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arXiv · 1308.0650

Frequency Domain Min-Max Optimization of Noise-Shaping Delta-Sigma Modulators

Masaaki Nagahara·Yutaka Yamamoto
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Abstract

This paper proposes a min-max design of noise-shaping delta-sigma modulators. We first characterize the all stabilizing loop-filters for a linearized modulator model. By this characterization, we formulate the design problem of lowpass, bandpass, and multi-band modulators as minimization of the maximum magnitude of the noise transfer function (NTF) in fixed frequency band(s). We show that this optimization minimizes the worst-case reconstruction error, and hence improves the SNR (signal-to-noise ratio) of the modulator. The optimization is reduced to an optimization with a linear matrix inequality (LMI) via the generalized KYP (Kalman-Yakubovich-Popov) lemma. The obtained NTF is an FIR (finite-impulse-response) filter, which is favorable in view of implementation. We also derive a stability condition for the nonlinear model of delta-sigma modulators with general quantizers including uniform ones. This condition is described as an H-infinity norm condition, which is reduced to an LMI via the KYP lemma. Design examples show advantages of our design.

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Masaaki Nagahara, Yutaka Yamamoto. 2013-08-03. Frequency Domain Min-Max Optimization of Noise-Shaping Delta-Sigma Modulators. https://doi.org/10.1109/tsp.2012.2188522

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