The Beta or Hairpin Match for Antennas

I have been hearing of Gamma Match ever since I attempted homebrewing a VHF Yagi initially and a UHF Yagi subsequently. Gamma Match is meant to match the lowered impedance of a multi-element Yagi compared to a dipole, with a 50 Ohms feedline running to a radio which also has a 50 Ohms impedance. But I came across a Beta Match, which is also known as a Hairpin Match a couple of days back while reading around another topic on antennas. Beta Match is nothing but a shorting stub at the feed point of the driven element in a Yagi antenna, which has the shape of a U or a Hairpin. This is of course, a very simplified explanation of a Beta Match and actual calculation of the size of the Beta Match will depend on the type of balun to be used at the feedpoint, operating frequency as well as conductivity, permeability, diameter, spacing, velocity factor and many other parameters of the Beta Match segment.

Beta Match is in fact a shunt inductance across the transmission line and driven element feed points. To give a matching capacitance, the driven element is shortened a bit to give capacitative reactance at the intended frequency. Beta Match can be made of a segment of transmission line which is shorted at the end opposite the feed point. This gives it a U shape and the other name of Hairpin Match. If the length of the stub is less than a quarter wavelength, the impedance at the open end of the stub will be purely inductive. Length of the stub for a Beta Match can be calculated for the design frequency, using a formula. As in the case of Gamma Match, tuning can be done by adjusting a movable shorting bar which will alter the effective length of the Beta Match segment. Hairpin Match can be used for matching Yagi antennas and end fed vertical antennas. In both cases, the length of the driven element is shortened to give a matching capacitative reactance.