On systematic wave digital modeling of passive hyperbolic partial differential equations
Christiane Leuer, Karlheinz Ochs · International Journal of Circuit Theory and Applications · 2011
SUMMARY Wave digital models are known to be most suitable for the digital emulation of passive physical systems. Starting from a system description in the form of a suited partial differential equation (PDE), a reference circuit having a one‐to‐one corresponding wave digital structure has to be synthesized. This synthesis transfers the principle of action at proximity and the passivity of the physical system into algorithms, which offer full parallelism, passivity, and robustness against signal and coefficient quantizations. Finding a reference circuit to a given PDE is an open problem, which has only partially been solved. In this paper, we present a schematic reference circuit synthesis for a special class of hyperbolic PDEs. In order to cut down the complexity of the synthesis, we introduce additional design parameters and decompose the PDE into an ordinary differential equation (ODE) and hyperbolic PDE subsystems. The parameters can be exploited to optimize the reference circuit and its corresponding wave digital structure. The method is applied to the Sine‐Gordon equation from the soliton theory and verified by simulation. Copyright © 2011 John Wiley & Sons, Ltd.