﻿ Impedance Transformation with Quarter-Wave Lines

# ARCTICPEAK

### ~ LA8OKA Martin ~

Quarter-wave transformer

# Impedance Transformation with Quarter-Wave Lines

The input impedance of a line an odd multiple of λ/4 long is where Zi is the input impedance and ZL is the load impedance. If ZL is a pure resistance, Zi will also be a pure resistance. Rearranging this equation gives This means that if we have two values of impedance that we wish to �match,� we can do so if we connect them together by a λ/4 transmission line having a characteristic impedance equal to the square root of their product. A λ /4 line is, in effect, a transformer, and in fact is often referred to as a quarter-wave transformer. It is frequently used as such in antenna work when it is desired, for example, to transform the impedance of an antenna to a new value that will match a given transmission line.

You can easily construct your own transmission lines with a suitable impedance to be used in a Quarter-wave transformer. This page tells you how to construct your own transmission line with the impedance you want:
Construction of air insulated transmission lines

When constructing a quarter-wave impedance transformer it is important to know the velocity factor of the transmission line to get the lenght of the quarter-wave impedance transformer right.

To calculate the quarter wave length of a certain transmission line with a known velocity factor and frequency you may use this calculator. Calculation of input impedance of a Quarter-wave transformer: Quarter-wave transformer impedance (Zo): Enter Value Output impedance (ZL): Enter Value Input impedance (Zi): Calculated Calculation of output impedance of a Quarter-wave transformer: Quarter-wave transformer impedance (Zo): Enter Value Input impedance (Zi): Enter Value Output impedance (ZL): Calculated Calculation of transformer impedance of a Quarter-wave transformer: Input impedance (Zi): Enter Value Output impedance (ZL): Enter Value Quarter-wave transformer impedance (Zo): Calculated Calculation of Quarter-wave stub lenght: Frequency (MHz): Enter Value Velocity factor: Enter Value Length of Quarter-wave stub (m): Calculated Length of Half-wave stub (m): Calculated Wave length in the transmission line (m): Calculated Wave length in free space (m): Calculated The velocity factor of RG-58, RG-59, RG-174, RG-213 and RG-214 is 0,66. The velocity factor of an open uninsulated wire is 0,95. Other transmission lines have other velocity factors.