### 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 signal power becomes inversely proportional to wave impedance:*invariant*with respect to time-varying branch impedances:

- 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. - The
*normalized wave*approach [297] 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) [174,297]. Unfortunately, four multiplications are obtained at each scattering junction. - The
*transformer-normalized waveguide*approach 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'' (defined in §C.16).

*equivalent*to those using normalized-wave junctions. Thus, the transformer-normalized DWF in Fig.C.27 and the wave-normalized DWF in Fig.C.22 are equivalent. One simple proof is to start with a transformer (§C.16) and a Kelly-Lochbaum junction (§C.8.4), move the transformer scale factors inside the junction, combine terms, and arrive at Fig.C.22. One practical benefit of this equivalence is that the normalized ladder filter (NLF) can be implemented using only three multiplies and three additions instead of the usual four multiplies and two additions. The transformer-normalized scattering junction is also the basis of the

*digital waveguide oscillator*(§C.17).

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Reflectance of an Impedance

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Conventional Ladder Filters