Capacitance and resistance minimization in one-port RC networks

Abstract

A complete topological characterization is given for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RC</tex> networks that realize an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RC</tex> driving-point impedance with minimum total capacitance or resistance. In particular, it is shown that for a constant input voltage, maximizing the steady-state capacitor voltages minimizes the total capacitance, and for a constant input current, maximizing the steady-state resistor currents minimizes the total resistance. It then follows that one of the Foster canonical forms is a minimum total capacitance structure and the other is a minimum total resistance structure. Explicit formulas for the minimum total capacitance and resistance are given.