RC admittance matrix realization by linear transformation

The problem of realizing an
RC
admittance matrix with a transformerless grounded
RC
network by linear transformation called Howitt transformation is studied. A new procedure for determining each element of the transformation matrix from the minimal realization of a given
RC
admittance matrix is presented. The positive inverse property of
M
-matrices and orthogonal matrices of a particular class play an important role there. The final results are summarized in Theorem 5 in Section IV-F. Theorem 5 makes clear the relation between the Howitt transformation matrix and the coefficient matrices of the minimal realization of a given
RC
admittance matrix, and provides us a new systematic synthesis method of the transformerless grounded
RC
networks. Based on Theorem 5, two numerical examples illustrate how to realize an
RC
admittance matrix by Howitt transformation.