How to Find Wave-Scattering Parameters from the Causal Bond Graph Model of a High Frequency Filter

Abstract

Problem statement: The aim of this study is to use the bond graph technique and the wave-scattering formalism, jointly, to determine the scattering matrix of a high frequency filter with cut-off frequency 10 GHz. Approach: The first step consist to model the high frequency filter by bond graph approach, afterward, we decomposed the obtained causal bond graph model under an elementary structures of a cascaded sub-model, where, each one containing only 0-junction (parallel admittance) and 1-junction (series impedance). The causal ways and algebraic loops present in each causal bond graph sub-model, allows us to derive the elementary wave matrix W(i) of each sub-model. Results: The total or global wave matrix W(T) of the high frequency filter is given by the product of all elementary wave matrixes W(i). Conclusion: The scattering matrix S of the studied filter can be inferred by use of the founded wave matrix W(T) which relates the incident and reflected waves at one port directly to the incident and reflected waves at the adjacent port and the relations linking the S coefficients to the W coefficients. Finally, the scattering parameters, founded from the wave matrix, will be checked by comparison of the simulation results.