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.
Highlights
The wave-scattering formalism (Paynter and Busch-Vishniac, 1988) has received great attention in microwave domain (Vendelin et al, 2005) and its application to low or high frequency circuits
We propose to use the causal bond graph model of a high frequency filter based on localized elements (Trabelsi et al, 2003) to find the integro-differentials operators (Khachatryan and Khachatryan, 2008) which based on the causal ways and algebraic loops present in the causal bond graph model and, on the other side, to extract the wave matrix (Magnusson et al, 2001) from these operators
Associated to a physical system, we showed the existence of an ideal structure junction of Kirchhoff (c) which includes a junction with common effort and flow known as a decomposition junction
Summary
The wave-scattering formalism (Paynter and Busch-Vishniac, 1988) has received great attention in microwave domain (Vendelin et al, 2005) and its application to low or high frequency circuits. The use of this scattering formalism, which intrinsically deals with causal relations and can explicitly include conservation laws, was advocated by Paynter (1992) as an alternative method for physical systems modeling. The propose of this study is to present and apply a new method to derive the scattering parameters of a high frequency filter from its causal and reduced bond graph model (Taghouti and Mami, 2009). We extract directly the scattering parameters (Newton, 2002) from the found wave matrix (Magnusson et al, 2001) by basing on the relations linking the S coefficients to the W coefficients
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