Active Distributed RC Realization of Low-Pass Magnitude Specifications

This paper introduces a design method that allows one to find easily an active distributed
RC
network transfer function whose magnitude approximates the magnitude of a specified lumped low-pass transfer function. The resulting distributed
RC(\overline{RC})
transfer function is a product of simple transfer functions rational in
P = \cosh \sqrt{sRC}
, each using a different
RC
product. The overall transfer function is then realized as a cascade of the realizations of the simple transfer functions using a variety of available synthesis techniques. In addition, the characterization of a distributed
RC
transfer function as a lumped transfer function times a delay factor, as presented herein, permits easy calculation of the transient response of the network. An example of the magnitude approximation is given together with the phase correction made by adding a delay term.