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′ 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 22″.
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.
Calculated performance is for a boom height of 20′ 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 58¼″ folded dipole 20′ 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
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 3511⁄16″ long. The diagonal wire slanted 45° is 53½″ long. The reflector loop is 3513⁄16″ 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.
The following table shows the degradation of average performance over 88, 93, 98, 103, and 108 MHz in dB when changing a single dimension by ±⅛″ (±1⁄16″ for symbols b and r, which represent half of a loop side).
Symbol Gain F/R 135°-225°
a 0.01 0.01
b 0.00 0.13
c 0.01 0.04
r 0.06 0.38
p 0.00 0.01
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 0.04 0.18
a 0.01 0.01
b 0.00 0.25
c 0.00 0.11
r 0.05 0.38
p 0.00 0.02
The change for ang was ±3°.
88–108 MHz