Abstract
A major problem with substrate crosstalk extraction methods in the literature is their lengthy computational time. This practically renders them useless for large circuits. This paper presents efficient substrate parasitic extraction techniques employing closed-form models derived using a quasi-static approach. We develop an integral equation model based on the Green's theorem utilizing a novel fast-convergent Green's function. In addition, we propose another modeling technique based on point approximation of the elements of the impedance matrix of the system. Although the proposed techniques speed the parasitic extraction process up, we show that it is unnecessary to run a full substrate parasitic extraction among all the devices for a system-on-a-chip. As such, by applying the new modeling technique to a multi-contact substrate structure, we develop a methodology that is a large-scale solution for substrate parasitic extraction in VLSI and mixed-signal circuits. Moreover, we demonstrate that the coupling among the contacts in a large system decreases faster than an exponential function of the distance among them. Using the proposed methodology, we introduce a decomposed two-contact problem set, associated with the original complex problem. Then, the total crosstalk of a device in the original problem is simply computed from the associated decomposed problem set.