A 3.5 Octave LPDA of High Potential Performance
But an Antenna that No One Will Build

L. B. Cebik, W4RNL (SK)





In my two part series in QEX (May and July, 2000) of relatively short boom 3.5 octave LPDAs (60 to 160 feet), I had occasion to note the shortcomings of such antennas. Lest anyone think that a good LPDA that covers 3 to 30 MHz is not possible, I employed LPCAD 2.7 by Roger Cox to begin design of a high performance LPDA for the entire HF range. This note presents a kind of picture show of the antenna performance as modeled on NEC-4. Since the graphics tell the story, commentary will be limited.

An Almost Adequate Design

The first design was a 60-element LPDA array of standard design with little or no modification. The normal modeling care went into element segmentation to ensure adequate numbers of segments on all elements on all frequencies within the passband. As well, element diameters were staggered from 6" for the longest elements to 0.5" for the shortest ones. Since most designs show a fall-off in gain at the higher end of the frequency range, I designed the first model for an upper limit of 35 MHz, and the software automatically calculated elements for up to 1.3 times this frequency. As we shall see, even this buffer was not fully sufficient for even performance across the entire working passband.

Modeling tests were done using transmission line characteristic impedances from 75 to 200 Ohms, with the last value being set as the standard. For an antenna with this much frequency coverage, pattern instabilities appeared whenever the phase line Zo was lowered to the 100-Ohm region or below. As a result, the feedpoint SWR values for selected frequencies checked are referenced to 160 Ohms, and a balun (transmission line transformer) would be required for use with a 50-Ohm feedline.

For reference, the EZNEC-4 model description of the first design follows.

 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-35 MHz Tau=.955 Sigma=.18 Frequency = 3.5 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,-83.640, 0.000 0.000, 83.640, 0.000 6.00E+00 111
2 60.221,-79.876, 0.000 60.221, 79.876, 0.000 5.88E+00 107
3 117.732,-76.282, 0.000 117.732, 76.282, 0.000 5.75E+00 101
4 172.654,-72.849, 0.000 172.654, 72.849, 0.000 5.62E+00 97
5 225.106,-69.571, 0.000 225.106, 69.571, 0.000 5.50E+00 93
6 275.197,-66.440, 0.000 275.197, 66.440, 0.000 5.38E+00 89
7 323.034,-63.450, 0.000 323.034, 63.450, 0.000 5.25E+00 85
8 368.718,-60.595, 0.000 368.718, 60.595, 0.000 5.12E+00 81
9 412.347,-57.868, 0.000 412.347, 57.868, 0.000 5.00E+00 77
10 454.012,-55.264, 0.000 454.012, 55.264, 0.000 4.88E+00 73
11 493.802,-52.777, 0.000 493.802, 52.777, 0.000 4.75E+00 71
12 531.802,-50.402, 0.000 531.802, 50.402, 0.000 4.62E+00 67
13 568.091,-48.134, 0.000 568.091, 48.134, 0.000 4.50E+00 63
14 602.748,-45.968, 0.000 602.748, 45.968, 0.000 4.38E+00 61
15 635.845,-43.900, 0.000 635.845, 43.900, 0.000 4.25E+00 59
16 667.453,-41.924, 0.000 667.453, 41.924, 0.000 4.12E+00 57
17 697.638,-40.038, 0.000 697.638, 40.038, 0.000 4.00E+00 53
18 726.465,-38.236, 0.000 726.465, 38.236, 0.000 3.88E+00 51
19 753.995,-36.515, 0.000 753.995, 36.515, 0.000 3.75E+00 49
20 780.286,-34.872, 0.000 780.286, 34.872, 0.000 3.62E+00 47
21 805.394,-33.303, 0.000 805.394, 33.303, 0.000 3.50E+00 45
22 829.372,-31.804, 0.000 829.372, 31.804, 0.000 3.38E+00 43
23 852.271,-30.373, 0.000 852.271, 30.373, 0.000 3.25E+00 41
24 874.140,-29.006, 0.000 874.140, 29.006, 0.000 3.12E+00 39
25 895.024,-27.701, 0.000 895.024, 27.701, 0.000 3.00E+00 37
26 914.969,-26.454, 0.000 914.969, 26.454, 0.000 2.88E+00 35
27 934.016,-25.264, 0.000 934.016, 25.264, 0.000 2.75E+00 33
28 952.206,-24.127, 0.000 952.206, 24.127, 0.000 2.75E+00 33
29 969.578,-23.041, 0.000 969.578, 23.041, 0.000 2.62E+00 31
30 986.167,-22.004, 0.000 986.167, 22.004, 0.000 2.50E+00 29
31 1002.01,-21.014, 0.000 1002.01, 21.014, 0.000 2.38E+00 27
32 1017.14,-20.069, 0.000 1017.14, 20.069, 0.000 2.25E+00 27
33 1031.59,-19.166, 0.000 1031.59, 19.166, 0.000 2.12E+00 25
34 1045.39,-18.303, 0.000 1045.39, 18.303, 0.000 2.12E+00 25
35 1058.57,-17.479, 0.000 1058.57, 17.479, 0.000 2.00E+00 23
36 1071.15,-16.693, 0.000 1071.15, 16.693, 0.000 2.00E+00 23
37 1083.17,-15.942, 0.000 1083.17, 15.942, 0.000 1.87E+00 21
38 1094.65,-15.224, 0.000 1094.65, 15.224, 0.000 1.87E+00 21
39 1105.61,-14.539, 0.000 1105.61, 14.539, 0.000 1.75E+00 19
40 1116.08,-13.885, 0.000 1116.08, 13.885, 0.000 1.75E+00 19
41 1126.08,-13.260, 0.000 1126.08, 13.260, 0.000 1.62E+00 17
42 1135.62,-12.663, 0.000 1135.62, 12.663, 0.000 1.62E+00 17
43 1144.74,-12.094, 0.000 1144.74, 12.094, 0.000 1.50E+00 17
44 1153.45,-11.549, 0.000 1153.45, 11.549, 0.000 1.50E+00 15
45 1161.77,-11.030, 0.000 1161.77, 11.030, 0.000 1.38E+00 15
46 1169.71,-10.533, 0.000 1169.71, 10.533, 0.000 1.38E+00 13
47 1177.29,-10.059, 0.000 1177.29, 10.059, 0.000 1.25E+00 13
48 1184.53, -9.607, 0.000 1184.53, 9.607, 0.000 1.25E+00 13
49 1191.45, -9.174, 0.000 1191.45, 9.174, 0.000 1.12E+00 13
50 1198.06, -8.762, 0.000 1198.06, 8.762, 0.000 1.12E+00 11
51 1204.36, -8.367, 0.000 1204.36, 8.367, 0.000 1.00E+00 11
52 1210.39, -7.991, 0.000 1210.39, 7.991, 0.000 1.00E+00 11
53 1216.14, -7.631, 0.000 1216.14, 7.631, 0.000 8.75E-01 11
54 1221.64, -7.288, 0.000 1221.64, 7.288, 0.000 8.75E-01 9
55 1226.88, -6.960, 0.000 1226.88, 6.960, 0.000 7.50E-01 9
56 1231.89, -6.647, 0.000 1231.89, 6.647, 0.000 7.50E-01 9
57 1236.68, -6.347, 0.000 1236.68, 6.347, 0.000 6.25E-01 9
58 1241.25, -6.062, 0.000 1241.25, 6.062, 0.000 6.25E-01 9
59 1245.61, -5.789, 0.000 1245.61, 5.789, 0.000 5.00E-01 9
60 1249.78, -5.529, 0.000 1249.78, 5.529, 0.000 5.00E-01 7

-------------- SOURCES --------------

Source Wire Wire #/Pct From End 1 Ampl.(V, A) Phase(Deg.) Type
Seg. Actual (Specified)

1 4 60 / 50.00 ( 60 / 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 20/50.0 ( 20/50.0) 21/50.0 ( 21/50.0) Actual dist 200.0 1.00 R
21 21/50.0 ( 21/50.0) 22/50.0 ( 22/50.0) Actual dist 200.0 1.00 R
22 22/50.0 ( 22/50.0) 23/50.0 ( 23/50.0) Actual dist 200.0 1.00 R
23 23/50.0 ( 23/50.0) 24/50.0 ( 24/50.0) Actual dist 200.0 1.00 R
24 24/50.0 ( 24/50.0) 25/50.0 ( 25/50.0) Actual dist 200.0 1.00 R
25 25/50.0 ( 25/50.0) 26/50.0 ( 26/50.0) Actual dist 200.0 1.00 R
26 26/50.0 ( 26/50.0) 27/50.0 ( 27/50.0) Actual dist 200.0 1.00 R
27 27/50.0 ( 27/50.0) 28/50.0 ( 28/50.0) Actual dist 200.0 1.00 R
28 28/50.0 ( 28/50.0) 29/50.0 ( 29/50.0) Actual dist 200.0 1.00 R
29 29/50.0 ( 29/50.0) 30/50.0 ( 30/50.0) Actual dist 200.0 1.00 R
30 30/50.0 ( 30/50.0) 31/50.0 ( 31/50.0) Actual dist 200.0 1.00 R
31 31/50.0 ( 31/50.0) 32/50.0 ( 32/50.0) Actual dist 200.0 1.00 R
32 32/50.0 ( 32/50.0) 33/50.0 ( 33/50.0) Actual dist 200.0 1.00 R
33 33/50.0 ( 33/50.0) 34/50.0 ( 34/50.0) Actual dist 200.0 1.00 R
34 34/50.0 ( 34/50.0) 35/50.0 ( 35/50.0) Actual dist 200.0 1.00 R
35 35/50.0 ( 35/50.0) 36/50.0 ( 36/50.0) Actual dist 200.0 1.00 R
36 36/50.0 ( 36/50.0) 37/50.0 ( 37/50.0) Actual dist 200.0 1.00 R
37 37/50.0 ( 37/50.0) 38/50.0 ( 38/50.0) Actual dist 200.0 1.00 R
38 38/50.0 ( 38/50.0) 39/50.0 ( 39/50.0) Actual dist 200.0 1.00 R
39 39/50.0 ( 39/50.0) 40/50.0 ( 40/50.0) Actual dist 200.0 1.00 R
40 40/50.0 ( 40/50.0) 41/50.0 ( 41/50.0) Actual dist 200.0 1.00 R
41 41/50.0 ( 41/50.0) 42/50.0 ( 42/50.0) Actual dist 200.0 1.00 R
42 42/50.0 ( 42/50.0) 43/50.0 ( 43/50.0) Actual dist 200.0 1.00 R
43 43/50.0 ( 43/50.0) 44/50.0 ( 44/50.0) Actual dist 200.0 1.00 R
44 44/50.0 ( 44/50.0) 45/50.0 ( 45/50.0) Actual dist 200.0 1.00 R
45 45/50.0 ( 45/50.0) 46/50.0 ( 46/50.0) Actual dist 200.0 1.00 R
46 46/50.0 ( 46/50.0) 47/50.0 ( 47/50.0) Actual dist 200.0 1.00 R
47 47/50.0 ( 47/50.0) 48/50.0 ( 48/50.0) Actual dist 200.0 1.00 R
48 48/50.0 ( 48/50.0) 49/50.0 ( 49/50.0) Actual dist 200.0 1.00 R
49 49/50.0 ( 49/50.0) 50/50.0 ( 50/50.0) Actual dist 200.0 1.00 R
50 50/50.0 ( 50/50.0) 51/50.0 ( 51/50.0) Actual dist 200.0 1.00 R
51 51/50.0 ( 51/50.0) 52/50.0 ( 52/50.0) Actual dist 200.0 1.00 R
52 52/50.0 ( 52/50.0) 53/50.0 ( 53/50.0) Actual dist 200.0 1.00 R
53 53/50.0 ( 53/50.0) 54/50.0 ( 54/50.0) Actual dist 200.0 1.00 R
54 54/50.0 ( 54/50.0) 55/50.0 ( 55/50.0) Actual dist 200.0 1.00 R
55 55/50.0 ( 55/50.0) 56/50.0 ( 56/50.0) Actual dist 200.0 1.00 R
56 56/50.0 ( 56/50.0) 57/50.0 ( 57/50.0) Actual dist 200.0 1.00 R
57 57/50.0 ( 57/50.0) 58/50.0 ( 58/50.0) Actual dist 200.0 1.00 R
58 58/50.0 ( 58/50.0) 59/50.0 ( 59/50.0) Actual dist 200.0 1.00 R
59 59/50.0 ( 59/50.0) 60/50.0 ( 60/50.0) Actual dist 200.0 1.00 R

Ground type is Free Space
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

The model was spot-checked at the HF region limits (3.0 and 30.0 MHz) and within each amateur band. The following table summarizes the results, with gain being the free space value.

Frequency         Gain        Front-to-Back     Source Impedance        160-Ohm
Mhz dBi dB R +/- jX Ohms VSWR
3.0 11.27 53.01 162.1 - j 0.8 1.014
3.5 11.28 55.40 163.2 - j 0.0 1.020
4.0 11.30 64.09 163.6 - j 2.3 1.027
7.15 11.31 59.19 164.6 - j 3.4 1.036
10.125 11.34 53.86 167.5 - j 6.4 1.062
14.175 11.32 50.29 161.8 - j 6.0 1.039
18.118 11.21 47.28 159.1 - j15.7 1.104
21.225 11.16 45.26 158.1 - j21.5 1.145
24.94 10.99 43.31 161.4 - j31.3 1.215
28.0 10.25 31.80 142.0 - j 8.7 1.142
28.5 10.25 32.59 156.6 - j 4.4 1.036
29.0 10.30 34.20 172.3 - j11.7 1.107
29.5 10.44 37.65 179.5 - j27.1 1.218
30.0 10.56 42.41 178.1 - j40.7 1.301

First, we shall display on this page only the 3 MHz and 30 MHz free-space azimuth patterns and the relative magnitudes of currents on the LPDA elements. However, you may examine similar graphics for each of the frequencies sampled by the "Gallery" link at the end of this note.

3 MHz:

30 MHz:

Let's just note two principle facts that you can derive from the table. First, above 12 meters, the gain and front-to-back ratios begin to drop relative to the lower HF values. Second, from 28 MHz up, the impedance values lose their systematic progression and begin to vary erratically. Now add in the relative current magnitude graphic for 30 MHz and see how many (or how few) elements are active at 30 MHz, compared to the 3 MHz graphic of the same data. At the upper end of the spectrum, there are still too few elements to achieve full performance from the LPDA, despite the 0.955 Tau and 0.18 Sigma values.

A More Nearly Adequate Design

Some redesign was certainly in order. I have elsewhere outline many of the techniques by which one can raise the performance of an LPDA at the higher frequency range. Due to the tediousness of some, I opted simply to add 4 more elements to the front end of the LPDA. The highest frequency (shortest) element is now independently resonant at approximately 50 MHz, and the array is now 64 elements long. Here is the model description.
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-35 MHz Tau=.955 Sigma=.18 Frequency = 3 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,-83.640, 0.000 0.000, 83.640, 0.000 6.00E+00 111
2 60.221,-79.876, 0.000 60.221, 79.876, 0.000 5.88E+00 107
3 117.732,-76.282, 0.000 117.732, 76.282, 0.000 5.75E+00 101
4 172.654,-72.849, 0.000 172.654, 72.849, 0.000 5.62E+00 97
5 225.106,-69.571, 0.000 225.106, 69.571, 0.000 5.50E+00 93
6 275.197,-66.440, 0.000 275.197, 66.440, 0.000 5.38E+00 89
7 323.034,-63.450, 0.000 323.034, 63.450, 0.000 5.25E+00 85
8 368.718,-60.595, 0.000 368.718, 60.595, 0.000 5.12E+00 81
9 412.347,-57.868, 0.000 412.347, 57.868, 0.000 5.00E+00 77
10 454.012,-55.264, 0.000 454.012, 55.264, 0.000 4.88E+00 73
11 493.802,-52.777, 0.000 493.802, 52.777, 0.000 4.75E+00 71
12 531.802,-50.402, 0.000 531.802, 50.402, 0.000 4.62E+00 67
13 568.091,-48.134, 0.000 568.091, 48.134, 0.000 4.50E+00 63
14 602.748,-45.968, 0.000 602.748, 45.968, 0.000 4.38E+00 61
15 635.845,-43.900, 0.000 635.845, 43.900, 0.000 4.25E+00 59
16 667.453,-41.924, 0.000 667.453, 41.924, 0.000 4.12E+00 57
17 697.638,-40.038, 0.000 697.638, 40.038, 0.000 4.00E+00 53
18 726.465,-38.236, 0.000 726.465, 38.236, 0.000 3.88E+00 51
19 753.995,-36.515, 0.000 753.995, 36.515, 0.000 3.75E+00 49
20 780.286,-34.872, 0.000 780.286, 34.872, 0.000 3.62E+00 47
21 805.394,-33.303, 0.000 805.394, 33.303, 0.000 3.50E+00 45
22 829.372,-31.804, 0.000 829.372, 31.804, 0.000 3.38E+00 43
23 852.271,-30.373, 0.000 852.271, 30.373, 0.000 3.25E+00 41
24 874.140,-29.006, 0.000 874.140, 29.006, 0.000 3.12E+00 39
25 895.024,-27.701, 0.000 895.024, 27.701, 0.000 3.00E+00 37
26 914.969,-26.454, 0.000 914.969, 26.454, 0.000 2.88E+00 35
27 934.016,-25.264, 0.000 934.016, 25.264, 0.000 2.75E+00 33
28 952.206,-24.127, 0.000 952.206, 24.127, 0.000 2.75E+00 33
29 969.578,-23.041, 0.000 969.578, 23.041, 0.000 2.62E+00 31
30 986.167,-22.004, 0.000 986.167, 22.004, 0.000 2.50E+00 29
31 1002.01,-21.014, 0.000 1002.01, 21.014, 0.000 2.38E+00 27
32 1017.14,-20.069, 0.000 1017.14, 20.069, 0.000 2.25E+00 27
33 1031.59,-19.166, 0.000 1031.59, 19.166, 0.000 2.12E+00 25
34 1045.39,-18.303, 0.000 1045.39, 18.303, 0.000 2.12E+00 25
35 1058.57,-17.479, 0.000 1058.57, 17.479, 0.000 2.00E+00 23
36 1071.15,-16.693, 0.000 1071.15, 16.693, 0.000 2.00E+00 23
37 1083.17,-15.942, 0.000 1083.17, 15.942, 0.000 1.87E+00 21
38 1094.65,-15.224, 0.000 1094.65, 15.224, 0.000 1.87E+00 21
39 1105.61,-14.539, 0.000 1105.61, 14.539, 0.000 1.75E+00 19
40 1116.08,-13.885, 0.000 1116.08, 13.885, 0.000 1.75E+00 19
41 1126.08,-13.260, 0.000 1126.08, 13.260, 0.000 1.62E+00 17
42 1135.62,-12.663, 0.000 1135.62, 12.663, 0.000 1.62E+00 17
43 1144.74,-12.094, 0.000 1144.74, 12.094, 0.000 1.50E+00 17
44 1153.45,-11.549, 0.000 1153.45, 11.549, 0.000 1.50E+00 15
45 1161.77,-11.030, 0.000 1161.77, 11.030, 0.000 1.38E+00 15
46 1169.71,-10.533, 0.000 1169.71, 10.533, 0.000 1.38E+00 13
47 1177.29,-10.059, 0.000 1177.29, 10.059, 0.000 1.25E+00 13
48 1184.53, -9.607, 0.000 1184.53, 9.607, 0.000 1.25E+00 13
49 1191.45, -9.174, 0.000 1191.45, 9.174, 0.000 1.12E+00 13
50 1198.06, -8.762, 0.000 1198.06, 8.762, 0.000 1.12E+00 11
51 1204.36, -8.367, 0.000 1204.36, 8.367, 0.000 1.00E+00 11
52 1210.39, -7.991, 0.000 1210.39, 7.991, 0.000 1.00E+00 11
53 1216.14, -7.631, 0.000 1216.14, 7.631, 0.000 8.75E-01 11
54 1221.64, -7.288, 0.000 1221.64, 7.288, 0.000 8.75E-01 9
55 1226.88, -6.960, 0.000 1226.88, 6.960, 0.000 7.50E-01 9
56 1231.89, -6.647, 0.000 1231.89, 6.647, 0.000 7.50E-01 9
57 1236.68, -6.347, 0.000 1236.68, 6.347, 0.000 6.25E-01 9
58 1241.25, -6.062, 0.000 1241.25, 6.062, 0.000 6.25E-01 9
59 1245.61, -5.789, 0.000 1245.61, 5.789, 0.000 5.00E-01 9
60 1249.78, -5.529, 0.000 1249.78, 5.529, 0.000 5.00E-01 7
61 1253.76, -5.280, 0.000 1253.76, 5.280, 0.000 5.00E-01 7
62 1257.57, -5.042, 0.000 1257.57, 5.042, 0.000 5.00E-01 7
63 1261.20, -4.815, 0.000 1261.20, 4.815, 0.000 5.00E-01 7
64 1264.67, -4.599, 0.000 1264.67, 4.599, 0.000 5.00E-01 7

-------------- SOURCES --------------

Source Wire Wire #/Pct From End 1 Ampl.(V, A) Phase(Deg.) Type
Seg. Actual (Specified)

1 4 64 / 50.00 ( 64 / 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 20/50.0 ( 20/50.0) 21/50.0 ( 21/50.0) Actual dist 200.0 1.00 R
21 21/50.0 ( 21/50.0) 22/50.0 ( 22/50.0) Actual dist 200.0 1.00 R
22 22/50.0 ( 22/50.0) 23/50.0 ( 23/50.0) Actual dist 200.0 1.00 R
23 23/50.0 ( 23/50.0) 24/50.0 ( 24/50.0) Actual dist 200.0 1.00 R
24 24/50.0 ( 24/50.0) 25/50.0 ( 25/50.0) Actual dist 200.0 1.00 R
25 25/50.0 ( 25/50.0) 26/50.0 ( 26/50.0) Actual dist 200.0 1.00 R
26 26/50.0 ( 26/50.0) 27/50.0 ( 27/50.0) Actual dist 200.0 1.00 R
27 27/50.0 ( 27/50.0) 28/50.0 ( 28/50.0) Actual dist 200.0 1.00 R
28 28/50.0 ( 28/50.0) 29/50.0 ( 29/50.0) Actual dist 200.0 1.00 R
29 29/50.0 ( 29/50.0) 30/50.0 ( 30/50.0) Actual dist 200.0 1.00 R
30 30/50.0 ( 30/50.0) 31/50.0 ( 31/50.0) Actual dist 200.0 1.00 R
31 31/50.0 ( 31/50.0) 32/50.0 ( 32/50.0) Actual dist 200.0 1.00 R
32 32/50.0 ( 32/50.0) 33/50.0 ( 33/50.0) Actual dist 200.0 1.00 R
33 33/50.0 ( 33/50.0) 34/50.0 ( 34/50.0) Actual dist 200.0 1.00 R
34 34/50.0 ( 34/50.0) 35/50.0 ( 35/50.0) Actual dist 200.0 1.00 R
35 35/50.0 ( 35/50.0) 36/50.0 ( 36/50.0) Actual dist 200.0 1.00 R
36 36/50.0 ( 36/50.0) 37/50.0 ( 37/50.0) Actual dist 200.0 1.00 R
37 37/50.0 ( 37/50.0) 38/50.0 ( 38/50.0) Actual dist 200.0 1.00 R
38 38/50.0 ( 38/50.0) 39/50.0 ( 39/50.0) Actual dist 200.0 1.00 R
39 39/50.0 ( 39/50.0) 40/50.0 ( 40/50.0) Actual dist 200.0 1.00 R
40 40/50.0 ( 40/50.0) 41/50.0 ( 41/50.0) Actual dist 200.0 1.00 R
41 41/50.0 ( 41/50.0) 42/50.0 ( 42/50.0) Actual dist 200.0 1.00 R
42 42/50.0 ( 42/50.0) 43/50.0 ( 43/50.0) Actual dist 200.0 1.00 R
43 43/50.0 ( 43/50.0) 44/50.0 ( 44/50.0) Actual dist 200.0 1.00 R
44 44/50.0 ( 44/50.0) 45/50.0 ( 45/50.0) Actual dist 200.0 1.00 R
45 45/50.0 ( 45/50.0) 46/50.0 ( 46/50.0) Actual dist 200.0 1.00 R
46 46/50.0 ( 46/50.0) 47/50.0 ( 47/50.0) Actual dist 200.0 1.00 R
47 47/50.0 ( 47/50.0) 48/50.0 ( 48/50.0) Actual dist 200.0 1.00 R
48 48/50.0 ( 48/50.0) 49/50.0 ( 49/50.0) Actual dist 200.0 1.00 R
49 49/50.0 ( 49/50.0) 50/50.0 ( 50/50.0) Actual dist 200.0 1.00 R
50 50/50.0 ( 50/50.0) 51/50.0 ( 51/50.0) Actual dist 200.0 1.00 R
51 51/50.0 ( 51/50.0) 52/50.0 ( 52/50.0) Actual dist 200.0 1.00 R
52 52/50.0 ( 52/50.0) 53/50.0 ( 53/50.0) Actual dist 200.0 1.00 R
53 53/50.0 ( 53/50.0) 54/50.0 ( 54/50.0) Actual dist 200.0 1.00 R
54 54/50.0 ( 54/50.0) 55/50.0 ( 55/50.0) Actual dist 200.0 1.00 R
55 55/50.0 ( 55/50.0) 56/50.0 ( 56/50.0) Actual dist 200.0 1.00 R
56 56/50.0 ( 56/50.0) 57/50.0 ( 57/50.0) Actual dist 200.0 1.00 R
57 57/50.0 ( 57/50.0) 58/50.0 ( 58/50.0) Actual dist 200.0 1.00 R
58 58/50.0 ( 58/50.0) 59/50.0 ( 59/50.0) Actual dist 200.0 1.00 R
59 59/50.0 ( 59/50.0) 60/50.0 ( 60/50.0) Actual dist 200.0 1.00 R
60 60/50.0 ( 60/50.0) 61/50.0 ( 61/50.0) Actual dist 200.0 1.00 R
61 61/50.0 ( 61/50.0) 62/50.0 ( 62/50.0) Actual dist 200.0 1.00 R
62 62/50.0 ( 62/50.0) 63/50.0 ( 63/50.0) Actual dist 200.0 1.00 R
63 63/50.0 ( 63/50.0) 64/50.0 ( 64/50.0) Actual dist 200.0 1.00 R

Ground type is Free Space
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

The performance table tells most of the story.

Frequency         Gain        Front-to-Back     Source Impedance        160-Ohm
Mhz dBi dB R +/- jX Ohms VSWR
3.0 11.27 52.92 163.5 - j 0.3 1.022
3.5 11.29 55.73 165.4 - j 0.1 1.034
4.0 11.30 64.98 164.4 - j 2.6 1.031
7.15 11.31 60.12 165.8 - j 6.3 1.054
10.125 11.31 54.81 161.4 - j11.8 1.077
14.175 11.29 50.03 161.3 - j16.9 1.111
18.118 11.21 46.71 161.1 - j16.9 1.111
21.225 11.10 44.48 158.8 - j19.0 1.127
24.94 11.00 43.87 159.2 - j22.9 1.154
28.0 10.75 37.12 158.0 - j16.8 1.112
28.5 10.73 37.90 163.7 - j18.6 1.124
29.0 10.77 39.74 166.8 - j25.9 1.178
29.5 10.85 43.39 163.6 - j33.4 1.230
30.0 10.93 46.74 157.8 - j36.2 1.256

The upper HF gain increase averages about a half dB, with about an average of 8 dB high front-to-back ratio. The original model resistive impedance varied by 37.5 Ohms: that value is down to 11 Ohms. In short, the LPDA is now better behaved (but not perfectly behaved) across its passband. 30 MHz:

The 30 MHz graphics demonstrate the improvement. (The 3.0 MHz through 18.118 MHz graphics are virtual replicas of those for the original model. The entire set of graphics for 21.225 MHz and up appear on the Gallery page for comparison with those for the first model.)

Conclusion

Needless to say, no ham will ever build either of these LPDAs, despite their high performance potential from 80 through 10 meters. Arrays between 1250' and 1265' long, with elements up to 167' long at the rear are too big for the average ham back yard. Although the array can be lightened by the use of multiple wires for elements rather than simple heavy tubular elements, it would still take an old railroad roundhouse turntable with several support towers at least 135' tall to handle and rotate the array.

However, the figures here and on the Gallery page make a few interesting points. First, the exceptional front-to-back ratio and the overall rear pattern gives us an understanding of one of the LPDA advantages: almost no power radiated to the rear. I have yet to model an antenna design with anything near to these rear patterns.

Second, we can see that the LPDA gain and front-to-back ratio are intimately connected. Although both values undulate and their peaks do not coincide relative to frequency, the general trend holds: the higher the gain, the higher the front-to-back ratio.

Third, the LPDA acquires its performance from the elements ahead of the element with the highest relative current. Every element in the array is active at 3.0 MHz, with only a few acting as the correlates to reflectors in parasitic beams. At the high end of the design spectrum, the rear elements are largely inert. Hence, to achieve high performance at the upper frequencies, one must ensure an adequate supply of "director-correlate" elements. (Otherwise, one must resort to one or more of the techniques of design revision that depart from standard LPDA design.)

Fourth, from 20 meters on up, notice how few of the elements are active. More than half of the array is active only at the lowest frequencies and above 14 MHz, only about 20% of the array is active. Therefore, a 14-30 MHz high performance LPDA might require perhaps 200-220' feet of boom--a considerably more manageable length. A rotating 1 acre plot might easily handle the array for just the 5 upper-end bands.

From a construction point of view, this has been an idle exercise. However, from a study perspective, the design illustrates the degree to which amateur-size LPDAs are deficient in performance relative to what an LPDA can do.

A Gallery of LPDA Graphics for 3-30 MHz

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