Questions of minimality in RLC circuit synthesis

Abstract

It is well known that the impedance of a passive circuit is necessarily positive-real.The Bott-Duffin procedure shows that any positive-real function has an RLC realisation, possibly with the number of reactive elements (inductors and capacitors) greatly exceeding the McMillan degree. It was recently shown that, for series-parallel circuits, that the Bott-Duffin procedure is minimal in the number of reactive elements (six) for the biquadratic minimum function. For general circuits, the best available result is the Reza-Pantell-Fialkow-Gerst simplification, published simultaneously in the 1954 papers, which reduces the number of reactive elements to five for the general biquadratic minimum function. In this extended abstract, we present an additional class of equivalent circuits which have not appeared previously in the literature. In the accompanying talk, we will show the remarkable result that the Reza-Pantell-Fialkow-Gerst simplification produces circuits which contain the least possible number of reactive elements for the realisation of certain biquadratic minimum functions.