The Transfer Matrix Method: Analysis of Nonuniform Multiport Systems

A ubiquitous tool in science, physics, and engineering at large, the transfer matrix method (TMM) is particularly suited to deal with complex nonuniform systems (NUS). In the field of electrical engineering, the method is employed in a variety of disciplines that span the electromagnetic spectrum, from power frequencies through RF, millimeter-waves, and terahertz. In this work, three nested goals are pursued. The first is to present a general comprehensive review of the transfer matrix method utilizing two distinct languages: the state space (via the matricant) and the modal analysis (via matrix diagonalization). The second goal, focused on electrical engineering issues, is the application of TMM to the interdisciplinary theme of nonuniform multiconductor transmission lines (MTL) –a good example of a complex reciprocal multiport system. The third goal is to offer the reader novel research results in the context of MTL analysis. Making use of a simple microwave stripline-coupler structure new theoretical results are presented showing that, in some cases, load impedance matching of nonuniform MTLs, using only passive components, may not be physically possible (negative resistors being required), even if the global NUS is longitudinally and transversally symmetric, with or without losses.