Destabilizing limit cycles in delta-sigma modulators with chaos

Limit cycles in delta-sigma modulators cause unwanted tones to appear in the quantization noise. Such limit cycles can be avoided by making a simple modification to the noise transfer function (NTF). Moving a zero of the NTF outside the unit circle destabilizes limit cycles and consequently reduces the tonality of the quantization noise. However, the in-band noise is increased by this modification. The SNR-tonality tradeoff is explored with simulations of first and second-order lowpass modulators