A matrix representation of linear amplifiers

The transfer matrices of linear bilateral and unilateral networks are distinguished by the vanishing of the determinant of the matrix, in the case of the latter, and the non-existence of the matrix of the reversed four-pole. Illustrative examples are given. The voltage gain, current gain, input impedance and output impedance of a four-pole are deduced in terms of the transfer matrix elements. Expressions are developed for the transfer matrices of the four-poles resulting from combining pairs of four-poles, which may be either bilateral or unilateral, in parallel - parallel, in series - parallel and in series - series connection. These expressions are used to obtain the transfer matrices of some passive and active networks, including feedback amplifiers, to illustrate the possibilities of the technique.