where the radial wires make good electrical contact, although the model suggests that electrical independence is the best method so far obtained.</p>
+  <p>Second, the radial system for each element will have to be fairly extensive to obtain more than mediocre performance from the LPMA. About 39 radials per element seems called for by the model for average to good soil (conductivity: 0.005 S/m; dielectric constant: 13). Worse soils will call for more extensive radial systems per element. A full field, as defined by the AM broadcast industry, would not be out of place for a serious installation of the LPMA. It is likely that poor performance from any lower-HF LPMA can be traced primarily to a poor ground treatment system (with room for poor-design causes as an additional factor).</p>
+  <p>The use of a MININEC ground in a model, then, is legitimate and the general performance predicted by such a model can be obtained. However, the cost in terms of modeling and especially in terms of required construction is very high. Consider the following alternatives. We examined a fixed-position horizontal LPDA of the same general design as the LPMA. To arrive at roughly equivalent performance levels, The LPDA would need to by 90-100 feet high, requiring 4 support towers, appropriate non-conductive support cables, and sundry materials. The comparable LPMA would require only 2 towers, but complex and extensive treatment of the ground at the element bases. Which option might be best for a given installation makes an interesting thought project.</p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p><i>Updated 06-01-2002. &COPY; L. B. Cebik, W4RNL. The original item appeared in</i> AntenneX <i>for May, 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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+<!DOCTYPE html>
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+  <meta charset="UTF-8">
+  <meta name="keywords" content="LPDA, HF Lower">
+  <title>80-Meter Wire LPDAs</title>
+  <link rel="stylesheet" href="../styles.css">
+</head>
+<body>
+  <center>
+    <h1>80-Meter Wire LPDAs</h1>
+  </center>
+  <center>
+    <h3>L. B. Cebik, W4RNL</h3>
+  </center><br>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  <p>For many years, the <i>ARRL Antenna Book</i> has contained an LPDA for 80 meters that uses 4 elements and is arranged as both a forward-sloping Vee and an inverted Vee, with its ends close to the ground. It was carefully designed from basic LPDA design equations with a Tau of 0.845 and a Sigma of 0.06, resulting in a #14 copper wire array close to 50' from front to rear (ignoring the forward Vee extension).</p>
+  <p>Unfortunately, this array has a number of properties that reduce its potential performance:</p>
+  <ul>
+    <li>1. The elements are Vee'd forward, reducing gain and decreasing the front-to-side ratio.</li>
+    <li>2. The elements are modified inverted Vees, again reducing gain and decreasing the front-to-side ratio.</li>
+    <li>3. The array uses thin wire, reducing gain relative to elements of an optimal diameter.</li>
+    <li>4. The combination of Tau (0.845) and Sigma (0.06) alone yield a maximum free-space gain potential to well under 6 dBi.</li>
+  </ul>
+  <p>The combination of performance-degrading factors in this array strongly suggest that a redesign is in order. In these notes, I shall explore more adequate arrays for 80 meters. However, each will presume standard linear elements at right angles to the main array axis. In the course of these notes, we shall look at the question of optimal element size and how to simulate it with a wire array. We shall also examine some limits (and the reasons for those limits) of improving thin wire lower HF arrays with simulated fatter elements.</p>
+  <p><b>An Improved 6-Element Wire LPDA for 80 Meters</b></p>
+  <center>
+    <img src="80w-1.gif" width="310" height="400" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 1</b> shows the outline of an LPDA using 6 elements, with a Tau of 0.8918 and a Sigma of 0.0702. The Tau and Sigma values are the initial values of the design. However, the element lengths have been optimized for the best performance across the 80-meter band (3.5-4.0 MHz) using standard circularized-Tau techniques. The final design--which might still be improved further with judicious experimentation--retains the original spacing, but 4 of the 6 elements have modified lengths.</p>
+  <p>Key to array performance is the element diameter, specified in the original design as 2". The elements are modeled as copper, although there is less than 0.02 dB difference between copper and aluminum when the elements are as fat as specified here.</p>
+  <p>The following table provides the wire specifications in the form of a NEC wire table. The phase line has a characteristic impedance of 100 Ohms.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+3.3-4.5 MHz t=.89 s=.07                  Frequency = 4  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1            0.000,-76.000,  0.000         0.000, 76.000,  0.000 2.00E+00  91
+2           21.346,-67.800,  0.000        21.346, 67.800,  0.000 2.00E+00  81
+3           40.382,-60.500,  0.000        40.382, 60.500,  0.000 2.00E+00  73
+4           57.358,-55.500,  0.000        57.358, 55.500,  0.000 2.00E+00  65
+5           72.498,-51.000,  0.000        72.498, 51.000,  0.000 2.00E+00  59
+6           86.000,-47.500,  0.000        86.000, 47.500,  0.000 2.00E+00  53
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          27     6 / 50.00   (  6 / 50.00)      0.707       0.000       V
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>The performance of this array is quite good for an 86' long LPDA on 80 meters, with an average free-space gain of about 6.9 dBi across the band. Whether the performance can be maintained in practice depends, of course, on the ability of the builder to raise the antenna to a height where horizontally polarized antennas perform well over desired propagation paths. The front-to-back ratio is above 20 dB across the band.</p>
+  <p>The use of 2" diameter elements on 80 meters is exceptionally rare, given the need for elements that are at their longest 152'. As an experiment, I took the same array and tested it in model form using #12 AWG wire (0.0808" diameter). Interestingly, the average free-space gain dropped to about 5.9 dBi with an average front-to-back ratio of about 13.5 dB. The loss of a full dB of gain in the move from 2" to 0.0808" element diameters seemed less than desirable.</p>
+  <p>Therefore, I reconstructed the elements from 2 parallel wires in accord with the sketch in <b>Fig. 2</b>.</p>
+  <center>
+    <img src="80w-2.gif" width="533" height="303" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The principle, as I have elsewhere noted, consists in taking a representative element in the array and finding its self-resonant frequency. Then, I constructed a model of a two-wire element of the same length and varied the spacing between the wires until it was resonant at the same frequency. In the present exercise, a spacing of between 10 and 12 inches proved to be close to precise, with a remnant reactance of under 10 Ohms at the widest spacing used.</p>
+  <p>For modeling simplicity, I used the 12" spacing, which translates into 1 foot (or a shortest segment length of 0.5'). See <b>Fig. 3</b>.</p>
+  <center>
+    <img src="80w-3.gif" width="632" height="168" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 3</b> shows the element model. The center portion is (for this model) 1.5' long and consists of 3 segments to ensure that the source segment is equal in length to the segments adjacent to it. The single wire is also necessary within the LPDA array, since the phase-line must meet a single wire segment at each element in the array. On each side of center, single segment wires, each 0.5' long, connect the center wire to the parallel wires that constitute the bulk of the elements. These wires, which have the same number of segments to sustain parallel segment junctions throughout, are connected together at the outer ends with 2-segment wires. The 11-wire element constitutes a reasonably fair model of the 2-wire element.</p>
+  <p>The attention to segment lengths at the center-most part of the element allowed me to reduce the number of segments in the long wires. Ideally, the segment length should be 0.5' throughout the model, which would have resulted in about 150 segments per long wire in the longest element. However, reducing the number to about 50 yielded a change of reactance in the test element of under 5 Ohms. So reduced segmentation--but still with parallel segment junctions--was used in the final array model. For reference, the following partial table shows just 2 elements of the modified array.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+80, t=.89 s=.07                              Frequency = 3.5  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1     W2E1   0.000,-76.000, -0.500  W3E1   0.000,-76.000,  0.500    # 12    2
+2     W1E1   0.000,-76.000, -0.500  W4E1   0.000, -0.750, -0.500    # 12   51
+3     W1E2   0.000,-76.000,  0.500  W5E1   0.000, -0.750,  0.500    # 12   51
+4     W2E2   0.000, -0.750, -0.500  W5E2   0.000, -0.750,  0.000    # 12    1
+5     W3E2   0.000, -0.750,  0.500  W6E1   0.000, -0.750,  0.000    # 12    1
+6     W4E2   0.000, -0.750,  0.000  W7E1   0.000,  0.750,  0.000    # 12    3
+7     W8E1   0.000,  0.750,  0.000  W9E1   0.000,  0.750, -0.500    # 12    1
+8     W6E2   0.000,  0.750,  0.000 W10E1   0.000,  0.750,  0.500    # 12    1
+9     W7E2   0.000,  0.750, -0.500 W11E1   0.000, 76.000, -0.500    # 12   51
+10    W8E2   0.000,  0.750,  0.500 W11E2   0.000, 76.000,  0.500    # 12   51
+11    W9E2   0.000, 76.000, -0.500 W10E2   0.000, 76.000,  0.500    # 12    2
+12   W13E1  21.346,-67.800, -0.500 W14E1  21.346,-67.800,  0.500    # 12    2
+13   W12E1  21.346,-67.800, -0.500 W15E1  21.346, -0.750, -0.500    # 12   46
+14   W12E2  21.346,-67.800,  0.500 W16E1  21.346, -0.750,  0.500    # 12   46
+15   W13E2  21.346, -0.750, -0.500 W16E2  21.346, -0.750,  0.000    # 12    1
+16   W14E2  21.346, -0.750,  0.500 W17E1  21.346, -0.750,  0.000    # 12    1
+17   W15E2  21.346, -0.750,  0.000 W18E1  21.346,  0.750,  0.000    # 12    3
+18   W19E1  21.346,  0.750,  0.000 W20E1  21.346,  0.750, -0.500    # 12    1
+19   W17E2  21.346,  0.750,  0.000 W21E1  21.346,  0.750,  0.500    # 12    1
+20   W18E2  21.346,  0.750, -0.500 W22E1  21.346, 67.800, -0.500    # 12   46
+21   W19E2  21.346,  0.750,  0.500 W22E2  21.346, 67.800,  0.500    # 12   46
+22   W20E2  21.346, 67.800, -0.500 W21E2  21.346, 67.800,  0.500    # 12    2
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>The use of the twin-wire (#12 AWG) elements restored much of the performance to the array--on average about 80% of the performance lost in going from a 2" element to a #12 single wire element. The average free-space gain rose to over 6.6 dBi, with an average front-to-back ratio of over 20 dB.</p>
+  <p>However, a better measure of appreciating how well the double-wire elements simulate the tubular elements can be gleaned from some graphs.</p>
+  <center>
+    <img src="80w-4.gif" width="644" height="527" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 4</b> shows the free-space gain across 80 meters a 0.05 MHz intervals. Not only is the double-wire curve much higher on average than the single wire curve; as well, it parallels the 2" element curve very closely. The single-wire curve peaks at a quite different frequency from the peak for the upper two curves.</p>
+  <center>
+    <img src="80w-5.gif" width="644" height="529" border="2" vspace="5" hspace="9">
+  </center>
+  <p>In <b>Fig. 5</b>, for the front-to-back ratio, we find a similar pattern, with the 2" element and the double-wire curves not only higher, but also more parallel than the curves for the single thin-wire version of the antenna.</p>
+  <center>
+    <img src="80w-6.gif" width="585" height="600" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Perhaps the least significant set of differences can be found in the 50-Ohm VSWR curve for the three versions of the array shown in <b>Fig. 6</b>. All would be acceptable 80-meter SWR curves. I shall note in passing that these curves are easy to obtain with experimental modeling shifts in the phase-line characteristic impedance. However, the original design equations called for a phase-line impedance of closer to 200 Ohms, with the illusion of needing a matching device for a coaxial feedline for the array.</p>
+  <p>The ability of a simple 2-wire element to restore most of the performance to the array arises from the fact that an LPDA--like any multi-element array--derives its performance not only from driving the elements, but as well from the mutual coupling between elements. The simulated fat elements, composed of wide-spaced wires, indeed has close to the same mutual coupling between array elements as the fat-wire model.</p>
+  <p>What differs between the 2-wire model and the fatter single-element version is the overall efficiency of the antenna. With 2" elements, the array is about 99.7% efficient, with losses due to material resistance that are a small fraction of 1%. The single #12 wire version is about 95.9% efficient, with over 4% material losses. The double-wire version reaches an efficiency of about 97.1%, which is only about a third of the way above the efficiency of the single-wire version toward the fat-element version. In short, the double-wire version of the antenna cannot restore all of the performance of the fat-wire version because it cannot decrease wire losses to the level of a single fat element. However, it can restore a large portion of the mutual coupling lost by using a single then wire for each element.</p>
+  <p>The process of restoring performance has a limit, and another LPDA design can illustrate this limit.</p>
+  <p><b>A 14-Element Wire LPDA for 80 Meters</b></p>
+  <p>By judiciously changing the values of Tau and Sigma, it is possible to arrive at an LPDA design with even better performance than we have so far attained. <b>Fig. 7</b> shows the outline of a 14-element 88.5' long array, again, initially using 2" elements.</p>
+  <center>
+    <img src="80w-7.gif" width="310" height="400" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The new array uses a Tau of 0.96 and a Sigma of 0.03 to pack the large number of elements into the prescribed space. Again, the phase-line characteristic impedance is 100 Ohms to arrive at a 50-Ohm feedpoint impedance. The following table shows the dimensions.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+80m t=.96 s=.03                              Frequency = 4  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1            0.000,-72.500,  0.000         0.000, 72.500,  0.000 2.00E+00  25
+2            8.603,-69.000,  0.000         8.603, 69.000,  0.000 2.00E+00  25
+3           16.862,-66.071,  0.000        16.862, 66.071,  0.000 2.00E+00  23
+4           24.790,-63.428,  0.000        24.790, 63.428,  0.000 2.00E+00  23
+5           32.402,-60.891,  0.000        32.402, 60.891,  0.000 2.00E+00  21
+6           39.709,-58.455,  0.000        39.709, 58.455,  0.000 2.00E+00  21
+7           46.723,-56.117,  0.000        46.723, 56.117,  0.000 2.00E+00  19
+8           53.457,-53.872,  0.000        53.457, 53.872,  0.000 2.00E+00  19
+9           59.922,-51.717,  0.000        59.922, 51.717,  0.000 2.00E+00  19
+10          66.128,-49.649,  0.000        66.128, 49.649,  0.000 2.00E+00  17
+11          72.086,-47.663,  0.000        72.086, 47.663,  0.000 2.00E+00  17
+12          77.805,-46.000,  0.000        77.805, 46.000,  0.000 2.00E+00  17
+13          83.296,-45.000,  0.000        83.296, 45.000,  0.000 2.00E+00  15
+14          88.567,-43.500,  0.000        88.567, 43.500,  0.000 2.00E+00  15
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           8    14 / 50.00   ( 14 / 50.00)      0.707       0.000       V
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>Like the smaller array, this design employs a measure of circularized Tau to obtain better performance than provided by the initial design taken from LPDA equations. The rear-most 2 and the forward-most 3 elements have been modified, and further refinement may be possible.</p>
+  <p>With 2" elements, the array has an average free-space gain across 80 meters of nearly 7.6 dBi, with an average front-to-back ratio of about 20 dB. A single #12 wire version of the antenna achieves an average free-space gain of about 6.75 dBi, about 0.8 dB lower than the fat-element version. Interestingly, the single-wire version of the antenna has an average front-to-back ratio of about 25 dB, about 5 dB higher than that of the fat-element version.</p>
+  <p>The same techniques used with the smaller array were applied to the 14-element LPDA to produce a double wire version. The resulting array model had over 2300 segments, even using the reduced levels of segmentation in the long parallel sections of each double-wire element. The resulting array showed an average free-space gain of about 7.1 dBi, less than half way toward the fat-element version from the single-wire model. The average front-to-back ratio was about 21 dB, close to the value of the fat-element version.</p>
+  <center>
+    <img src="80w-8.gif" width="646" height="527" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 8</b> shows the gain curves for the three models. The double-wire and fat-wire versions are very synchronous, while the single-wire model curve shows divergent frequencies for its peaks and valleys.</p>
+  <center>
+    <img src="80w-9.gif" width="646" height="525" border="2" vspace="5" hspace="9">
+  </center>
+  <p>In <b>Fig. 9</b>, we see much the same results. The fat-wire and double-wire curves are closely matched, while the single-wire takes a direction of its own--and at a higher average level of front-to-back ratio.</p>
+  <center>
+    <img src="80w-10.gif" width="585" height="600" border="2" vspace="5" hspace="9">
+  </center>
+  <p>In keeping with the front-to-back curves, <b>Fig. 10</b> shows 50-Ohm VSWR curves that are very similar for the fat-wire and double wire models. In contrast, although still a very flat curve, the single-wire SWR curve shows a progression of its own.</p>
+  <p>Initially, one might have expected a relatively uniform performance upgrade relative to that shown for the 6-element LPDA. However, 2 factors count against that expectation.</p>
+  <p>First, the efficiency of the larger array is inherently lower than that of the small LPDA. The fat-element version has an efficiency of about 99.2%, against a single #12 wire version efficiency of 88.5%. Doubling the wires for each element only raises the efficiency to 90.8%, a gain of 2.3% but still 8.4% shy of the fat wire model. From an efficiency perspective alone, the ability of the double-wire version to restore most of the performance of the fat-wire version is limited.</p>
+  <p>However, we should have also noted the fact that the LPDA front-to-back ratio decreased as we moved from the thin-wire to the fat-wire model. This fact suggests that the most closely spaced elements of the 14-element array are already over-coupled when using fat elements. Gain increases with wire size are largely functions of increased efficiency rather than superior mutual coupling between elements. The following table provides the key performance reports of NEC for the same 14-element array using a variety of element diameters ranging from the single-wire #12 AWG version up to and including the 2: element version. The progression may prove interesting for data taken at 3.75 Hz.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+El. Dia.    Gain        F-B Ratio         Feed Impedance          50-Ohm
+ inches     dBi         dB                R+/-jX Ohms             VSWR
+0.0808      6.80        26.25             62.9 - j 4.4            1.28
+0.25        7.24        23.57             60.2 - j 6.9            1.25
+0.5         7.37        21.91             55.0 - j 9.2            1.22
+1.0         7.45        20.65             46.8 + j 8.2            1.20
+1.5         7.48        20.03             42.3 - j 4.9            1.22
+2.0         7.50        19.68             40.1 - j 1.5            1.25
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>The largest increment of gain occurs with the first move that increases the element diameter by a factor of 3. As well, the front-to-back ratio also shows its steepest decrease. Above that level, performance stabilizes within a quite narrow range.</p>
+  <p>The result for this particular model is a set of alternative building strategies. One might go to the trouble of constructing 14 sets of double-wire elements. However, one can get as much performance improvement of the single-thin-wire model by simply using 0.25" wire, either copper or aluminum--the latter being lighter.</p>
+  <p><b>An Alternative Method of Modeling 2-Wire LPDA Elements</b></p>
+  <p>The method used in these notes to model the 2-wire substitute elements for an LPDA results in a very large model. The model of the 14-element array used 154 wires and 2334 segments. Even the smaller 6-element LPDA required 66 wires and 1010 segments for the 2-wire substitute.</p>
+  <p>There is a technique that results in smaller models with respect to the number of wires and segments, although the number of TL-transmission lines does increase. An increase in TL entries does not materially increase the run time of a model. Nor does it press any program limitations for the number of allowable segments. Consequently, the alternative method does have some advantages for the LPDA modeler. Therefore, consider <b>Fig. 11</b>.</p>
+  <center>
+    <img src="80w-11.gif" width="614" height="286" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The sketch shows the modeling structure--reduced to the forward 2 elements of a full array. The sketch presumes that the modeler creates a single 4-wire loop for each element, proceeding in a counter-clockwise direction as he adds wires to make the loop. With only 4 wires, the modeler has already saved 7 wires per element in the process. Moreover, each wire can use longer segment lengths, thus reducing the number of segments per element by as much as half to two-thirds.</p>
+  <p>The presumption that the element loop was created by going "around the horn" with wires creates an interesting situation with respect to the TL (transmission line) entries for the phase line. With a single wire assembly per element (or the single-wire central sections to the earlier technique for creating double-wire elements), each TL entry would be set to "Reverse" rather than to "Normal" in order to simulate the phase reversal between elements. In the new technique, using the presumed method of forming elements, we want to have both wires of each element connected in parallel, with a phase reversal between elements.</p>
+  <p>To achieve this goal, we must remember that our method of forming elements has reversed the direction of current. Therefore, to simulate a direct parallel connection between the two closely spaced wires, we must use a reverse connection of the tiny TL line between them. We can make the line that creates the parallel connection as short as we wish, since the line is mathematical only--and the physical distance between wires makes no difference. A TL entry for a length as short is 0.001 foot (since the model is in feet) will do fine.</p>
+  <p>Between elements, we wish to have a phase reversal. However, the current directions of the two wires we connect are already opposite in phase. Therefore, we use a "Normal" TL line entry for the "actual" distance between wires. The following extracts from an LPDA model using this technique will demonstrate the process further.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+3.3-4.5 MHz t=.89 s=.07                         Frequency = 4  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1     W4E2   0.000,-72.500,  0.000  W2E1   0.000, 72.500,  0.000    # 12   57
+2     W1E2   0.000, 72.500,  0.000  W3E1   0.000, 72.500,  1.000    # 12    1
+3     W2E2   0.000, 72.500,  1.000  W4E1   0.000,-72.500,  1.000    # 12   57
+4     W3E2   0.000,-72.500,  1.000  W1E1   0.000,-72.500,  0.000    # 12    1
+5     W8E2   8.603,-69.000,  0.000  W6E1   8.603, 69.000,  0.000    # 12   53
+6     W5E2   8.603, 69.000,  0.000  W7E1   8.603, 69.000,  1.000    # 12    1
+7     W6E2   8.603, 69.000,  1.000  W8E1   8.603,-69.000,  1.000    # 12   53
+8     W7E2   8.603,-69.000,  1.000  W5E1   8.603,-69.000,  0.000    # 12    1
+9    W12E2  16.862,-66.071,  0.000 W10E1  16.862, 66.071,  0.000    # 12   51
+10    W9E2  16.862, 66.071,  0.000 W11E1  16.862, 66.071,  1.000    # 12    1
+11   W10E2  16.862, 66.071,  1.000 W12E1  16.862,-66.071,  1.000    # 12   51
+12   W11E2  16.862,-66.071,  1.000  W9E1  16.862,-66.071,  0.000    # 12    1
+. . .
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          17    55 / 50.00   ( 55 / 50.00)      0.707       0.000       V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+
+Line  Wire #/% From End 1   Wire #/% From End 1    Length       Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)                Ohms Fact Norm
+
+1      1/50.0  (  1/50.0)    3/50.0  (  3/50.0)    0.001 ft   100.0  1.00  R
+2      3/50.0  (  3/50.0)    5/50.0  (  5/50.0)  Actual dist  100.0  1.00  N
+3      5/50.0  (  5/50.0)    7/50.0  (  7/50.0)    0.001 ft   100.0  1.00  R
+4      7/50.0  (  7/50.0)    9/50.0  (  9/50.0)  Actual dist  100.0  1.00  N
+5      9/50.0  (  9/50.0)   11/50.0  ( 11/50.0)    0.001 ft   100.0  1.00  R
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>The "wires" portion of the table shows the rear 3 elements of an LPDA composed of 2-wire elements. The 4 "Transmission Line" entries show the portions of the phase line connecting these elements. TLs 1, 3, and 5 are clearly the connections within each element, while lines 2 and 4 interconnect elements.</p>
+  <p>Some modelers run all long wires either left-to-right or right-to-left. Had we used this convention, the short TL within an element would require a "Normal" connection and the inter-element phase lines would require a "Reverse" connection. Either system will yield accurate results in terms of antenna performance, but mixed systems will result in bewildering outputs.</p>
+  <p>The alternative modeling system for LPDA double-wire elements may in fact produce more accurate results. At least the results are a bit more coincident with those for the single fat elements that the double-wire versions replace. The following short tables summarize for each of the two different LPDA designs the key parameters for 3.5, 3.75, and 4 MHz.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+6-element LPDA Model Performance
+Frequency     Gain     Front-to     Feedpoint Impedance     50-Ohm
+   MHz        dBi      Back Ratio     R +/- jX Ohms          VSWR
+2" Elements
+  3.5         7.04      23.91         59.9 - j 16.5          1.418
+  3.75        6.78      22.51         52.8 + j 11.1          1.248
+  4.0         6.78      27.13         92.2 + j 10.3          1.875
+Double-Wire Model: Initial Method
+  3.5         6.83      23.84         58.3 - j 13.3          1.336
+  3.75        6.49      19.99         55.8 + j 14.6          1.346
+  4.0         6.59      26.65         90.8 + j  4.6          1.822
+Double-Wire Model: Revised Method
+  3.5         6.87      23.18         60.4 - j 15.5          1.402
+  3.75        6.58      20.82         54.7 + j 12.6          1.291
+  4.0         6.57      25.46         90.8 + j 12.4          1.864
+
+14-element LPDA Model Performance
+Frequency     Gain     Front-to     Feedpoint Impedance     50-Ohm
+   MHz        dBi      Back Ratio     R +/- jX Ohms          VSWR
+2" Elements
+  3.5         7.67      18.84         61.5 + j  3.1          1.239
+  3.75        7.50      19.68         40.1 - j  1.5          1.250
+  4.0         7.49      21.52         58.4 - j  5.3          1.202
+Double-Wire Model: Initial Method
+  3.5         7.21      22.11         60.3 - j  3.8          1.220
+  3.75        7.06      20.54         44.3 + j  5.2          1.178
+  4.0         7.03      20.64         50.3 - j 15.2          1.352
+Double-Wire Model: Revised Method
+  3.5         7.27      20.33         60.7 + j  2.7          1.221
+  3.75        7.10      20.02         42.9 - j  0.0          1.165
+  4.0         7.10      21.33         58.7 - j  9.0          1.259
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>Operationally, the differences between the two double-wire substitutes for 2" tubular elements are insignificant. However, in terms of finding the most adequate model of the 2-wire substitute, both alternatively modeled 2-wire arrays show a slightly greater coincidence with the fat-wire model in terms of the parallel of changes of values. Note, for example, the dip in the gain curve of the original substitute element model, compared to the way in which the new model changes values. As well, the impedance values--in terms both of values and of the type of reactance--of the new method more closely match those of the basic model. In short, the alternate method of modeling double-wire LPDAs may result in both smaller and slightly more accurate models.</p>
+  <p><b>Alternative Designs</b></p>
+  <p>Between 6 and 14 elements, there is a great design space for the individual who wishes to eventually build an LPDA for 80 meters. To save some initial effort in evaluating what different designs might do within the space allocated for the array, I have calculated and then modified for relatively (but not perfectly) optimized performance a collection of LPDA designs ranging from 6 to 14 elements. All except the 14-element version are limited to 86' in length, with the longest one being about 88.5' in total length. All use 100-Ohm phase lines. Other values can be used but would require an impedance matching network or device at the array feedpoint. As well, higher phase line values may slightly alter the performance curves--in places showing slight gain reductions.</p>
+  <p>As we have seen from the graphs presented earlier, every LPDA exhibits peaks and valleys of gain, front-to-back ratio, feedpoint impedance, and SWR. However, for initial evaluations, we can use average values, since the gain changes are under 0.3 dB in the worst case. Only the longest LPDA in the collection shows front- to-back values under 20 dB. The average value of the 50-Ohm SWR is a reasonably good indicator of the impedance swing range. The "Model" label indicates the approximate values of Tau and Sigma. All models use 2" copper elements, and further on, we shall note the potential of these models for conversion to double- wire substitutes.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Average Performance Values of 80-Meter LPDAs
+Model       Gain        F-B         SWR
+8907-6      6.86        24.33       1.517
+9205-8      7.10        26.74       1.420
+9404-10     7.18        25.91       1.378
+9503-12     7.26        25.40       1.186
+9603-14     7.55        19.95       1.230
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>As we would expect, the gain increases steadily as we increase the number of elements. However, the front-to-back ratio peaks with the 8-element design. This peak is a rough indication that, with respect to the front-to-back ratio, optimal inter-element coupling occurs with the spacings of this array. We may also note that the average SWR decreases steadily until at the 1.25:1 region, differences no longer make a difference. As well, impedance swings decrease in step with the average SWR.</p>
+  <p>Selecting an array to replicate is always a composite judgment based on many factors. The more elements, the higher the gain, but not necessarily a higher the front-to-back ratio. If we translate the designs into double wire elements, then we must also consider the fact that as we increase the number of elements, the lower the return rate to full 2"-element performance due to a decreasing efficiency (added material losses) as we add more double-wire elements.</p>
+  <p>In broadest terms, perhaps the 8- and 10-element arrays show the most promise. They provide a useful increment of gain above the 6-element LPDA and provide peak front-to-back performance. Using double-wire elements will allow the wire array to more closely approximate the performance of the fat-element model with these smaller arrays than with the longest versions in the set. The prospective builder can interpolate from the 6-element and the 14-element figures the likely performance figures for double-wire versions of these intermediate arrays. The overall array weight of the 8- and 10-element LPDAs is also likely to be more manageable than the weight of larger models.</p>
+  <p>For reference, the following wire-tables of the models will provide enough guidance to replicate as models or in wire any of the designs discussed.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+8907-6 elements
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in)
+
+1            0.000,-76.000,  0.000         0.000, 76.000,  0.000 2.00E+00
+2           21.346,-67.800,  0.000        21.346, 67.800,  0.000 2.00E+00
+3           40.382,-60.500,  0.000        40.382, 60.500,  0.000 2.00E+00
+4           57.358,-55.500,  0.000        57.358, 55.500,  0.000 2.00E+00
+5           72.498,-51.000,  0.000        72.498, 51.000,  0.000 2.00E+00
+6           86.000,-47.500,  0.000        86.000, 47.500,  0.000 2.00E+00
+
+9205-8 elements
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in)
+
+1            0.000,-75.500,  0.000         0.000, 75.500,  0.000 2.00E+00
+2           15.494,-69.500,  0.000        15.494, 69.500,  0.000 2.00E+00
+3           29.771,-64.563,  0.000        29.771, 64.563,  0.000 2.00E+00
+4           42.928,-60.000,  0.000        42.928, 60.000,  0.000 2.00E+00
+5           55.050,-55.500,  0.000        55.050, 55.500,  0.000 2.00E+00
+6           66.221,-51.500,  0.000        66.221, 51.500,  0.000 2.00E+00
+7           76.515,-48.000,  0.000        76.515, 48.000,  0.000 2.00E+00
+8           86.000,-44.500,  0.000        86.000, 44.500,  0.000 2.00E+00
+
+9404-10 elements
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in)
+
+1            0.000,-75.500,  0.000         0.000, 75.500,  0.000 2.00E+00
+2           12.160,-71.000,  0.000        12.160, 71.000,  0.000 2.00E+00
+3           23.570,-66.953,  0.000        23.570, 66.953,  0.000 2.00E+00
+4           34.277,-62.826,  0.000        34.277, 62.826,  0.000 2.00E+00
+5           44.324,-58.700,  0.000        44.324, 58.700,  0.000 2.00E+00
+6           53.752,-55.800,  0.000        53.752, 55.800,  0.000 2.00E+00
+7           62.599,-53.000,  0.000        62.599, 53.000,  0.000 2.00E+00
+8           70.900,-49.500,  0.000        70.900, 49.500,  0.000 2.00E+00
+9           78.690,-47.500,  0.000        78.690, 47.500,  0.000 2.00E+00
+10          86.000,-45.000,  0.000        86.000, 45.000,  0.000 2.00E+00
+
+9503-12 elements
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in)
+
+1            0.000,-75.500,  0.000         0.000, 75.500,  0.000 2.00E+00
+2           10.006,-71.800,  0.000        10.006, 71.800,  0.000 2.00E+00
+3           19.504,-68.519,  0.000        19.504, 68.519,  0.000 2.00E+00
+4           28.521,-65.044,  0.000        28.521, 65.044,  0.000 2.00E+00
+5           37.081,-61.746,  0.000        37.081, 61.746,  0.000 2.00E+00
+6           45.206,-58.614,  0.000        45.206, 58.614,  0.000 2.00E+00
+7           52.919,-55.641,  0.000        52.919, 55.641,  0.000 2.00E+00
+8           60.241,-53.000,  0.000        60.241, 53.000,  0.000 2.00E+00
+9           67.192,-52.000,  0.000        67.192, 52.000,  0.000 2.00E+00
+10          73.790,-48.500,  0.000        73.790, 48.500,  0.000 2.00E+00
+11          80.054,-46.500,  0.000        80.054, 46.500,  0.000 2.00E+00
+12          86.000,-44.500,  0.000        86.000, 44.500,  0.000 2.00E+00
+
+
+9603-14 elements
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in)
+
+1            0.000,-72.500,  0.000         0.000, 72.500,  0.000 2.00E+00
+2            8.603,-69.000,  0.000         8.603, 69.000,  0.000 2.00E+00
+3           16.862,-66.071,  0.000        16.862, 66.071,  0.000 2.00E+00
+4           24.790,-63.428,  0.000        24.790, 63.428,  0.000 2.00E+00
+5           32.402,-60.891,  0.000        32.402, 60.891,  0.000 2.00E+00
+6           39.709,-58.455,  0.000        39.709, 58.455,  0.000 2.00E+00
+7           46.723,-56.117,  0.000        46.723, 56.117,  0.000 2.00E+00
+8           53.457,-53.872,  0.000        53.457, 53.872,  0.000 2.00E+00
+9           59.922,-51.717,  0.000        59.922, 51.717,  0.000 2.00E+00
+10          66.128,-49.649,  0.000        66.128, 49.649,  0.000 2.00E+00
+11          72.086,-47.663,  0.000        72.086, 47.663,  0.000 2.00E+00
+12          77.805,-46.000,  0.000        77.805, 46.000,  0.000 2.00E+00
+13          83.296,-45.000,  0.000        83.296, 45.000,  0.000 2.00E+00
+14          88.567,-43.500,  0.000        88.567, 43.500,  0.000 2.00E+00
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p><b>Conclusion</b></p>
+  <p>80-meter wire LPDAs can be effective horizontally polarized antennas for the entire band if they are better designed than past versions. Minimally, I would recommend the 6-element 86' long model as an array whose effort at construction and mounting would be rewarded by decent performance. The double-wire version is apt for fixed installations, while--for certain builders with abilities matching the mass--the use of large tubular elements might well permit rotation of the antenna.</p>
+  <p>Further increments of performance will require larger arrays, such as the 14-element 88' LPDA noted in the design exercise. However, because the elements have already reached the limits of their inter-element coupling, the double-wire version may be more work than is worth the effort. The use of a larger wire size--0.25" or greater--may be the best way to improve performance above the level one can obtain from a single #12 wire.</p>
+  <p>Along the way, we have seen that the double-wire simulation of fat elements has a limit. The more elements to the array, the less the double-wire element can effectively restore performance lost when using single thin wires. Mutual coupling varies with several variables, including element spacing, element diameter, and frequency. The peaks and valleys evident in both gain and front-to-back curves for LPDAs arise largely because the mutual coupling among the most active elements does vary with frequency--variations which also yield changes in the current magnitude on each element in the array. The peaks and valleys in the performance curves are not coincident for both gain and the front-to-back ratio, suggesting that the optimal mutual coupling conditions for one parameter are not necessarily optimum for the other. However, since many elements are simultaneously active to a significant, if not controlling, degree, exacting formulations of the relationships lie beyond the realm of modeling. Nevertheless, in revealing the coincidence and displacement of curves as we vary the element diameter of the elements, modeling can show the effects of changes in coupling among elements.</p>
+  <p>The upshot of these exercises is this: it pays to explore a given design in many different kinds of models before deciding on the best method of construction.</p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p><i>Updated 04-01-2002. &COPY; L. B. Cebik, W4RNL. The original item appeared in</i> AntenneX <i>for March, 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>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
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content/lpda/9556.html

@@ -0,0 +1,326 @@
+<!DOCTYPE html>
+<html lang="en">
+<head>
+  <meta charset="UTF-8">
+  <meta name="keywords" content="LPDA, HF Upper">
+  <title>Long-Boom LPDAs for 14-30 MHz</title>
+  <link rel="stylesheet" href="../styles.css">
+</head>
+<body>
+  <center>
+    <h1>Long-Boom LPDAs for 14-30 MHz</h1>
+  </center>
+  <center>
+    <h3>L. B. Cebik, W4RNL</h3>
+  </center><br>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  <p>In this note, I want to discuss a pair of long-boom LPDA designs to cover all of the amateur bands from 20 through 10 meters. Long-boom means (for our purposes) anything over 45' or so. We know that 5-6-element monoband Yagis can achieve a little over 10.1 dBi free-space gain with better than 20 dB front-to-back ratios across 20 meters with boom lengths between 45 and 53 feet. The question before us is this: what can we achieve using a similar boom length in a multi-band antenna?</p>
+  <p><b>Standards of Comparison</b></p>
+  <p>In the tri-band category, Force 12 has a 49-foot model with excellent performance on 20, 15, and 10 meters. However, the standard for comparison for an LPDA would need to cover all 5 upper HF bands.</p>
+  <p>The only single-boom design with high performance on all 5 amateur bands is the ON4ANT forward-stagger design, which has recently appeared in journals and also appears at my web site. <b>Fig. 1</b> shows the general outline of the "final" 14-element, 60'-boom model designed by Johan Van de Velde.</p>
+  <center>
+    <img src="9556-1.gif" width="611" height="373" border="2" vspace="5" hspace="9">
+  </center>
+  <p>For each band below 10 meters, the director also serves as the reflector for the next higher band. As well, for all bands above 20 meters, the director serves as the reflector for the next higher band. Additional directors have been added to improve 10-meter performance.</p>
+  <p>For reference, the following EZNEC-4 model description will provide the dimensions (in meters):</p>
+  <pre>
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+ON4ANT 5-b Yagi:  14-28 Final              Frequency = 14.175  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : m )  Conn. --- End 2 (x,y,z : m )   Dia(mm) Segs
+
+1           -5.450,  0.000,  0.000         5.450,  0.000,  0.000 3.20E+01  37
+2           -5.200,  2.000,  0.000         5.200,  2.000,  0.000 3.20E+01  35
+3           -4.900,  3.600,  0.000         4.900,  3.600,  0.000 3.20E+01  34
+4           -4.150,  5.250,  0.000         4.150,  5.250,  0.000 2.50E+01  28
+5           -4.020,  6.400,  0.000         4.020,  6.400,  0.000 2.50E+01  27
+6           -3.800,  7.200,  0.000         3.800,  7.200,  0.000 2.50E+01  25
+7           -3.395,  8.400,  0.000         3.395,  8.400,  0.000 2.50E+01  23
+8           -3.020,  9.500,  0.000         3.020,  9.500,  0.000 2.50E+01  21
+9           -2.910, 10.800,  0.000         2.910, 10.800,  0.000 2.50E+01  21
+10          -2.680, 12.000,  0.000         2.680, 12.000,  0.000 2.30E+01  19
+11          -2.550, 13.014,  0.000         2.550, 13.014,  0.000 2.30E+01  19
+12          -2.470, 13.816,  0.000         2.470, 13.816,  0.000 2.30E+01  17
+13          -2.440, 15.775,  0.000         2.440, 15.775,  0.000 2.30E+01  16
+14          -2.310, 18.250,  0.000         2.310, 18.250,  0.000 2.30E+01  16
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          18     2 / 50.00   (  2 / 50.00)      1.000       0.000       I
+
+No loads specified
+No transmission lines specified
+Ground type is Free Space
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+</pre>
+  <p>More important is the performance potential, which the following table reveals:</p>
+  <pre>
+Freq.     Gain      F-B       Feed Impedance
+MHz       dBi       dB        R +/- jX Ohms
+20
+14.0      8.30      36.74     28.8 - j 0.4
+14.175    8.41      27.35     24.7 + j 7.9
+14.35     8.55      20.57     19.0 + j18.8
+17
+18.118    8.35      23.06     31.7 - j 4.9
+15
+21.0      8.73      23.12     34.1 + j 2.0
+21.225    8.86      23.15     35.9 + j10.3
+21.45     8.99      23.04     37.4 + j18.6
+12
+24.94     9.70      37.50     23.4 + j14.6
+10
+28.0      9.92      26.58     30.0 - j 8.8
+28.35     9.99      39.15     33.5 - j 4.7
+28.7      9.69      34.30     20.3 - j12.2
+</pre>
+  <p>Because elements must do double duty, performance improves with frequency. Even the 20-meter performance improves as one moves up the band, since the 20-meter director must be cut and positioned also to serve as the 17-meter reflector. 15 meters shows a similar pattern. The 180-degree front-to-back value exceeds 20 dB throughout the passband.</p>
+  <p>No SWR figures appear since the antenna's 5 feedpoints (one for each band) are designed for use with a gamma match. The significant limitation (from the perspective of broadband design, but not from the perspective of some kinds of operating interests) is the "cut-off" of 10-meter coverage somewhere between 28.7 and 28.8 MHz, as gain continues to decrease and the feedpoint resistive component of the impedances continues to decrease.</p>
+  <p>The ON4ANT design makes a good standard against which to compare a high-performance LPDA.</p>
+  <p><b>Version 1: Circular-Tau-Modified Standard LPDA Design</b></p>
+  <p>The initial version of the LPDA uses a Tau of 0.95 and a Sigma of 0.056. Ideally, one should use a Tau of 0.96 and an optimized Sigma somewhat higher than 0.18. However, the boom length for such an antenna becomes well over 3 times the length of the present design. With the Tau and Sigma values given, the boom length is about 51.5' with 21 elements, all of which are uniformly 0.5" in diameter. Fig. 2 shows the general outline of the array.</p>
+  <center>
+    <img src="9556-2.gif" width="612" height="420" border="2" vspace="5" hspace="9">
+  </center>
+  <p>For reference and element dimensions (in inches), the EZNEC model description follows:</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+14-30 MHz .95/.056 21 el 51.5'             Frequency = 14  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+
+1            0.000,-216.30,  0.000         0.000,216.300,  0.000 5.00E-01  25
+2           48.177,-205.00,  0.000        48.177,205.000,  0.000 5.00E-01  23
+3           93.944,-194.00,  0.000        93.944,194.000,  0.000 5.00E-01  23
+4          137.424,-184.40,  0.000       137.424,184.399,  0.000 5.00E-01  21
+5          178.729,-175.18,  0.000       178.729,175.179,  0.000 5.00E-01  21
+6          217.969,-166.42,  0.000       217.969,166.420,  0.000 5.00E-01  19
+7          255.248,-158.10,  0.000       255.248,158.099,  0.000 5.00E-01  19
+8          290.662,-150.19,  0.000       290.662,150.194,  0.000 5.00E-01  17
+9          324.306,-142.68,  0.000       324.306,142.685,  0.000 5.00E-01  17
+10         356.267,-135.55,  0.000       356.267,135.550,  0.000 5.00E-01  15
+11         386.630,-128.77,  0.000       386.630,128.773,  0.000 5.00E-01  15
+12         415.475,-122.33,  0.000       415.475,122.334,  0.000 5.00E-01  15
+13         442.878,-116.22,  0.000       442.878,116.217,  0.000 5.00E-01  13
+14         468.911,-110.41,  0.000       468.911,110.407,  0.000 5.00E-01  13
+15         493.642,-104.89,  0.000       493.642,104.886,  0.000 5.00E-01  13
+16         517.136,-99.642,  0.000       517.136, 99.642,  0.000 5.00E-01  11
+17         539.456,-94.660,  0.000       539.456, 94.660,  0.000 5.00E-01  11
+18         560.660,-89.927,  0.000       560.660, 89.927,  0.000 5.00E-01  11
+19         580.804,-85.431,  0.000       580.804, 85.431,  0.000 5.00E-01   9
+20         599.940,-81.159,  0.000       599.940, 81.159,  0.000 5.00E-01   9
+21         618.120,-77.101,  0.000       618.120, 77.101,  0.000 5.00E-01   9
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           5    21 / 50.00   ( 21 / 50.00)      0.707       0.000       V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+
+Line  Wire #/% From End 1   Wire #/% From End 1    Length       Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)                Ohms Fact Norm
+
+1      1/50.0  (  1/50.0)    2/50.0  (  2/50.0)  Actual dist  100.0  1.00  R
+2      2/50.0  (  2/50.0)    3/50.0  (  3/50.0)  Actual dist  100.0  1.00  R
+3      3/50.0  (  3/50.0)    4/50.0  (  4/50.0)  Actual dist  100.0  1.00  R
+4      4/50.0  (  4/50.0)    5/50.0  (  5/50.0)  Actual dist  100.0  1.00  R
+5      5/50.0  (  5/50.0)    6/50.0  (  6/50.0)  Actual dist  100.0  1.00  R
+6      6/50.0  (  6/50.0)    7/50.0  (  7/50.0)  Actual dist  100.0  1.00  R
+7      7/50.0  (  7/50.0)    8/50.0  (  8/50.0)  Actual dist  100.0  1.00  R
+8      8/50.0  (  8/50.0)    9/50.0  (  9/50.0)  Actual dist  100.0  1.00  R
+9      9/50.0  (  9/50.0)   10/50.0  ( 10/50.0)  Actual dist  100.0  1.00  R
+10    10/50.0  ( 10/50.0)   11/50.0  ( 11/50.0)  Actual dist  100.0  1.00  R
+11    11/50.0  ( 11/50.0)   12/50.0  ( 12/50.0)  Actual dist  100.0  1.00  R
+12    12/50.0  ( 12/50.0)   13/50.0  ( 13/50.0)  Actual dist  100.0  1.00  R
+13    13/50.0  ( 13/50.0)   14/50.0  ( 14/50.0)  Actual dist  100.0  1.00  R
+14    14/50.0  ( 14/50.0)   15/50.0  ( 15/50.0)  Actual dist  100.0  1.00  R
+15    15/50.0  ( 15/50.0)   16/50.0  ( 16/50.0)  Actual dist  100.0  1.00  R
+16    16/50.0  ( 16/50.0)   17/50.0  ( 17/50.0)  Actual dist  100.0  1.00  R
+17    17/50.0  ( 17/50.0)   18/50.0  ( 18/50.0)  Actual dist  100.0  1.00  R
+18    18/50.0  ( 18/50.0)   19/50.0  ( 19/50.0)  Actual dist  100.0  1.00  R
+19    19/50.0  ( 19/50.0)   20/50.0  ( 20/50.0)  Actual dist  100.0  1.00  R
+20    20/50.0  ( 20/50.0)   21/50.0  ( 21/50.0)  Actual dist  100.0  1.00  R
+
+Ground type is Free Space
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>As one decreases the characteristic impedance of the phasing line from 200 Ohms downward, the array draws closer to having an acceptable 50-Ohm or 75-Ohm SWR throughout its passband (14-30 MHz). However, these same reductions often reveal frequencies at which an LPDA will show a weakness. A weakness means that the elements to the rear of the element with the highest current magnitude begin to operate in a harmonic mode. The result is a reduction in forward gain and a very significant reduction in front-to-back ratio. In short, rearward radiation becomes quite large at frequencies of weakness. The design uses a 100-Ohm phase line, which is physically practical for either double boom construction or for a separate phase line structure. The array shows potential weaknesses at about 19.75 MHz and again at 26.5 MHz. Since these frequencies lie between amateur bands, no compensatory treatments were applied.</p>
+  <p>To enhance performance in the upper HF region, the forward elements were subjected to circularization, a process of decreasing the value of Tau with respect to be element length and spacing for the affected elements. The result was a small increase in upper HF gain, but a more useful improvement in the feedpoint SWR curve.</p>
+  <p>The following table provides the potential performance figures for the NEC-4 model:</p>
+  <pre>
+Freq.     Gain      F-B       Feed Impedance    50-Ohm      75-Ohm
+MHz       dBi       dB        R +/- jX Ohms     VSWR        VSWR
+20
+14.0      8.82      25.45     75.0 + j 0.1      1.50        1.00
+14.175    8.82      31.25     73.9 - j 2.9      1.48        1.04
+14.35     8.78      42.54     72.5 - j 6.3      1.47        1.10
+17
+18.118    8.74      40.48     69.1 - j 7.6      1.42        1.14
+15
+21.0      8.52      34.31     60.6 + j 1.3      1.21        1.24
+21.225    8.50      34.54     65.9 + j 4.2      1.33        1.15
+21.45     8.50      34.73     71.3 + j 1.4      1.43        1.06
+12
+24.94     8.39      32.03     61.7 - j 8.9      1.28        1.25
+10
+28.0      8.00      25.31     66.6 - j16.8      1.50        1.30
+28.5      8.05      26.38     54.1 - j 3.3      1.11        1.39
+29.0      7.97      25.35     73.6 - j 0.8      1.47        1.02
+29.5      7.79      23.27     63.6 - j30.7      1.80        1.60
+</pre>
+  <p>As the frequency approaches 30 MHz, the 75-Ohm VSWR exceed 2:1 by a small amount, although the 50-Ohm SWR remains at about 1.8:1. The feedpoint resistance begins to sink rapidly above 29.5 MHz.</p>
+  <p>Below 15 meters, the gain performance of the LPDA exceeds the ON4ANT forward-stagger Yagi. More generally, the LPDA front-to-back ratio is more stable, as it tracks the gain of the antenna at each frequency. 10-meter performance is down considerably relative to the Yagi. This phenomenon is quite normal for an LPDA where the upper design frequency is less than 1.6 times the highest frequency used. Adding further elements (to a self-resonant frequency of about 50 MHz) would have significantly lengthened the boom. At least 5 further elements would have been required.</p>
+  <p>The reduction in gain (and front-to-back) at higher frequencies stems in large measure from the fact that in a wide-band LPDA array, all of the elements forward of the one with the highest current magnitude at a given frequency are active, essentially adding many "directors" to the array. As we increase frequency, the element with the highest current magnitude moves forward, leaving fewer elements to serve as "directors." Circularizing the value of Tau for the forward-most elements can improve the upper-end gain, but it cannot fully compensate for all of the reduction.</p>
+  <p>As a consequence of the gain fall-off, further design was undertaken.</p>
+  <p><b>Version 2: Circular-Tau-Modified Standard LPDA Design With a Parasitic Director</b></p>
+  <p>I added a director to the array, as shown in <b>Fig. 3</b>. The director adds only 4.3' to the boom length, but equalizes performance at both ends of the passband.</p>
+  <center>
+    <img src="9556-3.gif" width="633" height="427" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The resulting array is described in EZNEC-4 terms:</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+14-30 MHz .95/.056 21+dir 55.8'              Frequency = 14  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+
+1            0.000,-216.30,  0.000         0.000,216.300,  0.000 5.00E-01  25
+2           48.177,-205.00,  0.000        48.177,205.000,  0.000 5.00E-01  23
+3           93.944,-194.00,  0.000        93.944,194.000,  0.000 5.00E-01  23
+4          137.424,-184.40,  0.000       137.424,184.399,  0.000 5.00E-01  21
+5          178.729,-175.18,  0.000       178.729,175.179,  0.000 5.00E-01  21
+6          217.969,-166.42,  0.000       217.969,166.420,  0.000 5.00E-01  19
+7          255.248,-158.10,  0.000       255.248,158.099,  0.000 5.00E-01  19
+8          290.662,-150.19,  0.000       290.662,150.194,  0.000 5.00E-01  17
+9          324.306,-142.68,  0.000       324.306,142.685,  0.000 5.00E-01  17
+10         356.267,-135.55,  0.000       356.267,135.550,  0.000 5.00E-01  15
+11         386.630,-128.77,  0.000       386.630,128.773,  0.000 5.00E-01  15
+12         415.475,-122.33,  0.000       415.475,122.334,  0.000 5.00E-01  15
+13         442.878,-116.22,  0.000       442.878,116.217,  0.000 5.00E-01  13
+14         468.911,-110.41,  0.000       468.911,110.407,  0.000 5.00E-01  13
+15         493.642,-104.89,  0.000       493.642,104.886,  0.000 5.00E-01  13
+16         517.136,-99.642,  0.000       517.136, 99.642,  0.000 5.00E-01  11
+17         539.456,-94.660,  0.000       539.456, 94.660,  0.000 5.00E-01  11
+18         560.660,-89.927,  0.000       560.660, 89.927,  0.000 5.00E-01  11
+19         580.804,-85.431,  0.000       580.804, 85.431,  0.000 5.00E-01   9
+20         599.940,-81.159,  0.000       599.940, 81.159,  0.000 5.00E-01   9
+21         618.120,-77.101,  0.000       618.120, 77.101,  0.000 5.00E-01   9
+22         670.000,-88.700,  0.000       670.000, 88.700,  0.000 5.00E-01  11
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           5    21 / 50.00   ( 21 / 50.00)      0.707       0.000       V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+
+Line  Wire #/% From End 1   Wire #/% From End 1    Length       Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)                Ohms Fact Norm
+
+1      1/50.0  (  1/50.0)    2/50.0  (  2/50.0)  Actual dist  100.0  1.00  R
+2      2/50.0  (  2/50.0)    3/50.0  (  3/50.0)  Actual dist  100.0  1.00  R
+3      3/50.0  (  3/50.0)    4/50.0  (  4/50.0)  Actual dist  100.0  1.00  R
+4      4/50.0  (  4/50.0)    5/50.0  (  5/50.0)  Actual dist  100.0  1.00  R
+5      5/50.0  (  5/50.0)    6/50.0  (  6/50.0)  Actual dist  100.0  1.00  R
+6      6/50.0  (  6/50.0)    7/50.0  (  7/50.0)  Actual dist  100.0  1.00  R
+7      7/50.0  (  7/50.0)    8/50.0  (  8/50.0)  Actual dist  100.0  1.00  R
+8      8/50.0  (  8/50.0)    9/50.0  (  9/50.0)  Actual dist  100.0  1.00  R
+9      9/50.0  (  9/50.0)   10/50.0  ( 10/50.0)  Actual dist  100.0  1.00  R
+10    10/50.0  ( 10/50.0)   11/50.0  ( 11/50.0)  Actual dist  100.0  1.00  R
+11    11/50.0  ( 11/50.0)   12/50.0  ( 12/50.0)  Actual dist  100.0  1.00  R
+12    12/50.0  ( 12/50.0)   13/50.0  ( 13/50.0)  Actual dist  100.0  1.00  R
+13    13/50.0  ( 13/50.0)   14/50.0  ( 14/50.0)  Actual dist  100.0  1.00  R
+14    14/50.0  ( 14/50.0)   15/50.0  ( 15/50.0)  Actual dist  100.0  1.00  R
+15    15/50.0  ( 15/50.0)   16/50.0  ( 16/50.0)  Actual dist  100.0  1.00  R
+16    16/50.0  ( 16/50.0)   17/50.0  ( 17/50.0)  Actual dist  100.0  1.00  R
+17    17/50.0  ( 17/50.0)   18/50.0  ( 18/50.0)  Actual dist  100.0  1.00  R
+18    18/50.0  ( 18/50.0)   19/50.0  ( 19/50.0)  Actual dist  100.0  1.00  R
+19    19/50.0  ( 19/50.0)   20/50.0  ( 20/50.0)  Actual dist  100.0  1.00  R
+20    20/50.0  ( 20/50.0)   21/50.0  ( 21/50.0)  Actual dist  100.0  1.00  R
+
+Ground type is Free Space
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>The parasitic director length and position represent a design compromise. Further gain is achievable, but at the cost of unacceptable 10-meter SWR values. A parasitic element also decreases the front-to-back ratio at upper frequencies of the passband. The design goals included a front-to-back ratio at 29.5 MHz of at least 20 dB plus a 50-Ohm SWR no higher than 2:1 across 10 meters. The following performance table reveals that both objectives were met.</p>
+  <pre>
+Freq.     Gain      F-B       Feed Impedance    50-Ohm      75-Ohm
+MHz       dBi       dB        R +/- jX Ohms     VSWR        VSWR
+20
+14.0      8.85      24.83     75.6 + j 0.2      1.51        1.01
+14.175    8.85      30.27     74.2 - j 3.5      1.49        1.05
+14.35     8.81      38.97     71.9 - j 6.5      1.46        1.10
+17
+18.118    8.83      38.07     67.2 - j 6.9      1.38        1.16
+15
+21.0      8.72      42.38     64.8 + j 0.1      1.30        1.16
+21.225    8.71      41.41     66.9 - j 0.6      1.34        1.12
+21.45     8.72      40.76     67.1 - j 1.8      1.34        1.12
+12
+24.94     8.81      32.04     73.6 - j 2.4      1.48        1.04
+10
+28.0      8.92      24.94     72.3 + j16.5      1.58        1.26
+28.5      9.02      22.35     82.3 - j31.3      1.99        1.50
+29.0      9.04      20.97     39.6 - j22.4      1.73        2.12
+29.5      9.04      20.03     38.7 + j 8.8      1.38        1.97
+</pre>
+  <p>Although the LPDA does not achieve all of the upper-end gain of the ON4ANT Yagi, it does achieve a remarkably smooth free-space gain curve with only about 0.3 dB variation across the entire passband of the array.</p>
+  <p><b>Some Comparisons</b></p>
+  <p>In order to assess the full potential of the LPDA arrays, I performed frequency sweeps of them in 0.25 MHz increments from 13 through 31 MHz. The following graphics are very nearly self-explanatory. Except where values on the tables above coincide with frequency markers in the graphs below, expect to find very slight differences in values, since all properties of an LPDA undulate across the passband.</p>
+  <center>
+    <img src="9556-4.gif" width="646" height="529" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 4</b> shows the free-space gain curve of the arrays in dBi. Note the frequencies (19.75 MHz and 26.5 MHz) at which the gain shows an abnormal decrease. If one wishes to eliminate these dips, then the weakness can be suppressed with a single stub on the lower frequency element that shows the highest harmonic mode operation.</p>
+  <p>The graph also shows performance deterioration at both upper and lower ends of the band, except for the gain on the version with the director. However, that increasing high frequency gain will be offset by decreases in the front-to-back ratio.</p>
+  <p>The most significant feature of the gain curve is a revelation of the effects of the parasitic director. The director improves gain (although insignificantly so) even at the lowest design frequency of the array. Given the current magnitude on it, the director must be considered an active element through the design spectrum.</p>
+  <center>
+    <img src="9556-5.gif" width="649" height="527" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The 180-degree front-to-back curve, shown in <b>Fig. 5</b>, shows far more variation than the gain curve relative to the two array designs. However, the "unnatural" dips in the front-to-back ratio reach their lowest values at same frequencies as the gain dip minima: 19.75 MHz and 26.5 MHz. In actuality, the minima occur at very slightly different frequencies. The peaks and nulls in the undulating gain and front-to-back curves do not exactly coincide.</p>
+  <p>Above 20 MHz, the presence of the director most significantly alters the front-to-back performance of the array, shifting the overall curve so that the peaks are lower in frequency relative to the version without the director. As well, above 28 MHz, the array with the director shows a much more rapid drop in front-to-back ratio. The overall front-to-back curve can be altered further with changes in director length and spacing. However, balancing goals for gain, front-to-back ratio, feedpoint impedance, and overall boom length require a design compromise. The closer the spacing of the director to the forward LPDA element, the more radical its effect upon performance at the upper end of the passband.</p>
+  <center>
+    <img src="9556-6.gif" width="645" height="527" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 6</b> shows 2 pairs of SWR curves, with 50-Ohm curves and 75-Ohm curves shown for each version of the array. To distinguish the designs, in the legend, "ND" means "no director," and "D" means "director." Despite the fact the impedance values seem to track a 75-Ohm impedance center across most of the passband, a 50-Ohm feedline appears to be the better choice at the passband edges. Both versions of the LPDA show a 50-Ohm 2:1 SWR or better from 14 through 29.7 MHz.</p>
+  <p><b>Conclusion</b></p>
+  <p>The Director-LPDA offers somewhat better low-end performance but slightly inferior high-end performance relative to the ON4ANT Yagi. However, the LPDA 10-meter performance extends across the entire band. The LPDA has the advantage of requiring only a single feedline. However, it does require the construction of a phasing line and element-to-boom insulating plates for all elements. Of course, the LPDA is usable at all frequencies between 14 and 30 MHz (with a corrective for the weaknesses noted). Even with a director, the array is 4' shorter than the "final" forward-stagger Yagi.</p>
+  <p>Although the design employs a value for Tau (0.95) close to the maximum recommended value, the array does not achieve all of its potential gain. With the use of an optimized value for Sigma (rather than the 0.056 value actually used in the design), free-space gain would increase to a maximum close to 11.5 dBi, with some front-to-back (and averaged front-to-rear) figures exceeding 50 dB. As noted initially, however, such an array would require 3 to 4 times the boom length.</p>
+  <p>The LPDA with no director is not so inferior to the director array that it should be ignored. At a height of 70' or so, the gain of the array across the entire passband is remarkably equal, allowing for the lowering of the take-off angle with increasing frequency. There is under 0.4 dB difference in maximum among 14, 21, and 28 MHz values.</p>
+  <p>At present, these LPDA arrays are design exercises, since I lack the facilities to construct and the robust tower and rotator to support a long-boom LPDA. Therefore, I shall not include potential mechanical design considerations in these notes. However, the arrays are samples of what an LPDA can do within the limitations of what amateurs consider to be long-boom antennas. Although the long-boom LPDA presents mechanical challenges, it achieves performance competitive with stacks of 2 ordinary multi-band Yagis without the extended mast. In short, it is one more option within the amateur arsenal of high performance multi-band arrays.</p>
+  <center>
+    <img src="../images/colorbar.gif" width="591" height="3">
+  </center>
+  <p><small>Note: The purpose of this article is to disseminate information and ideas. The author retains all design rights associated with the subject arrays, including modifications for improved performance over standard arrays of a similar type and including all reasonable variations upon them both stated or implied by the text or the designs themselves.</small></p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p><i>Updated 07-01-2001. &COPY; L. B. Cebik, W4RNL. The original item appeared in</i> AntenneX <i>for June, 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>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p><a href="../radio.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Go to Main Index</a></p>
+  <p class="topics-footer">Topics: <a href='../topics.html#hf-upper'>HF Upper</a>, <a href='../topics.html#lpda'>LPDA</a></p><br>
+</body>
+</html>

content/lpda/cad.html

@@ -0,0 +1,280 @@
+<!DOCTYPE html>
+<html lang="en">
+<head>
+  <meta charset="UTF-8">
+  <meta name="keywords" content="LPDA, HF Multi Band">
+  <title>LPCAD Designs and NEC Models of LPDAs</title>
+  <link rel="stylesheet" href="../styles.css">
+</head>
+<body>
+  <center>
+    <h1><img src="../images/lpda.gif" align="left" width="150" height="83" border="2" vspace="5" hspace="10"><img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10">LPCAD Designs and NEC Models of LPDAs</h1>
+  </center>
+  <center>
+    <h3>L. B. Cebik, W4RNL</h3>
+  </center><br>
+  <br>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  <p>The log-periodic dipole array (LPDA) arouses amateur interest every so often. Based on a series of mathematical relationships, the LPDA design is amenable to computerized calculations for all element lengths and spacings. One program that has found wide use is LPCAD by Roger Cox, WB0DGF.</p>
+  <p>The point of this note is not to discuss basic LPDA design. This information can be found in the <i>ARRL Antenna Book</i>, Chapter 10, and in many standard antenna texts and references, for example, Kraus or Johnson and Jasik.</p>
+  <p>This note is devoted to a number of precautions we should take when moving from a page of design calculations, such as those produced by LPCAD, to a NEC model of the antenna design. To ease the transition, LPCAD provides a save function to capture the antenna design in standard NEC format (as well as in other formats). This model description will run on almost any version of NEC, -2 and above. Those having a version of EZNEC that translates from the .NEC format can import the file to that program.</p>
+  <p>The save function is undoubtedly offered as a convenience to designers. However, the designer who models the antenna in NEC must take responsibility for ensuring that the model meets all of the requirements for being a good NEC model. Let's use an example: a 20-element 100' long 3-30 MHz LPDA of standard design. The value of Tau for this example is about 0.8737 and the value of Sigma is about 0.0409. <b>Fig. 1</b> provides an outline of the general antenna design.</p>
+  <center>
+    <img src="cad-1.gif" width="626" height="387" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The LPCAD NEC file provides both a wires table and a TL transmission line table. The most accurate way to model LPDA designs that do not have unusual mechanical features, such as overlapping element ends, is to create each element at the correct spacing. Then use the TL facility of NEC-2 and higher to create the phasing line between each element pair, being sure to reverse connections of the line at each element. LPCAD adheres to this procedure in creating its NEC file.</p>
+  <p>The LPCAD NEC-file does not specify any wire loss, since material specifications are not used in the element calculations. Therefore, the first step for the modeler is to specify the wire material for the elements. Second, modeler should check the output azimuth plot specification. LPCAD uses a standard 10-degree step in the pattern, and the user may wish to reduce the step to 1 or 2 degrees to obtain smoother patterns with more detail.</p>
+  <p>With just these steps, an EZNEC description of the resulting file will look like the following listing.</p>
+  <pre>20 el 100' 3-30 MHz                      Frequency = 3  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : in)  Conn.--- End 2 (x,y,z : in)  Dia(in) Segs
+
+1          0.000,-1003.7,  0.000         0.000,1003.68,  0.000 3.50E+00  15
+2        164.166,-876.93,  0.000       164.166,876.934,  0.000 3.50E+00  15
+3        307.601,-766.19,  0.000       307.601,766.193,  0.000 3.50E+00  15
+4        432.923,-669.44,  0.000       432.923,669.437,  0.000 3.50E+00  15
+5        542.419,-584.90,  0.000       542.419,584.899,  0.000 3.50E+00  15
+6        638.087,-511.04,  0.000       638.087,511.037,  0.000 3.50E+00  15
+7        721.675,-446.50,  0.000       721.675,446.503,  0.000 3.50E+00  15
+8        794.707,-390.12,  0.000       794.707,390.118,  0.000 3.50E+00  15
+9        858.516,-340.85,  0.000       858.516,340.853,  0.000 3.50E+00  15
+10       914.267,-297.81,  0.000       914.267,297.810,  0.000 3.50E+00  15
+11       962.978,-260.20,  0.000       962.978,260.202,  0.000 3.50E+00  15
+12       1005.54,-227.34,  0.000       1005.54,227.343,  0.000 3.50E+00  15
+13       1042.72,-198.63,  0.000       1042.72,198.634,  0.000 3.50E+00  15
+14       1075.21,-173.55,  0.000       1075.21,173.550,  0.000 3.50E+00  15
+15       1103.60,-151.63,  0.000       1103.60,151.634,  0.000 3.50E+00  15
+16       1128.40,-132.49,  0.000       1128.40,132.485,  0.000 3.50E+00  15
+17       1150.07,-115.75,  0.000       1150.07,115.755,  0.000 3.50E+00  15
+18       1169.00,-101.14,  0.000       1169.00,101.137,  0.000 3.50E+00  15
+19       1185.55,-88.365,  0.000       1185.55, 88.365,  0.000 3.50E+00  15
+20       1200.00,-77.206,  0.000       1200.00, 77.206,  0.000 3.50E+00  15
+
+               -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           8    20 / 50.00   ( 20 / 50.00)      0.707       0.000       V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+
+Line  Wire #/% From End 1   Wire #/% From End 1    Length     Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)              Ohms Fact Norm
+
+1    1/50.0  (  1/50.0)    2/50.0  (  2/50.0)  Actual dist  200.0  1.00  R
+2    2/50.0  (  2/50.0)    3/50.0  (  3/50.0)  Actual dist  200.0  1.00  R
+3    3/50.0  (  3/50.0)    4/50.0  (  4/50.0)  Actual dist  200.0  1.00  R
+4    4/50.0  (  4/50.0)    5/50.0  (  5/50.0)  Actual dist  200.0  1.00  R
+5    5/50.0  (  5/50.0)    6/50.0  (  6/50.0)  Actual dist  200.0  1.00  R
+6    6/50.0  (  6/50.0)    7/50.0  (  7/50.0)  Actual dist  200.0  1.00  R
+7    7/50.0  (  7/50.0)    8/50.0  (  8/50.0)  Actual dist  200.0  1.00  R
+8    8/50.0  (  8/50.0)    9/50.0  (  9/50.0)  Actual dist  200.0  1.00  R
+9    9/50.0  (  9/50.0)   10/50.0  ( 10/50.0)  Actual dist  200.0  1.00  R
+10  10/50.0  ( 10/50.0)   11/50.0  ( 11/50.0)  Actual dist  200.0  1.00  R
+11  11/50.0  ( 11/50.0)   12/50.0  ( 12/50.0)  Actual dist  200.0  1.00  R
+12  12/50.0  ( 12/50.0)   13/50.0  ( 13/50.0)  Actual dist  200.0  1.00  R
+13  13/50.0  ( 13/50.0)   14/50.0  ( 14/50.0)  Actual dist  200.0  1.00  R
+14  14/50.0  ( 14/50.0)   15/50.0  ( 15/50.0)  Actual dist  200.0  1.00  R
+15  15/50.0  ( 15/50.0)   16/50.0  ( 16/50.0)  Actual dist  200.0  1.00  R
+16  16/50.0  ( 16/50.0)   17/50.0  ( 17/50.0)  Actual dist  200.0  1.00  R
+17  17/50.0  ( 17/50.0)   18/50.0  ( 18/50.0)  Actual dist  200.0  1.00  R
+18  18/50.0  ( 18/50.0)   19/50.0  ( 19/50.0)  Actual dist  200.0  1.00  R
+19  19/50.0  ( 19/50.0)   20/50.0  ( 20/50.0)  Actual dist  200.0  1.00  R
+
+Ground type is Free Space</pre>
+  <p>Judging from some correspondence, many modelers would accept this model at face value as a proper model and proceed to check the performance at frequencies of interest. In fact, this model would show up as acceptable of better on the Average Gain Test, since this test does not pick up segmentation flaws unless they are wildly flagrant. However, there are two important modifications that one should make to this model before trusting any outputs.</p>
+  <p>First, the model is uniformly specified with 15 segments per wire throughout the 20 elements. However, every element is a different length. Hence, segmentation should vary from one element to the next. How many segments each element should have is a function of the length of the longest element and the highest frequency at which the antenna will operate. The longest element is a little over 2000" and the highest frequency is 30 MHz. We need conservatively about 10 segments per half wavelength, but because we shall place a transmission line along the exact center line of the antenna, we need for each element an odd number of segments. The requirement for an odd number of elements will limit the precision of our segmentation.</p>
+  <p>Since the longest element is a bit over 5 wl long at 30 MHz, let's assign 107 segments to the longest element. For each shorter element, in order, we simply multiply by Tau, using the preceding element answer as the basis for the next element. We shall have to round upward or downward to the closest odd number to obtain the segment number for the element in question. For the example in question, the shortest two elements each receive 9 segments, since their 1/2 wl resonant frequencies are above 30 MHz.</p>
+  <p>Second, consider the element diameter. The value in the diameter column is the average element diameter that the user specified as an input to the calculations. However, this value is very often not an accurate reflection of the intended element diameter for the actual antenna. Hence, we should replace the average diameter with value as close to reality as possible.</p>
+  <p>For the model in question, I specified a range of diameters from 0.5" for the shortest element to 6.5" for the longest. The design required that each element change according to Tau in the descent from 6.5" to 0.5". Once more, this is a simply matter of successive multiplication of preceding values by Tau to obtain the next smaller diameter. (The design purpose in this case was to have a constant element length-to-diameter ratio for the entire model. In any event, you should use element diameter values as close to reality as the stage of design will allow.)</p>
+  <p>The modified antenna model then took on this appearance.</p>
+  <pre>20 el 100' 3-30 MHz                       Frequency = 3  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : in)  Conn.--- End 2 (x,y,z : in)  Dia(in) Segs
+
+1          0.000,-1003.7,  0.000         0.000,1003.68,  0.000 6.50E+00 107
+2        164.166,-876.93,  0.000       164.166,876.934,  0.000 5.68E+00  93
+3        307.601,-766.19,  0.000       307.601,766.193,  0.000 4.96E+00  81
+4        432.923,-669.44,  0.000       432.923,669.437,  0.000 4.34E+00  71
+5        542.419,-584.90,  0.000       542.419,584.899,  0.000 3.79E+00  63
+6        638.087,-511.04,  0.000       638.087,511.037,  0.000 3.31E+00  55
+7        721.675,-446.50,  0.000       721.675,446.503,  0.000 2.89E+00  47
+8        794.707,-390.12,  0.000       794.707,390.118,  0.000 2.53E+00  41
+9        858.516,-340.85,  0.000       858.516,340.853,  0.000 2.21E+00  37
+10       914.267,-297.81,  0.000       914.267,297.810,  0.000 1.93E+00  31
+11       962.978,-260.20,  0.000       962.978,260.202,  0.000 1.69E+00  27
+12       1005.54,-227.34,  0.000       1005.54,227.343,  0.000 1.47E+00  25
+13       1042.72,-198.63,  0.000       1042.72,198.634,  0.000 1.29E+00  21
+14       1075.21,-173.55,  0.000       1075.21,173.550,  0.000 1.12E+00  19
+15       1103.60,-151.63,  0.000       1103.60,151.634,  0.000 9.80E-01  17
+16       1128.40,-132.49,  0.000       1128.40,132.485,  0.000 8.60E-01  15
+17       1150.07,-115.75,  0.000       1150.07,115.755,  0.000 7.50E-01  13
+18       1169.00,-101.14,  0.000       1169.00,101.137,  0.000 6.50E-01  11
+19       1185.55,-88.365,  0.000       1185.55, 88.365,  0.000 5.70E-01   9
+20       1200.00,-77.206,  0.000       1200.00, 77.206,  0.000 5.00E-01   9
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           5    20 / 50.00   ( 20 / 50.00)      0.707       0.000       V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+
+Line  Wire #/% From End 1   Wire #/% From End 1    Length     Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)              Ohms Fact Norm
+
+1    1/50.0  (  1/50.0)    2/50.0  (  2/50.0)  Actual dist  200.0  1.00  R
+2    2/50.0  (  2/50.0)    3/50.0  (  3/50.0)  Actual dist  200.0  1.00  R
+3    3/50.0  (  3/50.0)    4/50.0  (  4/50.0)  Actual dist  200.0  1.00  R
+4    4/50.0  (  4/50.0)    5/50.0  (  5/50.0)  Actual dist  200.0  1.00  R
+5    5/50.0  (  5/50.0)    6/50.0  (  6/50.0)  Actual dist  200.0  1.00  R
+6    6/50.0  (  6/50.0)    7/50.0  (  7/50.0)  Actual dist  200.0  1.00  R
+7    7/50.0  (  7/50.0)    8/50.0  (  8/50.0)  Actual dist  200.0  1.00  R
+8    8/50.0  (  8/50.0)    9/50.0  (  9/50.0)  Actual dist  200.0  1.00  R
+9    9/50.0  (  9/50.0)   10/50.0  ( 10/50.0)  Actual dist  200.0  1.00  R
+10  10/50.0  ( 10/50.0)   11/50.0  ( 11/50.0)  Actual dist  200.0  1.00  R
+11  11/50.0  ( 11/50.0)   12/50.0  ( 12/50.0)  Actual dist  200.0  1.00  R
+12  12/50.0  ( 12/50.0)   13/50.0  ( 13/50.0)  Actual dist  200.0  1.00  R
+13  13/50.0  ( 13/50.0)   14/50.0  ( 14/50.0)  Actual dist  200.0  1.00  R
+14  14/50.0  ( 14/50.0)   15/50.0  ( 15/50.0)  Actual dist  200.0  1.00  R
+15  15/50.0  ( 15/50.0)   16/50.0  ( 16/50.0)  Actual dist  200.0  1.00  R
+16  16/50.0  ( 16/50.0)   17/50.0  ( 17/50.0)  Actual dist  200.0  1.00  R
+17  17/50.0  ( 17/50.0)   18/50.0  ( 18/50.0)  Actual dist  200.0  1.00  R
+18  18/50.0  ( 18/50.0)   19/50.0  ( 19/50.0)  Actual dist  200.0  1.00  R
+19  19/50.0  ( 19/50.0)   20/50.0  ( 20/50.0)  Actual dist  200.0  1.00  R
+20   1/50.0  (  1/50.0)  Short ckt (Short ck)   90.000 in   200.0  1.00
+
+Ground type is Free Space</pre>
+  <p>Besides the changes to the element segments and element diameter columns, one other addition to the model is evident. I added a shorted transmission line stub to the phasing line at the rearmost element. Actually, I ran this model with and without the stub to see the difference in performance at selected frequencies.</p>
+  <p>Notice that the stub has a specific length and is not the oft-used 1/4 wl (or the length of 1/2 the longest element). The stub was chosen to improve low frequency performance while having the least effect on upper frequency performance.</p>
+  <p>The modification significantly increase the segment count for the entire model (with or without the stub). The example above uses 792 segments, which may be beyond the common 500-segment limit of many entry-level NEC programs. However, it is the minimal satisfactory model of the LPDA design in question. In fact, convergence testing should check the model up to at least 1.5 times the segmentation density used here. (See the end of this note for the convergence test.)</p>
+  <p>Is all this really necessary? To find out, let's run frequency sweeps of the original model (with the aluminum elements and smaller plot step level in place) and of the two modified models (without and with a stub). If the original model formulation is satisfactory, then its curves should track the curves of the modified models except for any stub effects. As a preliminary set of checks, let's plot the following parameters: free-space gain in dBi, 180-degree front-to-back ratio in dB, source resistance in Ohms, source reactance in Ohms, and VSWR relative to some standard.</p>
+  <p>For a real design, we would run detailed frequency sweeps across each intended band of operation. For this general profile, we can use a sweep that checks the values of interest at 1 MHz intervals from 3 through 30 MHz, the design range of the model. In the following graphs, "20100" refers to the unmodified model, "20100A" refers to the stubless modified model, and "20100ATL" refers to the modified model with a shorted stub.</p>
+  <center>
+    <img src="cad-2.gif" width="644" height="527" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 2</b> provides graphs of the gain values for the three models. Except for the 6 MHz region, the stub and no-stub modified models track each other very well, with the stub model having the highest gain at 3 MHz. The original model using a constant 15-segments per element erroneously predicts a gain peak at 6 MHz. More significantly, above about 12 MHz, the original model provides significantly over-optimistic values for the gain of the antenna, a typical result of inadequate segmentation. However, note that the values occur in the frequency region in which we might think that the segmentation is adequate. This is a lesson to the effect that all of the elements of an LPDA design play a role at all frequencies.</p>
+  <center>
+    <img src="cad-3.gif" width="645" height="525" border="2" vspace="5" hspace="9">
+  </center>
+  <p>In <b>Fig. 3</b>, we see the generally coincident curves for all three models with respect to front-to-back ratio. The original model is once more a bit over-optimistic at the highest frequencies, but these high reports are confined to the 25 to 29 MHz region. The most serious anomaly is at 6 MHz, where the original model predicts a very low front-to-back ratio (the same frequency on which it predicted an unusually high gain value). The stubless model that corresponds to the initial model (which is also without a shorted stub) predicts exactly the opposite--an unusually high front-to- back ratio. Addition of the stub smoothes the curve considerably.</p>
+  <center>
+    <img src="cad-4.gif" width="647" height="524" border="2" vspace="5" hspace="9">
+  </center>
+  <p>When we turn to the resistance and reactance components (<b>Fig. 4</b> and <b>Fig. 5</b>) of the source impedance, the odd performance of the original model shows itself most vividly. The curves for the stub and stubless models are so close together above the lowest region of the passband that one curve obscures the other. This phenomenon makes all the more evident that fact that the initial model tends to dip and peak in a rhythm directly opposite that of the more adequately segmented model. The resistance values reported by the 15- segment per element model would have to be accounted wholly unreliable.</p>
+  <center>
+    <img src="cad-5.gif" width="645" height="526" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The graph of reactance values tells a very similar story. Again, the stubbed and stubless models coincide above the lowest frequencies, but the initial model fails to track these curves. In fact, it tends to take just the opposite turn. It is well to remember that the larger model more closely approaches convergence than the smaller model and hence must be accounted a more proper model of the antenna than the smaller model.</p>
+  <center>
+    <img src="cad-6.gif" width="646" height="527" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Because the resistance and reactance values were at such odds, it was necessary to track VSWR against different reference values in <b>Fig. 6</b>. The initial model used a 75-Ohm standard, suggesting that it might be directly fed with a coaxial cable. However, both larger models are referenced to 95 Ohms, a value taken as close to the mean between the extremes of the resistive components of the source impedance. Incidentally, the LPCAD prediction for a source impedance is 103 Ohms.</p>
+  <p>The importance of the difference in VSWR reference standards lies in the consequences for designing the impedance matching required for connecting a main feedline to the antenna. The initial model's prediction that a 75-Ohm cable would be sufficient is unlikely to be fulfilled. More likely is the potential for using a wide-band 2:1 impedance matching device to connect the antenna to a 50-Ohm cable.</p>
+  <p>The inadequacies of uncritically adopting the transfer model as a proper NEC model are all too evident from the comparative graphs. This is not a criticism of LPCAD, since the main function of saving the LPDA design as a NEC model is to release the designer from the tedium of entering every element length, space, and transmission line without omission, slippage, or transposition of numbers. However, it remains the responsibility of the modeler to use sufficient care to ensure that the resulting model meets all applicable NEC standards for being a proper model within the guidelines for the core. If a model turns out to be too big for the limits of a software package, it is dangerous to trust the results of a model squeezed down in segmentation to fit those limits. Instead, the model needs to be whatever size is required for it to yield reliable results--and sometimes, that calls for a software package with larger limits. Most especially, models should never be shrunken just to reduce the time it takes to make a set of runs.</p>
+  <p>Programs like LPCAD are exceptionally useful design tools. However, like NEC itself, they have limitations. When using them, it pays to find and understand those limitations so that they do not impede design progress. Translating LPCAD designs into NEC models is a fascinating case in point.</p>
+  <h3>A Note on the Convergence of Large Models</h3>It is always useful to perform a convergence test on a model to determine its reliability. The convergence test is a necessary but not sufficient test of reliability: a model that fails to converge should be considered unreliable, but one that does converge might have problems that the convergence test cannot detect.
+  <p>In the present case, we are dealing with relatively large models--relative, that is, to normal amateur radio modeling practices, although these models would be small in the confines of some engineering projects. The modified models--with and without a stub--have 792 segments overall, distributed in 20 elements. A reasonable convergence test might add 50% to that number as a basic convergence check.</p>
+  <p>However, the segmentation of the model must meet special requirements. The number of segments per element is determined by a rolling Tau calculation starting from the longest element. The calculation is then rounded to the nearest odd-number of segments. To avoid double rounding errors, I performed the Tau-based calculations, beginning with 161 segments on the rear element, up from 107 on the models considered above. The result appears in the partial model description below:</p>
+  <pre>              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : in)  Conn.--- End 2 (x,y,z : in)  Dia(in) Segs
+
+1          0.000,-1003.7,  0.000         0.000,1003.68,  0.000 6.50E+00 161
+2        164.166,-876.93,  0.000       164.166,876.934,  0.000 5.68E+00 141
+3        307.601,-766.19,  0.000       307.601,766.193,  0.000 4.96E+00 123
+4        432.923,-669.44,  0.000       432.923,669.437,  0.000 4.34E+00 107
+5        542.419,-584.90,  0.000       542.419,584.899,  0.000 3.79E+00  93
+6        638.087,-511.04,  0.000       638.087,511.037,  0.000 3.31E+00  81
+7        721.675,-446.50,  0.000       721.675,446.503,  0.000 2.89E+00  71
+8        794.707,-390.12,  0.000       794.707,390.118,  0.000 2.53E+00  63
+9        858.516,-340.85,  0.000       858.516,340.853,  0.000 2.21E+00  55
+10       914.267,-297.81,  0.000       914.267,297.810,  0.000 1.93E+00  47
+11       962.978,-260.20,  0.000       962.978,260.202,  0.000 1.69E+00  41
+12       1005.54,-227.34,  0.000       1005.54,227.343,  0.000 1.47E+00  37
+13       1042.72,-198.63,  0.000       1042.72,198.634,  0.000 1.29E+00  31
+14       1075.21,-173.55,  0.000       1075.21,173.550,  0.000 1.12E+00  27
+15       1103.60,-151.63,  0.000       1103.60,151.634,  0.000 9.80E-01  25
+16       1128.40,-132.49,  0.000       1128.40,132.485,  0.000 8.60E-01  21
+17       1150.07,-115.75,  0.000       1150.07,115.755,  0.000 7.50E-01  19
+18       1169.00,-101.14,  0.000       1169.00,101.137,  0.000 6.50E-01  17
+19       1185.55,-88.365,  0.000       1185.55, 88.365,  0.000 5.70E-01  15
+20       1200.00,-77.206,  0.000       1200.00, 77.206,  0.000 5.00E-01  13</pre>
+  <p>I then took a long walk while I frequency swept the enlarged model from 3 to 30 MHz in 1 MHz steps. The results were then entered into a spreadsheet. Differentials between the values for the smaller and the larger model covered gain and front-to-back ratio (in dB), source resistance and reactance (in Ohms), and 95-Ohm VSWR. The results form the basis for a judgment of whether the smaller model is sufficiently converged with the larger to be considered reliable.</p>
+  <center>
+    <img src="cad-7.gif" width="646" height="526" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 7</b> shows the differentials for gain and front-to-back ratio. The maximum gain difference is under 0.15 dB or less than 3% of the average gain. The maximum front-to-back differential is 0.49 dB, again, less than 3% of the average front-to-back level.</p>
+  <p>Whether these numbers represent significant differences is a question of judgment related to the purposes for which one is doing the modeling. A gain difference of 0.15 dB is certainly not operationally detectable. Nor is a front-to-back differential of 0.49 dB. Since these maximum figures do not represent a general trend in the curves, they are unlikely to be meaningful for any design work one might do on an antenna of this sort. In fact, the most notable fact about the two curves in Fig. 7 is how closely they coincide, that is, how much of the curves remains within +/-.05 dB of zero.</p>
+  <center>
+    <img src="cad-8.gif" width="646" height="527" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The resistance and reactance curves appear in <b>Fig. 8</b>. The maximum resistance and reactance deviations are about 6 Ohms each, within 5% of the total range of values for each parameter. What the graph of differences cannot show is that differences are largest where the values compared are large. The resistance ranges from about 49 Ohms to over 170 Ohms, and the 6-Ohm peaks occur with the largest values. Likewise, reactance ranges from about -55 Ohms to nearly +70 Ohms, and once more, peak differences attach to the highest values. We may have noticed that in the progression of source impedance values for an LPDA, most instances of high reactance occur when the resistance is most distant from its mean value. Hence, the resistance and reactance peak values appear at different points on the basic graphs.</p>
+  <center>
+    <img src="cad-9.gif" width="645" height="505" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The result is a 95-Ohm VSWR graph of differences (<b>Fig. 9</b>) that peaks at values less than 0.025, a truly insignificant differential for any operational antenna consideration with which I am acquainted.</p>
+  <p>The general conclusion one might reach here is that the smaller model converges well with the larger and may be considered reliable for most purposes. This kind of test--and the results--give confidence that the graphed results for the modified models are far more usable than those for the unmodified model using a standard 15 elements per element.</p>
+  <p>Nevertheless, the general conclusion represents a "smoothed" judgment. There are still a few values on the difference graphs that call attention to themselves. In such cases, we may usefully do two things: 1. We can keep our eye out in further modeling for significant anomalies that occur at the same frequencies. 2. Should we implement the design used for discussion here, we might make a few special checks at these frequencies during the field testing and adjustment to ensure that operational values do not exceed whatever limits might be specified in the final design.</p>
+  <h3>A Note on Design Method in LPCAD</h3>When designing LPDAs in LPCAD, you have a choice: to use values of Tau and Sigma or to use specifications of the number of elements desired and the total length of the array. Now, suppose you initially design an LPDA using Tau and Sigma. Then, suppose you use the number of elements and the length given in that design report to design a new LPDA. You might expect to get a design whose element lengths and spacings were identical to the first design, with precisely the same values for Tau and Sigma.
+  <p>You will not. There will be slight differences in the two designs. As an example, here are the element descriptions for two LPDAs, the first designed by entering a Tau of 0.85 and a Sigma of 0.04. The second design was derived by entering 7 elements and 294.185" as the length, both figures taken from the first design. The frequency range for the design is 6.8 to 15 MHz.</p>
+  <pre>1.  Designed with Tau = 0.85; Sigma = 0.04
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+
+1            0.000,-442.80,  0.000         0.000,442.800,  0.000 1.00E+00  29
+2           70.848,-376.38,  0.000        70.848,376.380,  0.000 1.00E+00  25
+3          131.069,-319.92,  0.000       131.069,319.923,  0.000 1.00E+00  21
+4          182.257,-271.93,  0.000       182.257,271.935,  0.000 1.00E+00  17
+5          225.766,-231.14,  0.000       225.766,231.144,  0.000 1.00E+00  15
+6          262.749,-196.47,  0.000       262.749,196.473,  0.000 1.00E+00  13
+7          294.185,-167.00,  0.000       294.185,167.002,  0.000 1.00E+00  11
+
+2.  Designed with 7 Elements and 294.185" Length
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+
+1            0.000,-442.80,  0.000         0.000,442.800,  0.000 1.00E+00  29
+2           72.738,-371.50,  0.000        72.738,371.495,  0.000 1.00E+00  25
+3          133.763,-311.67,  0.000       133.763,311.673,  0.000 1.00E+00  21
+4          184.961,-261.48,  0.000       184.961,261.484,  0.000 1.00E+00  17
+5          227.915,-219.38,  0.000       227.915,219.377,  0.000 1.00E+00  15
+6          263.951,-184.05,  0.000       263.951,184.050,  0.000 1.00E+00  13
+7          294.185,-154.41,  0.000       294.185,154.413,  0.000 1.00E+00  11</pre>
+  <p>The calculated values for the second design are Tau = 0.840 and Sigma = 0.041. These small changes result in a 10" shortening of the second element (the prime current carraier at the low end of the passband) and a 26" shortening of the 7th element. These changes are not minor, as <b>Fig. 10</b> demonstrates.</p>
+  <center>
+    <img src="cad-10.gif" width="646" height="527" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Lowering the value of Tau shortens every element in the array except the rear one. One consequence is to lower gain everywhere in the passband. Whether the amount is significant is a user judgment based on design goals. However, it is sufficient to be noticeable and designers should be alerted to this facet of LPCAD operation.</p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p><i>Updated 09-26-99; 10-7-99. &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><br>
+  <br></p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p><a href="../radio.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Go to Main Index</a></p>
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+  <title>Notes on the Extended Aperture Log-Periodic Array</title>
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+<body>
+  <h1 style="text-align: center;">Notes on the Extended Aperture Log-Periodic Array</h1>
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+  <p style="text-align: center; font-weight: bold;"><a href="ealpda1.pdf">Part 1: The Extended Element and the Standard LPDA</a></p>
+  <p style="text-align: center; font-weight: bold;"><a href="ealpda2.pdf">Part 2: The Extended Aperture LPDA</a></p>
+  <p style="text-align: center;">This page exists to include the PDF in the topic index</p>
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+<!DOCTYPE html>
+<html lang="en">
+<head>
+  <meta charset="UTF-8">
+  <meta name="keywords" content="LPDA, HF Upper">
+  <title>HF General Coverage LPDAs Using 30-35' Booms</title>
+  <link rel="stylesheet" href="../styles.css">
+</head>
+<body>
+  <center>
+    <h1>Notes on HF General Coverage LPDAs Using 30-35' Booms</h1>
+  </center>
+  <center>
+    <h3>L. B. Cebik, W4RNL</h3>
+  </center><br>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  <p>The most popular range for LPDAs among radio amateurs is 14-30 MHz. Within that range, boom lengths of 30-35' hold considerable interest, since these booms are similar to the ones used for advanced multi-element, multi-band Yagis. In fact, it is quite possible to construct an LPDA with a 30' boom that provides better than 7 dBi free-space gain and better than 20 dB front-to-back ratio across all of the amateur bands included in the passband.</p>
+  <center>
+    <img src="l30-1.gif" width="313" height="367" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 1</b> shows the outline of one such design. Because the design is proprietary, I cannot provide exact dimensions. However, the outline shows--if you look carefully--signs of Tau circularization on the longest and shortest elements. To maximize gain on the amateur bands, the designs employs a 100-Ohm phase line, for direct connection to either a 50-Ohm or 70-Ohm feedline.</p>
+  <p>A quick survey of amateur-band performance, as modeled on NEC-4 will show the potential of the design.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+         Amateur-Band Performance Potential of a 12-Element LPDA
+
+Freq.      Gain       180-Deg.   Feed Impedance   50-Ohm    70-Ohm
+ MHz       dBi        F-B dB     R +/- jX Ohms     SWR       SWR
+14.175     7.33       27.66      84.9 + j 10.7    1.74      1.27
+18.118     7.17       25.41      62.8 - j  5.0    1.28      1.14
+21.225     7.04       27.39      65.4 - j  9.7    1.37      1.17
+24.94      7.37       23.18      47.6 - j 11.9    1.28      1.55
+28.0       6.88       22.98      66.1 - j  3.2    1.33      1.08
+28.85      7.32       25.22      43.4 - j 10.0    1.29      1.67
+29.7       7.67       20.62      94.0 - j  8.1    1.90      1.37
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>Because 10 meters is such a wide band, I have given 3 check points. Changes in performances are very small for the other bands. Although 50-Ohm SWR is generally acceptable, the 70-Ohm SWR performance is superior. Only at the low end of 10 meters does the gain drop below 7 dBi, but not by much.</p>
+  <p>Suppose, however, that the design goals for our 30-35' long LPDA go beyond simple amateur-band performance. Suppose that we wish to develop a general coverage LPDA from 14-30 MHz. We might set up the criteria in the following manner:</p>
+  <ul>
+    <li>1. Gain: &gt;7 dBi everywhere across the passband</li>
+    <li>2. Gain Differential: &lt;0.5 dB across the passband</li>
+    <li>3. Front-to-Back (Worst-Case): &gt;20 dB</li>
+    <li>4. SWR: &lt;1.5:1 relative to an impedance standard across the passband</li>
+  </ul>
+  <p>The significance of these design criteria stem from the needs of some services to use frequency-nimble communications techniques. Wide divergence of performance from one frequency to the next may jeopardize communications, especially with marginal signal levels. Hence, we may legitimately set these goals and then see if we can meet them.</p>
+  <p>Our outstanding 12-element LPDA ham-band performer unfortunately does not meet these more stringent criteria.</p>
+  <center>
+    <img src="l30-2.gif" width="744" height="407" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 2</b> shows the free-space gain and both the 180-degree and the worst- case front-to-back ratios at intervals of 0.25 MHz from 14-30 MHz. Since the LPDA has no secondary forward lobes, the front/sidelobe ratio curve reliably tracks the strongest rear lobe and thus presents a picture of the worst-case front-to-back performance of the array.</p>
+  <p>Immediately apparent is the anomaly in the curves in the region of 24.5 MHz. The array employs a shorted stub on the rear element. The length of the stub can move the frequency of the anomaly, but cannot eliminate it. Even if we ignore the anomaly, the gain range runs from 6.75 dBi to 7.67 dBi, a 0.92 dB range. The front-to-back performance is also subject to the anomaly. In addition, the worst-case value drops below 20 dB from 26.75 to 28.0 MHz and again above 29.75 MHz.</p>
+  <center>
+    <img src="l30-3.gif" width="744" height="407" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 3</b> shows both the 50-Ohm and the 70-Ohm SWR curves for the array across the entire passband. The 70-Ohm curve is superior--relative to the 1.5:1 standard--below the anomalous frequency region, while the 50-Ohm curve is superior from the anomaly up to 29.5 MHz. Above 29.5 MHz, the SWR climbs rapidly, and it goes completely to pot in the region of 24.5 MHz.</p>
+  <p>Relative to the general coverage standards, the 12-element, 30' LPDA does not fill the bill, despite its high utility as an amateur band array. Indeed, if we re-examine the design, we can see several reasons for the failure. The 100-Ohm phase line value is too low to ensure stable performance across the entire passband: hence, the anomaly. Of equal importance is the gain curve in general--apart from the anomaly. Element length changes on the shortest elements improve high-end performance. However, they also occasion wider gain swings than we see in the lower portions of the passband. We also detect a gradual lowering of the average gain and worst-case front-to-back ratio as we increase frequency until the high-end compensation kicks into action--and the compensation improves the gain more than the worst-case front-to-back ratio.</p>
+  <p>To achieve a general-coverage LPDA with a boom length in the 30-35' region, we shall have to look at other design options.</p>
+  <p><b>A 12-Element Hybrid LPDA</b></p>
+  <p>In volume 1 of <i>LPDA Notes</i> on the <a href="../bookant.html">Books Page</a>, I presented a family of basic LPDA designs--at the proof-of-principle level--and included a 12-element, 32' long array that used 11 LPDA elements plus a parasitic director. The original design used 0.5" diameter elements. I have adjusted the element diameters to 0.8" for the longest elements down to 0.5" for the shortest, since this range of element diameters reflects the uniform-diameter element equivalents for common element structures that might survive 120 mph winds. The potential users who might insist upon the high performance criteria would likely also insist upon high wind survival values for the elements.</p>
+  <center>
+    <img src="l30-4.gif" width="333" height="349" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 4</b> shows the general outline of the array. A careful scrutiny of the outline created by the LPDA element ends will show that some degree of tau-circularization has been employed--along with a shorted stub--to tailor the low and high frequency performance of the array. The array uses a 250-Ohm phase line, the lowest value of impedance that will ensure stable performance across the entire passband. The SWR reference impedance therefore becomes 100 Ohms, with the presumed use of a 2:1 balun device for a 50-Ohm feedline.</p>
+  <p>Within the amateur bands, the array is a solid performer.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+     Amateur-Band Performance Potential of a 12-Element Hybrid LPDA
+
+Freq.      Gain       180-Deg.   Feed Impedance   100-Ohm
+ MHz       dBi        F-B dB     R +/- jX Ohms     SWR
+14.175     7.11       27.28      132.8 + j 21.9   1.41
+18.118     7.04       25.56      123.5 - j 22.5   1.34
+21.225     7.19       28.75      106.3 - j 17.2   1.20
+24.94      7.21       27.01      152.3 + j  3.2   1.52
+28.0       7.45       30.76       71.8 - j 22.4   1.53
+28.85      7.51       27.03       84.6 - j  5.9   1.20
+29.7       7.89       20.56      114.0 - j 63.6   1.82
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>The range of SWR values suggests that a 250-Ohm phase line is not ideal for a 100-Ohm feedpoint impedance. In the bands through 12 meters, the reference impedance--roughly, the median value of feedpoint resistance values--is closer to 110-120 Ohms. When the parasitic director begins to show its influence on performance--above 28 MHz--the median feedpoint resistance drops considerably, a natural phenomenon with the use of parasitic elements ahead of LPDA arrays. Already, we can see that the design, even as improved, will not meet all of the more stringent standards set of a general coverage array with a 30-35' boom length.</p>
+  <center>
+    <img src="l30-5.gif" width="744" height="407" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 5</b> shows the free-space gain and the front-to-back curves across the entire passband of the array. The gain curve has a total range of 6.95 to 8.09 dBi, for a 1.14 dB differential. More significantly, we can see that the curve shows increasing swings from gain maxima to gain minima as we increase frequency, with a radical upswing above 28.0 MHz. The notch in the curve just below 28 MHz does not indicate an anomaly, but it does indicate where one occurs (with the length of shorted stub used in the design) if we decrease the phase line impedance down to 200 Ohms or lower.</p>
+  <p>The 180-degree front-to-back curve also shows the notch below 28 MHz, although the worst-case curve does not show any deviation from a smooth curve in this region of the operating spectrum. However, both front-to-back curves drop below 20 dB as we approach 30 MHz.</p>
+  <center>
+    <img src="l30-6.gif" width="744" height="407" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The feedpoint performance curves in <b>Fig. 6</b> show no notches and serve to confirm that the array has no anomalous frequencies. However, they do show other weaknesses of the design. As we increase frequency, the average feedpoint resistance decreases, and the average feedpoint reactance becomes increasingly capacitive. (In an ideal LPDA using a very high value for Tau and its corresponding ideal Sigma, the reactance will remain capacitive throughout the operating range, although it will vary over a very small range.) In the region where the parasitic director is most effective, the slope of the resistance and reactance curves combine to yield relatively high SWR values as we near 30 MHz. As already noted, the use of a 250-Ohm phase line alone is sufficient to yield SWR values in excess of 1.5:1 in several regions throughout the operating passband.</p>
+  <p><b>Why the Hybrid Design is Unlikely to be Successful at the 30-35' Boom Length</b></p>
+  <p>Before we look at any alternative designs, let's pause to understand why this design--and similar ones--are unlikely to meet the rigorous design specifications. The exercise gains some importance because if we increase the boom length to greater than 40', we can obtain a satisfactory array. Such arrays typically average from 7.5 to 8.0 dBi free-space gain using either pure or hybrid LPDA techniques. Since LPDA front-to-back ratios increase with increases in gain, meeting that standard is no major problem. However, careful design is required to meet the narrow gain differential limit and the SWR limit. Nonetheless, boom lengths in the 42' range are sufficient to meet the goal.</p>
+  <p>If we shorten the boom by about 10', our design tendency is also to reduce the element population. With 16 elements, a 42' boom has about 3.8 elements per 10' of boom length. At a similar element rate, we obtain about 12 elements for a 32' boom. However, the frequency span remains the same--14 to 30 MHz--and the value of Tau must therefore be lowered. With lower values of Tau, we tend to find reduced low-end performance prior to compensation and slightly higher upper-end performance, relative to similar values of Sigma.</p>
+  <p>The design that we just examined used a Tau of 0.909 and a Sigma of 0.055 prior to compensation. If we try to smooth the upper end performance prior to compensation by increasing the upper frequency limit, we end up with a lower value of Tau, with decreases in the low-end performance. Even though circularization of Tau and a well-designed stub can restore the performance in the 14-18 MHz range, there will be a decrease in performance in the 20-23 MHz range. On the other hand, if we increase Tau and reduce the upper-end frequency limit, then the influence of the parasitic director more radically affects the feedpoint impedance, and the SWR curve exceeds limits at a lower frequency.</p>
+  <p>Although there may be a workable compromise among the design values that go into a hybrid LPDA that will achieve the desired goals, I have yet to find it in several dozen designs for hybrid LPDAs with 30-35' boom lengths. Each design has been subjected to a considerable number of compensatory variations. If there is a hybrid LPDA design in the 30-35' boom length range that will meet all specifications, I should like to be enlightened. In the mean time, meeting the desired specifications may require other design directions.</p>
+  <p><b>A 16-Element Pure LPDA on a 35' Boom</b></p>
+  <p>My experiences with LPDA designs strongly suggests that the original design calculations must be modified for arrays using far less than the ideal Sigma value for a given value of Tau. Ordinarily, computations set the shortest element to be resonant at a frequency of about 1.3 times the highest operating frequency. For a 30 MHz upper operating limit, the shortest element will be self-resonant at about 39 MHz.</p>
+  <p>Even with high values of Tau and close-to-ideal values of Sigma, pure LPDAs will show a performance decrease with increasing frequency using the traditional multiplier. The decrease in performance becomes more pronounced with shorter boom lengths and sparse element populations. For the region of LPDAs most commonly used in the upper HF region, a multiplier of 1.6 times the highest operating is closer to optimal for the shortest element in an array. This multiplier sets the self-resonant frequency of the shortest element at about 48 MHz for a 14-30 MHz array. There is no magic in this value: it may range from 46 to 50 MHz, depending upon the particular values of Tau and Sigma used in a given design.</p>
+  <p>Based upon this re-formulation of the upper design limit, I reconstructed the original 11-element LPDA design (omitting the parasitic director) that used a Tau of 0.909 and a Sigma of 0.055, adding elements until the performance met specifications. Interestingly, 16 elements fit on a boom under 35' long, since the new elements required fairly close spacing. The elements used a modification of the usual circularization of Tau procedures to arrive at their final lengths. <b>Fig. 7</b> shows the outline of the array. The array uses a 200-Ohm phase line with a 100-Ohm reference feedpoint impedance for the SWR values.</p>
+  <center>
+    <img src="l30-7.gif" width="338" height="335" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The amateur band performance of the resulting array is remarkable smooth, as the following table shows.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+      Amateur-Band Performance Potential of a 16-Element Pure LPDA
+
+Freq.      Gain       180-Deg.   Feed Impedance   100-Ohm
+ MHz       dBi        F-B dB     R +/- jX Ohms     SWR
+14.175     7.27       23.88      130.2 + j  1.4   1.30
+18.118     7.27       25.82       91.1 - j 13.8   1.19
+21.225     7.32       26.63      115.8 - j 13.7   1.21
+24.94      7.28       28.74       94.6 - j  5.6   1.08
+28.0       7.27       29.41       90.2 - j 16.2   1.22
+28.85      7.18       27.62       83.8 - j  7.9   1.22
+29.7       7.19       26.67       87.7 + j  2.6   1.14
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>The gain range across the entire operating spectrum reflects the smooth performance shown in the ham-band table. The minimum free-space gain is 7.15 dBi, while the maximum is 7.45 dBi, for a differential of only 0.3 dB. <b>Fig. 8</b> provides the relevant curves. With adjustments to the element-length compensation used at both the long and the short ends of the array, we might narrow that range even more. However, the array meets both the minimum gain and gain differential criteria that we set earlier for general coverage LPDAs.</p>
+  <center>
+    <img src="l30-8.gif" width="744" height="407" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The array also meets the front-to-back standards with ease. The bump in the gain curve and the notch in the front-to-back curves indicate that if we reduce the phase line impedance too much below 200 Ohms, we may encounter an anomaly. The overall worst-case front-to-back ratio curve (indicated by the front/sidelobe ratio line) is remarkable smooth.</p>
+  <center>
+    <img src="l30-9.gif" width="744" height="407" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 9</b> shows the feedpoint values across the operating passband of the array. The maximum 100-Ohm SWR value is 1.318:1, with the average SWR only 1.16:1. Although the average feedpoint resistance decreases slowly with increasing frequency, the reactance tends to fall within an ever-narrowing range as we increase the operating frequency. Hence, we obtain a very well-behaved SWR curve, despite the small notch that corresponds to notches in the gain and front-to-back curves.</p>
+  <p>Like the hybrid LPDA examined earlier, the element diameters taper from 0.8" for the longest element to 0.5" for the shortest. In any final design, we would replace these elements with fully structured stepped diameter elements reflecting the physical design of an intended array. Because we find a slight rise in performance, we might even experiment with removing the 16th element and shortening the boom by about a foot. For now, the present design meets the general-coverage performance criteria that we established earlier. The following table provides the element dimensions in EZNEC model-description format for the 16-element array.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+16 el LPDA 14-30 200tl
+
+         --------------- ANTENNA DESCRIPTION ---------------
+
+Frequency = 14 MHz
+Wire Loss: Aluminum (6061-T6) -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+No.            End 1     Coord. (in)              End 2     Coord. (in)       Dia (in)  Segs
+          Conn.      X       Y       Z       Conn.      X       Y       Z
+1                      0,   -213,      0                  0,    213,      0       0.8   33
+2                   49.8, -205.5,      0               49.8,  205.5,      0       0.8   31
+3                   95.1,   -188,      0               95.1,    188,      0       0.8   29
+4                  136.3, -170.8,      0              136.3,  170.8,      0       0.8   27
+5                  173.8, -155.4,      0              173.8,  155.4,      0       0.7   25
+6                    208, -141.3,      0                208,  141.3,      0       0.7   23
+7                  239.1, -128.5,      0              239.1,  128.5,      0       0.7   21
+8                  267.4, -116.8,      0              267.4,  116.8,      0       0.7   19
+9                  293.1, -106.2,      0              293.1,  106.2,      0       0.6   17
+10                 316.5,    -97,      0              316.5,     97,      0       0.6   15
+11                 337.8,    -89,      0              337.8,     89,      0       0.6   13
+12                 357.2,  -81.7,      0              357.2,   81.7,      0       0.6   11
+13                 374.8,    -78,      0              374.8,     78,      0       0.5   11
+14                 390.8,  -71.7,      0              390.8,   71.7,      0       0.5   9
+15                 405.3,    -66,      0              405.3,     66,      0       0.5   9
+16                 418.5,  -60.7,      0              418.5,   60.7,      0       0.5   9
+
+Total Segments: 302
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>The high number of elements on a shorter (but not short) boom likely will disturb some LPDA designers and home builders. However, the population density assures performance well within the design specifications. We might wish to look toward the borderline to try to find the minimal configuration that meets the standards that we set early in this exploration.</p>
+  <p><b>A 14-Element 32' Pure LPDA for 7-dBi General Coverage</b>e</p>
+  <p>I have tested a number of designs using NEC-4 and have found some candidates for a borderline general coverage LPDA with at least 7.0 dBi free-space gain, less than 0.5 dB gain differential across the passband, better than 20 dB front-to-back ratio, and less than 1.5:1 SWR within the operating spectrum. The model selected is truly a borderline case. Its outline appears in <b>Fig. 10</b>.</p>
+  <center>
+    <img src="l30-10.gif" width="338" height="355" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The array consists of 14 elements on a 32' boom. The shortest element is resonant in the region of 46-48 MHz for smooth upper frequency performance. I modified the longest two elements to bring the low end performance above minimal levels, and placed a 12" stub on the longest element. The phase line is 200 Ohms for a feedpoint reference impedance of 100 Ohms. For comparison with the other models, let's show the ham-band performance.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+      Amateur-Band Performance Potential of a 14-Element Pure LPDA
+
+Freq.      Gain       180-Deg.   Feed Impedance   100-Ohm
+ MHz       dBi        F-B dB     R +/- jX Ohms     SWR
+14.175     7.12       27.91      106.8 + j  7.5   1.10
+18.118     7.26       25.73      118.9 + j  2.9   1.19
+21.225     7.10       26.45      107.4 - j 15.1   1.18
+24.94      7.06       27.38      109.3 - j 12.9   1.16
+28.0       7.07       23.60      122.4 - j  9.3   1.25
+28.85      7.15       25.13      106.5 - j 25.2   1.29
+29.7       7.09       25.78       97.7 - j 14.4   1.16
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>The average free-space gain is 7.14 dBi (compared to 7.26 for the larger array), with a gain range that runs from 6.93 to 7.28, a differential of 0.35 dB. The gain drops below the 7.0 dBi minimum from 25.5 to 27.25 MHz, but hovers within 0.05 dB of the standard throughout the range. As <b>Fig. 11</b> shows, there is a notch in performance in the 28.5-MHz region, with a minimum gain value of 6.93 dBi at 28.55 MHz. Adjustment of the stub length can move the notch and even prevent it from showing the lowest gain by placing it at a frequency where the gain is well above 7 dBi. The gain curve itself shows the most rapid and wide variation above 25 MHz, with a rapid drop to 7.05 dBi at 30 MHz. From a gain perspective, this design and variations on it represent a true borderline array.</p>
+  <center>
+    <img src="l30-11.gif" width="744" height="407" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The front-to-back curves are quite well behaved. The worst-case front-to-back value ranges only between 20.72 and 22.89 dB, for an average value of 21.95 dB. As is typical of LPDA designs with extended upper frequency elements, the 180-degree front-to-back shows fewer sharp peaks and lesser valleys than typical designs, with only a 4-dB difference between maximum and minimum values.</p>
+  <center>
+    <img src="l30-12.gif" width="744" height="407" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The feedpoint conditions appear in <b>Fig. 12</b>. The 100-Ohm SWR exceeds 1.4:1 only from 15 to 15.25 MHz and is well below 1.45:1 in that region. All of the remaining values are less than 1.35:1. In general, both the resistance and reactance values make only small excursions all the way across the passband.</p>
+  <p>For reference, the following table shows the elements used in this borderline model--using the EZNEC model description format.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+14-37 14el t=0.909 s=0.057
+
+         --------------- ANTENNA DESCRIPTION ---------------
+
+Frequency = 14 MHz
+Wire Loss: Aluminum (6061-T6) -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+No.            End 1     Coord. (in)              End 2     Coord. (in)       Dia (in)  Segs
+          Conn.      X       Y       Z       Conn.      X       Y       Z
+1                      0,   -210,      0                  0,    210,      0       0.8   37
+2                49.0591,   -194,      0            49.0591,    194,      0       0.8   35
+3                93.6748,-177.88,      0            93.6748,177.879,      0       0.8   31
+4                134.249,-161.77,      0            134.249,161.768,      0       0.7   29
+5                171.149,-147.12,      0            171.149,147.116,      0       0.7   25
+6                204.707,-133.79,      0            204.707,133.792,      0       0.7   23
+7                235.225,-121.67,      0            235.225,121.674,      0       0.6   21
+8                262.979,-110.65,      0            262.979,110.653,      0       0.6   19
+9                 288.22,-100.63,      0             288.22,100.631,      0       0.6   17
+10               311.174,-91.517,      0            311.174,91.5167,      0       0.5   17
+11               332.049,-83.228,      0            332.049,83.2278,      0       0.5   15
+12               351.034, -75.69,      0            351.034,75.6896,      0       0.5   13
+13               368.299,-68.834,      0            368.299,68.8342,      0       0.5   13
+14                   384,  -62.6,      0                384,62.5997,      0       0.5   11
+
+Total Segments: 306
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>I have left the excessively long decimal values for element coordinate entries to show clearly which elements (1 and 2) have received modifications.</p>
+  <p>Model 143714 represents a truly borderline design relative to the standard set for general coverage LPDAs in the 30-35' boom length category. Fewer elements or a shorter boom appears to inevitably yield lower performance levels for more significant portions of the operating passband. Even this model has shown small dips below the minimum gain levels. On the other hand, extending the boom by a foot or so or increasing the number of elements by 1 would likely ensure performance above the minimum gain level everywhere in the passband.</p>
+  <p>The notch in performance can be moved, but I left it to warn against lowering the phase line impedance below the 200-Ohm level. A 100-Ohm phase line will show an uneliminable anomaly in performance. At the other end of the phase-line possibility range, we might consider raising the phase-line impedance for unconditional stability. However, this move is subject to several cautions. First, the gain and front-to-back performance will decrease with significant increases in phase-line impedance. Second, the average gain may change in different parts of the operating spectrum. Hence, for high-impedance phase lines, one should design an LPDA from scratch, with enough iterations to ensure not only stable performance, but smooth performance across the operating passband.</p>
+  <p><b>Conclusion</b></p>
+  <p>We may design both pure and hybrid LPDAs in the 40-45' boom-length range for smooth general coverage--using the standards suggested here, but with an increase in gain. However, reducing the boom length to the 30-35' range, with a reduction also in the number of elements, tends to reduce our design options. The most promising designs for shorter-boom arrays involve extending the upper frequency limit of the basic design, and they inevitably result in a higher number of elements than we require for ham-band-only operation of an LPDA.</p>
+  <p>The designs presented for study are by no means final. They require adaptation to the element taper schedule to be used in any physical implementation. As well, they are subject to further optimization procedures. Nevertheless, they do serve to illustrate the design principles and procedures in attempting to develop a 14-30 MHz LPDA that meets rigorous general coverage performance criteria.</p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p><i>Updated 09-01-2003. &COPY; L. B. Cebik, W4RNL. The original item appeared in</i> AntenneX <i>for August, 2003. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.</i></p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
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