Modeling of non-ideal switch-capacitor integrator and its effect on baseband sigma-delta modulator stability and output dynamic range

As the sigma-delta modulator integrators would be implemented by switch-capacitor circuits typically, integrator non-idealities such as the low amount of overall integrator gain, the effect of finite gain of op-amp which causes the integrator voltage leakage and degrading the overall integrator gain, and the capacitance voltage dependency, would result in debilitating the output dynamic range and endanger the modulator stability. In this paper, the non ideal integrator transfer function based on mentioned drawbacks would be calculated elaborately and by followings, the modulator output dynamic range and stability would be verified based on calculated non-idealities effects. The results are obtained using the general model for the quantizer and modulator and are validated by performing direct simulations.