Tone suppression in general double-loop ΣΔ modulators using chaos

Chaotic ΣΔ modulators, in which at least one internal integrator is unstable, have recently been proposed to combat spurious, detrimental “tones” appearing in the modulator output. This paper employs a semi-analytical technique to solve the design problem for general chaotic double-loop modulators with constant inputs. For given integrator pole locations, scaling factors are found which maximize an approximate performance measure subject to bounds on internal state variables. The results clarify an explicit trade-off between tone rejection through chaos, system stability and practiced performance