Analysis of Opamp Non-Idealities in Quadrature Bandpass Sigma-Delta Modulators

The performance of continuous-time ΣΔ modulators dramatically depends on the non-idealities of operational amplifiers (opamps) used within the loop filter. In this paper, the limitations stemming from the opamps regarding the loop filter transfer function (TF) as well as the Noise-Transfer-Function (NTF) are studied. By evoking the impulse-invariant transform a derivation of the non-ideal NTF prior to lengthy simulations is possible, enabling a pre-design study of the NTF's pole and zero placement affected by the opamps non-idealities. Based on the pre-design study precise settings for the opamps can be found without the need for time-consuming simulations on the circuit level. Furthermore, the developed mathematical model can also be utilized for top-level verification.