Error bounds for reduction of multi‐port resistor networks

Abstract

SUMMARYThe 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.

Model Reduction of Networked Multiagent Systems by Cycle Removal

“…where V is an orthogonal matrix that diagonalizes the matrixL e in (18). Again using the Woodbury inversion formula, we find that the inverse of I + T T T is given by I − T (I + T T T ) −1 T T .…”

“…For resistor networks with scalar agent dynamics, the problem of model reduction by edge-removal was studied in [17] and [18].…”

“…In [17], an efficient method (reduceR) was introduced for finding an equivalent resistor network with the same number of external nodes, but with a reduced number of internal nodes. In [18], the number of external and internal nodes is kept the same for the reduced network. The approximation error that is considered is the worst case relative error between the steady-state voltages over the nodes of the original and reduced network.…”

“…The approximation error that is considered is the worst case relative error between the steady-state voltages over the nodes of the original and reduced network. The upper bound on the approximation error given in [18] depends on the conductance matrices of both the original and the reduced network.…”