A passive synthesis for time-invariant transfer functions

A passive transfer-function synthesis based upon statespace techniques is presented. The method rests upon the formation of a coupling admittance that, when synthesized by resistors and gyrators, is to be loaded by capacitors whose voltages form the state. By the use of a Lyapunov transformation, the coupling admittance is made positive real, while further transformations allow internal dissipation to be moved to the source or the load. A general class of configurations applicable to integrated circuits and using only grounded gyrators, resistors, and a minimal number of capacitors is obtained. The minimum number of resistors for the structure is also obtained. The technique illustrates how state-variable theory can be used to obtain results not yet available through other methods.