Sampled data simulation of linear and nonlinear circuits

In this paper, an efficient, accurate, stable, and explicit method for transient analysis of lumped linear time invariant circuits is given. The method formulates a set of finite difference equations in the analog domain for sampled data simulation of the circuit. The solution of these equations gives the network response at fixed and equally spaced discrete instants of time. The fixed-time interval between each solution can be chosen arbitrarily and does not depend on the circuit time constants. The transient solution at each time point requires one matrix/vector multiplication and vector addition only. The algorithm is a general computer oriented formulation method that can be applied to any linear circuit. In addition to linear time invariant circuits, the method can be applied to a restricted class of time varying and/or nonlinear circuits. It is directly applicable to linear networks containing periodically clocked ideal switches, for example, switched capacitor and switched current circuits. In these networks, the circuit is linear inside each phase and changes its topology at fixed discrete instants of time. All nonlinear elements allowed in analysis must be clocked, such that their characteristics change only at discrete instants of time. For example, clocked digital circuits, such as, ideal comparators, A/D and D/A blocks are allowed. In particular, the method is applied to the simulation of oversampled delta-sigma modulators. The method can be used to study the effect of clock feed through, finite switch resistance, and finite gain bandwidth of operational amplifiers on the performance of these modulators. In addition, the algorithm can be used for analysis of continuous time delta-sigma modulators. Examples of simulation results are given.