A Rigorous Approach to the Robust Design of Continuous-Time $\Sigma\Delta$ Modulators

Abstract

Abstract-In this paper we present a framework for robust design of continuous-time Σ∆ modulators. The approach allows to find a modulator which maintains its performance (stability, guaranteed peak SNR, . . . ) over all the foreseen parasitic effects, provided it exists. For this purpose, we have introduced the S-figure as a criterion for the robustness of a continuous-time Σ∆ modulator. This figure, inspired by the worst-case-distance methodology, indicates how close a design is to violating one of its performance requirements. Optimal robustness is obtained by optimizing this S-figure. The approach is illustrated through various design examples and is able to find modulators that are robust to excess loop delay, clock jitter and coefficient variations. As an application of the approach, we have quantified the effect of coefficient trimming. Even with poor trim resolution, good performance can be achieved provided beneficial initial system parameters are chosen. Another example illustrates the fact that also the out-of-band peaking behaviour of the signal transfer function can be controlled with our design framework.

A selectable-bandwidth 3.5 mW, 0.03 mm2 self-oscillating Sigma Delta modulator with 71 dB dynamic range at 5 MHz and 65 dB at 10 MHz bandwidth

“…Note that no integrator time constant tuning or trimming was used. It is clear that the measured robustness of this pulse width modulation scheme is very good especially compared to comparable conventional continuous-time sigma delta modulators where the time constants must be tuned with an accuracy of the order of a few percents relative to the clock frequency [15].…”

Compensation method of the excess loop delay in continuous‐time delta‐sigma analog‐to‐digital converters based on model matching approach

“…It is hard to know how much this technique can compensate for low pass modulators. Some other techniques for excess loop delay compensation are presented in [3] (based on control theory), [14] (using Nyguist criterion), [16][17][18][19][20][21] (circuit level implementation) and [15] (S-figure criterion compensation). An innovative compensation technique is presented in this paper, which is designed in the framework of control engineering using the model matching method [22].…”

Estimation of Non-Idealities in Sigma-Delta Modulators for Test and Correction Using Unscented Kalman Filters

“…First, the modulator can already be designed for a robust and stable performance even in the presence of worst case manufacturing and run-time conditions. Following this approach, remarkable design techniques have been proposed in the literature [3], [5]- [9]. However, design robustness must be commonly traded for aggressiveness of the noise-shaping and hence performance of the modulator.…”