Nonidealities in Continuous‐Time Delta‐Sigma Modulators

This chapter discusses how the analog to digital converter (ADC) thresholds and digital to analog converters (DAC) levels deviate from their desired values due to element mismatch during continuous‐time delta‐sigma modulation. The chapter assumes that quantization noise suppression within the signal band should not be affected since the magnitude of the loop‐gain does not change with delay. It is important to note that only the samples of the compensated loop‐filter are equal to ideal samples. The shape of the DAC pulse influences the sampled response of the loop‐filter. Other commonly used pulses are the return‐to‐zero (RZ) and impulsive shapes. A third‐order CIFF modulator will be used as an example to illustrate the basic idea. Simple formulae, amenable even to hand‐calculations, and valid for arbitrary DAC pulse shapes, yield the coefficients of the compensated filter in terms of those of the delay‐free design. The deleterious consequences of delay can be easily addressed by tuning the loop‐filter's coefficients and by adding a direct path around the quantizer. Coefficient tuning and the direct path, in amplifier parlance, add zeros or move existing ones to the loop‐gain function and restore stability.