Circularly Polarized Crossed Yagis

Circularly polarized cubical quads provide a simple and inexpensive way to extract orthogonal power from circularly polarized FM signals that linearly polarized antennas ignore. However, the patterns degrade for signals with nonideal circularity. Rear-signal rejection is mostly due to cancellation of orthogonal signal components, not to inherent antenna directivity. You can obtain good patterns for nonideal signals by phasing a crossed pair of Yagis with decent individual patterns.

This array uses crossed five-element Yagis. The boom length is 60″. Tilting the Yagis 45° equalizes ground interaction and any residual coupling to the feedline (the mast section near the antenna should be nonconductive). Blue dots mark analysis segments. Red dots mark the 75Ω feedpoints.

I used the AO 9.61 Antenna Optimizer to optimize both forward gain and the pattern. F/R during optimization used the right-circular field in the forward direction and the total field in the rear quarter-plane. This models interference to the rear with worst-case polarization. I optimized the array at a boom height of 20 feet over average-quality ground (dielectric constant 13, conductivity 5 mS/m). All results are at 1° elevation angle.

Coincident crossed Yagis require a 90° phase shift between antennas. The model uses a phasing line not shown in the image above. I adjusted the conductor spacing for a characteristic impedance of 75Ω in a transmission line model. Then I optimized the phasing line length and the other antenna dimensions in the crossed Yagi model.

Crossed Yagis offset a quarter wavelength require no phasing line, but in addition to larger size they have a major drawback: rear response is right-circular, not left-circular. Rear rejection comes only from inherent directivity, not crosspolarization. This will increase interference from most unwanted signals.

Modeling Results

Calculated performance is for the right-circular field using 28 analysis segments per conductor halfwave. 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 power. H/V is the ratio of horizontal to vertical forward power. F/R is the ratio of forward power 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    73.9 + j9.2   1.13     0.02      0.01     -0.89      1.68       1.26     16.00
    89    71.7 + j7.1   1.11     0.01      0.01     -0.79      0.88       0.86     15.81
    90    70.0 + j6.8   1.12     0.01      0.01     -0.70      0.59       0.48     15.70
    91    68.7 + j7.0   1.14     0.02      0.01     -0.60      0.66       0.16     15.77
    92    67.8 + j7.7   1.16     0.02      0.01     -0.48      0.80      -0.07     16.01
    93    68.6 + j8.5   1.16     0.02      0.01     -0.34      0.81      -0.20     16.47
    94    68.7 + j9.3   1.17     0.03      0.01     -0.18      0.87      -0.37     17.01
    95    69.2 + j9.9   1.17     0.03      0.01      0.00      0.90      -0.47     17.71
    96    68.8 + j10.0  1.18     0.03      0.01      0.20      1.04      -0.67     18.50
    97    69.5 + j10.1  1.17     0.03      0.01      0.41      0.99      -0.71     19.66
    98    70.6 + j9.9   1.16     0.02      0.01      0.65      0.87      -0.71     21.20
    99    72.8 + j9.8   1.14     0.02      0.01      0.90      0.50      -0.48     23.55
   100    73.7 + j9.0   1.13     0.02      0.02      1.16      0.29      -0.26     26.78
   101    74.6 + j8.2   1.12     0.01      0.02      1.43      0.47       0.18     27.05
   102    74.2 + j6.7   1.10     0.01      0.02      1.70      0.88       0.71     25.83
   103    75.9 + j5.2   1.07     0.01      0.02      1.95      1.72       1.65     24.17
   104    78.5 + j2.0   1.05     0.00      0.03      2.15      2.73       2.73     22.39
   105    79.3 - j4.9   1.09     0.01      0.03      2.29      3.76       3.58     20.67
   106    77.3 - j11.5  1.17     0.03      0.04      2.33      4.56       3.83     18.89
   107    68.6 - j7.5   1.15     0.02      0.06      2.37      3.98       2.47     16.98
   108    79.2 + j6.9   1.11     0.01      0.11      2.01      1.98       1.54     15.65

These patterns show the response to interfering signals with worst-case polarization.

These curves show how boom height affects F/R in the rear quarter-plane for average-quality ground.

These curves show how ground quality affects F/R in the rear quarter-plane for a boom height of 20 feet.

Dielectric  Conductivity  Ground
 Constant       mS/m       Type
    81        5000        Salt water
    80           1        Fresh water
    20          30        Pastoral, low hills, rich soil (Dallas TX to Lincoln NE)
    13           5        Pastoral, medium hills and forestation, heavy clay soil (central VA)
    10           2        Sandy, dry, flat, coastal
     5           1        Cities, industrial areas
     3           0.55     Desert (southwest ID)

Antenna File

CP Crossed Yagis
20' High
88 90 92 94 96 99 102 105 107 108 MHz
15 6063-T832 wires, inches
ang = 22.31157		; driven element angle
r = 32.57215		; element half-lengths
de = 31.1078
d1 = 26.47018
d2 = 25.69514
d3 = 23.71135
dep = 19.80202		; elements positions
d1p = 24.73639
d2p = 34.39471
d3p = 59.04991
p = .665578		; phasing line spacing
f = p / 2
pl = 31.92993		; phasing line length
tx = dep - pl
n = pl / p
shift z 20'		; boom height above ground
rotate x 45
1      0  -r  0      0   r  0    .375
rotate end1 z -ang
1    dep   0  0    dep  de  0    .375
rotate end1 z ang
1    dep   0  0    dep -de  0    .375
rotate z end
1    d1p -d1  0    d1p  d1  0    .375
1    d2p -d2  0    d2p  d2  0    .375
1    d3p -d3  0    d3p  d3  0    .375
shift x -1		; boom offset
rotate x -45
1      0  -r  0      0   r  0    .375
rotate end1 z -ang
1    dep   f  0    dep  de  0    .375
rotate end1 z ang
1    dep  -f  0    dep -de  0    .375
rotate z end
n    dep   f  0     tx   f  0      1
n    dep  -f  0     tx  -f  0      1
2     tx   f  0     tx  -f  0    .375
1    d1p -d1  0    d1p  d1  0    .375
1    d2p -d2  0    d2p  d2  0    .375
1    d3p -d3  0    d3p  d3  0    .375
2 sources
Wire 3, end1
Wire 12, center

Construction

Use ⅜″ elements supported by insulated mounting brackets. Symbols r, de, d1, d2, and d3 are element half-lengths (center to tip), dep, d1p, d2p, and d3p are element positions relative to the reflector (center to center), and ang is the driven element angle. Split the driven elements leaving a gap no greater than ¼″ and angle each half 22°. Offset the Yagis 1″ along the boom and orient them 45° to the ground. The rear-Yagi elements should go from upper left to lower right as viewed from the rear.

Connect the feedpoints to a power combiner using 75Ω coax. The coax from the rear Yagi should be longer by 31.93″ multiplied by its velocity factor. For example, the extra length for Belden 1530A RG-6 with 83% velocity factor is 26˝″. For right-circular polarization, connect the coax center conductors to driven element halves on the same side of the boom. Keep the stripped coax leads as short as possible. Use a 75Ω current balun at each feedpoint. To decouple the feedline, starting at the power combiner 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.

An alternative is to run two feedlines of equal length to a power combiner at the receiver. Let Q be the extra line length calculated above and H an electrical half-wavelength at 98 MHz (50″ for Belden 1530A). Add Q to the feedline from the rear Yagi for right-circular polarization. Add Q + H for left-circular. Add H for vertical polarization and no extra length for horizontal. If you include a phase shifter and variable-gain amplifiers, you can exactly match polarization to maximize the strength of any desired signal or precisely crosspolarize to null any interfering signal.

Sensitivity Analysis

The following table shows the largest performance degradation over 88, 93, 98, 103, and 108 MHz in dB when altering a symbol value by Tol.

Symbol      Tol   Gain    F/R
   ang   1.0000   0.03   0.45
     r   0.0197   0.01   0.04
    de   0.0394   0.00   0.03
    d1   0.0197   0.02   0.03
    d2   0.0197   0.08   0.08
    d3   0.0197   0.01   0.03
   dep   0.0394   0.01   0.08
   d1p   0.0394   0.01   0.08
   d2p   0.0394   0.01   0.02
   d3p   0.0394   0.00   0.02
     p   0.0394   0.27   0.26
    pl   0.0394   0.01   0.01

Gain Comparison

This compares the crossed Yagis, four circularly polarized cubical quads, Antennacraft FM6, small 5-element Yagi, Antenna Performance Specialties APS-13, 10-element Home Depot Yagi, and Körner 9.2, 15.12, and 19.3 for a right-circular field with the booms 20 feet above average-quality ground. Boom length precedes the antenna name.

Crossed Yagis vs Quads

Transmit Polarization

The following table lists antenna polarization percentages by service class for U.S. FM broadcast stations.

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         Percent   C   H   V   h   v
All               100  83   5  10   1   1 
Full service       57  90   3   4   2   1
LPFM                8  98   2   0   0   0  
Translator         33  68  10  21   0   0 
Booster             2  57   9  33   1   0 

If you build a right-circular antenna and a favorite station is left-circular, you'll be disappointed. To prevent this, look up important stations in the FCC database. Check the horizontal and vertical transmit power to determine polarization. To determine circularity sense, check the specifications for the antenna make and model at the manufacturer's website. Some manufacturers do not list circularity sense. As far as I can tell, current antenna models from the following are right-circular: ERI, Jampro, Micronetixx, PSI nonpanel, SWR nonpanel except the FM1, Progressive Concepts except the CIRPA, Nicom except the BKG 88, and Shively Labs except the 6832, 6842, and Versa2une. Exceptions are left-circular. Some interleaved Dielectric antennas are right-circular for analog and left-circular for HD Radio. Harris FMH and Bext antennas are left-circular.

If you're unable to identify a station's antenna, try to find an image of its tower, perhaps with Google Street View.

These antennas are right-circular.

These antennas are left-circular.

If you can receive a station with a tilted dipole, you can determine its circularity sense by finding whether a left or right tilt maximizes signal strength. When all else fails, contact the station chief engineer.


November 27, 201688–108 MHz