Log-Yagis

A log-Yagi is a log-periodic driver cell with parasitic elements. It can provide an excellent wideband pattern at lower material cost than a Yagi with similar performance. However, log-Yagis are more complex and difficult to build, and their performance can be sensitive to certain dimensions and ground proximity. Consider building one if you can verify the pattern and don't mind some tinkering to achieve best performance.

Five-Element Log-Yagi

This antenna has one reflector, two driven elements, and two directors on a 79″ boom. Bending three elements improves both forward gain and the pattern. The red dot is the 75Ω feedpoint and the green dot is an inductor. A hairpin match uses another inductor across the feedpoint. I designed the antenna with the AO 9.61 Antenna Optimizer, trading forward gain for low backlobes.

This shows phasing line detail. Blue dots mark analysis segments.

Modeling Results

Calculated performance is for 28 analysis segments per element halfwave and phasing 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    54.6 - j27.4  1.70     0.30      0.03      5.98      30.02
    89    61.6 - j10.8  1.29     0.07      0.03      6.02      31.44
    90    66.9 + j0.5   1.12     0.01      0.02      5.93      31.67
    91    71.0 + j8.4   1.14     0.02      0.02      5.83      30.13
    92    74.4 + j14.1  1.21     0.04      0.02      5.73      30.16
    93    77.1 + j18.1  1.27     0.06      0.02      5.66      31.14
    94    79.5 + j20.7  1.31     0.08      0.02      5.61      32.62
    95    81.4 + j22.3  1.34     0.09      0.01      5.59      32.22
    96    83.1 + j23.2  1.36     0.10      0.01      5.59      31.83
    97    84.7 + j23.3  1.37     0.11      0.01      5.61      31.21
    98    85.8 + j22.7  1.37     0.11      0.01      5.65      30.74
    99    86.6 + j21.5  1.35     0.10      0.01      5.72      30.33
   100    87.3 + j19.8  1.33     0.09      0.01      5.80      30.06
   101    87.8 + j17.1  1.30     0.07      0.01      5.91      29.90
   102    88.1 + j13.2  1.26     0.06      0.02      6.03      29.85
   103    87.0 + j8.0   1.19     0.03      0.02      6.17      29.99
   104    84.7 - j0.0   1.13     0.02      0.02      6.34      30.35
   105    78.4 - j9.2   1.14     0.02      0.02      6.49      30.89
   106    66.4 - j17.6  1.32     0.08      0.03      6.60      31.42
   107    49.4 - j20.9  1.71     0.31      0.03      6.54      31.53
   108    31.6 - j16.4  2.51     0.89      0.04      6.13      30.03

Ground Effects

I designed the antenna in free space. This shows how ground proximity affects F/R at 1 elevation angle for boom heights between 15 and 50 feet.

Reoptimizing the design at 20 feet above ground improves F/R for practical installation heights. This design has a boom length of 77″.

These curves are for an installation height of 20 feet above ground at 1 elevation angle. The gain reference is an isotropic antenna in free space.

Bent vs Straight Elements

Using the same performance trade-offs and constraints, I reoptimized the design with straight elements. These curves show the benefit of bent elements.

Construction

Space ⅛″ aluminum wire ″ center-to-center for the phasing lines. Orient them symmetrically with respect to the boom. Cross the wires midway between elements over a 1″ span with the wire surfaces ⅛″ apart. Support and space the wires at crossover with low-loss dielectric, such as polystyrene.

Form the phasing line into the rear coil. Use three turns with an inside diameter of 1″ and an outside length of 1316″. The shunt feedpoint coil uses three turns of the ⅛″ wire with an inside diameter of 1″ and an outside length of ″ (⅝″ for the over-ground design). Use ″ leads and center the coil above the element. To align test coils with leads with a network analyzer, adjust the rear coil for a reactance of 142Ω at 98 MHz and the feedpoint coil for 150Ω (146Ω and 167Ω for the over-ground design).

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 the edge of two washers and secure the phasing line between them on top of the element. Use galvanized or cad-plated hardware and apply an antioxidation compound. Bend each side of three elements in the forward direction as follows: reflector 13.7, rear driven element 3.5, and first director 4.2 (10.5, 3.2, and 3.8 for the over-ground design). Total parasitic element bend doubles when done exactly at the center. Use two bends, each up to 1″ from center, to reduce metal stress and simplify element mounting. Angle the driven element mounts to implement that bend.

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 phasing line crossover to approximately cancel any coupling.

Connect 75Ω coax to the forward driven element. Keep the stripped coax leads as short as possible. Use a current balun at the feedpoint. Route the coax on the boom side opposite the phasing lines.

Antenna Files

5-Element Log-Yagi
Free Space
88 91.5 98 103 108 MHz
19 6063-T832 wires, inches
angr = 13.7225		; element angles
angde1 = 3.476124
angd1 = 4.243591
r = 32.56746		; reflector half-length
de1 = 27.43906		; boom center to driven-element tips
de2 = 26.01785
d1 = 25.35547		; director half-lengths
d2 = 22.94104
rp = 0			; element positions
de1p = 22.12118
de2p = 43.42033
d1p = 52.48478
d2p = 79.41011
p = .5			; phasing line spacing
f = p / 2
xc = (de1p + de2p) / 2	; position of crossover center
xr = xc - f
xf = xc + f
n = (xr - de1p) / p	; number of phasing line segments
rotate end1 z angr
1      rp   0  0      rp    r  0    .375
rotate end1 z -angr
1      rp   0  0      rp   -r  0    .375
rotate end1 z angde1
1    de1p   f  0    de1p  de1  0    .375
rotate end1 z -angde1
1    de1p  -f  0    de1p -de1  0    .375
rotate end
1    de2p   f  0    de2p  de2  0    .375
1    de2p  -f  0    de2p -de2  0    .375
rotate end1 z angd1
1     d1p   0  0     d1p   d1  0    .375
rotate end1 z -angd1
1     d1p   0  0     d1p  -d1  0    .375
rotate end
1     d2p -d2  0     d2p   d2  0    .375
2    de1p  -f  0    de1p    f  0    .1315	; rear coil jumper
n    de1p   f  0      xr    f  0    .1315	; phasing line
1      xr   f  0      xc    0  f    .1315
1      xc   0  f      xf   -f  0    .1315
n      xf  -f  0    de2p   -f  0    .1315	; 0.1315" in AO yields
n    de1p  -f  0      xr   -f  0    .1315	; correct line Z for
1      xr  -f  0      xc    0 -f    .1315	; 0.125" wires spaced 0.5"
1      xc   0 -f      xf    f  0    .1315
n      xf   f  0    de2p    f  0    .1315
2    de2p  -f  0    de2p    f  0    .1315	; feedpoint jumper
1 source
lf = 243.8945
Wire 19, center lf nH				; feedpoint coil
1 load
lr = 229.922
Wire 10, center lr nH				; rear coil


5-Element Log-Yagi Optimized at 20'
Over Ground
88 93 98 101 103 108 MHz
19 6063-T832 wires, inches
angr = 10.47858		; element angles
angde1 = 3.204839
angd1 = 3.797056
r = 32.75512		; reflector half-length
de1 = 27.8726		; boom center to driven-element tips
de2 = 26.38708
d1 = 25.5825		; director half-lengths
d2 = 22.96665
rp = 0			; element positions
de1p = 25.08253
de2p = 45.33577
d1p = 52.28618
d2p = 77.28246
p = .5			; phasing line spacing
f = p / 2
xc = (de1p + de2p) / 2	; position of crossover center
xr = xc - f
xf = xc + f
n = (xr - de1p) / p	; number of phasing line segments
shift z 20'
rotate end1 z angr
1      rp   0  0      rp    r  0    .375
rotate end1 z -angr
1      rp   0  0      rp   -r  0    .375
rotate end1 z angde1
1    de1p   f  0    de1p  de1  0    .375
rotate end1 z -angde1
1    de1p  -f  0    de1p -de1  0    .375
rotate end
1    de2p   f  0    de2p  de2  0    .375
1    de2p  -f  0    de2p -de2  0    .375
rotate end1 z angd1
1     d1p   0  0     d1p   d1  0    .375
rotate end1 z -angd1
1     d1p   0  0     d1p  -d1  0    .375
rotate end
1     d2p -d2  0     d2p   d2  0    .375
2    de1p  -f  0    de1p    f  0    .125	; rear coil jumper
n    de1p   f  0      xr    f  0    .1315	; phasing line
1      xr   f  0      xc    0  f    .1315
1      xc   0  f      xf   -f  0    .1315
n      xf  -f  0    de2p   -f  0    .1315	; 0.1315" in AO yields
n    de1p  -f  0      xr   -f  0    .1315	; correct line Z for
1      xr  -f  0      xc    0 -f    .1315	; 0.125" wires spaced 0.5"
1      xc   0 -f      xf    f  0    .1315
n      xf   f  0    de2p    f  0    .1315
2    de2p  -f  0    de2p    f  0    .125	; feedpoint jumper
1 source
lf = 271.0583
Wire 19, center lf nH				; feedpoint coil
1 load
lr = 237.4339
Wire 10, center lr nH				; rear coil

Sensitivity Analysis

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

Symbol      Tol   Gain    F/R
  angr   1.0000   0.00   2.35
angde1   1.0000   0.02   2.67
 angd1   1.0000   0.13   1.72
     r   0.0197   0.00   0.46
   de1   0.0394   0.03   0.60
   de2   0.0394   0.01   0.43
    d1   0.0197   0.06   1.08
    d2   0.0197   0.01   0.16
    rp   0.0394   0.00   0.09
  de1p   0.0394   0.00   0.06
  de2p   0.0394   0.01   0.13
   d1p   0.0394   0.00   0.21
   d2p   0.0394   0.00   0.07
     p   0.0394   0.05   0.81
    lf  24.3895   0.05   0.00
    lr  22.9922   0.28   3.28

These are the sensitivities for the over-ground design at 20 feet:

Symbol      Tol   Gain    F/R
  angr   1.0000   0.00   1.29
angde1   1.0000   0.01   1.67
 angd1   1.0000   0.22   1.80
     r   0.0197   0.00   0.41
   de1   0.0394   0.01   0.42
   de2   0.0394   0.01   0.40
    d1   0.0197   0.08   1.06
    d2   0.0197   0.01   0.21
    rp   0.0394   0.00   0.03
  de1p   0.0394   0.00   0.07
  de2p   0.0394   0.01   0.16
   d1p   0.0394   0.00   0.19
   d2p   0.0394   0.00   0.06
     p   0.0394   0.03   0.70
    lf  27.1058   0.04   0.00
    lr  23.7434   0.09   2.50

Ten-Element Log-Yagi

This antenna has three reflectors, three driven elements, and four directors on a 129″ boom. A shorted stub adds inductance across the rear driven element. A hairpin match uses an inductor across the feedpoint. I designed the antenna with the AO 9.64 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 phasing 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    69.0 - j2.3   1.09     0.01      0.05      7.15      39.00
    89    70.5 - j5.8   1.11     0.01      0.04      7.15      39.91
    90    67.3 - j7.6   1.17     0.03      0.04      7.15      39.63
    91    62.6 - j6.8   1.23     0.05      0.04      7.15      39.24
    92    58.3 - j4.1   1.30     0.07      0.04      7.15      39.02
    93    54.9 - j0.3   1.37     0.11      0.03      7.15      39.01
    94    52.5 + j3.9   1.43     0.14      0.03      7.17      39.37
    95    51.3 + j8.6   1.50     0.17      0.03      7.18      39.27
    96    50.8 + j12.8  1.55     0.21      0.03      7.22      39.09
    97    51.1 + j16.9  1.60     0.24      0.03      7.27      38.98
    98    51.8 + j20.6  1.64     0.26      0.03      7.33      39.01
    99    53.7 + j24.4  1.66     0.27      0.03      7.41      38.98
   100    56.5 + j27.9  1.66     0.28      0.03      7.51      38.99
   101    60.7 + j31.4  1.66     0.27      0.03      7.63      39.05
   102    67.1 + j34.2  1.63     0.26      0.03      7.76      39.02
   103    76.7 + j34.8  1.58     0.22      0.04      7.90      39.01
   104    89.6 + j30.8  1.51     0.18      0.04      8.05      39.00
   105     103 + j17    1.45     0.15      0.05      8.17      38.97
   106     105 - j5     1.40     0.12      0.06      8.22      38.92
   107    97.9 - j17.2  1.39     0.12      0.07      8.16      39.00
   108     121 - j38    1.85     0.41      0.12      7.60      40.06

Ground Effects

I designed the antenna in free space. This shows how ground proximity affects F/R at 1 elevation angle for boom heights between 15 and 50 feet.

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. Cross the wires 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 at crossover with low-loss dielectric, such as polystyrene.

The shunt feedpoint coil uses three turns of the ⅛″ wire with an inside diameter of 1″ and an outside length of 1⅜″. Use ″ leads and center the coil above the element. To align a test coil with leads with a network analyzer, adjust it for a reactance of 117Ω at 98 MHz.

For the elements use ⅜″ aluminum tubing supported by insulated mounts. Drill a screw hole through the top surface of each driven element inner end. Use a lockwasher and nut inside the tubing. Bend the edge of two washers and secure the phasing line between them. 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 first director and last driven element 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 forward driven element. Keep the stripped coax leads as short as possible. Use a current balun at the feedpoint. Route the coax on the boom side opposite the phasing lines.

Antenna File

10-Element Log-Yagi
Free Space
88 93 98 103 107 108 MHz
33 6063-T832 wires, inches
z = 19.02283		; outer reflector height
rp = 0			; element positions
de1p = 20.607875
de2p = 36.23055
de3p = 48.23532
d1p = 50.3294
d2p = 67.626431
d3p = 94.63474
d4p = 129.30383
r0 = 37.033267		; inner reflector half-length
r1 = 36.061686		; outer reflector half-length
de1 = 30.316967		; boom center to driven-element tips
de2 = 25.818328
de3 = 24.989362
d1 = 25.816858		; director half-lengths
d2 = 25.223362
d3 = 24.042474
d4 = 20.450674
p = .5			; phasing line spacing
f = p / 2
s = 4.7204345		; stub length
sp = de1p - s
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 = (de1p - sp) / p	; number of phasing line segments
n1 = (c1a - de1p) / p
n2 = (c2a - de2p) / 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
2    de3p   -f  0    de3p    f  0    .125	; feedpoint jumper
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
1 source
lf = 189.98988
Wire 13, center lf nH				; feedpoint coil

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
     z   0.0394   0.00   0.15
    rp   0.0394   0.00   0.11
  de1p   0.0394   0.00   0.18
  de2p   0.0394   0.01   0.06
  de3p   0.0394   0.01   0.17
   d1p   0.0394   0.02   0.48
   d2p   0.0394   0.02   0.41
   d3p   0.0394   0.00   0.27
   d4p   0.0394   0.00   0.14
    r0   0.0197   0.00   0.10
    r1   0.0197   0.00   0.15
   de1   0.0394   0.01   0.55
   de2   0.0394   0.01   0.90
   de3   0.0394   0.03   0.88
    d1   0.0197   0.10   2.30
    d2   0.0197   0.05   3.14
    d3   0.0197   0.02   1.68
    d4   0.0197   0.00   0.30
     p   0.0394   0.03   0.91
     s   0.0394   0.00   0.21
    lf  18.9990   0.07   0.00

Stacked Six-Element Log-Yagis

This antenna rejects interference by combining a narrow main lobe with very low secondary forward lobes and backlobes. Each log-Yagi has a bent reflector, two driven elements, and three directors on a 114″ boom. Boom spacing is 78″. Red dots are 75Ω feedpoints and green dots are inductors. A hairpin match uses another inductor across each feedpoint. I designed the antenna with the AO 9.62 Antenna Optimizer.

Modeling Results

Calculated performance is for 28 analysis segments per element halfwave and phasing line segment length equal to the line spacing. Forward gain includes mismatch and conductor losses. Subtract 0.3 dB to account for the loss of a ferrite power combiner. 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    80.8 - j34.2  1.56     0.21      0.03      8.75      30.07
    89    79.3 - j13.6  1.20     0.04      0.02      8.85      34.08
    90    78.7 - j0.2   1.05     0.00      0.02      8.83      36.04
    91    78.8 + j9.2   1.14     0.02      0.02      8.79      31.96
    92    79.2 + j15.8  1.24     0.05      0.02      8.76      30.44
    93    79.9 + j20.3  1.31     0.08      0.01      8.74      30.02
    94    80.8 + j23.3  1.36     0.10      0.01      8.74      30.27
    95    81.6 + j24.8  1.39     0.12      0.01      8.77      30.98
    96    82.4 + j25.2  1.39     0.12      0.01      8.83      32.37
    97    83.0 + j24.5  1.38     0.11      0.01      8.90      34.53
    98    82.9 + j22.9  1.36     0.10      0.01      9.00      34.43
    99    82.0 + j20.7  1.32     0.08      0.01      9.12      33.82
   100    80.1 + j18.2  1.28     0.06      0.01      9.25      33.26
   101    77.5 + j15.8  1.23     0.05      0.01      9.40      32.75
   102    74.3 + j13.7  1.20     0.04      0.02      9.54      32.32
   103    70.8 + j11.9  1.19     0.03      0.02      9.69      31.95
   104    67.0 + j10.3  1.20     0.04      0.02      9.84      30.76
   105    64.1 + j7.9   1.22     0.04      0.02      9.99      30.01
   106    60.3 + j3.3   1.25     0.05      0.03     10.13      30.99
   107    52.4 - j4.3   1.44     0.14      0.03     10.18      31.88
   108    34.9 - j9.0   2.19     0.65      0.05      9.77      31.77

I optimized the array as a whole. Rear rejection for a single log-Yagi is much worse than for the array.

Ground Effects

I designed the antenna in free space. This shows how ground proximity affects F/R at 1 elevation angle for boom heights between 15 and 50 feet.

Reoptimizing the design at 30 feet above ground improves F/R for practical installation heights. This design has a boom length of 107″ and a boom spacing of 76″.

These curves are for an installation height of 30 feet above ground at 1 elevation angle. The gain reference is an isotropic antenna in free space.

Construction

Space ⅛″ aluminum wire ″ center-to-center for the phasing lines. Orient them symmetrically with respect to the boom. Cross the wires midway between elements over a 1″ span with the wire surfaces separated ⅛″. Support and space the wires at crossover with low-loss dielectric, such as polystyrene.

Form the phasing line into the rear coil. Use three turns with an inside diameter of 1″ and an outside length of 1″ (⅞″ for the over-ground design). The shunt feedpoint coil uses three turns of the ⅛″ wire with an inside diameter of 1″ and an outside length of 1″ (1″ for the over-ground design). Use ″ leads and center the coil above the element. To align test coils with leads with a network analyzer, adjust the rear coil for a reactance of 133Ω at 98 MHz and the feedpoint coil for 124Ω (140Ω and 110Ω for the over-ground design).

For the elements use ⅜″ aluminum tubing supported by insulated mounts. Bend each side of the reflector 11 in the forward direction (16 for the over-ground design). Total element bend doubles when done exactly at the center. Use two bends, each up to 1″ from center, to reduce metal stress and simplify element mounting. Drill a screw hole through the top of each driven element inner end. Use a lockwasher and nut inside the tubing. Bend the edge of two washers and secure the phasing line between them on top of the element. 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.

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.

Connect equal lengths of 75Ω coax to the forward driven elements. Keep the stripped coax leads as short as possible. Use a current balun at each feedpoint and add more at 30″ intervals along each feeder. Drop the feeders vertically for several feet and connect them to a power combiner at the mast. Use a nonconductive crossboom.

SWR for a single log-Yagi is very close to that for the array so you can check each antenna individually during construction.

Antenna Files

Stacked 6-El Log-Yagis
Free Space Symmetric
88 93 98 100 103 105 106 107 108 MHz
19 6063-T832 wires, inches
angr = 10.97231		; reflector angle
r = 32.68768		; reflector half-length
de1 = 27.4109		; boom center to driven-element tips
de2 = 25.77784
d1 = 25.02346		; director half-lengths
d2 = 24.70072
d3 = 22.44673
rp = 0			; element positions
de1p = 24.75507
de2p = 46.90845
d1p = 60.14999
d2p = 85.70532
d3p = 114.0106
p = .5			; phasing line spacing
f = p / 2
xc = (de1p + de2p) / 2	; position of crossover center
xr = xc - f
xf = xc + f
n = (xr - de1p) / p	; number of phasing line segments
s = 38.79003		; array half-spacing
shift y s
rotate end1 z angr
1      rp   0  0      rp    r  0    .375
rotate end1 z -angr
1      rp   0  0      rp   -r  0    .375
rotate end
1    de1p   f 0     de1p  de1  0    .375
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     d1p -d1  0     d1p   d1  0    .375
1     d2p -d2  0     d2p   d2  0    .375
1     d3p -d3  0     d3p   d3  0    .375
2    de1p  -f  0    de1p    f  0    .125	; rear coil jumper
n    de1p   f  0      xr    f  0    .1315	; phasing line
1      xr   f  0      xc    0  f    .1315
1      xc   0  f      xf   -f  0    .1315
n      xf  -f  0    de2p   -f  0    .1315	; 0.1315" in AO yields
n    de1p  -f  0      xr   -f  0    .1315	; correct line Z for
1      xr  -f  0      xc    0 -f    .1315	; 0.125" wires spaced 0.5"
1      xc   0 -f      xf    f  0    .1315
n      xf   f  0    de2p    f  0    .1315
2    de2p  -f  0    de2p    f  0    .125	; feedpoint jumper
1 source
lf = 200.9906
Wire 19, center lf nH				; feedpoint coil
1 load
lr = 215.8895
Wire 10, center lr nH				; rear coil


Stacked 6-El Log-Yagis Optimized at 30'
Over Ground
88 93 98 100 103 105 106 107 108 MHz
38 6063-T832 wires, inches
angr = 16.2158		; reflector angle
r = 32.70866		; reflector half-length
de1 = 26.88994		; boom center to driven-element tips
de2 = 25.71161
d1 = 25.29992		; director half-lengths
d2 = 24.859
d3 = 22.29509
rp = 0			; element positions
de1p = 24.65184
de2p = 49.16114
d1p = 60.97778
d2p = 81.72629
d3p = 106.6172
p = .5			; phasing line spacing
f = p / 2
xc = (de1p + de2p) / 2	; position of crossover center
xr = xc - f
xf = xc + f
n = (xr - de1p) / p	; number of phasing line segments
s = 37.87296		; array half-spacing
shift z 30' y s
rotate end1 z angr
1      rp   0  0      rp    r  0    .375
rotate end1 z -angr
1      rp   0  0      rp   -r  0    .375
rotate end
1    de1p   f 0     de1p  de1  0    .375
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     d1p -d1  0     d1p   d1  0    .375
1     d2p -d2  0     d2p   d2  0    .375
1     d3p -d3  0     d3p   d3  0    .375
2    de1p  -f  0    de1p    f  0    .125	; rear coil jumper
n    de1p   f  0      xr    f  0    .1315	; phasing line
1      xr   f  0      xc    0  f    .1315
1      xc   0  f      xf   -f  0    .1315
n      xf  -f  0    de2p   -f  0    .1315	; 0.1315" in AO yields
n    de1p  -f  0      xr   -f  0    .1315	; correct line Z for
1      xr  -f  0      xc    0 -f    .1315	; 0.125" wires spaced 0.5"
1      xc   0 -f      xf    f  0    .1315
n      xf   f  0    de2p    f  0    .1315
2    de2p  -f  0    de2p    f  0    .125	; feedpoint jumper
shift y -s
rotate end1 z angr
1      rp   0  0      rp    r  0    .375
rotate end1 z -angr
1      rp   0  0      rp   -r  0    .375
rotate end
1    de1p   f 0     de1p  de1  0    .375
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     d1p -d1  0     d1p   d1  0    .375
1     d2p -d2  0     d2p   d2  0    .375
1     d3p -d3  0     d3p   d3  0    .375
2    de1p  -f  0    de1p    f  0    .125
n    de1p   f  0      xr    f  0    .1315
1      xr   f  0      xc    0  f    .1315
1      xc   0  f      xf   -f  0    .1315
n      xf  -f  0    de2p   -f  0    .1315
n    de1p  -f  0      xr   -f  0    .1315
1      xr  -f  0      xc    0 -f    .1315
1      xc   0 -f      xf    f  0    .1315
n      xf   f  0    de2p    f  0    .1315
2    de2p  -f  0    de2p    f  0    .125
2 sources
lf = 178.983
Wire 19, center lf nH				; feedpoint coils
Wire 38, center lf nH
2 loads
lr = 227.3235
Wire 10, center lr nH				; rear coils
Wire 29, center lr nH

Sensitivity Analysis

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

Symbol      Tol   Gain    F/R
  angr   1.0000   0.00   1.26
     r   0.0197   0.00   0.48
   de1   0.0394   0.02   0.33
   de2   0.0394   0.02   0.71
    d1   0.0197   0.06   1.20
    d2   0.0197   0.02   1.06
    d3   0.0197   0.01   0.40
    rp   0.0394   0.00   0.04
  de1p   0.0394   0.01   0.04
  de2p   0.0394   0.01   0.03
   d1p   0.0394   0.00   0.22
   d2p   0.0394   0.01   0.44
   d3p   0.0394   0.00   0.15
     p   0.0394   0.03   0.52
     s   0.0394   0.00   0.05
    lf  20.0991   0.06   0.00
    lr  21.5889   0.28   2.76

These are the sensitivities for the over-ground design at 30 feet:

Symbol      Tol   Gain    F/R
  angr   1.0000   0.00   1.78
     r   0.0197   0.00   0.29
   de1   0.0394   0.02   0.26
   de2   0.0394   0.02   0.66
    d1   0.0197   0.08   1.52
    d2   0.0197   0.01   0.20
    d3   0.0197   0.00   0.11
    rp   0.0394   0.00   0.09
  de1p   0.0394   0.00   0.19
  de2p   0.0394   0.01   0.17
   d1p   0.0394   0.00   0.11
   d2p   0.0394   0.01   0.37
   d3p   0.0394   0.01   0.13
     p   0.0394   0.02   0.53
     s   0.3937   0.03   0.44
    lf  17.8983   0.07   0.00
    lr  22.7324   0.20   3.06

Performance Comparison



Stacked Vertically Polarized Log-Yagis

Vertically polarized directional antennas often have poor azimuth patterns. Side nulls don't invariably occur as for horizontal antennas and the main beam usually is broad. Stacking two antennas side-by-side can reduce beamwidth and side response, but secondary forward lobes may appear and mutual coupling can greatly increase the backlobes. To address these issues, I optimized a stacked pair of six-element log-Yagis with AO 9.62.

Each log-Yagi has one reflector, three driven elements, and two directors. A shorted stub adds inductance across the rear driven element. Boom length is 90″ and boom spacing is 57″. Red dots mark the 75Ω feedpoints.

This shows phasing line and stub detail. Blue dots mark analysis segments.

Modeling Results

Calculated performance is for 28 analysis segments per element halfwave and phasing line segment length equal to the line spacing. Forward gain includes mismatch and conductor losses. Subtract 0.3 dB to account for the loss of a ferrite power combiner. 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    46.3 + j1.6   1.62     0.25      0.06      8.50     27.52
    89    52.5 + j1.4   1.43     0.14      0.05      8.54     29.03
    90    57.7 + j0.7   1.30     0.07      0.04      8.55     28.41
    91    62.0 - j0.5   1.21     0.04      0.03      8.55     27.99
    92    65.0 - j2.0   1.16     0.02      0.03      8.55     27.80
    93    66.8 - j3.6   1.13     0.02      0.03      8.54     27.42
    94    67.6 - j4.8   1.13     0.02      0.02      8.54     26.97
    95    67.6 - j5.7   1.14     0.02      0.02      8.55     26.79
    96    67.1 - j6.0   1.15     0.02      0.02      8.56     26.84
    97    66.2 - j5.9   1.16     0.02      0.02      8.58     27.07
    98    65.3 - j5.3   1.17     0.03      0.02      8.60     27.46
    99    64.3 - j4.3   1.18     0.03      0.02      8.63     27.93
   100    63.4 - j3.0   1.19     0.03      0.02      8.67     28.40
   101    62.8 - j1.7   1.20     0.03      0.02      8.71     28.08
   102    62.3 - j0.3   1.20     0.04      0.02      8.76     27.77
   103    62.1 + j0.2   1.21     0.04      0.02      8.81     27.37
   104    62.0 - j0.3   1.21     0.04      0.02      8.87     26.95
   105    60.9 - j2.5   1.23     0.05      0.02      8.93     26.64
   106    57.3 - j6.8   1.33     0.09      0.03      8.97     26.56
   107    48.7 - j11.2  1.60     0.24      0.03      8.90     26.79
   108    34.8 - j11.3  2.22     0.67      0.04      8.55     27.44

This illustrates how stacking narrows the main beam, reduces side response, and improves forward gain. Note that it also increases the backlobe.

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. Cross the wires midway between elements over a 1″ span with the wire surfaces separated ⅛″. Support and space the wires at crossover 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 surface of each driven element inner end. Use a lockwasher and nut inside the tubing. Bend the edge of two washers and secure the phasing line between them. 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.

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.

The crossboom can be metallic, but for best pattern use a nonconductive mast section near the antenna. Connect the feedpoints to a power combiner using 75Ω cables of equal length. Install a current balun at each feedpoint. Route the cables on the boom side opposite the phasing lines. Install a current balun immediately after the power combiner and another 30″ down the feedline to help isolate it from vertical fields.

Antenna File

Vertically Polarized Log-Yagi Stack
Free Space Symmetrix	; image antenna has in-phase currents
88 93 98 103 108 MHz
29 6063-T832 wires, inches
r = 33.19663		; reflector half-length
de1 = 30.71209		; boom center to driven-element tips
de2 = 25.40404
de3 = 26.31992
d1 = 25.35208		; director half-lengths
d2 = 23.87683
rp = 0			; element positions
de1p = 24.56485
de2p = 42.19891
de3p = 61.00068
d1p = 68.92586
d2p = 90.30688
sd = 28.56487		; stacking half-distance
p = .5			; phasing line spacing
f = p / 2
s = 2.987003		; stub length
sp = de1p - s
m1b = (de1p + de2p) / 2	; phasing line crossover points
m1a = m1b - f
m1c = m1b + f
m2b = (de2p + de3p) / 2
m2a = m2b - f
m2c = m2b + f
n0 = s / p		; # segments for phasing lines
n1 = (m1a - de1p) / p
n2 = (m2a - de2p) / p
shift y sd
rotate x 90
1      rp   -r  0      rp    r  0   .375
1    de1p    f  0    de1p  de1  0   .375
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
1     d2p  -d2  0     d2p   d2  0   .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
n1   de1p    f  0     m1a    f  0   .1315	; phasing lines
1     m1a    f  0     m1b    0  f   .1315
1     m1b    0  f     m1c   -f  0   .1315
n1    m1c   -f  0    de2p   -f  0   .1315	; 0.1315" in AO yields
n1   de1p   -f  0     m1a   -f  0   .1315	; correct line Z for
1     m1a   -f  0     m1b    0 -f   .1315	; 0.125" wires spaced 0.5"
1     m1b    0 -f     m1c    f  0   .1315
n1    m1c    f  0    de2p    f  0   .1315
n2   de2p    f  0     m2a    f  0   .1315
1     m2a    f  0     m2b    0  f   .1315
1     m2b    0  f     m2c   -f  0   .1315
n2    m2c   -f  0    de3p   -f  0   .1315
n2   de2p   -f  0     m2a   -f  0   .1315
1     m2a   -f  0     m2b    0 -f   .1315
1     m2b    0 -f     m2c    f  0   .1315
n2    m2c    f  0    de3p    f  0   .1315
2    de3p   -f  0    de3p    f  0   .125	; feedpoint jumper
1 source
Wire 29, 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.

Symbol      Tol   Gain    F/R
     r   0.0197   0.00   0.23
   de1   0.0394   0.01   0.13
   de2   0.0394   0.02   0.16
   de3   0.0394   0.00   0.24
    d1   0.0197   0.06   0.28
    d2   0.0197   0.01   0.20
    rp   0.0394   0.00   0.01
  de1p   0.0394   0.00   0.05
  de2p   0.0394   0.08   0.06
  de3p   0.0394   0.04   0.11
   d1p   0.0394   0.00   0.05
   d2p   0.0394   0.00   0.06
    sd   0.0394   0.00   0.04
     p   0.0394   0.23   0.37
     s   0.0394   0.01   0.15

Gallery

Ivan installed this vertically polarized five-element log-Yagi near Pskov, Russia.

Mark erected an earlier version of the ten-element log-Yagi 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.


April 3, 201788108 MHz