Quantization noise and limit cycle patterns in single-bit delta-sigma modulators

Abstract

This paper presents a quantitative analysis of limit cycle patterns, which plague single-stage single-bit delta-sigma modulators. To quantify these elusive phenomena and to reveal the frequency distribution of the corresponding tonal patterns, we have analyzed the output streams of 3 frequently used single-stage topologies. The numerical results show that the spectral distribution of the detected cyclic patterns closely follows the modulator noise shaping function. The data also reveal that most tones occur outside the modulator passband, where they cause relatively little harm. The few passband tones are typically less powerful than the total in-band quantization noise. Hence, the tonal patterns are unlikely to affect the maximum signal to noise ratio. However, the unwanted cycles do limit the spurious free dynamic range.