Mesh analysis for extracting the S-parameters of lumped element RF and microwave circuits

Abstract

This paper demonstrates the applicability of basic mesh current circuit analysis techniques, usually learned in the first year of engineering studies, to lumped element RF circuits, which are usually taught with more sophisticated analysis techniques. As an example, the S-parameters of the 90° lumped element hybrid coupler is derived using the traditional mesh current analysis, and compared to that of the distributed micro-strip response. The distributed transmission line coupler is transformed into equivalent lumped element PI sections, and then combined for the resulting lumped element coupler. Mesh current analysis is then utilized to demonstrate the equivalence between the lumped element coupler and the micro-strip coupler as well as the ability to easily simulate the effects of finite inductor Q on the circuit's performance.