The Realization of the A-Matrix of a Certain Class of RLC Networks

Necessary and sufficient conditions for a matrix to be realizable as the A-matrix of an RLC network are developed. The RLC network is assumed to have no cut-set of inductors, no circuit of capacitors, and is assumed to have a connected resistive part. It is shown that if there exists a realization then the given matrix A can be factored into two matrices: one, a diagonal matrix of positive entries, and the other a symmetric-skew-symmetric (hybrid) matrix. The former determines directly the values of capacitances and inductances in the network. A technique is given by which the terminal matrix of the resistive part and the fundamental circuit matrix of the reactive part can be obtained from the other factor. It is shown that the given matrix A has a realization with a half-degenerate RLC network which has a connected resistive part if and only if the factorization exists and both the terminal matrix and the circuit matrix are realizable with the same terminal tree.