Application Of Neural Networks To Computer-Aided Design Of Electronic Circuits: Solution Of Linear Equations

Abstract

The objective of this research is to investigate the application of Artificial Neural Network techniques to the area of computer-aided design of electronic circuits. A major problem in this area is the analysis (especially statistical) of large integrated circuits, taking a substantial amount of the CPU time even on the most powerful computers available today. Two most time consuming tasks responsible for this situation are: calculation of model parameters of semiconductor devices, and solving systems of linear equations (required for all types of analyses available from such circuit analysis programs as, e.g., SPICE). Therefore, it is very important to look for methods of improving the efficiency of performing these two major tasks. In the development of this project, the main emphasis has been directed toward solving a system of linear equations. ANNs are applicable because optimization can be used to obtain a solution to these equations. Currently, solving a system of linear equations usually involves iterative numerical techniques in the form of an algorithm implemented in a computer program. The time needed for the computer to yield an exact solution can grow exponentially with the number of equations for which the solution is desired. With ANNs, a good approximation to the solution can be obtained directly in hardware (an electrical circuit) in a parallel architecture. With a parallel architecture, operations are performed simultaneously in parallel rather than serially. As a result, expanding the number of equations to solve in parallel does not increase the time required to reach a solution. Thus the efficiency in solving a large system of linear equations is much greater with the parallel ANN. Applying Artificial Neural Networks to the solution of a system of linear equations provides a new hardware approach which is faster and more efficient than conventional iterative implementations in software programs. One obvious disadvantage is that the accuracy of the solution obtained is limited by the accuracy of the ANN element values and the measurements of the solution voltages, since the ANN is an analog circuit.