Impedance and matching

More than one number in ohms

ImpedanceImpedance×Impedance is complex opposition to alternating current: it includes resistance and a frequency-dependent reactance. Antenna input impedance is therefore more than a DC resistance reading.Example & full explanation → is written Z = R + jX. R is resistance and X reactance. In the usual convention, positive X is inductive and negative X capacitive. Two loads with the same impedance magnitude can therefore behave differently on a line.

Resonance means X = 0 at the reference plane being considered. A resonant 100 Ω load is still not matched to a 50 Ω line. Conversely, a matching network can present a suitable impedance at the transmitter even when the antenna feed point itself has reactance.

A narrowband transformer

An ideal lossless quarter-wave line transforms a resistive load according to Zin = Zt²/Rload. To join 50 and 100 Ω it therefore needs Zt = √(50·100) ≈ 70.71 Ω. Physical length then depends on frequency and velocity factor. Both characteristic impedance and length are part of the solution.

The quarter-wave condition applies at the design frequency and corresponding recurring electrical lengths. Changing frequency changes the transformation. The calculator assumes purely resistive terminations; entering the magnitude of a complex antenna load is not a valid substitute.

Always identify the reference plane

A measurement at the radio includes the feed line’s effect. A measurement directly at the antenna connector observes a different plane. Calibrate suitable equipment at the intended plane or account for the line with an appropriate model. Otherwise the same antenna may appear to have different impedances merely because the measurement location changed.