Zero Cancellation Synthesis Using Impedance Operators

Abstract

Through an extension of Richards' theorem, an RLC driving-point impedance function, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z</tex> , is synthesized by a prescribed, realizable, four-terminal network terminated with another drivingpoint impedance function, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\zeta</tex> , four less in rank than <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z</tex> . <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z</tex> is completely arbitrary except that it may not have a pole or a zero at the origin or infinity. The initial four-terminal network consists of a capacitor, a perfectly-coupled transformer, and an ideal gyrator. Other equivalent networks are derived which do not require transformers and gyrators but in which the cascade nature of the synthesis is lost.