In a recent article, "Notes on HF General Coverage LPDAs Using 30-35' Booms," I explored the design factors involved in obtaining smooth general coverage from 14-30 MHz from a relatively short-boom array. In this exercise, I should like to explore the same goal, but to employ a much longer boom to obtain a gain level average at least 1.5 dB higher than we could get from the shorter boom. The boom lengths involved in the new exercise fall in the 55-60 foot range. As one might expect, we shall increase the number of elements accordingly.
In the preceding exploration, I defined--not without reason, but somewhat arbitrarily--the concept of general LPDA coverage in terms of a set of operational standards:
Obtaining these goals might seem easier with so much boom length and so many elements at our disposal, but, as we shall see, the task is not as simple as it may seem.
Model 9556143X: a Hybrid LPDA Using 21 LPDA Elements and 1 Director
In Vol. 1 of LPDA Notes on the Books Page, I presented a hybrid high-performance LPDA using 21 LPDA elements and a parasitic director on a 55.8' boom. The array used a Tau of 0.95 and a Sigma of 0.056. The design (and all of the others in this exercise) will use no shorted stub. The overall appearance of the array follows the outline sketch in Fig. 1.
Although the dimensions appear in the book, the following partial EZNEC wire table will serve as a reminder of the array dimensions.
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14-30 MHz .95/.056 21+dir 55.8
--------------- ANTENNA DESCRIPTION ---------------
Frequency = 14 MHz
Wire Loss: Aluminum (6061-T6) -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
--------------- WIRES ---------------
No. End 1 Coord. (ft) End 2 Coord. (ft) Dia (in) Segs
Conn. X Y Z Conn. X Y Z
1 0,-18.025, 0 0, 18.025, 0 0.8 25
2 4.01472,-17.083, 0 4.01472,17.0833, 0 0.8 23
3 7.8287,-16.167, 0 7.8287,16.1667, 0 0.8 23
4 11.452,-15.367, 0 11.452,15.3666, 0 0.8 21
5 14.8941,-14.598, 0 14.8941,14.5983, 0 0.7 21
6 18.1641,-13.868, 0 18.1641,13.8684, 0 0.7 19
7 21.2706,-13.175, 0 21.2706,13.1749, 0 0.7 19
8 24.2218,-12.516, 0 24.2218,12.5162, 0 0.7 17
9 27.0255, -11.89, 0 27.0255,11.8904, 0 0.7 17
10 29.6889,-11.296, 0 29.6889,11.2959, 0 0.6 15
11 32.2192,-10.731, 0 32.2192,10.7311, 0 0.6 15
12 34.6229,-10.195, 0 34.6229,10.1945, 0 0.6 15
13 36.9065,-9.6848, 0 36.9065,9.68479, 0 0.6 13
14 39.0759,-9.2006, 0 39.0759,9.20056, 0 0.6 13
15 41.1368,-8.7405, 0 41.1368,8.74052, 0 0.5 13
16 43.0947,-8.3035, 0 43.0947, 8.3035, 0 0.5 11
17 44.9547,-7.8883, 0 44.9547,7.88833, 0 0.5 11
18 46.7217,-7.4939, 0 46.7217,7.49391, 0 0.5 11
19 48.4003,-7.1192, 0 48.4003,7.11922, 0 0.5 9
20 49.995,-6.7633, 0 49.995,6.76325, 0 0.5 9
21 51.51,-6.4251, 0 51.51,6.42509, 0 0.5 9
22 55.8333,-7.3917, 0 55.8333,7.39167, 0 0.5 11
Total Segments: 340
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The dimensions above are in feet. The array employs a 100-Ohm phase line for use with either 50-Ohm or 75-Ohm feedlines. Note that for this exercise, I have modified the proof-of-principle design from a uniform element diameter of 0.5" to graduated diameters running from 0.8" for the longest element to 0.5" for the shortest. This adjustment represents one step toward more adequately modeling a full array and including the stepped-diameter elements in detail.
The amateur-band performance of the array shows a significant gain improvement over the 30-35 foot boom arrays in the preceding exercise.
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Amateur-Band Performance Potential of a 22-Element Hybrid LPDA
Freq. Gain 180-Deg. Feed Impedance 50-Ohm 75-Ohm
MHz dBi F-B dB R +/- jX Ohms SWR SWR
14.175 8.89 29.93 74.8 - j 6.3 1.51 1.09
18.118 8.83 37.14 66.5 - j 6.2 1.36 1.16
21.225 8.70 41.54 65.6 - j 3.2 1.32 1.15
24.94 8.79 31.08 71.8 + j 2.5 1.44 1.06
28.0 8.92 25.02 72.5 + j 16.6 1.58 1.25
28.85 9.04 21.33 47.3 - j 30.7 1.87 1.98
29.7 9.05 19.63 50.2 + j 20.9 1.51 1.67
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The free-space forward gain averages about 1.5 dB more than for the shorter-boom models. Many--but not all--of the front-to-back ratios exhibit a parallel improvement. Below 10 meters, the design favors the use of a 70-75-Ohm feedline, but above 28 MHz, a 50-Ohm line shows the better SWR curve. Although the array provides good amateur band performance, we can already see that we have not met the more stringent standards set for a general coverage array. We obtain a more complete picture of these failings from a general graph of free-space gain and front-to-back ratios, as shown in Fig. 2.
The gain varies from 8.42 to 9.05 dBi, a 0.68 dB differential. More significantly, the use of the low impedance phase line results in two suspect frequencies: 20.0 MHz and 26.75 MHz. Here we have potentially anomalous array operation. Moreover, the front-to-back ratio (both 180-degree and worst-case) drops below 20 dB at 20.0 MHz and above 29.5 MHz. (Note: the front/sidelobe ratio indicates the worst-case front-to-back ratio, since the array nowhere exhibits any secondary forward lobes.)
The addition of a parasitic director almost always adversely affects the SWR curve at the upper end of the operating spectrum. Above 28 MHz, the SWR--shown in Fig. 3--exceeds 1.5:1, and the 70-Ohm SWR actually exceeds 2:1 from 29.0 to 29.25 MHz. The source of these swings is apparent in the wide variations in both the resistance and reactance curves at the high end of the operating spectrum.
Rather than modifying this array as a hybrid to see if a higher phase line impedance and readjustments to the parasitic director would stabilize performance within the desired limits, I decided to see if a pure LPDA might fulfill the need in a more straightforward way.
Model 9556Z: a 26-Element Pure LPDA with a 100-Ohm Phase Line
For maximum gain, I initially retained the 100-Ohm phase line. I added elements up to a total of 26 in order to set the self-resonant frequency of the shortest element in the 46-48 MHz region. I retained the same values of Tau and Sigma (0.95 and 0.056) throughout. The general outline of the new array appears in Fig. 4.
The boom length of the array grew to 58', which is long, but not too much longer than the nearly 56' boom of the hybrid array. For reference, the following model description shows the element dimensions.
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14-30 MHz .95/.056 26 el
--------------- ANTENNA DESCRIPTION ---------------
Frequency = 30 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, -216.3, 0 0, 216.3, 0 0.8 29
2 48.1766, -205, 0 48.1766, 205, 0 0.8 27
3 93.9445, -194, 0 93.9445, 194, 0 0.8 27
4 137.424, -184.4, 0 137.424,184.399, 0 0.8 25
5 178.729,-175.18, 0 178.729,175.179, 0 0.7 23
6 217.969,-166.42, 0 217.969, 166.42, 0 0.7 23
7 255.248, -158.1, 0 255.248,158.099, 0 0.7 21
8 290.662,-150.19, 0 290.662,150.194, 0 0.7 21
9 324.306,-142.68, 0 324.306,142.685, 0 0.7 19
10 356.267,-135.55, 0 356.267, 135.55, 0 0.6 19
11 386.63,-128.77, 0 386.63,128.773, 0 0.6 17
12 415.475,-122.33, 0 415.475,122.334, 0 0.6 17
13 442.878,-116.22, 0 442.878,116.217, 0 0.6 15
14 468.911,-110.41, 0 468.911,110.407, 0 0.6 15
15 493.642,-104.89, 0 493.642,104.886, 0 0.5 15
16 517.136,-99.642, 0 517.136, 99.642, 0 0.5 13
17 539.456, -94.66, 0 539.456,94.6599, 0 0.5 13
18 560.66,-89.927, 0 560.66,89.9269, 0 0.5 13
19 580.804,-85.431, 0 580.804,85.4306, 0 0.5 11
20 599.94,-81.159, 0 599.94, 81.159, 0 0.5 11
21 618.12,-77.101, 0 618.12,77.1011, 0 0.5 11
22 635.39,-73.246, 0 635.39, 73.246, 0 0.5 9
23 651.8,-69.584, 0 651.8, 69.584, 0 0.5 9
24 667.39,-66.105, 0 667.39, 66.105, 0 0.5 9
25 682.2, -62.8, 0 682.2, 62.8, 0 0.5 9
26 696.27, -59.66, 0 696.27, 59.66, 0 0.5 9
Total Segments: 430
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Dimensions are in inches. All of the new elements use a 0.5" diameter, since this is likely to be close to the equivalent uniform diameter of a stepped-diameter physical element with the smallest diameter being 0.5". A presumed wind survival of 120 mph guides my thinking here.
The amateur-band performance of the array remains very high for an LPDA.
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Amateur-Band Performance Potential of a 26-Element Pure LPDA
100-Ohm Phase Line
Freq. Gain 180-Deg. Feed Impedance 50-Ohm 75-Ohm
MHz dBi F-B dB R +/- jX Ohms SWR SWR
14.175 8.88 31.34 67.2 - j 6.3 1.37 1.15
18.118 8.87 37.80 68.5 - j 2.3 1.37 1.10
21.225 8.77 33.34 64.1 - j 0.1 1.28 1.17
24.94 8.68 44.15 68.8 - j 10.9 1.45 1.19
28.0 8.57 35.28 68.8 - j 5.9 1.40 1.13
28.85 8.64 37.30 66.9 - j 2.4 1.34 1.13
29.7 8.49 30.12 60.7 - j 13.2 1.36 1.33
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The ham-band table shows that a pure LPDA with the shortest element self-resonant in the region of 1.6 times the highest operating frequency results in a remarkably stable set of feedpoint impedances, even with the low 100-Ohm phase line. The values favor a 75-Ohm line, but the 50-Ohm performance is completely acceptable relative to our standards. As well, the gain exhibits only modest excursions and the front-to-back ratio is everywhere above 30 dB. The remaining question is whether this performance holds up across the entire operating spectrum.
Fig. 5 shows the gain and front-to-back curves. The gain variation is exactly 0.5 dB. However, just as we did with the hybrid array, we find suspect frequencies: 20.0 MHz and 26.75 MHz. At 20 MHz, the front-to-back ratio drops to under 17.5 dB. Whether or not we have a true anomaly at either suspect frequency, we can see performance drops below the standards.
The feedpoint conditions in Fig. 6 show reasonably good stability. The 50-Ohm SWR rises above 1.5:1 in the 24.5-24.75 MHz region. Otherwise, the spectrum is clean.
Overall, then, the array very nearly meets all standards almost everywhere in the operating spectrum. However, "almost" and "nearly" need not be "good enough" in an exercise like this one.
Model 9556Z200: a 26-Element Pure LPDA with a 200-Ohm Phase Line
For improved stability, I raised the phase-line impedance to 200 Ohms. The feedpoint reference impedance thus becomes 100 Ohms, with a presumed 2:1 balun device for use with a 50-Ohm supply cable. The element dimensions otherwise remained the same. This modest revision yielded the following amateur-band performance table.
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Amateur-Band Performance Potential of a 26-Element Pure LPDA
200-Ohm Phase Line
Freq. Gain 180-Deg. Feed Impedance 100-Ohm
MHz dBi F-B dB R +/- jX Ohms SWR
14.175 8.81 28.53 121.9 - j 12.8 1.26
18.118 8.77 34.99 103.1 - j 2.6 1.04
21.225 8.74 41.77 112.7 - j 12.3 1.18
24.94 8.72 34.88 112.6 - j 9.1 1.16
28.0 8.64 35.77 110.2 - j 14.3 1.18
28.85 8.46 30.97 88.8 - j 20.7 1.28
29.7 8.31 29.39 96.2 + j 5.5 1.07
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In the process of raising the phase line impedance, we lost little performance at the lower end of the operating spectrum. However, we have lost performance in the upper range. The free-space gain and front-to-back curves for the entire operating spectrum more vividly portray these losses.
In Fig. 7, we can observe the increasing acceleration in the reduction of gain with increases in frequency. The gain differential has actually increased to 0.55 dB across the range, even though there are no suspect frequencies. Except for the region near 14 MHz, the front-to-back ratios remain above 30 dB.
The feedpoint conditions appear in Fig. 8. The 100-Ohm SWR never reaches 1.3:1, and the small variations in the resistance and reactance provide the basis for the stable SWR conditions.
Increasing the phase line impedance thus had two effects. It stabilize the array, but it also changed the gain curve. At 100-Ohms, the gain remained nearly constant, with only a small drop-off at the higher frequencies of operation. Doubling the line impedance produced a gain curve whose average value shows a nearly linear drop with increasing frequency. This is one of the phenomena that LPDA designers should bear in mind, one that often requires some redesign of an entire array to smooth performance.
Of course, we have not done any modifications to the calculated design. Hence, circularizing Tau for the forward-most elements still remains an option. We have spare SWR with which to maneuver, since our limit is 1.5:1, and adjusting the lengths of the forward elements very often produces somewhat less optimal SWR values.
Model 9556Z201: a 26-Element Pure LPDA with a 200-Ohm Phase Line and Modified Forward Elements
Since the basic array with the extended frequency coverage has so many elements whose self-resonant frequencies are above 30 MHz, I circularized the Tau of the forward-most 7 elements. The results show up in the outline sketch in Fig. 9. As with the other models in the exercise, the array uses no shorted stub on the longest element.
The following wire table from EZNEC shows more clearly how much revision occurred.
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14-30 MHz .95/.056 26 el: 200-Ohm phase line; modified
--------------- 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, -216.3, 0 0, 216.3, 0 0.8 29
2 48.1766, -205, 0 48.1766, 205, 0 0.8 27
3 93.9445, -194, 0 93.9445, 194, 0 0.8 27
4 137.424, -184.4, 0 137.424,184.399, 0 0.8 25
5 178.729,-175.18, 0 178.729,175.179, 0 0.7 23
6 217.969,-166.42, 0 217.969, 166.42, 0 0.7 23
7 255.248, -158.1, 0 255.248,158.099, 0 0.7 21
8 290.662,-150.19, 0 290.662,150.194, 0 0.7 21
9 324.306,-142.68, 0 324.306,142.685, 0 0.7 19
10 356.267,-135.55, 0 356.267, 135.55, 0 0.6 19
11 386.63,-128.77, 0 386.63,128.773, 0 0.6 17
12 415.475,-122.33, 0 415.475,122.334, 0 0.6 17
13 442.878,-116.22, 0 442.878,116.217, 0 0.6 15
14 468.911,-110.41, 0 468.911,110.407, 0 0.6 15
15 493.642,-104.89, 0 493.642,104.886, 0 0.5 15
16 517.136,-99.642, 0 517.136, 99.642, 0 0.5 13
17 539.456, -94.66, 0 539.456,94.6599, 0 0.5 13
18 560.66,-89.927, 0 560.66,89.9269, 0 0.5 13
19 580.804,-85.431, 0 580.804,85.4306, 0 0.5 11
20 599.94, -81.5, 0 599.94, 81.5, 0 0.5 11
21 618.12, -78, 0 618.12, 78, 0 0.5 11
22 635.39, -74.7, 0 635.39, 74.7, 0 0.5 9
23 651.8, -70.5, 0 651.8, 70.5, 0 0.5 9
24 667.39, -68.5, 0 667.39, 68.5, 0 0.5 9
25 682.2, -65.8, 0 682.2, 65.8, 0 0.5 9
26 696.27, -63.1, 0 696.27, 63.1, 0 0.5 9
Total Segments: 430
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The object of the exercise was not to radically alter array performance, but only to bring it within the initial specifications and limits. The following table of potential amateur-band performance gives an indication of the degree of performance change.
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Amateur-Band Performance Potential of a 26-Element Pure LPDA
200-Ohm Phase Line; Modified Forward Elements
Freq. Gain 180-Deg. Feed Impedance 100-Ohm
MHz dBi F-B dB R +/- jX Ohms SWR
14.175 8.82 28.23 119.1 - j 15.0 1.25
18.118 8.78 34.01 100.2 - j 3.1 1.03
21.225 8.77 40.78 109.2 - j 13.7 1.17
24.94 8.79 32.16 110.2 - j 14.4 1.18
28.0 8.75 31.74 109.8 - j 21.3 1.25
28.85 8.56 28.14 77.4 - j 19.3 1.40
29.7 8.43 27.59 102.2 + j 10.0 1.11
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The most noticeable effect is the slight hitch in the impedance at 28.85 MHz, although the SWR remains well below the 1.5:1 limit. The array produced usable SWR values--at reduced performance levels down to 13.5 MHz and well above 35 MHz, although the SWR rises above the 1.5:1 level around 32 MHz.
Fig. 10 shows the overall gain and front-to-back curves. As is evident, the decreasing gain curve did not come close to flattening. However, free-space gain now ranges from 8.43 dBi to 8.88 dBi, a differential of 0.45 dB. The average gain is 8.74 dBi, the same value as for the 100-Ohm phase-line version and 0.05 dB higher than for the initial 200-Ohm phase-line version. Due to element length modifications, the average worst-case front-to-back ratio drops by about 1 dB, from 34.86 dB to 33.88 dB. Although numerically interesting, these differences are not operationally significant.
In Fig. 11, we have the feedpoint conditions. As noted in connection with ham-band performance, there is on region where the SWR exceeds 1.4:1--28.5 to 28.75 MHz), but the average 100-Ohm SWR is 1.16:1. The upshot is that the revised array now meets all of the general coverage criteria set forth at the beginning of the exercise.
Conclusion
It is not at all clear that the final stage of array revision is necessary to achieve an adequate general coverage LPDA on a boom between 55 and 60'. However, the move to a 200-Ohm phase line and the extension of the upper design frequency appear to be advisable steps to achieve the general goals. The initial array, however, would be quite suitable for amateur band and SWL use, as well as any other use imposing less stringent standards of performance smoothness.
Perhaps the easiest way to design LPDAs with extended upper frequency limits, especially when the calculation program presumes a design limit of 1.3 times the upper operating frequency, is simply to trick the system. Multiply the upper operating frequency by 1.6. Then divide the new frequency by 1.3 to obtain the upper operating frequency you will plug into a design program, such as LPCAD. For an operating limit of 30 MHz, the highest self-resonant frequency will be 48 MHz. Hence, the virtual upper operating frequency will be about 37 MHz.
How much above or below the virtual upper operating frequency you should go depends on the values of Tau and Sigma used in the design. For reasonably high values of Tau, the higher the value of Sigma, the better the inherent upper range performance. Hence, the designer may not need to raise the upper limit so high. For reasonable values of Sigma, the higher the value of Tau, the better the low end performance, and the greater the performance fall-off with increasing frequency. Such design may need a higher upper limit. Since the phase-line impedance will alter these rules-of-thumb somewhat, the final design may require some trial and error.
Nonetheless, the exercise does demonstrate that it is possible--without excessive additions to the weight of an array--to achieve smooth general coverage performance within rigorous standards.
Updated 11-01-2003. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for October, 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.
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