Theory on Matching Network in Viewpoint of Transmission Phase Shift

In this paper, the concept of the transmission phase shift of an impendance-matching network (IMN) has been introduced. The generalized two-port network parameters of the matching circuit, which matches an arbitrary complex load to a different complex source impedance incorporating the transmission phase, has been derived. In general, the IMNs are electrically asymmetric; however, there exist only two distinct values of phase shifts (180° apart) for a given source and load impedance for which the networks are symmetric, irrespective of the choice of design topology. Simple examples of symmetric matching networks like single and parallel transmission lines (TLs) have been studied. The design equations of several asymmetric matching networks like the stepped-impedance, the $\Pi $ -type, and the T-type network for a given load and source impedance with desired phase shift have been derived. The concepts of allowed and forbidden regions for such matching circuits, in the impedance phase-shift plane, have been established. Two prototype impedance transformers have been fabricated and measured to establish the proposed concept.