A Reduced-Order Modeling Technique for Substrate Coupling in Mixed-Signal VLSI

Finite Element Method (FEM) is one of the well-known methods used to solve the problem of substrate coupling modeling. In this method the whole body of the substrate becomes descretized, therefore the resulting modeling matrix is overwhelmingly large. This calls for developing new methods which can efficiently reduce the dimensions of the modeling matrix. In this paper, we propose two approaches which reduce the order of the impedance modeling matrix by at least a number of 4. One is to reduce horizontal resistances to one equivalent resistance. The other is a circle-wise modeling leading to a resistor ladder for the total substrate. The approximation incurred by our method results in a minor error, allowing the simulation results to track the exact values properly.