Realization of the A-Matrix of Halfdegenerate Rlc Networks

摘要

The 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 be nondegenerate or half-degenerate and is assumed to have a connected resistive part. First 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-skewsymmetric (hybrid) matrix. It is shown that the given matrix A has a realization with a half-degenerate or non-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. It is also shown that for a certain factorization if a realization exists, then the reactive part is unique within two-isomorphism and the resistive part can always be reduced to a complete polygon in general. In an appendix, a way of writing the A-matrix by inspection in the active half-degenerate RLC case is given and the necessary and sufficient conditions that the order of complexity be equal to the number of reactive elements in the network are developed. (Author)