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 driven element is configured 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 8.51 Antenna Optimizer to maximize both forward gain and F/B over the FM band. Free-space models are not entirely adequate for circularly polarized designs because height above ground and ground quality affect circularity. To represent a typical installation, I optimized the antenna 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 23″.
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, propagation over irregular terrain may cause multiple diffraction and reflection that affect the horizontal and vertical fields differently. 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. Forward gain also may decline, although it is less sensitive.
Calculated performance is for a boom height of 20′ over average-quality ground (dielectric constant 13, conductivity 5 mS/m), an elevation angle of 1°, and 17 analysis segments per halfwave. Forward gain includes mismatch and conductor losses. The gain reference is a horizontal 58¼″ folded dipole 20′ high in a right-circular field. F/R 150°-210° is the ratio of forward power to that of the worst backlobe in the rear sixth-plane. Axial ratio is the ratio of maximum to minimum linearly polarized forward response.
88.000 MHz: Impedance 256 + j40 Ω
SWR 1.24
Mismatch Loss 0.05 dB
Conductor Loss 0.06 dB
Forward Gain 9.21 dB
F/R 150°-210° 22.86 dB
Axial Ratio 8.45 dB
93.000 MHz: Impedance 396 - j13 Ω
SWR 1.32
Mismatch Loss 0.09 dB
Conductor Loss 0.03 dB
Forward Gain 7.31 dB
F/R 150°-210° 23.69 dB
Axial Ratio 3.66 dB
98.000 MHz: Impedance 394 - j17 Ω
SWR 1.32
Mismatch Loss 0.08 dB
Conductor Loss 0.02 dB
Forward Gain 6.33 dB
F/R 150°-210° 22.83 dB
Axial Ratio 2.75 dB
103.000 MHz: Impedance 377 + j8 Ω
SWR 1.26
Mismatch Loss 0.06 dB
Conductor Loss 0.02 dB
Forward Gain 6.53 dB
F/R 150°-210° 25.57 dB
Axial Ratio 1.27 dB
108.000 MHz: Impedance 345 + j54 Ω
SWR 1.24
Mismatch Loss 0.05 dB
Conductor Loss 0.02 dB
Forward Gain 7.57 dB
F/R 150°-210° 22.88 dB
Axial Ratio 1.28 dB
These plots show the response to linearly polarized signals. 80% of FM signals in the U.S. are circularly polarized, 7% are horizontal or mostly horizontal, and 12% are vertical or mostly vertical. For full-service stations only, the figures are 90%, 4%, and 6%.
This shows how the pattern at 98 MHz varies with ground quality.
This shows pattern variation with antenna height.
This shows how the wire currents vary with frequency. At each frequency the peak current is normalized to the same trace amplitude.
Circularly Polarized Cubical Quad 20' High 88 93 98 103 108 MHz 9 copper wires, inches a = 15.25598 b = 19.90258 c = 17.28933 r = 17.92655 p = -21.20724 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 39¾″ on three sides. The bottom wire is 353⁄16″ long. The diagonal wire slanted 45° is 52⅝″ long. The reflector loop is 35⅞″ on each side and is spaced 213⁄16″ from the driven loop. At the feedpoint install a 75:300Ω balun (if it's a voltage balun, follow it with a 75Ω current balun). To further isolate the feedline, install another current balun 30″ from the feedpoint. Use a nonconductive mast section near the antenna.
The following table shows the performance degradation when changing a single dimension by 1⁄16″ (1⁄32″ for symbols b and r, which represent half of a loop side). AO calculated the performance drop when increasing and decreasing a symbol value, keeping the worst results. Listed are degradations for average and worst performance over 88, 93, 98, 103, and 108 MHz. Gain includes mismatch loss (listed separately as MML) and F/R is over 150°-210°. Values are in dB.
----- Average ---- ------ Worst -----
Symbol Gain F/R MML Gain F/R MML
a 0.00 0.03 0.00 0.00 0.01 0.00
b 0.00 0.08 0.00 0.00 0.11 0.00
c 0.00 0.02 0.00 0.00 0.05 0.00
r 0.01 0.14 0.00 0.02 0.16 0.00
p 0.00 0.01 0.00 0.00 0.00 0.00
88–108 MHz