Circularly Polarized Cubical Quad

This two-element circularly polarized cubical quad is configured for right-circular polarization and optimized for the low end of the FM broadcast band.

This image shows the antenna geometry. The forward lobe is along the X axis.

This shows details of the inner loop and analysis segmentation. Blue dots indicate segment boundaries. The red dot locates the 75-ohm feedpoint, which is across the parallel wires. A 300-ohm loop design attributed to Ethan Funk inspired the driven element.

I optimized the design with the AO-Pro 8.05 Antenna Optimizer for good gain and small backlobes at the low end of the band. Because the antenna captures orthogonal power unavailable to a linearly polarized antenna, forward gain from 88-92 MHz is similar to that of a ten-foot Yagi. Although performance degrades higher in frequency, the antenna remains surprisingly usable over the entire band. This is remarkable for a compact directive antenna with a boom length of two feet.

Modeling Results

Below are calculated performance figures for a segmentation density of 54 segments per halfwave. Mismatch loss is due to SWR. Wire loss is due to conductor resistance. Mismatched gain is forward gain, including wire and mismatch losses. The gain reference is a linear dipole in a free-space circular field. F/B is the ratio of forward power to that directly to the rear. The SWR reference impedance is 75 ohms.

88.000 MHz:   Impedance          79.5 + j1.1 ohms
              SWR                 1.06
              Mismatch Loss       0.00 dB
              Wire Loss           0.08 dB
              Mismatched Gain     7.80 dBd
              F/B                30.00 dB

90.000 MHz:   Impedance          73.2 + j0.1 ohms
              SWR                 1.02
              Mismatch Loss       0.00 dB
              Wire Loss           0.06 dB
              Mismatched Gain     7.41 dBd
              F/B                34.80 dB

92.000 MHz:   Impedance          72.2 - j0.2 ohms
              SWR                 1.04
              Mismatch Loss       0.00 dB
              Wire Loss           0.05 dB
              Mismatched Gain     6.94 dBd
              F/B                29.20 dB

94.000 MHz:   Impedance          71.0 - j0.4 ohms
              SWR                 1.06
              Mismatch Loss       0.00 dB
              Wire Loss           0.05 dB
              Mismatched Gain     6.54 dBd
              F/B                26.13 dB

96.000 MHz:   Impedance          69.0 + j1.2 ohms
              SWR                 1.09
              Mismatch Loss       0.01 dB
              Wire Loss           0.05 dB
              Mismatched Gain     6.22 dBd
              F/B                23.26 dB

98.000 MHz:   Impedance          67.4 + j4.4 ohms
              SWR                 1.13
              Mismatch Loss       0.02 dB
              Wire Loss           0.04 dB
              Mismatched Gain     5.92 dBd
              F/B                20.58 dB

100.000 MHz:  Impedance          67.4 + j8.9 ohms
              SWR                 1.18
              Mismatch Loss       0.03 dB
              Wire Loss           0.04 dB
              Mismatched Gain     5.65 dBd
              F/B                18.26 dB

102.000 MHz:  Impedance          69.5 + j13.9 ohms
              SWR                 1.23
              Mismatch Loss       0.05 dB
              Wire Loss           0.04 dB
              Mismatched Gain     5.40 dBd
              F/B                16.33 dB

104.000 MHz:  Impedance          73.7 + j18.2 ohms
              SWR                 1.28
              Mismatch Loss       0.07 dB
              Wire Loss           0.04 dB
              Mismatched Gain     5.17 dBd
              F/B                14.74 dB

106.000 MHz:  Impedance          79.7 + j20.6 ohms
              SWR                 1.31
              Mismatch Loss       0.08 dB
              Wire Loss           0.04 dB
              Mismatched Gain     4.96 dBd
              F/B                13.44 dB

108.000 MHz:  Impedance          87.0 + j20.1 ohms
              SWR                 1.34
              Mismatch Loss       0.09 dB
              Wire Loss           0.04 dB
              Mismatched Gain     4.77 dBd
              F/B                12.34 dB

Patterns

The gain reference for the pattern plots is a circularly polarized dipole in free space. It has 3.01 dB gain over the linearly polarized dipole the listed results use as a gain reference.

Antenna File

CP Cubical Quad
Free Space
90 MHz
17 copper wires, inches
s = .5
f = 7.426954
x = 17.17732
r = 18.0908
v = -23.70532
1	0  0 -x		0  f -x		#14	; Driven element
1	0  f -x		0  x -x		#14
1	0  x -x		0  x  0		#14
1	s  0 -x		s  f -x		#14
1	s  f -x		s  x -x		#14
1	s  x -x		s  x  x		#14
1	0  x  0		s  0  0		#14
1	s  0  0		s  0 -x		#14
1	s  x  x		s -x  x		#14
1	s -x  x		s -x -x		#14
1	s -x -x		s  0 -x		#14
1	s  0 -x		0  0 -x		#14
1	0  f -x		s  f -x		#14	; Feedpoint
1	v -r -r		v  r -r		#14	; Reflector
1	v  r -r		v  r  r		#14
1	v  r  r		v -r  r		#14
1	v -r  r		v -r -r		#14
1 source
Wire 13, end2
1 load
c = 19.40773
Wire 13, end2 c pF

Optimized at 88, 90, and 92 MHz
Gain 50%, F/B 50%
F/B OK > 30 dB
F/B region = 120 deg
54 segments per halfwave
No bent-wire correction

Use #14 bare copper wire. The reflector loop is 36-3/16" on a side, while the driven loop is 34-3/8". The inner loop is exactly half the size of the outer loop and is spaced 1/2" toward the reflector. The outer loops are 24-3/16" apart. The feedpoint is 7-7/16" from the centerline of the driven loop. Across the two wires at this point solder 75-ohm coax with a 20-pF capacitor in series with the center conductor. Coil the coax into a current balun at the feedpoint.

More is here.

Updated March 6, 2008