Notes on HF General Coverage LPDAs Using 30-35' Booms

L. B. Cebik, W4RNL (SK)




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.

Fig. 1 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.

A quick survey of amateur-band performance, as modeled on NEC-4 will show the potential of the design.

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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
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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.

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:

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.

Our outstanding 12-element LPDA ham-band performer unfortunately does not meet these more stringent criteria.

Fig. 2 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.

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.

Fig. 3 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.

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.

To achieve a general-coverage LPDA with a boom length in the 30-35' region, we shall have to look at other design options.

A 12-Element Hybrid LPDA

In volume 1 of LPDA Notes, 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.

Fig. 4 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.

Within the amateur bands, the array is a solid performer.

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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
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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.

Fig. 5 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.

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.

The feedpoint performance curves in Fig. 6 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.

Why the Hybrid Design is Unlikely to be Successful at the 30-35' Boom Length

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.

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.

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.

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.

A 16-Element Pure LPDA on a 35' Boom

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.

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.

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. Fig. 7 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.

The amateur band performance of the resulting array is remarkable smooth, as the following table shows.

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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
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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. Fig. 8 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.

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.

Fig. 9 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.

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.

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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
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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.

A 14-Element 32' Pure LPDA for 7-dBi General Coveragee

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 Fig. 10.

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.

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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
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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 Fig. 11 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.

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.

The feedpoint conditions appear in Fig. 12. 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.

For reference, the following table shows the elements used in this borderline model--using the EZNEC model description format.

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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
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I have left the excessively long decimal values for element coordinate entries to show clearly which elements (1 and 2) have received modifications.

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.

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.

Conclusion

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.

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.

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