Circularly Polarized Cubical Quads

Circular polarization is widely used for FM broadcast signals in the U.S. It's easy to take advantage of it with an end-fire array of square loops. Parasitic loops respond to circular fields without modification, while the addition of a diagonal conductor to the driven loop promotes a traveling wave. Power recovered from the orthogonal field increases forward gain and helps cancel rear signals. The antennas respond to horizontal and vertical linear fields, used mostly by booster and translator stations. I designed the antennas for right-circular polarization, which seems far more common than left-circular. They will attenuate right-circular signals that become left-circular upon reflection. This includes multipath reflections, which is desirable, and ionospheric reflections, which may or may not be. Rotate the driven element 180° in the horizontal plane to reverse the circularity sense.

Free-space models are inadequate for circularly polarized designs because antenna height and ground quality affect circularity. To represent a typical installation, I optimize designs at a boom height of 20 feet over average-quality ground (dielectric constant 13, conductivity 5 mS/m).

Calculated performance is for a perfectly circular transmit signal with a single ground reflection. But transmit antennas may exhibit an axial ratio of several dB, especially when the tower structure is not properly accounted for. In addition, scattering may occur multiple times during propagation over irregular terrain. Each instance differentially alters the orthogonal fields. Finally, antenna height and ground characteristics may differ from those modeled. Because of these factors, rear rejection is likely to be substantially lower than calculated for many signals. Although it is less sensitive, forward gain also may decline. Axial ratio measurements in irregular terrain showed wide variation among broadcast signals.

Given the expected axial ratio variability, I used the AO 9.60 Antenna Optimizer to maximize forward gain without regard for the pattern. The two-element design is suitable for urban or suburban reception in a small space. Performance is remarkable for a compact antenna with a turning radius of two feet. The larger designs are suitable for weak-signal reception in rural locations with few interfering signals.

Two Elements

Blue dots mark analysis segments. The red dot is the 300Ω feedpoint.

Modeling Results

Calculated performance is for a boom height of 20 feet over average-quality ground at 1° elevation angle. The model used 17 analysis segments per halfwave with bent-wire correction. The gain reference is a circularly polarized isotropic antenna in free space. Forward gain includes mismatch and conductor losses. Axial ratio is the ratio of maximum to minimum linearly polarized forward response. H/V is the ratio of horizontal to vertical forward response. F/R is the ratio of forward response to that of the worst backlobe in the rear half-plane.

Frequency  Impedance    SWR   Mismatch  Conductor  Forward    Axial       H/V       F/R
   MHz       ohms              Loss dB   Loss dB  Gain dBic  Ratio dB      dB        dB
    88     222 + j59    1.46     0.15      0.07     -1.66      9.27       1.05     13.30
    89     312 + j82    1.31     0.08      0.06     -1.27      7.59      -0.10     14.55
    90     387 + j55    1.35     0.10      0.05     -1.18      6.00      -0.79     13.72
    91     422 + j9     1.41     0.13      0.04     -1.22      4.65      -1.00     13.34
    92     428 - j27    1.44     0.14      0.03     -1.31      3.61      -0.91     12.83
    93     424 - j49    1.45     0.15      0.03     -1.40      2.84      -0.70     12.19
    94     415 - j63    1.45     0.15      0.03     -1.51      2.29      -0.45     11.68
    95     407 - j71    1.44     0.14      0.02     -1.57      1.90      -0.28     11.26
    96     398 - j74    1.42     0.14      0.02     -1.61      1.61      -0.19     10.89
    97     389 - j75    1.40     0.12      0.02     -1.64      1.36      -0.13     10.54
    98     380 - j74    1.38     0.11      0.02     -1.64      1.13      -0.13     10.20
    99     371 - j70    1.34     0.09      0.02     -1.63      0.90      -0.18      9.87
   100     361 - j65    1.31     0.08      0.02     -1.61      0.65      -0.25      9.55
   101     351 - j58    1.27     0.06      0.02     -1.59      0.43      -0.34      9.24
   102     341 - j49    1.22     0.04      0.02     -1.55      0.41      -0.40      8.95
   103     331 - j39    1.17     0.03      0.02     -1.52      0.70      -0.47      8.65
   104     320 - j28    1.12     0.01      0.02     -1.50      1.14      -0.53      8.36
   105     309 - j14    1.06     0.00      0.02     -1.48      1.64      -0.52      8.08
   106     299 + j2     1.01     0.00      0.03     -1.48      2.20      -0.46      7.81
   107     288 + j20    1.08     0.01      0.03     -1.50      2.81      -0.34      7.54
   108     279 + j41    1.17     0.03      0.03     -1.54      3.44      -0.16      7.28

Antenna File

2-el CP Quad
20' High
88 93 98 103 108 MHz
9 copper wires, inches
a = 13.10174
b = 20.26189
c = 19.44813
r = 17.63084
p = -22.90194
shift z 20'
1  p -r -r  p  r -r  #14	; reflector
1  p  r -r  p  r  r  #14
1  p  r  r  p -r  r  #14
1  p -r  r  p -r -r  #14
1  0 -a -b  0  b -b  #14	; driven element
1  0  b -b  0  b  b  #14
1  0  b  b  0 -b  b  #14
1  0 -b  b  0 -b -b  #14
1  0 -b -b  0  c  c  #14
1 source
Wire 5, end2

Construction

You can use the PVC construction described below for the larger designs, but the antenna will be rather conspicuous in a neighborhood setting. Thin fiberglass spreaders and a small-diameter boom, both with muted color, might be more suitable.

Use #14 bare copper wire supported by nonconductive spreaders. The driven loop is 40½″ on three sides. The bottom wire is 33⅜″ long. The diagonal wire slanted 45° is 56316″ long. The reflector loop is 35¼″ on each side and spaced 22⅞″ from the driven loop. Use a 75:300Ω balun. To decouple the feedline, starting at the feedpoint install current baluns at 30″ intervals. The last one should be several feet from the antenna. Use a nonconductive mast section near the antenna.

Sensitivity Analysis

The following table shows the change in average performance over 88, 93, 98, 103, and 108 MHz in dB when altering a single dimension by ⅛″ (116″ for symbols b and r, which represent half of a loop side).

Symbol    Gain    F/R
     a    0.00   0.01
     b    0.00   0.05
     c    0.00   0.01
     r    0.01   0.27
     p    0.00   0.00

Five Elements

You can build this five-element maximum-gain design with inexpensive parts from a hardware store. The boom length is 115″.

Modeling Results

Calculated performance is for a boom height of 20 feet over average-quality ground at 1° elevation angle. The model used 17 analysis segments per halfwave with bent-wire correction. The gain reference is a circularly polarized isotropic antenna in free space. Forward gain includes mismatch and conductor losses. Axial ratio is the ratio of maximum to minimum linearly polarized forward response. H/V is the ratio of horizontal to vertical forward response. F/R is the ratio of forward response to that of the worst backlobe in the rear half-plane.

Frequency  Impedance    SWR   Mismatch  Conductor  Forward    Axial       H/V       F/R
   MHz       ohms              Loss dB   Loss dB  Gain dBic  Ratio dB      dB        dB
    88     292 + j41    1.15     0.02      0.05     -0.04      7.11       0.39     17.61
    89     344 + j31    1.18     0.03      0.04      0.22      5.81      -0.09     16.65
    90     372 + j9     1.24     0.05      0.04      0.33      4.75      -0.21     16.17
    91     384 - j8     1.28     0.07      0.03      0.39      3.99      -0.22     15.98
    92     387 - j18    1.30     0.07      0.03      0.44      3.50      -0.11     15.96
    93     387 - j23    1.30     0.08      0.03      0.50      3.18      -0.04     15.41
    94     388 - j25    1.31     0.08      0.03      0.58      2.99      -0.12     14.98
    95     388 - j24    1.31     0.08      0.03      0.70      2.80      -0.23     14.58
    96     389 - j23    1.31     0.08      0.03      0.84      2.61      -0.44     14.21
    97     390 - j23    1.31     0.08      0.03      1.00      2.42      -0.73     13.87
    98     390 - j25    1.31     0.08      0.03      1.17      2.22      -1.08     13.54
    99     388 - j29    1.31     0.08      0.03      1.36      2.09      -1.47     13.24
   100     380 - j34    1.29     0.07      0.03      1.55      2.02      -1.84     12.95
   101     364 - j37    1.25     0.05      0.04      1.73      2.11      -2.11     12.68
   102     342 - j33    1.18     0.03      0.04      1.90      2.40      -2.20     12.46
   103     319 - j20    1.09     0.01      0.04      2.03      2.82      -2.00     12.29
   104     299 + j2     1.01     0.00      0.05      2.14      3.28      -1.49     12.24
   105     287 + j27    1.11     0.01      0.06      2.29      3.54      -0.74     12.40
   106     281 + j49    1.20     0.04      0.07      2.63      3.21       0.02     12.91
   107     269 + j66    1.29     0.07      0.12      3.36      1.61      -0.38     13.77
   108     255 + j21    1.20     0.04      0.27      3.35      6.41      -6.15     14.82

Antenna File

5-el CP Quad
20' High
88 90 98 106 108 MHz
21 copper wires, inches
r = 17.71214				; reflector half-side
a = 14.49214				; driven element lower wire
b = 20.20037				; driven element half-side
c = 21.99771				; driven element diagonal wire
d1 = 13.7816				; director half-sides
d2 = 13.88908
d3 = 14.00479
dep = 27.06915				; driven element position
dex = dep + 1				; diagonal wire tip position
d1p = 51.54301				; director positions
d2p = 82.69584
d3p = 114.5893
shift z 20'
1    0  -r  -r    0   r  -r  #14	; reflector
1    0   r  -r    0   r   r  #14
1    0   r   r    0  -r   r  #14
1    0  -r   r    0  -r  -r  #14
1  dep  -a  -b  dep   b  -b  #14	; driven element
1  dep   b  -b  dep   b   b  #14
1  dep   b   b  dep  -b   b  #14
1  dep  -b   b  dep  -b  -b  #14
1  dep  -b  -b  dex   c   c  #14
1  d1p -d1 -d1  d1p  d1 -d1  #14	; director 1
1  d1p  d1 -d1  d1p  d1  d1  #14
1  d1p  d1  d1  d1p -d1  d1  #14
1  d1p -d1  d1  d1p -d1 -d1  #14
1  d2p -d2 -d2  d2p  d2 -d2  #14	; director 2
1  d2p  d2 -d2  d2p  d2  d2  #14
1  d2p  d2  d2  d2p -d2  d2  #14
1  d2p -d2  d2  d2p -d2 -d2  #14
1  d3p -d3 -d3  d3p  d3 -d3  #14	; director 3
1  d3p  d3 -d3  d3p  d3  d3  #14
1  d3p  d3  d3  d3p -d3  d3  #14
1  d3p -d3  d3  d3p -d3 -d3  #14
1 source
Wire 5, end2

Construction

Use #14 bare copper wire supported by ½″ PVC pipe (0.84″ OD). The length of the driven element lower wire is 341116″. The length of the diagonal wire is 59⅝″. It extends 2½″ past the loop corner. Place the diagonal wire and the corner on opposite sides of the spreader. For the boom use a 10-foot piece of 1½″ PVC pipe (1.9″ OD). Drill two offset holes through it for each spreader. Secure with PVC cement or bolts. Use a halfwave coaxial balun. Form the balun into a small-diameter coil and mount it perpendicular to the driven element. To decouple the feedline, starting at the feedpoint install current baluns at 30″ intervals. The last one should be several feet from the antenna. The mast section near the antenna should be nonconductive.

Sensitivity Analysis

The following table shows the change in average performance over 88, 93, 98, 103, and 108 MHz in dB when altering a single dimension by ⅛″ (116″ for symbols r, b, and d1-d3, which represent half of a loop side).

Symbol    Gain    F/R
     r    0.01   0.09
     a    0.00   0.01
     b    0.02   0.08
     c    0.01   0.04
    d1    0.06   0.18
    d2    0.09   0.14
    d3    0.03   0.09
   dep    0.00   0.01
   d1p    0.00   0.01
   d2p    0.00   0.01
   d3p    0.00   0.01

Seven Elements

This maximum-gain design uses seven elements on a 186″ boom.

Modeling Results

Calculated performance is for a boom height of 20 feet over average-quality ground at 1° elevation angle. The model used 17 analysis segments per halfwave with bent-wire correction. The gain reference is a circularly polarized isotropic antenna in free space. Forward gain includes mismatch and conductor losses. Axial ratio is the ratio of maximum to minimum linearly polarized forward response. H/V is the ratio of horizontal to vertical forward response. F/R is the ratio of forward response to that of the worst backlobe in the rear half-plane.

Frequency  Impedance    SWR   Mismatch  Conductor  Forward    Axial       H/V       F/R
   MHz       ohms              Loss dB   Loss dB  Gain dBic  Ratio dB      dB        dB
    88     293 + j35    1.13     0.02      0.05      0.60      7.03       0.37     18.96
    89     342 + j30    1.17     0.03      0.04      0.91      5.90      -0.11     18.59
    90     372 + j12    1.24     0.05      0.04      1.07      4.97      -0.31     18.25
    91     385 - j3     1.28     0.07      0.03      1.18      4.27      -0.37     18.21
    92     391 - j14    1.31     0.08      0.03      1.27      3.75      -0.39     17.72
    93     395 - j20    1.32     0.09      0.03      1.37      3.36      -0.43     17.32
    94     398 - j25    1.34     0.09      0.03      1.49      3.07      -0.59     17.09
    95     400 - j29    1.35     0.10      0.03      1.63      2.75      -0.73     16.92
    96     400 - j33    1.35     0.10      0.03      1.79      2.41      -0.90     16.82
    97     397 - j39    1.35     0.10      0.03      1.97      2.05      -1.07     16.77
    98     389 - j45    1.34     0.09      0.03      2.16      1.69      -1.19     16.74
    99     377 - j49    1.31     0.08      0.03      2.37      1.38      -1.24     16.71
   100     361 - j47    1.26     0.06      0.04      2.59      1.15      -1.15     16.66
   101     343 - j39    1.20     0.04      0.04      2.83      1.05      -0.92     16.51
   102     326 - j27    1.13     0.02      0.04      3.11      1.04      -0.64     16.20
   103     312 - j10    1.05     0.00      0.05      3.47      0.99      -0.44     15.92
   104     300 + j8     1.03     0.00      0.06      3.93      0.91      -0.58     15.64
   105     295 + j25    1.09     0.01      0.08      4.50      1.55      -1.46     15.23
   106     283 + j25    1.11     0.01      0.12      4.93      3.48      -3.14     14.44
   107     232 + j48    1.37     0.11      0.17      4.60      5.62      -3.37     13.06
   108     244 + j70    1.39     0.12      0.38      4.10      3.66      -2.89     12.51

Antenna File

7-el CP Quad
20' High
88 89 90 98 106 107 108 MHz
29 copper wires, inches
r = 17.68041		; reflector half-side
a = 14.47533
b = 20.19889		; driven element half-side
c = 22.44163
d1 = 13.8335		; director half-sides
d2 = 14.07744
d3 = 13.784
d4 = 13.74143
d5 = 13.91304
dep = 29.19122		; element positions
dex = dep + 1		; DE tip offset
d1p = 50.496
d2p = 78.3315
d3p = 116.5934
d4p = 151.7725
d5p = 186.4434
shift z 20'
1    0  -r  -r    0   r  -r  #14	; reflector
1    0   r  -r    0   r   r  #14
1    0   r   r    0  -r   r  #14
1    0  -r   r    0  -r  -r  #14
1  dep  -a  -b  dep   b  -b  #14	; driven element
1  dep   b  -b  dep   b   b  #14
1  dep   b   b  dep  -b   b  #14
1  dep  -b   b  dep  -b  -b  #14
1  dep  -b  -b  dex   c   c  #14
1  d1p -d1 -d1  d1p  d1 -d1  #14	; director 1
1  d1p  d1 -d1  d1p  d1  d1  #14
1  d1p  d1  d1  d1p -d1  d1  #14
1  d1p -d1  d1  d1p -d1 -d1  #14
1  d2p -d2 -d2  d2p  d2 -d2  #14	; director 2
1  d2p  d2 -d2  d2p  d2  d2  #14
1  d2p  d2  d2  d2p -d2  d2  #14
1  d2p -d2  d2  d2p -d2 -d2  #14
1  d3p -d3 -d3  d3p  d3 -d3  #14	; director 3
1  d3p  d3 -d3  d3p  d3  d3  #14
1  d3p  d3  d3  d3p -d3  d3  #14
1  d3p -d3  d3  d3p -d3 -d3  #14
1  d4p -d4 -d4  d4p  d4 -d4  #14	; director 4
1  d4p  d4 -d4  d4p  d4  d4  #14
1  d4p  d4  d4  d4p -d4  d4  #14
1  d4p -d4  d4  d4p -d4 -d4  #14
1  d5p -d5 -d5  d5p  d5 -d5  #14	; director 5
1  d5p  d5 -d5  d5p  d5  d5  #14
1  d5p  d5  d5  d5p -d5  d5  #14
1  d5p -d5  d5  d5p -d5 -d5  #14
1 source
Wire 5, end2

Construction

Construct like the five-element design, but use a two-section spliced boom and nonconductive boom guys. The length of the driven element lower wire is 341116″. The length of the diagonal wire is 60516″. It extends 3316″ past the loop corner.

Sensitivity Analysis

The following table shows the change in average performance over 88, 93, 98, 103, and 108 MHz in dB when altering a single dimension by ⅛″ (116″ for symbols r, b, and d1-d5, which represent half of a loop side).

Symbol    Gain    F/R
     r    0.01   0.14
     a    0.00   0.01
     b    0.01   0.05
     c    0.01   0.01
    d1    0.03   0.10
    d2    0.09   0.16
    d3    0.04   0.02
    d4    0.02   0.04
    d5    0.00   0.03
   dep    0.00   0.00
   d1p    0.00   0.00
   d2p    0.00   0.00
   d3p    0.00   0.00
   d4p    0.00   0.00
   d5p    0.00   0.00

Gain Comparison

This compares the three quads, Antennacraft FM6, Antenna Performance Specialties APS-13, Körner 15.12, and Körner 19.3 for a right-circular field at 1° elevation angle with the booms 20 feet above average-quality ground.

Transmit Polarization

The following table lists the number of stations and transmit polarization percentages by U.S. FM broadcast service class.

C  Circular           Hpwr = Vpwr
H  Horizontal         Vpwr = 0
V  Vertical           Hpwr = 0
h  Mostly horizontal  Hpwr > Vpwr > 0
v  Mostly vertical    Vpwr > Hpwr > 0

Class          Number   C   H   V   h   v
Full service    10788  90   3   4   2   1
Translator       6014  67  11  22   0   0
Booster           344  57  10  32   1   0
LPFM             1149  98   2   0   0   0
All             18295  82   5  10   1   1

To determine circularity sense, look up a station's antenna make and model in the FCC database.


July 4, 201588–108 MHz