Passive reciprocal state-space synthesis using a minimum number of resistors

The paper presents a state-space synthesis of multiport passive reciprocal networks using a minimum number of resistors. The method relies on a Gauss-factorisation procedure similar to Bayard´s classical synthesis procedure. After a brief review of state-space formulation of the synthesis problem, a construction of a state-space realisation for a prescribed symmetric impedance is developed with the aid of a Gauss factorisation. The realisation constructed is nonminimal in general, but it is passive and used a minimal number of resistors. The constraint on the Gauss factorisation imposed by symmetry is then examined and interpreted in state-space terms to give a reciprocal synthesis.