Real-time-capable Emulation of Nonlinear Analog Circuits by Means of Novel Wave Digital Filters

点击翻译按钮获取中文摘要

The concept of Wave Digital Filters, introduced by Alfred Fettweis (1926-2015), provides an elegant approach to interrelate analog circuits and recursive digital structures in a unique fashion. The underlying idea is to discretize each electric component of the circuit individually and solely based on its local definition. The resulting digital building blocks then are connected in accordance with the wiring of the analog components in the reference circuit, forming a digital structure, the Wave Digital Filter. This physical model of the analog circuit is able to recreate its dynamic properties accurately and in real-time. Due to the modular construction principles, a number of unique positive properties like passivity, stability, robustness and the topology of the reference system are preserved in the corresponding Wave Digital Filter. Here, instead of using the usual Kirchhoff quantities voltage and current, wave variables are utilized to achieve a readily computable signal flow graph. Unfortunately, the set of reference circuits that are directly translatable into a Wave Digital structure is limited significantly: Even very simple nonlinear networks or circuits containing more complex, ring-like topologies are not representable by means of classic Wave Digital Filters, as non-computable delay-free loops are introduced. This unsolved problem rendered the application of the Wave Digital concept to the field of generic circuit simulation impossible in spite of all its favourable properties.The objective of the proposed research project is to counteract these realization problems and to allow for a real-time capable and generic circuit simulation based on Wave Digital Filters. The scientific approach chosen here is based on a novel iteration method of the applicants that exploits the contractivity property of Wave Digital Filters. This results in completely modular digital structures which emulate the underlying analog reference structure with very high accuracy. The theoretic fundament of the method is so substantial that convergence can even be guaranteed mathematically for whole classes of reference circuits (e.g. all diode circuits and arbitrary topologies). For other circuits of great technical relevance, for example highly nonlinear transistor circuits, an analogous proof is still missing and therefore is to be developed within the scope of the proposed project. Additionally, further questions are to be answered which relate to the design of highly efficient real-time structures. This includes implementation principles that minimize the number of iterations by construction or analyses of the scaling behaviour of the approach with respect to very large circuits. The expected results are of great interest for both the scientific community and practical applications.