Stability Analysis of Bandpass Sigma-Delta Modulators for Single and Dual Tone Sinusoidal Inputs

In this paper, the stability boundaries of higher order 1-bit bandpass (BP) Σ-Δ modulators for single- and dual-sinusoidal inputs are determined using quasi-linear modeling together with the describing-function method. Closed-form mathematical expressions are derived for the stability curves for dif...

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Bibliographic Details
Published in:IEEE transactions on instrumentation and measurement 2011-05, Vol.60 (5), p.1546-1554
Main Authors: Altinok, G D, Al-Janabi, M, Kale, I
Format: Article
Language:English
Subjects:
Analog-digital conversion
Analytical models
Attenuation
Chebyshev approximation
Modulation
Noise
nonlinear systems
Quantization
signal processing
Stability analysis
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Summary:In this paper, the stability boundaries of higher order 1-bit bandpass (BP) Σ-Δ modulators for single- and dual-sinusoidal inputs are determined using quasi-linear modeling together with the describing-function method. Closed-form mathematical expressions are derived for the stability curves for different quantizer gain values. The stability prediction for the maximum stable input limits for eighth- and tenth-order (i.e., effective fourth- and fifth-order) inverse-Chebyshev- and Butterworth-based BP Σ-Δ modulators for different stopband attenuation and bandwidths are established. The theoretical results are shown to be in good agreement with the simulation results for a variety of input amplitudes, bandwidths, and modulator orders. The proposed mathematical models of the quantizer will immensely help speed up the design of higher order BP Σ-Δ modulators.
ISSN:0018-9456
1557-9662
DOI:10.1109/TIM.2010.2102395