Designing a Gamma Match – Simsmith design tool and confirmation of as-built antenna posted a Simsmith design tool to assist in designing a Gamma Match.
Let’s walk through an example.
Above is an example for discussing the Gamma Match. In this case, the assumed feed point impedance of a simple split dipole feed is 17+j2Ω, and the challenge is to design a practical Gamma Match to match it to 50+j0Ω.
The design tool assumes that the connections to the open circuit stub are at the feed point, ie that the gap in the gamma arm outer is at the inboard end. There are other ways to build a gamma match and the model may not suit them without tweaking.
It can be approximated as three distinct steps of impedance transformation:
- impedance transformation by virtue of the parallel dipole conductor and gamma conductor, the diameters of each and their spacing are used in the calculation;
- shunt short circuit stub formed by the gamma arm and dipole conductor; and
- series open circuit stub.
Step 1 is the transformation due to two parallel conductors with mutual inductance and self inductance, immersed in an approximately uniform electric field. The ratio of the current in both (in common) to the current in the gamma arm sets up Step 1 of the transformation. Choose practical values for Dood, Gdia, and Gspa to get a transformed G of <0.02, the example above uses 0.0117.
Step 2 is the transformation due to the shunt short circuit stub. Choose practical values for Ciod and Coid (the dimensions of the coaxial line so formed) and adjust its length so the the magenta arc just intersects the R=50 circle.
Step 3 is the transformation due to the series open circuit stub. Set the VF2 and stub length to land on the chart centre, 50+j0Ω.
This can be an iterative process, especially for instance if the length of the open circuit stub is greater than the length of the short circuit stub. Optimisation may involve changing some of the Step 1 parameters to stage for easier transformations in Steps 2 and 3.