Polynomial Approximation Of Circuit Responses For Optimal Design Of VLSI Circuits

Abstract

An approximation scheme that uses 2nd order polynomials is presented. The approximation is used to obtain circuit responses without having to continuously refer to circuit simulation programs which are very time consuming. In building up the coefficients of the approximating polynomial, a number of points in the circuit parameter space are sampled and the circuit responses are evaluated using a circuit analysis program. Once the polynomial is determined substution of circuit parameters in the polynomial gives the approximated value for the circuit response to which the polynomial corresponds. The approximation scheme allows the approximation to be updated and makes use of all available sampled and analyzed points without being restrained by having exactly the right number of points necessary for unique interpolation, either linear or quadratic. The method is based on an interpolation where the unique polynomial is obtained by adding the constraint that the function should be maximally flat while at the same time satisfying all the available sampled and analyzed points. The approximation presented behaves much better than the linear and even the full quadratic interpolation when only a few additional points more than the number needed for the rather inaccurate linear interpolation are added. The savings in the computer time needed for VLSI circuit optimization gained when using this method arc invaluable. Software implementation and a practical example demonstrating the approximation scheme are presented in this thesis.