Distributed RC Networks with Rational Transfer Functions

A distributed RC circuit analogous to a continuously tapped transmission line can be made to have a rational short-circuit transfer admittance and one rational short-circuit driving-point admittance. A subcircuit of the same structure has a rational open-circuit transfer impedance and one rational open-circuit driving-point impedance. Hence, rational transfer functions may be obtained while considering either generator impedance or load impedance. The functions have poles only along the negative real axis. Although the number of poles is arbitrary, only two may be chosen with complete freedom in a single unit. The realization of a transfer function with many poles may require a number of units either connected in parallel or isolated. Even for a structure with only two poles, there is a considerable saving in the number of interconnections over the lumped circuit. The loss and total capacity required is often the same order of magnitude as those for lumped circuits.