The Transfer Matrix Method: Analysis of Nonuniform Multiport Systems

Abstract

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.

Analysis of a nonuniform guiding structure by the adaptive finite‐difference and singular value decomposition methods

“…Note that there is no exact solution for the catenary TL. Figure 5 shows the magnitude and phase of the calculated voltage and current versus frequency and position from the proposed and TMM methods in [23]. There is excellent agreement between the results of the proposed and theoretical approaches.…”

A new method for analyzing non-uniform guiding structures

“…The analytical solution of the catenary TL is not available. However, the catenary TL can be analyzed using the Transfer Matrix Method (TMM) 23 or UCS technique with excellent accuracy. The magnitude and phase of the calculated V ( x ) and I ( x ) using the proposed and TMM/UCS method are shown in Fig.…”

Investigation of n-ZnO/p-Si and n-TiO2/p-Si Heterojunction Solar Cells: TCAD + DFT

“…Only, when modeling the solar cell, it is necessary to take into account the effect of light. Ray Tracing [54], Transfer Matrix Method (TMM) [55] and Beam Propogation [56] methods are widely used for optical modeling of solar cells. In this paper, the optical modeling was performed using the TMM method.…”