DBDF: An implicit numerical differentiation algorithm for integrated circuit simulation

Abstract

Frequently, the design of integrated circuits cannot be accomplished by purely analytical techniques. Accurate and efficient algorithms for numerical circuit simulation are important tools. Several circuit simulators, such as SPICE, have been made available for this task. Contrary to many other applications of numerical system simulation, integrated circuit problems don't lend themselves to a formulation of state-space models, since the space charge in a p-n junction is a nonlinear and noninvertible function of the voltage across the junction. Therefore, it is necessary to employ numerical differentiation instead of numerical integration in this type of simulation study. The numerical algorithms employed in today's circuit simulators are fairly primitive. SPICE, for example, offers only two very simple implementations of the trapezoidal rule and of the backwards differentiation formula. This thesis describes the design and implementation of DBDF, a specification of a numerical method in Nordsieck format for solving circuit simulation problems. A formal stability and truncation error analysis are included.