Generalized Series–Parallel 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.