Asymptotic MSE law of nth-order ΣΔ modulators

The mean squared error (MSE) of an nth-order ΣΔ modulator is classically understood to decay with the oversampling ratio M at the rate α/M²ⁿ⁺¹. In this paper, we demonstrate by experimental evidence and basic analytical explanations that the accurate general MSE law is in fact in (β/M²ⁿ)+(γ/M²ⁿ⁺¹) instead. The coefficient β is in general not zero, except when the input is rigorously constant, or when using the ideal standard nonoverloaded n-bit n-loop modulator. The term β/M²ⁿ is dominant starting from low values of M when using a one-bit quantizer.