Small Yagi
If you don't need high performance, the Antennacraft FM6 is hard to beat for value. But you may want something smaller, something with a better pattern, or something to build just for fun. The small Yagi described here has 5-7 dBd gain and better than 20 dB F/B across the FM band. It uses five elements on a five-foot boom.Balun loss drops the FM6 output 0.85 dB when using a 75-ohm feedline. In contrast, the small Yagi has a 75-ohm feedpoint and needs only a simple coax balun, which adds no loss if you have a couple extra feet of feedline to coil. Including balun loss, the small Yagi has better gain than the FM6, as well as better F/B, across the entire FM band. Compare gain and F/B curves here.
I designed the antenna using the global optimizer and response flattener of the AO 8.04 Antenna Optimizer program. This image shows the antenna geometry. The red dot indicates the feedpoint. The driven element is bent toward the reflector to increase F/B at the low end of the band.
Modeling Results
Below are calculated performance figures for a segmentation density of 28 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. 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 59.4 - j17.6 ohms
SWR 1.42
Mismatch Loss 0.13 dB
Wire Loss 0.01 dB
Mismatched Gain 5.22 dBd
F/B 20.70 dB
90.000 MHz: Impedance 79.4 - j13.7 ohms
SWR 1.20
Mismatch Loss 0.04 dB
Wire Loss 0.01 dB
Mismatched Gain 5.20 dBd
F/B 36.40 dB
92.000 MHz: Impedance 90.6 - j14.1 ohms
SWR 1.29
Mismatch Loss 0.07 dB
Wire Loss 0.01 dB
Mismatched Gain 5.16 dBd
F/B 24.83 dB
94.000 MHz: Impedance 95.6 - j14.7 ohms
SWR 1.35
Mismatch Loss 0.10 dB
Wire Loss 0.01 dB
Mismatched Gain 5.23 dBd
F/B 21.76 dB
96.000 MHz: Impedance 95.4 - j14.1 ohms
SWR 1.34
Mismatch Loss 0.09 dB
Wire Loss 0.01 dB
Mismatched Gain 5.41 dBd
F/B 21.02 dB
98.000 MHz: Impedance 91.5 - j11.2 ohms
SWR 1.27
Mismatch Loss 0.06 dB
Wire Loss 0.01 dB
Mismatched Gain 5.70 dBd
F/B 21.66 dB
100.000 MHz: Impedance 84.1 - j5.2 ohms
SWR 1.14
Mismatch Loss 0.02 dB
Wire Loss 0.01 dB
Mismatched Gain 6.06 dBd
F/B 23.66 dB
102.000 MHz: Impedance 74.6 + j5.3 ohms
SWR 1.07
Mismatch Loss 0.01 dB
Wire Loss 0.02 dB
Mismatched Gain 6.44 dBd
F/B 26.90 dB
104.000 MHz: Impedance 67.3 + j21.9 ohms
SWR 1.38
Mismatch Loss 0.11 dB
Wire Loss 0.02 dB
Mismatched Gain 6.72 dBd
F/B 25.64 dB
106.000 MHz: Impedance 69.3 + j39.4 ohms
SWR 1.73
Mismatch Loss 0.32 dB
Wire Loss 0.03 dB
Mismatched Gain 6.80 dBd
F/B 21.42 dB
108.000 MHz: Impedance 69.7 + j12.9 ohms
SWR 1.21
Mismatch Loss 0.04 dB
Wire Loss 0.07 dB
Mismatched Gain 6.94 dBd
F/B 22.83 dB
Patterns
Stacked Yagis
The small Yagi is quite suitable for stacking. Vertical stacking adds little gain because elevation patterns of antennas at different heights are dissimilar unless the antennas are rather high. But horizontal stacking is effective at any height. It also minimizes Yagi-to-Yagi interaction.
The yellow pattern is for two small Yagis with their booms stacked 8' apart and red is for a single antenna. Forward gain is 2.73 dB greater for the stack. The much narrower main lobe can reduce interference and multipath distortion.
Connect the two Yagis with equal lengths of 75-ohm line to a power splitter, using a coax balun at each feedpoint. The coax center conductor should go to the same side of each Yagi. Typical loss of a 75-ohm consumer power splitter is 0.5 dB. An alternative with less than 0.1 dB loss is to parallel the 75-ohm feeders and transform back to approximately 75 ohms with an electrical quarter-wavelength of 50-ohm coax (20" for cable with a velocity factor of 0.66). The stacking boom should be nonconductive and the feeders should drop vertically for a few feet before running parallel to the elements.
Circular Polarization
Two small Yagis oriented at right angles and offset a quarter wavelength make a compact circularly polarized array with a boom shorter than eight feet. At a height of 30 feet over average-quality ground, array gain for signals with matching polarization is about 2.8 dB. Cross-polarized signals, including multipath reflections, are rejected at least 20 dB in the forward direction. This method of arraying two Yagis is more compact than horizontal or vertical stacking and may provide more benefit.
Run two 75-ohm cables of equal length to a 75-ohm power splitter. Coil each cable into a current balun at the driven element. From the splitter run a single 75-ohm feedline to the rear of the boom. Form another current balun there and drop the feedline vertically, keeping it away from the vertical elements. Use a nonconductive mast. Swap the connections at one driven element to reverse the circularity sense. For a typical power-splitter loss of 0.5 dB, array gain is about 2.3 dB for a signal with matching circularity. For a linearly polarized signal, the array delivers about 3.5 dB less power than a polarization-aligned Yagi. To eliminate power-splitter loss, connect the 75-ohm cables in parallel and transform back to 75 ohms with 20" of 50-ohm RG-58 cable.
Hardwired as described, the array will receive signals with horizontal, vertical, and either right- or left-circular polarization. It will reject signals of opposite circularity. Most signals on the air today are right-circular, some are left-circular, and a few are horizontal or vertical. Check that the signals you want to receive have the same circularity sense or are linearly polarized.
A more complex installation uses two 75-ohm feedlines and a switching arrangement to receive all polarizations, as well as eliminate the penalty for linear polarization. The feedlines are combined in phase for right-circular polarization and out of phase for left circular. For horizontal and vertical polarization, the feedlines are used individually.
The switching arrangement uses a three-pole, four-throw switch. The RG-58 is a quarterwave section that matches 37.5 to 75 ohms. (A 50-ohm line would work just as well.) The RG-59 is a halfwave phasing line to reverse circularity. A velocity factor of 0.66 is assumed for both lines.
An even more complex arrangement combines the signals from two feedlines with adjustable amplitude and phase. This method can exactly cancel an interfering signal by compensating for transmit circularity errors, attenuation of vertical polarization due to propagation over hills or mountains, variation in ground quality or antenna height, or off-axis signal arrival.
The first three patterns below show the response of a pair of small Yagis offset 33-1/2" with outputs summed at a boom height of 30 feet. The yellow traces are for matched polarization, while red is for orthogonal polarization. Note that off-axis rejection of orthogonal signals is not nearly as good as for an array of Antennacraft FM6s, shown here. While off-axis rejection for the FM6 array is much better with the Yagis tilted 45 degrees, the small Yagis work best when parallel and perpendicular to the ground.
The gain figures for these antennas over ground are not comparable with the figures for free-space antennas given earlier, but you can use the last plot for a single horizontal antenna at 30 feet as a gain reference. Not counting power-splitter losses, in a right-circular field the circularly polarized array has 2.8 dB gain over the single antenna.
Antenna File
Small Yagi Free Space Symmetric 98 MHz 6 6063-T832 wires, inches ang = -18.93766 r = 32.31071 de = 29.63062 d1 = 26.26223 d2 = 25.38989 d3 = 23.05096 rp = 2.729484 dep = 19.92724 d1p = 25.04834 d2p = 36.52914 d3p = 63.3664 1 rp -r 0 rp r 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 shift x dep rotate z ang 1 0 0 0 0 de 0 .375 rotate z -ang 1 0 0 0 0 -de 0 .375 1 source Wire 5, end1 28 segments/halfwave best matches NEC Optimized at 88 90 92 94 96 99 102 105 107 108 MHz Trade-offs: 20% gain, 80% F/B Weighting: average for gain, worst-case for F/B Enable bent-wire correctionUse 3/8"-diameter elements and a nonconducting boom. Symbols r, de, d1, d2, and d3 are element half-lengths, while rp, dep, d1p, d2p, and d3p are element positions. Split the driven element, angle the halves, and feed with 75-ohm coax through a current balun.
More is here.
Updated July 8, 2007
