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.