Abstract
Problem statement: Further to research works made previously and which use collectively the scattering formalism and bond graph technique for the modeling of a physical systems often working in high frequencies, we propose, in this article, a comparative study (discussion) for the scattering matrix realization of a high-frequency physical system. Approach: This discussion is based, on the one hand, on a non-causal (acausal) bond graph model which represents the starting model for the determination of the scattering parameters. On the other hand, we shall use a causal bond graph model richer in information and to which we shall apply what we called in former articles: the analytical procedure of the scattering parameters exploitation with the aim of showing the importance of the causality notion in the physical systems study by the bond graph approach, as well as the importance of the ways and causal loops notion. Results: We will, initially, apply this discussion, to an elementary transmission line; in the second place, the application is carried out on the equivalent circuit of a band pass filter based on localized elements often used like microwave filters in high frequencies studies. Conclusion: We will finish this discussion by realizing the scattering bond graph model of a quadruple by pointing out the procedure used for the construction of this new type of bond graph model.
Highlights
The development of the bond graph technique was articulated around two basic concepts which are the reticulation assumption and the power continuity principle (Mota and Mota, 2011), without forgetting the importance of the causality concept, which reveals the relations of cause for purpose (Cause with effect) between the various modules of the system and returns the bond graph model richer in information than a simple graph model (Birkett, 2009)
In this article, to apply the new modeling technique, described in former articles, which uses collectively the scattering formalism and the bond graph approach for a modeling of the physical systems often working in high frequencies
Applied Sci., 9 (4): 459-467, 2012 modeling of the physical systems since it enables us to organize the relations constitutive of the elements in an Inputs-outputs form and to analyze the variables of powers effort and flow in terms of dependence, we propose in the continuation of this study to build the “Scattering Bond Graph” model by taking account of the causality concept contrary with what was carried out in the study of Professor (Kamel and DauphinTanguy, 1996) which completely cancelled the concept of causality in spite of its importance
Summary
The development of the bond graph technique was articulated around two basic concepts which are the reticulation assumption and the power continuity principle (Mota and Mota, 2011), without forgetting the importance of the causality concept, which reveals the relations of cause for purpose (Cause with effect) between the various modules of the system and returns the bond graph model richer in information than a simple graph model (Birkett, 2009). To apply the analytical exploitation procedure which takes account of the causality concept, we start by assigning an integral causality on the bond graph above while supposing that the linear and reduced impedance and admittance have respectively the. We detect, on this reduced and causal bond graph model, by going through the causal ways, a single causal loop B1 where the associated integro-differential operator is Eq 15: characteristics of an inductance and a capacity. The operator associated with the causal way connecting the reduced variable φ2 with the P2 port to the variable ε2 with the same port is Eq 20:
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