15/4 Wavelength Transformer

A wavelength/4 transformer -or (2n+1) wavelength/4 –  is a classical circuit scheme which allow us to match a real impedance to a transmission line (TL). The transformer impedance is the geometric average of the real impedance and the TL impedance. What happens inside the transformer? In the transitory state, an imping wave flows to the transformer. Part of the energy flows to the load, and part goes back to the generator, that is a backward wave does exist inside the TL (t=6s). The wave inside the transformer arrives the load and part of it returns to the TL (t=14s). During this time, a quasi-standing wave is made in the TL. But at t=24s, the backward wave from the load “compensates” the reflection from the transformer, and a flowing wave is formed in the TL, that is, in the steady state, all the energy that comes from the generator goes to the transformer, and it will be consumed in the load.


Standing Waves in a Transmission Line

These three videos show the behavior of a standing wave.  In this first one we can see a perfect standing wave. This wave is produced as a sum of two waves of the same amplitude, flowing in the same direction but in opposite sense. You can observe that there are positions where the wave amplitude is always zero and also, that there are instants that the amplitude is zero everywhere.

A voltage standing wave can be generated when a transmission line ended in a pure imaginary load, as for example a short circuit:

It is easy to realize that it is a short circuit, because the voltage is equal to zero at the end.

What happens if these waves have different amplitude? This is the general case, when a transmission line is ended in an arbitrary load:

We can see that a wave is flowing towards the positive sense. Also, a backward wave with lower amplitude is flowing in the line. The sum of both waves produce a net flux of energy toward the positive sense and also standing wave.