Sensitivity Analysis of Microstrip Tree S-Parameters by Using Tensorial Analysis of Networks

Abstract

This paper introduces a tensorial analysis of networks (TAN) applied to a tree asymmetrical structure. To illustrate the TAN concept easily, the present investigation is applied to a three-port structure represented by a Y-tree topology. The unfamiliar method of TAN circuit modelling is elaborated from the graph topology. The fast formulation of the Y-matrix model of the structure is established from branch and mesh space TAN analyses. The TAN model is validated with commercial tool simulation and measurements from DC up to 0.5 GHz in the frequency domain and two different waveform signals in the time domain. The proof of concept circuit is implemented in microstrip technology on an FR4-epoxy dielectric substrate. Mapping sensitivity analysis with respect to the Y-tree RLC-parameters is realized by showing that local variations around initial set of R, L, and C do not equally influence reflection and transmission coefficients over the frequency bandwidth. If a similar impact is observed at the lowest frequency, maximum variations up to 250% show the importance of parameters ranking to improve both microstrip design and modelling.