OVERVIEW

The study of coupled TEM or quasi-TEM transmission lines is important in microwave and digital electrical engineering. Traditionally, coupled transmission lines have been extensively used in RF circuits to design directional couplers and electric filters ^{[1] [3]}. Directional couplers implemented using rectangular waveguides were an extremely useful tool for microwave engineers because of their unique property of separating forward- and backward-traveling waves. Perhaps the most important device made using directional couplers was the reflectometer, which enabled the invention of many important devices such as power detectors and network analyzers.

The coupling theory developed by physicist Hans Albrecht Bethe during his brief appointment in the radiation laboratory at the Massachusetts Institute of Technology during World War II, explaining the coupling mechanisms through small apertures between two waveguides, was the first rigorous way of designing waveguide directional couplers. Although rectangular waveguides were extensively used in designing directional couplers, TEM structures, such as coaxial lines, were also employed ^[1]. Then, as the development of printed circuits advanced, printed TEM or quasi-TEM structures started to be used extensively in designing directional couplers, although for very high-power applications hollow waveguides were still employed. The fast development of printed circuit technology eventually enabled compact and cost-effective designs of filters in microstrip or stripline structures. Microwave filter design using coupled lines also has a very well-established theory in RF and microwave engineering ^{[4] [7]}. The book by Matthaei, Young, and Jones has been a classic reference for electrical engineers in this...