Modeling harmonic distortions caused by nonlinear op-amp DC gain for switched-capacitor sigma-delta modulators

Op-amps are crucial components in sigma-delta modulators (SDMs). As device dimensions and supply voltages continue to scale down, it is increasingly critical to determine a suitable op-amp dc gain. If the dc gain is set too high, then the op-amp consumes too much power; if the dc gain is too small, then nonlinear distortion becomes serious. However, there exists no efficient approach for selecting dc gains. In this brief, we propose to use a nonlinear function to model nonlinear op-amp dc gain curves. Then, this nonlinear function is employed to derive an SDM nonlinear distortion model as a function of SDM system parameters. The obtained SDM nonlinear distortion model can subsequently be used to compute the minimum required op-amp dc gain such that nonlinear distortions are kept under a tolerable value. The nonlinear dc gain curve model and the SDM nonlinear distortion model proposed in this brief are verified by behavior simulations and transistor-level simulations.