In some applications (e.g. ), 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 , 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  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) [3,4]. 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
The transformer-normalized DWF junction is shown in Fig.4a. We can now modulate a single junction, even in arbitrary network topologies, by inserting a transformer immediately to the left or right of the junction. Conceptually, the wave impedance is not changed over the delay-line portion of the waveguide section; instead, it is changed to the new time-varying value just before (or after) it meets the junction. When velocity is the wave variable, the coefficients and in Fig.4a are swapped (or inverted).
So, as in the normalized waveguide case, for the price of two extra multiplies per section, we can implement time-varying digital filters which do not modulate stored signal energy. Moreover, transformers enable the scattering junctions to be varied independently, without having to propagate time-varying impedance ratios throughout the waveguide network.
It can be shown  that cascade waveguide chains built using transformer-normalized waveguides are equivalent to those using normalized-wave junctions. Thus, the transformer-normalized DWF in Fig.4a and the wave-normalized DWF in Fig.4b are equivalent. One simple proof is to start with a transformer and a Kelly-Lochbaum junction, move the transformer scale factors inside the junction, combine terms, and arrive at Fig.4b. One practical benefit of this equivalence is that the normalized ladder filter (NLF) can be implemented with only three multiplies and three additions instead of four multiplies and two additions.