Measurement and enhancement of multistage sigma-delta modulators

Oversampled sigma-delta modulators as a solution to realizing high-resolution (>16 b) analog-to-digital (A/D) converters are dealt with. Their theoretical basis is well founded. However, effects such as gain mismatch of the stages, timing, jitter, input noise, instability of thresholders, and the asymmetry in the rise/fall times of the pulses generated have not been considered. The differential-comparison method is used here to examine the system behavior and the sensitivity of the modulator to circuit nonlinearities. It is found that the primary influence on accuracy comes from 1-b digital-to-analog (D/A) converters in the feedback path. Identical circuit nonidealities have greater influence at the output, when they appear further from the input. Simulation has shown that the key factor for a successful spectrum analysis is a coherent measurement with a rectangular window. Compensation is sometimes needed for phase imbalances between channels of a coherent digital spectrum analyzer. Thus, the concept of a fractional delay could be useful for alignment of measurements from instrumentation