Power-Normalized Waveguide Filters

Above, we adopted the convention that the time variation of the wave impedance did not alter the traveling force waves . In this case, the power represented by a traveling force wave is modulated by the changing wave impedance as it propagates. The actual power becomes inversely proportional to wave impedance:

In some applications (e.g. [439]), it may be desirable to compensate for the power modulation so that changes in the wave impedances of the waveguides do not affect the power of the signals propagating within.

In [441], three methods are discussed for making signal power invariant with respect to time-varying branch impedances: (1) The normalized waveguide scheme compensates for power modulation by scaling the signals leaving the delays so as to give them the same power coming out as they had going in. It requires two additional scaling multipliers per waveguide junction. (2) The normalized wave approach [301] propagates rms-normalized waves in the waveguide. In this case, each delay-line contains and . In this case, the power stored in the delays does not change when the wave impedance changes. This is the basis of the normalized ladder filter (NLF) [176,301]. Unfortunately, four multiplications are obtained at each scattering junction. (3) The transformer-normalized waveguide approach to normalization changes the wave impedance at the output of the delay back to what it was at the time it entered the delay using a ``transformer.''

A transformer 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, and from the definition of power waves, we see that to bridge an impedance discontinuity with no power change and no scattering requires the relations

Therefore, the junction equations for a transformer [34] can be chosen as

where