On the stability of a 1-bit-quantized feedback system

The performance of a Delta(-Sigma)- Modulator can be greatly improved by increasing the effectiveness of the low-pass or band-pass filter which is placed in the feedback loop around the 1-bit quantizer. However, too steep an attenuation of the filter will cause the system to exhibit limit cycle oscillations, which have a detrimental effect on the performance. These are characterized by a periodic sequence of
\frac{1}{2}L
positive 1-bit samples followed by
\frac{1}{2}L
negative output samples. This paper presents a sufficient phase condition of the loop filter for the nonexistence of these limit cycles. A simple interpretation in the time domain is given.