Much is written about the virtue of the Gamma Match, and near as much about how they work, and the difficulty in design and implementation.
Designing a Gamma match using a Smith chart showed a design method for a simple Gamma Match using a Smith chart as the design tool.
This article visits the implementation on a pair of antennas that I built 50 years ago, and are still in use today (albeit with some small preventative maintenance once during that interval). The basic antenna is a four element Yagi for 144MHz copied from an ARRL handbook of the time, probably based on NBS 688. It was designed to deliver a split dipole feed point impedance of 50+j0Ω.
I built them using a Gamma Match, partly to get some familiarity, but mostly to implement a Gamma Match that was reliable, weatherproof and lasting… features that are alien to most implementations I had seen at that point.
Both antennas were constructed and the Gamma Match adjusted for VSWR<1.1 using a Bird 43 directional wattmeter. The dimensions of each (including the key gamma dimensions) are the same, not surprising, but a confirmation of repeatability. See Novel Gamma Match Construction for more discussion.
Above is a dimensioned drawing of the construction.
The design will be reviewed using the method set out at Designing a Gamma match using a Smith chart.
Smith chart method
We can calculate the Zo of the series coaxial section.
Parameters | |
Conductivity | 5.800e+7 S/m |
Rel permeability | 1.000 |
Inner diameter | 0.00650 m |
Outer diameter | 0.00880 m |
Velocity factor | 0.750 |
Loss tangent | 0.000e+0 |
Frequency | 144.000 MHz |
Length | 0.060 m |
Zload | 1.000e+100+j0.000e+0 Ω |
Yload | 0.000000+j0.000000 S |
Results | |
Zo | 13.62-j0.03 Ω |
Velocity Factor | 0.7500 |
Length | 13.834 °, 0.038427 λ, 0.060000 m, 2.669e+2 ps |
Line Loss (matched) | 5.10e-3 dB |
Line Loss | >100 dB |
Efficiency | ~0 % |
Zin | 5.374e-3-j5.532e+1 Ω |
Yin | 1.756e-6+j1.808e-2 S |
We can calculate the Zo of the two wire line section.
Parameters | |
Conductivity | 5.800e+7 S/m |
Rel permeability | 1.000 |
Diameter | 0.012000 m |
Spacing | 0.038000 m |
Velocity factor | 1.000 |
Loss tangent | 0.000e+0 |
Frequency | 10.000 MHz |
Twist rate | 0 t/m |
Length | 100.000 m |
Results | |
Zo | 218.49-j0.11 Ω |
Velocity Factor | 1.0000 |
Length | 1200.831 °, 3.335641 λ, 100.000000 m, 3.336e+5 ps |
Line Loss (matched) | 9.18e-2 dB |
If the conductors were not equal diameter, Folded dipole step up ratio calculator can be used to calculate Zo and the step up ratio.
A solution using the Smith chart for a near ideal match of a nominal 50+j0Ω antenna to 50+j0Ω using the Gamma Match and the calculated Zo for both line sections is as follows.
The lengths of the gamma arm and series sections reconcile well with the built and adjusted antennas.