Impedance synthesis via state-space techniques

Abstract

The paper deals with the synthesis of passive networks and relies on general systems theory and control concepts. The network-synthesis problem is first interpreted in state-variable terminology, solved as a control problem and the solution is then translated back into network-theory terms. After a review of state-space formulations, an algebraic theory of synthesis is developed, beginning with a minimal state-space realisation, perhaps obtained through control-theory procedures, from which a synthesis of rational positive-real impedance matrices is obtained through a transformation on the state. The method rests upon an appropriate basis change, in the state-space, obtained by factoring the Pmatrix of the control-theory positive real lemma. The minimum number of resistors and reactive elements is used. The paper also serves as a review of the ‘state-of-the-art’ for formal nport synthesis; the results lead to new methods of attacking open problems, as well as to methods of analysis and synthesis via digital computers.