A. Opal, SAMPLED-DATA SIMULATION OF LINEAR AND NONLINEAR CIRCUITS, IEEE transactions on computer-aided design of integrated circuits and systems, 15(3), 1996, pp. 295-307
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 ana
log domain for sampled data simulation of the circuit, The solution of
these equations gives the network response at fixed and equally space
d discrete instants of time, The fixed-time interval between each solu
tion can be chosen arbitrarily and does not depend on the circuit time
constants, The transient solution at each time point requires one mat
rix/vector multiplication and vector addition only, The algorithm is a
general computer oriented formulation method that can be applied to a
ny linear circuit, In addition to linear time invariant circuits, the
method can be applied to a restricted class of time varying and/or non
linear circuits, It is directly applicable to linear networks containi
ng periodically clocked ideal switches, for example, switched capacito
r and switched current circuits, In these networks; the circuit is lin
ear inside each phase and changes its topology at fixed discrete insta
nts of time, All nonlinear elements allowed in analysis must be clocke
d, such that their characteristics change only at discrete instants of
time, For example, clocked digital circuits, such as, ideal comparato
rs, A/D and D/A blocks are allowed, In particular, the method is appli
ed 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 us
ed for analysis of continuous time delta-sigma modulators, Examples of
simulation results are given.