State-trajectory behavior in high-order, lowpass sigma-delta modulators with distinct NTF zeros
2002 14th International Conference on Digital Signal Processing Proceedings. DSP 2002 (Cat. No.02TH8628) - Tập 2 - Trang 1053-1056 vol.2
Tóm tắt
This paper presents a generic, scalable approach to obtain closed-form state-trajectory expressions for high-order (order > 2) lowpass sigma-delta (/spl Sigma//spl Delta/) modulators with distinct noise transfer function (NTF) zeros. Constant modulator input is assumed. The techniques of state-space diagonalization, continuous-time embedding, and Poincare map analysis are combined and extended. It is shown that an even-order modulator can be decomposed into individual second-order subsystems with circular trajectories about two half-plane centers, while an odd-order modulator will result in an additional first-order subsystem represented by an oscillating quantity. The trajectory and half-plane transition expressions thus obtained provide effective tools for stability analysis of /spl Sigma//spl Delta/ modulators.
Từ khóa
#Delta-sigma modulation #Stability analysis #Transfer functions #Bridges #Noise shaping #Linearity #Signal to noise ratio #Chaos #Limit-cycles #Matrix decompositionTài liệu tham khảo
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