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Simulation of oversampled sigma delta convertors

A method for simulation of oversampled sigma-delta modulators is described. The algorithm makes use of the clocked operation of these circuits to formulate a set of finite difference equations in the time domain. The solution of these equations requires matrix multiplication and addition only. In addition, the circuit response is computed only at discrete instants of time, usually once per clock cycle. The combination of simple matrix algebra and discrete time operation results in fast and accurate simulation of oversampled sigma-delta modulators. The algorithms have been implemented in a computer program SDSIM. The modulator is described at the circuit level using a combination of linear and nonlinear elements. The program can be used to study the effect of circuit nonidealities, such as, switch resistance, clock feed through, finite gain-bandwidth of operational amplifiers, and the use of multi-bit quantizers on the signal to noise ratio of a modulator.