Conjugate Image Impedance Of Lossless or Low-loss Two-Port System with Desired Phase Shift and Application to Transmission Line and Impedance Matching Theory

This work proposes the concept of an optimal port impedance, also known as the conjugate image impedance, of a two-port network. The optimum port impedance of a two-port network is defined in terms of the ABCD parameters of the network. The optimum port impedance is obtained by considering that both the source and load sides' conjugate matching holds. It has been shown that a lossless reciprocal network has an infinite set of port impedances. In contrast, a lossy network has a unique set of port impedances. It has been shown that if both ports of a two-port network are matched, maximum power can be transferred through the network. A closed-form expression of the port impedance of the lossy transmission line is given. In a lossless two-port network, a unique set of port impedances for the desired phase shift can be obtained for a given source or load angle. The desired phase shift in a low-loss network can be obtained by selecting the port impedance based on the reactive part of the network.