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:
In some applications (such as timevarying waveguide reverberation [434]), it may be preferable 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 [436,437], three methods are discussed for making signal power invariant with respect to timevarying branch impedances:
The transformernormalized DWF junction is shown in Fig.C.27 [436]. As derived in §C.16, the transformer ``turns ratio'' is given by
We can now modulate a single scattering 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 delayline portion of the waveguide section; instead, it is changed to the new timevarying value just before (or after) it meets the junction. When velocity is the wave variable, the coefficients and in Fig.C.27 are swapped (or inverted).

So, as in the normalized waveguide case, for the price of two extra multiplies per section, we can implement timevarying digital filters which do not modulate stored signal energy. Moreover, transformers enable the scattering junctions to be varied independently, without having to propagate timevarying impedance ratios throughout the waveguide network.
It can be shown [437] that cascade waveguide chains built using transformernormalized waveguides are equivalent to those using normalizedwave junctions. Thus, the transformernormalized DWF in Fig.C.27 and the wavenormalized DWF in Fig.C.22 are equivalent. One simple proof is to start with a transformer (§C.16) and a KellyLochbaum 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 transformernormalized scattering junction is also the basis of the digital waveguide oscillator (§C.17).