Passivity and electric circuits: a behavioral approach

Abstract

We present the element extraction approach to electric circuit analysis and synthesis using the behavioral framework. Explicit descriptions are obtained of the behavior and the driving-point behavior of a general circuit comprising resistors, inductors, capacitors, transformers, and gyrators (an RLCTG circuit). It is shown that the internal currents and voltages are always properly eliminable to obtain a driving-point behavior which is the set of locally integrable (weak) solutions to a linear differential equation. We also review a recently introduced trajectory level definition of passivity, and we show that a behavior is passive if and only if it is the driving-point behavior of an RLCTG circuit.