Stefan Ludwig

Efficient model reduction of passive electrical networks with a large number of independent sources

This work will present a method for the efficient description of a large number of independent sources in electrical networks for a model order reduction. With the help of controlled sources, the number of ports is reduced, which enables a high order reduction. The proposed description guarantees the passivity and reciprocity of the system, which are preserved in the order reduced system. Synthesizing the reduced system with the proposed algorithm into a passive electrical RC-network enables for fast simulations with circuit simulators to be made. The whole procedure is validated by reducing an IC conducted emission model of a 32 Bit microcontroller.

Two-step order reduction of IC conducted emission models

This paper addresses the order reduction of IC conducted emission models. These models are mathematically described by singular matrices of high order. Usually the order of the matrices can be reduced by the multipoint Krylov based order reduction. To achieve an even lower order we introduce a two step order reduction. The first step is the order reduction method based on the multipoint approximation of system matrices by utilizing the Krylov subspace. The second step is based on the rejection of the dispensable part of a system. To recognize the remaining dispensable system part Lyapunov equations are used. Thus this paper introduces the efficient solutions of the Lyapunov equations. With two-step order reduction a high speed-up in frequency analysis can be achieved.

Passive and reciprocal network description of independent sources for efficient model reduction

This work will present a method for the efficient description of independent sources in electrical networks for a model reduction. The number of ports of the model is reduced with the help of controlled sources and the resulting network is passive and reciprocal. The model is then reduced with model order reduction methods. The lower number of ports hereby allows for a higher reduction. Passivity and reciprocity are preserved in the reduced model. The passivity enables guaranteed stable time-domain simulations. An efficient synthesis of the reduced model is enabled by the reciprocity of the model. The high efficiency of the presented description is validated by reducing an IC conducted emission model of a 32 bit microcontroller.

Model Reduction Methods for Linear Network Models of Distributed Systems with Sources

Distributed systems with distributed sources are modeled as large electrical networks with linear RLC-elements, independent sources and pins for the connection with other network models. Often these networks are too large to be simulated efficiently. Model reduction can be used to reduce these networks while approximating the behavior at the pins for the connection with other nonlinear and linear network models. In the standard model reduction the independent sources are extracted and connected by ports with the RLC-part of the network which is to be reduced. This extraction only enables a weak reduction for networks with a large number of independent sources, as the number of ports is very high. In this article an efficient reduction of networks with a large number of sources is proposed by taking the waveforms of the sources into account. The method is based on the reduction of the dimension of the function space of the waveforms with the help of function approximation. The basis functions of the function approximation are used in the network, which results a lower number of independent sources. Extracting this lower number of independent sources and reducing the network enables a higher model reduction with state of the art techniques. With the proposed method a smaller size and higher accuracy of the reduced model can be achieved. The validity and efficiency of the proposed method is shown by reducing example models.

Model reduction of parasitic coupling networks of mixed‐signal VLSI circuits

Purpose – This paper aims to present a method for the efficient reduction of networks modelling parasitic couplings in very‐large‐scale integration (VLSI) circuits.Design/methodology/approach – The parasitic effects are modelled by large RLC networks and current sources for the digital switching currents. Based on the determined behaviour of the digital modules, an efficient description of these networks is proposed, which allows for a more efficient model reduction than standard methods.Findings – The proposed method enables a fast and efficient simulation of the parasitic effects. Additionally, an extension of the reduction method to elements, which incorporate some supply voltage dependence to model the internal currents more precisely than independent current sources is presented.Practical implications – The presented method can be applied to large electrical networks, used in the modelling of parasitic effects, for reducing their size. A reduced model is created which can be used in investigations wi...

Network modelling of electromagnetic field distribution using a statistical mechanical approach

This paper we discuss the concept of model reduction in statistical mechanics and interpret certain concepts of model reduction in this framework. Some examples illustrate our considerations.

Model reduction of linear networks with nonlinear elements

In this paper a method for the reduction of linear networks with a large number of nonlinear elements is presented. In the standard approach the nonlinear elements are extracted from the linear part and the linear part is reduced. A large number of nonlinear elements leads to a large number of ports for the interconnection of linear and nonlinear network parts which is a strong limitation for the reduction. A method for the reduction of the number of ports of the linear part which enables a more efficient model order reduction with standard projection techniques is presented. The method is based on decomposition of the equations of the nonlinear elements which are explicitly described by one current or voltage function. By reducing an example model the method is illustrated and validated.

Efficient description of RLC-macromodels with a large number of independent sources for model order reduction

This paper introduces an efficient description of electromagnetic macromodels that contain passive electrical elements and a large number of independent sources. This description allows for much higher order reduction than the standard description. In the proposed description the behavior at the pins of the model as well as the passivity are preserved. With model order reduction algorithms the proposed description of the network can be reduced more efficiently and therewith a higher speed-up in simulations can be achieved. The whole procedure is validated by applying it to an macromodel of the electromagnetic behavior of a 32 Bit microcontroller.