Zero Cancellation Synthesis Using Impedance Operators

Through an extension of Richards' theorem, an RLC driving-point impedance function,
Z
, is synthesized by a prescribed, realizable, four-terminal network terminated with another drivingpoint impedance function,
\zeta
, four less in rank than
Z
.
Z
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.