E9E: Impedance Matching

Connecting a transmitter to an antenna efficiently requires matching their impedances. Mismatches cause reflections that reduce power transfer and can damage transmitters. Several matching systems have been developed for specific antenna configurations.

This lesson covers the gamma match, beta (hairpin) match, stub match, delta match, T-match, quarter-wave Q-section, reflection coefficient, Wilkinson divider, shunt feeding a grounded tower, and phasing lines for pattern control.

Gamma Match

The gamma match connects the coaxial cable shield to the center of the antenna element and the center conductor to a point a fraction of a wavelength to one side, through a series capacitor. The series capacitor cancels the unwanted inductive reactance introduced by the gamma rod. Because the driven element does not need to be split or insulated at the center, the gamma match is compatible with elements that are electrically connected to the boom — and it is also the technique used to shunt feed a grounded tower at its base.

Beta (Hairpin) Match

The beta or hairpin match is used when the Yagi's driven element is insulated from the boom (a requirement for this match). It requires the driven element to present a capacitive feed point impedance — meaning the driven element must be made electrically shorter than 1/2 wavelength. The hairpin is a short shunt inductor (a U-shaped wire or rod) connected across the feed point that resonates with the element's capacitive reactance and transforms the resulting resistive impedance to 50 ohms.

Stub Match

A stub match uses a short length of transmission line connected in parallel with the feed line at or near the feed point. By choosing the stub's length and whether its far end is open or shorted, the stub presents a specific reactive impedance that cancels the antenna's feed point reactance, leaving a purely resistive load for the transmission line.

Quarter-Wave Q-Section

A quarter-wave Q-section (also called a quarter-wave transformer) is a transmission line section that transforms impedance. The required characteristic impedance of the Q-section is:

Z_Q = √(Z_source × Z_load)

Reflection Coefficient

The reflection coefficient is the parameter that describes the interaction of a load and a transmission line. It quantifies what fraction of the forward-traveling wave is reflected back toward the source when the line's characteristic impedance does not match the load impedance. The reflection coefficient (Γ) ranges from 0 (perfect match, no reflection) to 1 (total reflection, complete mismatch). SWR is related to the reflection coefficient by: SWR = (1 + |Γ|) / (1 − |Γ|).

Wilkinson Divider

A Wilkinson divider is a power-splitting network that divides input power equally between two 50-ohm loads while maintaining 50-ohm input impedance. Unlike a simple T-junction, the Wilkinson divider also provides isolation between its two output ports, preventing signals entering one output from appearing at the other. It is widely used in antenna arrays and combiner networks.

Shunt Feeding a Grounded Tower

A grounded tower can be used as a vertical antenna on HF bands by shunt feeding it at the base with a gamma match. The gamma rod connects from the coax center conductor to a point up the tower, with the coax shield connected to the tower base (ground). The series capacitor in the gamma match tunes out the inductive reactance.

Phasing Lines

When multiple driven elements are connected through phasing lines, the purpose is to control the antenna's radiation pattern. By selecting phasing line lengths to produce specific phase differences between elements, the antenna array can be made to favor certain directions, produce nulls in others, or steer the main lobe. This is the fundamental principle behind phased vertical arrays, directional AM broadcast antennas, and steerable antenna systems.

E9E Practice Questions