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

由Alfred Fettweis（1926-2015）提出的波数字滤波器的概念提供了一种以独特的方式将模拟电路和递归数字结构相互关联的优雅方法。其基本思想是将电路的每个电子元件单独离散化，并且仅基于其局部定义。然后，根据参考电路中的模拟元件的布线，连接所得到的数字构建块，形成数字结构，即波数字滤波器。该模拟电路的物理模型能够准确且实时地再现其动态特性。由于模块化的结构原则，一些独特的积极的属性，如无源性，稳定性，鲁棒性和参考系统的拓扑结构被保留在相应的波数字滤波器。这里，而不是使用通常的基尔霍夫量电压和电流，波变量被用来实现一个容易计算的信号流图。不幸的是，可直接转换为Wave Digital结构的参考电路集受到很大限制：即使是非常简单的非线性网络或包含更复杂的环状拓扑的电路也无法通过经典Wave Digital滤波器表示，因为引入了不可计算的无延迟环路。这个未解决的问题，使波数字概念的应用领域的通用电路仿真不可能，尽管其所有的有利properties.The拟议的研究项目的目的是抵消这些实现问题，并允许一个实时的能力和通用电路仿真的基础上波数字滤波器。这里选择的科学方法是基于申请人的一种新颖的迭代方法，该方法利用了波数字滤波器的收缩特性。这导致完全模块化的数字结构，其以非常高的精度仿真底层模拟参考结构。该方法的理论基础是如此的坚实，甚至可以保证收敛数学为整个类的参考电路（例如，所有二极管电路和任意拓扑结构）。对于其他具有重大技术意义的电路，例如高度非线性晶体管电路，类似的证明仍然缺失，因此将在拟议项目的范围内进行开发。此外，进一步的问题是要回答的高效的实时结构的设计。这包括通过构造或分析该方法相对于非常大的电路的缩放行为来最小化迭代次数的实施原则。预期的结果是科学界和实际应用的极大兴趣。

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.