Designing a Gamma Match – confirmation of as-built antennas was based on some online calculators to provide key values to a Simsmith model of a Gamma Match.
This article provides an updated Simsmith model that incorporates the necessary calculations (ie without depending on external calculators).
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.
Above, the 1970 build pictured in 2023.
The design will be reviewed using the method set out at Designing a Gamma match using a Smith chart.
Simsmith model
The Simsmith model defines some key parameters in the Parameters element:
- Dood: outside diameter of the dipole tube;
- Gdia: outside diameter of the gamma tube;
- Gspa: centre to centre spacing of dipole and gamma tubes;
- Ciod: outside diameter of inside conductor of capacitive stub;
- Coid: inside diameter of outside conductor of capacitive stub; and
- VF2: velocity factor of capacitive stub.
The Parameters element calculates some intermediate values and populates fields of the following elements.
Above is the solution of the example 144MHz 4el gamma matched Yagi.
The lengths of the gamma arm and series sections reconcile well with the built and adjusted antennas.
The Simsmith file is here: GammaArm144Yagi.7z .