Frequency Domain Min-Max Optimization of Noise-Shaping Delta-Sigma Modulators
Frequency Domain Min-Max Optimization of Noise-Shaping Delta-Sigma Modulators
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DOI：
10.1109/tsp.2012.2188522
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发表时间：
2012-06
影响因子：
5.4
通讯作者：
M. Nagahara;Y. Yamamoto
中科院分区：
文献类型：
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作者：
M. Nagahara;Y. Yamamoto
本文提出了噪声整形 Delta-Sigma 调制器的最小-最大设计。我们首先表征线性化调制器模型的所有稳定环路滤波器。通过这种表征，我们将低通、带通和多频带调制器的设计问题表述为最小化固定频带中噪声传递函数 (NTF) 的最大幅度。我们表明，这种优化最大限度地减少了最坏情况下的重建误差，从而提高了调制器的 SNR（信噪比）。通过广义 KYP（卡尔曼-雅库博维奇-波波夫）引理，优化被简化为线性矩阵不等式 (LMI) 的优化。所获得的NTF是FIR(有限脉冲响应)滤波器，其在实现方面是有利的。我们还推导了具有通用量化器（包括均匀量化器）的 Delta-Sigma 调制器非线性模型的稳定性条件。该条件被描述为范数条件，通过 KYP 引理简化为 LMI。设计实例展示了我们设计的优势。
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 norm condition, which is reduced to an LMI via the KYP lemma. Design examples show advantages of our design.