Tiny-Backlobe Log-Yagi

This antenna has three reflectors, three driven elements, and four directors on a 134″ boom. A shorted stub adds inductance across the rear driven element. A matching line extends below the front driven-element. I designed the antenna with the AO 9.67 Antenna Optimizer, trading forward gain for very low backlobes.

This shows phasing line and stub detail. Blue dots mark analysis segments. The red dot marks the feedpoint.

The phasing lines cross midway between driven elements.

Modeling Results

Calculated performance is for 28 analysis segments per element halfwave and parallel line segment length equal to the line spacing. Forward gain includes mismatch and conductor losses. 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     F/R 
   MHz        ohms             Loss dB   Loss dB   Gain dBd      dB 
    88     55.8-j12.8   1.43     0.14      0.04      7.06      38.42
    89     51.9-j8.0    1.48     0.16      0.04      7.03      38.93
    90     50.4-j2.7    1.49     0.17      0.04      7.02      38.81
    91     50.6+j2.4    1.48     0.17      0.04      7.04      38.52
    92     51.9+j7.2    1.47     0.16      0.03      7.08      38.42
    93     54.1+j11.5   1.45     0.15      0.03      7.13      38.56
    94     57.2+j15.2   1.43     0.14      0.03      7.19      39.00
    95     61.0+j18.2   1.40     0.12      0.03      7.26      38.90
    96     65.3+j20.3   1.38     0.11      0.03      7.34      38.66
    97     69.9+j21.4   1.35     0.10      0.03      7.43      38.54
    98     75.0+j21.1   1.32     0.09      0.03      7.54      38.46
    99     80.3+j19.0   1.29     0.07      0.03      7.66      38.45
   100     85.4+j15.0   1.25     0.06      0.03      7.78      38.44
   101     89.1+j8.1    1.22     0.04      0.03      7.91      38.45
   102     89.9-j1.3    1.20     0.04      0.03      8.04      38.47
   103     85.7-j12.1   1.22     0.04      0.04      8.15      38.43
   104     76.5-j20.8   1.32     0.08      0.04      8.23      38.42
   105     64.1-j24.5   1.47     0.16      0.05      8.24      38.36
   106     53.3-j22.4   1.63     0.26      0.06      8.17      38.25
   107     48.2-j20.8   1.75     0.33      0.08      8.03      38.43
   108     37.2-j31.9   2.47     0.86      0.13      7.21      40.10

Construction

Space ⅛″ aluminum wire ″ center-to-center for the phasing lines. Orient them symmetrically with respect to the boom. Extend the phasing lines past the rear driven element to form the shorted stub. Extend them beyond the front driven-element to form the matching line. (They are modeled in the vertical plane, but any orientation that keeps them away from the first director is fine.) Cross the phasing lines midway between elements over a 1″ span with the wire surfaces separated ⅛″. To minimize boom coupling, connect the top wire at each crossover to the same side of the middle driven element. Support and space the wires with low-loss dielectric, such as polystyrene.

For the elements use ⅜″ aluminum tubing supported by insulated mounts. Drill a screw hole through the top of each driven element inner end. Use a lockwasher and nut inside the tubing. Bend one edge of two aluminum washers and secure the phasing line between them on top. Use galvanized or cad-plated hardware and apply an antioxidation compound. Measure driven element half-length from the center of the boom to the element tips. The last driven element and first director are very close. Make sure the elements are exactly parallel.

At crossover the phasing lines are not equidistant from the boom. The proximity imbalance can couple stray signals. Modeling suggests that elevating the phasing line plane ″ above the boom surface causes negligible pattern degradation. Use Stauff clamps with the mounting method described above to do this. Position the mast next to the forward phasing line crossover to approximately cancel any coupling.

Connect 75Ω coax to the end of the matching line. Keep the stripped coax leads as short as possible. Waterproof the connections and coax. Use a current balun at the feedpoint. Keep the coax away from the phasing lines.

Antenna File

10-Element Log-Yagi
Free Space
88 92 98 101 103 107 108 MHz
35 6063-T832 wires, inches
z = 19.8879		; outer reflector height
rp = 0		        ; element positions
de1p = 20.47588
de2p = 38.68067
de3p = 51.72175
d1p = 54.01671
d2p = 71.4959
d3p = 98.88953
d4p = 133.4537
r0 = 36.64897		; inner reflector half-length
r1 = 36.19538		; outer reflector half-length
de1 = 30.41594	        ; boom center to driven-element tips
de2 = 25.84483
de3 = 25.26526
d1 = 25.82585		; director half-lengths
d2 = 25.19954
d3 = 23.94531
d4 = 20.168
p = .5		        ; parallel line spacing
f = p / 2
s = 6.272795		; stub length
sp = de1p - s
m = 2.789245		; matching line length
c1 = (de1p + de2p) / 2	; position of crossover centers
c2 = (de2p + de3p) / 2
c1a = c1 - f		; position of crossover ends
c1b = c1 + f
c2a = c2 - f
c2b = c2 + f
n0 = s / p		; number of phasing line segments
n1 = (c1a - de1p) / p
n2 = (c2a - de2p) / p
n3 = m / p
1      rp  -r1  z      rp   r1  z    .375	; reflectors
1      rp  -r0  0      rp   r0  0    .375
1      rp  -r1 -z      rp   r1 -z    .375
1      sp   -f  0      sp    f  0    .125	; stub short
n0     sp   -f  0    de1p   -f  0    .1315	; stub lines
n0     sp    f  0    de1p    f  0    .1315
1    de1p    f  0    de1p  de1  0    .375	; driven elements
1    de1p   -f  0    de1p -de1  0    .375
1    de2p    f  0    de2p  de2  0    .375
1    de2p   -f  0    de2p -de2  0    .375
1    de3p    f  0    de3p  de3  0    .375
1    de3p   -f  0    de3p -de3  0    .375
1     d1p  -d1  0     d1p   d1  0    .375	; directors
1     d2p  -d2  0     d2p   d2  0    .375
1     d3p  -d3  0     d3p   d3  0    .375
1     d4p  -d4  0     d4p   d4  0    .375
n1   de1p    f  0     c1a    f  0    .1315	; phasing lines
1     c1a    f  0      c1    0  f    .1315
1      c1    0  f     c1b   -f  0    .1315
n1    c1b   -f  0    de2p   -f  0    .1315
n1   de1p   -f  0     c1a   -f  0    .1315
1     c1a   -f  0      c1    0 -f    .1315
1      c1    0 -f     c1b    f  0    .1315
n1    c1b    f  0    de2p    f  0    .1315	; 0.1315" in AO yields
n2   de2p    f  0     c2a    f  0    .1315	; correct line Z for
1     c2a    f  0      c2    0 -f    .1315	; 0.125" wires spaced 0.5"
1      c2    0 -f     c2b   -f  0    .1315
n2    c2b   -f  0    de3p   -f  0    .1315
n2   de2p   -f  0     c2a   -f  0    .1315
1     c2a   -f  0      c2    0  f    .1315
1      c2    0  f     c2b    f  0    .1315
n2    c2b    f  0    de3p    f  0    .1315
n3   de3p    f  0    de3p    f -m    .1315	; matching lines
n3   de3p   -f  0    de3p   -f -m    .1315
2    de3p   -f -m    de3p    f -m    .125	; feedpoint jumper
1 source
Wire 35, center

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. Note the high F/R sensitivity to the first two director lengths.

Symbol      Tol   Gain    F/R
     z   0.0394   0.00   0.15
    rp   0.0394   0.00   0.11
  de1p   0.0394   0.00   0.14
  de2p   0.0394   0.01   0.05
  de3p   0.0394   0.02   0.08
   d1p   0.0394   0.03   0.22
   d2p   0.0394   0.02   0.29
   d3p   0.0394   0.01   0.18
   d4p   0.0394   0.00   0.06
    r0   0.0197   0.00   0.10
    r1   0.0197   0.00   0.07
   de1   0.0394   0.02   0.29
   de2   0.0394   0.01   0.72
   de3   0.0394   0.03   0.52
    d1   0.0197   0.16   1.30
    d2   0.0197   0.05   2.33
    d3   0.0197   0.03   0.79
    d4   0.0197   0.00   0.10
     p   0.0394   0.03   1.10
     s   0.0394   0.00   0.12
     m   0.0394   0.02   0.12

Gallery

Mark erected an earlier version of the antenna in New Jersey. He used a lockwasher between McMaster-Carr 2993T83 single-bolt clamps and the boom to help keep the elements parallel. Mark consistently gets 35 dB F/B despite using a short middle reflector and deviant phasing lines.


February 23, 201988108 MHz