Extraction of Poles and Zeros of an $RC$ Circuit With Roots on the Real Axis

A graphical/numerical technique is presented for the extraction of roots (poles and zeros) of an RC circuit, where the roots lay on the left-hand side of the real axis (RLHP) in the s-plane. The method constructs a corresponding LC circuit for the RC circuit and, as shown, all the RLHP roots in the RC circuit are shifted to the jω axis, where the swiping-frequency signals exist. It is also shown that the magnitude of the corresponding roots in the two circuits are related by a scaling factor. The technique is also extended to study the behavior of real-axis RHP roots in RC circuits. Several examples demonstrate the performance of the proposed technique.