Computer Aided Analysis of Periodically Switched Linear Networks

Interest in analysing periodically switched linear networks has developed in response to the rapid development of sampled data communications systems. In particular, integrated circuit switched capacitor networks play an important part in modern analogue signal processing systems. This thesis addresses the problem of developing techniques for analysing periodically switched linear networks in the time and frequency domains that are suited to computer implementation and therefore facilitate the development of efficient computer aided analysis tools for these networks. Systems of large sparse complex linear equations arise in many network analysis problems and efficient techniques for solving these systems are crucial to the analysis methods developed in this thesis. By extending the concept of sparsity to include the type of the nonzero elements, very efficient solution and optimal ordering algorithms are developed. A new method for computing the time domain response of linear networks is presented. The method is based on numerical inversion of the Laplace transform and polynomial approximation of the excitations. This high accuracy method is well suited to solving large stiff systems and is extremely efficient. The method is extended to periodically switched linear networks and provides the basis for frequency domain analysis. A new frequency domain analysis method is presented that is orders of magnitude faster than existing techniques. This efficiency is achieved by developing a formulation such that AC analysis is not required, which allows the system to be solved as a discrete system. A special system compression reduces the solution of this discrete system to the solution of the network in one phase only. This solution step, which ordinarily requires O(N3) operations, is made more efficient by reducing the system to upper Hessenberg form in a preprocessing step, which then reduces the solution cost to O(N2) operations