A bound on limit cycles in digital filters which exploits a particular structural property of the quantization

This paper presents an improved upper bound on the rms value of self-sustained limit cycles due to quantization in those implementations of digital filter sections where the quantization possesses a particular structural property. An important example wherein this property exists and our results apply is quantization by a single magnitude-truncation quantizer. The main result is a closed form bound which can be easily evaluated for the important case of second-order sections. The bound also has an extremely appealing geometrical interpretation. A feature of the bound is that its value is zero, implying the absence of limit cycles, for certain choices of the filter coefficients. A comparison with the Sandberg-Kaiser bound shows that the bound given here always yields a lower value.