Analysis of Gain and Bandwidth Limitations of Operational Amplifiers in Sigma-Delta Modulators

In Sigma-Delta modulator system design the loop filter coefficients are calculated based on ideal circuit behavior. Advancing to an actual circuit implementation based on operational amplifiers, which show finite gain bandwidth products, a deviation of these coefficients is observed. These influences which were not considered during initial coefficient development can lead to performance degradation or even instability. This paper presents an analysis of the influence of the 3dB bandwidth and the DC gain of an opamp to the signal and noise transfer function of a third order Sigma-Delta modulator. Based on a mathematical analysis of the transfer functions the opamp's influences on a complex integrator and a Tow-Thomas biquad are discussed in order to give a target specification for a circuit implementation.