Analysis of error mechanisms in switched-current Sigma-Delta modulators

Abstract

This paper presents a systematic analysis of the major switched-current (SI) errors and their influence on the performance degradation of ΣΔ Modulators (ΣΔMs). The study is presented in a hierarchical systematic way. First, the physical mechanisms behind SI errors are explained and a precise modeling of the memory cell is derived. Based on this modeling, the analysis is extended to other circuits of higher level in the modulator hierarchy such as integrators and resonators. After that, the study is extended to the modulator level, considering two fundamental architectures: a 2nd-order LowPass ΣΔM (2nd-LPΣΔM) and a 4th-order BandPass ΣΔM (4th-BPΣΔM). The noise shaping degradation caused by the linear part of SI errors is studied in the first part of the paper. This study classifies SI non-idealities in different categories depending on how they modify the zeroes of the quantization noise transfer function. As a result, closed-form expressions are found for the degradation of the signal-to-noise ratio and for the change of the notch frequency position in the case of 4th-BPΣΔMs. The analysis is treated considering both the isolated and the cumulative effect of errors. In the second part of the paper the impact of non-linear errors on the modulator performance is investigated. Closed-form expressions are derived for the third-order harmonic distortion and the third-order intermodulation distortion at the output of the modulator as a function of the different error mechanisms. In addition to the mentioned effects, thermal noise is also considered. The most significant noise sources of SI ΣΔMs are identified and their contributions to the input equivalent noise are calculated. All these analyses have been validated by SPICE electrical simulations at the memory cell level and by time-domain behavioural simulations at the modulator level. As an experimental illustration, measurements taken from a 0.8 μm CMOS SI 4th-BPΣΔM silicon prototype validate our approach.