A complete multimode equivalent-circuit theory for electrical design

Abstract

This work presents a complete equivalent-circuit theory for lossy multimode transmission lines. Its voltages and currents are based on general linear combinations of standard normalized modal voltages and currents. The theory includes new expressions for transmission line impedance matrices, symmetry and lossless conditions, source representations, and the thermal noise of passive multiports.

Traveling Waves and Power Waves: Building a Solid Foundation for Microwave Circuit Theory

“…I suggest that you then look through [4] and [5] to find out more about how the theory can address lossy printed transmission lines. You might also look at [6] if you fancy lossy multimode transmission lines.…”

Planar Directional Couplers and Filters

“…With the results from 2D EM Eigenmode analysis as a starting point, the modal impedance Z mt = Z m and scattering S mt = S m matrices of uniformly 1 coupled asymmetric lines are derived [1,2]. The nonuniform case is covered by cascading a sufficiently high number of short uniform lines.…”

A Thru-Only De-Embedding Method Foron-Wafer Characterization of Multiport Networks

“…This development naturally leads to the idea that the same de-embedding method should be applicable to 2n-ports, where n is a positive integer, provided that the S-matrix of the THRU (n coupled nonuniform TLs) can somehow be blockdiagonalized with 2 × 2 diagonal blocks ). Modal analysis of multiconductor transmission lines (MTLs) have been a subject of intensive study for decades (Faria, 2004;Kogo, 1960;Paul, 2008;Williams et al, 1997). MTL equations are typically written in terms of per-unit-length equivalent-circuit parameters.…”