The Normalized Lossless Junction

In some applications it is worthwhile to normalize the traveling waves so that all waveguides effectively have unit impedance, ${{\mbox{\boldmath$R$}}(z)} = {\mbox{\boldmath$I$}}$. To normalize, pressure waves are multiplied by a (matrix) square root of the wave admittance, and velocity waves are multiplied by a (matrix) square root of the wave impedance. Conservation of power at a lossless junction implies that the signal dynamic range is conserved in a mean square sense for normalized waves. This can be very useful in fixed-point implementations of large networks, especially in the time-varying case, since signal scaling problems are avoided and the full dynamic range can be achieved at every point of the network. Normalized waveguide networks can be seen as a generalization of the normalized ladder filter [35].