A CRITICAL EXAMINATION OF METHODS OF FORMULATING NONLINEAR RESISTIVE NETWORK EQUATIONS

ARNOLD W NORDSIECK, Purdue University

Abstract

With the advent of very large scale integration, simulation of electronic networks has presented a formidable challenge. Limited core memory and expensive computer run time has prompted a reexamination of present simulation techniques. One controversial aspect of simulation concerns the methods of equation formulation. The available methods fall into three general classes according to the size and sparsity of the Jacobian matrix (assuming the use of the popular Newton-Raphson algorithm). The methods with a very large and very sparse Jacobian matrix are represented by the Component Connection Model and the Sparse Tableau which is implemented in the program ASTAP. The methods generating a large and sparse Jacobian are represented by the Modified Nodal Analysis which is implemented in the program SPICE 2. And finally, the methods with a small and dense Jacobian matrix are represented by the Hybrid Multiport. An explicit equation formulation is developed for each method. Transformations are then developed to convert one set of equations to another via block elimination and permutation matrices. Among the transformations developed and implemented is the conversion of the Modified Nodal Analysis to a Hybrid Multiport. This research has developed a methodology for comparisons using sparse matrix techniques. The comparison simulations of eighteen are based on benchmark circuits. These circuits are bipolar networks ranging in size from one transistor to a TTL JK flip flop. The data obtained are the number of multiplications per Newton iteration, the number of multiplications for the Newton algorithm to converge, and the amount of memory allocated. The results of the benchmark circuit simulations are then extrapolated to cover a wide range of circuit sizes. Since at each time step a nonlinear dynamical network is equivalent to a nonlinear resistive network, only the latter network is considered, but the results are then extended to include dynamic circuits as well.

Degree

Ph.D.

Subject Area

Electrical engineering

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