On approximate reduction of multi-port resistor networks

Simulation of the influence of interconnect structures and substrates is essential for a good understanding of modern chip behavior. Sometimes such simulations are not feasible with current circuit simulators. We propose an approach to reduce the large resistor networks obtained from extraction of the parasitic effects that builds upon the work in (Rommes and Schilders, IEEE Trans. CAD Circ. Syst. 29:28–39, 2010). The novelty in our approach is that we obtain improved reductions, by developing error estimations which enable to delete superfluous resistors and to control accuracy. An industrial test case demonstrates the potential of the new method

Error bounds for reduction of multi-port resistor networks

The interconnect layouts of chips can be modeled by large resistor networks. In order to be able to speed up simulations of such large networks, reduction techniques are applied to reduce the size of the networks. For some class of networks, an existing reduction strategy does not provide sufficient reduction in terms of the number of resistors appearing in the final network. In this paper, we propose an approach for obtaining a further reduction in the amount of resistors. The suggested approach improves sparsity of the conductance matrix by neglecting resistors that do not contribute significantly to the behavior of the circuit. Explicit error bounds, which give an opportunity to control the errors due to approximation, have been derived. Numerical examples show that the suggested approach appears promising for multi-terminal resistor networks, and in combination with the existing reduction strategy, leads to better reduction. Keywords: resistor networks; model order reduction; generalized eigenvalue problem; Cholesky factorization; singular valu

Error bounds for reduction of multi-port resistor networks

The interconnect layouts of chips can be modeled by large resistor networks. In order to be able to speed up simulations of such large networks, reduction techniques are applied to reduce the size of the networks. For some class of networks, an existing reduction strategy does not provide sufficient reduction in terms of the number of resistors appearing in the final network. In this paper we propose an approach for obtaining a further reduction in the amount of resistors. The suggested approach improves sparsity of the conductance matrix by neglecting resistors which do not contribute significantly to the behavior of the circuit. Explicit error bounds, which give an opportunity to control the errors due to approximation, have been derived. Numerical examples show that the suggested approach appears promising for multi-terminal resistor networks and, in combination with the existing reduction strategy, leads to better reduction