Matching networks using transmission lines

Transmission line derived versions of the 'L', 'PI' and 'T' networks are possible. They allow greater repeatability than those built around coil inductors once the frequency goes beyond 40MHz, as only the line length is variable, other parameters remain fixed. Accurate repeatable power inductors are difficult to construct beyond 30MHz.

A simple transmission line output

This circuit has limited application but should be considered in order to clear up some misconceptions. If the characteristic impedance of the cable matches the generator but not the load then the cable can not match  the load impedance to the generator.

Two things will happen though: The phase of the mismatch will change, to the extent that an open circuit will be transformed into a short circuit. A  mismatch at an unacceptable phase may be transformed into a tolerable one. At extreme lengths the impedance mismatch will be diminished as the cable will attenuate reflected power by an amount that will be twice its loss. 

If the cable can be made to have a different impedance and a length equal to 1/4 wavelength at the working frequency then a transformation is possible. For example a cable 1/4 wave long and 25 ohm will match a 12.5ohm load to a 50 ohm source. This technique is not practical at HF frequencies but can be invaluable at 80MHz and beyond.

The Transmission line 'L' network.

In this variation on the 'L' network the required inductance is provided by the output cable, with the result that the system appears to consist entirely of capacitors. At first glance it appears as if it should not work. 

The configuration will work with a long enough cable. A potential difference may be developed between the ends of the cable shield which may lead to some RF current flowing through the chassis of a system.

The Transmission line 'T' network.

In this variation on the 'T' network the required inductance is provided by the output cable, with the result that the system appears to consist entirely of capacitors. At first glance it appears as if it should not work. 

The configuration will work, however in a T network application the cable is likely to be operating nowhere near its characteristic impedance and so cable losses and leakage will be greater than expected. An appreciable potential difference would be expected between the ends of the cable shield which may lead to RF current flowing through the chassis of a system.