Circularly Polarized Cubical Quad

This two-element cubical quad takes advantage of the widespread use of circular polarization for FM broadcast signals in the U.S. The antenna recovers power from the orthogonal field to increase forward gain and to help cancel rear signals. The reflector loop responds to circular fields without modification, while the addition of a diagonal conductor to the driven loop promotes a traveling wave. Blue dots mark analysis segments. The red dot is the 300Ω feedpoint. The antenna is designed for right-circular polarization, which seems far more common than left-circular. Rotate the driven element 180 in the horizontal plane to invert the circularity sense.

I used the AO 9.50 Antenna Optimizer to maximize forward gain and minimize backlobes over the band. Free-space models are not entirely adequate for circularly polarized designs because antenna height and ground quality affect circularity. To represent a typical installation, I optimized the design at a boom height of 20 feet over average-quality ground. The reflector is most effective at the low end of the band, where polarization is mainly linear and mostly horizontal. Higher in the band, crosspolarization from the increasingly circular response contributes to rear rejection. The overall performance is remarkable for a compact antenna with a turning radius of less than two feet.

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 may be lower than calculated, perhaps substantially lower for some signals. Although it is less sensitive, forward gain also may decline. Axial ratio measurements in irregular terrain showed wide variation among broadcast signals.

Modeling Results

Calculated performance is for a boom height of 20 feet over average-quality ground (dielectric constant 13, conductivity 5 mS/m), 1 elevation angle, and 17 analysis segments per halfwave. Forward gain includes mismatch and conductor losses. The gain reference for the plot above is a linearly polarized isotropic antenna in free space. For the results below it is a horizontal 58″ folded dipole 20 feet high. F/R 135-225 is the ratio of forward response to that of the worst backlobe in the rear quarter-plane. Axial ratio is the ratio of maximum to minimum linearly polarized forward response. H/V is the ratio of horizontal to vertical forward response.

Frequency  Impedance    SWR   Mismatch  Conductor  Forward   F/R dB    Axial     H/V 
      MHz       ohms              Loss dB   Loss dB   Gain dB  135-225 Ratio dB    dB    
   88     237 + j5     1.26     0.06      0.06      9.15     22.03     8.73     3.21
   89     296 + j17    1.06     0.00      0.05      8.81     26.78     7.01     2.50
   90     338 + j12    1.13     0.02      0.04      8.42     24.13     5.74     2.20
   91     363 + j1     1.21     0.04      0.03      8.01     23.11     4.89     2.14
   92     378 - j7     1.26     0.06      0.03      7.62     22.74     4.36     2.19
   93     387 - j14    1.30     0.07      0.03      7.27     22.44     4.08     2.24
   94     392 - j19    1.32     0.08      0.02      7.01     22.37     3.84     2.29
   95     394 - j20    1.32     0.08      0.02      6.75     22.26     3.68     2.30
   96     394 - j20    1.32     0.08      0.02      6.55     22.13     3.55     2.30
   97     392 - j18    1.32     0.08      0.02      6.38     21.99     3.41     2.25
   98     390 - j15    1.31     0.08      0.02      6.28     21.88     3.24     2.16
   99     387 - j11    1.29     0.07      0.02      6.20     21.69     3.04     2.04
  100     384 - j5     1.28     0.07      0.02      6.20     21.65     2.80     1.89
  101     381 + j2     1.27     0.06      0.02      6.25     21.73     2.54     1.73
  102     377 + j10    1.26     0.06      0.02      6.35     22.01     2.22     1.55
  103     375 + j20    1.26     0.06      0.02      6.49     22.40     1.91     1.38
  104     371 + j29    1.26     0.06      0.02      6.68     23.09     1.53     1.21
  105     367 + j38    1.26     0.06      0.02      6.89     23.80     1.18     1.06
  106     363 + j48    1.27     0.06      0.02      7.12     24.18     0.95     0.95
  107     357 + j59    1.29     0.07      0.02      7.34     22.59     1.01     0.88
  108     351 + j73    1.31     0.08      0.02      7.55     21.20     1.36     0.87

This shows how the gain and pattern at 98 MHz vary with boom height. The gain reference is a circularly polarized isotropic antenna in free space.

Antenna File

Circularly Polarized Cubical Quad
20' High
88 93 98 103 108 MHz
9 copper wires, inches
a = 16.24859
b = 19.42513
c = 18.4075
r = 17.90678
p = -21.11868
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

Use #14 bare copper wire supported by nonconductive spreaders. The driven loop is 38⅞″ on three sides. The bottom wire is 351116″ long. The diagonal wire slanted 45 is 53″ long. The reflector loop is 351316″ on each side and spaced 21⅛″ 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 135-225
     a    0.00       0.03
     b    0.01       0.15
     c    0.00       0.04
     r    0.03       0.27
     p    0.00       0.00

Skewed Driven Element

Rotating the driven element 12 in the horizontal plane improves the pattern and slightly improves forward gain. Use the plots below to decide whether the benefit is worth the mechanical complexity. Keep in mind the modeling limitations described earlier. The gain reference is a circularly polarized isotropic antenna in free space.

Antenna file:

Skewed Driven Element
20' High
88 93 98 103 108 MHz
9 copper wires, inches
ang = -11.79481
a = 15.40325
b = 19.99364
c = 16.92573
r = 17.9645
p = -22.30329
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
rotate z ang
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

Sensitivity analysis:

Symbol    Gain   F/R 135-225
   ang    0.02       0.13
     a    0.00       0.02
     b    0.01       0.19
     c    0.00       0.09
     r    0.03       0.18
     p    0.00       0.02

The change for ang was 3.


May 31, 201488108 MHz