Title :
MSE law of nth order ΣΔ modulators
Author_Institution :
Dept. of Electr. Eng., New York Univ., NY, USA
Abstract :
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 show 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.
Keywords :
error analysis; mean square error methods; modulators; sigma-delta modulation; MSE law; centroid function; error analysis; mean squared error law; nth order ΣΔ modulators; oversampling ratio; Convolution; Delta modulation; Equations; Error analysis; Filters; Linearity; Noise figure; Sampling methods; Testing; Transfer functions;
Conference_Titel :
Circuits and Systems, 2002. MWSCAS-2002. The 2002 45th Midwest Symposium on
Print_ISBN :
0-7803-7523-8
DOI :
10.1109/MWSCAS.2002.1187232
