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.