Another way to define the ideal waveguide transformer is to ask for a two-port element that joins two waveguide sections of differing wave impedance in such a way that signal power is preserved and no scattering occurs. From Ohm's Law for traveling waves (Eq.(6.6)), and from the definition of power waves (§C.7.5), we see that to bridge an impedance discontinuity between and with no power change and no scattering requires the relations
Therefore, the junction equations for a transformer can be chosen as
The dualizer is readily derived from Ohm's Law for traveling waves:
In this case, velocity waves in section are converted to force waves in section , and vice versa (all at wave impedance ). The wave impedance can be changed as well by cascading a transformer with the dualizer, which changes to (where we assume ). Finally, the velocity waves in section can be scaled to equal their corresponding force waves by introducing a transformer on the left, which then coincides Eq.(C.123) (but with a minus sign in the second equation).