RC and RL to LC circuit conversion, and its application in poles and zeros identification

Abstract

A new technique is presented to convert an RC or RL circuit to its corresponding LC circuit. It is shown that while this conversion keeps the coefficients of a transfer function unaltered, it maps the roots (poles and zeros) of the transfer function to desirable locations for further processing. The technique provides different results for different types of (real, imaginary, and complex) roots on the s-plain, which in fact lends itself to identifying and even extract the circuit roots directly from a Bode plot. Some applications of the methodology with examples are given to demonstrate the capability of the technique.