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The corresponding variation form of the Z-domain transfer function of switched - capacitor integrator(behavioral simulation model) under the impact of op-amp's four nonlinearities are explored in detail in this paper, which are finite direct-current gain(FDCG), nonlinear direct-current gain(NLDCG), slew rate(SR) and gain-bandwidth product(GBW) respectively. It's a ssumed that the integrator is free from the effect of SR and GBW when dealing with the FDCG and NLDCG, namely, in other words, the sampling and integrating can be finished in a very short ti me slot. Then based on the total charge conservation in sampling capacitor and integrating one, we find out the relationship between the input and output of the switched-capacitor integrator. After that, the relational expression is further translated into the Z-domain model. Especially, when looking into the effect of the finite SR and GBW, in order to establish the zero-input response during integration phase, we convert the issue into the zero-status response of the equivalent step input utilizing the equivalence principle between the charge and discharge of the sampling capacitor. In such a way, the complexity of the analyzing and calculating is effectively simplified. The presented mathematical analysis in this paper is the theoretical foundation of behavioral modeling and simulation for op-amp's four nonlinear properties employing MATLAB/SIMULINK software tools.

Z-domain Analysis about the Impact of Op-Amp FDCG, NLDCG, GBW and SR on Performance of Switched-Capacitor Integrator