A 3.5 Octave LPDA of High Potential Performance
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.
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.
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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
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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.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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.)
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
Updated 04-14-2000. © 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.
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