Generalized Series–Parallel $RLC$ Synthesis Without Minimization for Biquadratic Impedances

This brief is concerned with the realization problem of biquadratic impedances, motivated by the recent development in passive mechanical control. This brief generalizes a realization procedure of a special class of biquadratic impedances to a more general form, and the resulting series-parallel
RLC
networks whose elements are no more than those in Bott-Duffin's networks are obtained without minimization. The realizability condition is proven by providing a constructive synthesis procedure. The series-parallel network obtained contains elements no more than those of Bott-Duffin's network when the impedance is nonregular.