The hybrid matrix in linear multiple-loop feedback networks

This paper presents the relationship between the determinant of the hybrid matrix and that of the conventional cutset-admittance or loop-impedance matrix. It is shown that the determinant of the return-difference matrix can be elegantly and compactly expressed as the ratio of the two functional values assumed by the determinant of the hybrid matrix under the condition that the elements of interest assume their nominal and reference values. The significance of the present approach is that it avoids the necessity of interpreting the loop gain in terms of the actual signal transmission around the closed loops in a signal-flow graph.