Optimal design of both multi-input multi-output loop filter and multi-input single-output reconstruction filter of sigma delta modulator,International Journal of Circuit Theory and Applications

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Optimal design of both multi-input multi-output loop filter and multi-input single-output reconstruction filter of sigma delta modulator
International Journal of Circuit Theory and Applications ( IF 1.8 ) Pub Date : 2022-07-28 , DOI: 10.1002/cta.3384
Qing Miao ₁ , Bingo Wing‐Kuen Ling ₂ , Heidi Hai Huyen Dam ₃

Affiliation

This paper considers a sigma delta modulator (SDM) with the outputs of the quantizers directly fedback to the inputs of the loop filter without being subtracted from the input sequence. The design of the multi-input multi-output (MIMO) loop filter is formulated as an optimization problem. In particular, the sum of the inner products between the elements in the signal transfer function (STF) and the corresponding elements in the noise transfer function (NTF) of the SDM is minimized. The constraints of the optimization problem are defined based on the specifications on the maximum absolute difference between the magnitude response of the designed STF and that of the desirable STF as well as that between the magnitude response of the designed NTF and that of the desirable NTF of the SDM. Similarly, the design of the multi-input single-output (MISO) reconstruction filter is also formulated as an optimization problem. In particular, the sum of the total absolute difference between the designed magnitude response of the reconstruction filter and the desirable magnitude response of the STF of the SDM is minimized. The constraint of the problem is defined based on the specification on maximum absolute difference between the designed magnitude response of the reconstruction filter and the desirable magnitude response of the STF of the SDM. In this paper, the genetic algorithm is employed to find a near global solution of the formulated optimization problems. In order to reduce the required computational power, the matrix inversion lemma is applied. The computer numerical simulation results show that the SDM designed by our proposed method outperforms the SDMs designed by the Matlab function in terms of the signal to noise ratio (SNR) performance.

中文翻译：

sigma delta调制器多输入多输出环路滤波器和多输入单输出重构滤波器的优化设计

本文考虑了一个 sigma delta 调制器 (SDM)，其量化器的输出直接反馈到环路滤波器的输入，而无需从输入序列中减去。多输入多输出 (MIMO) 环路滤波器的设计被表述为一个优化问题。特别地，信号传递函数(STF)中的元素与SDM的噪声传递函数(NTF)中的对应元素之间的内积之和被最小化。优化问题的约束是根据设计的 STF 的幅度响应与理想的 STF 的幅度响应之间以及设计的 NTF 的幅度响应与理想的 NTF 的幅度响应之间的最大绝对差的规范来定义的SDM。相似地，多输入单输出 (MISO) 重建滤波器的设计也被表述为优化问题。特别地，重构滤波器的设计幅度响应与SDM的STF的期望幅度响应之间的总绝对差之和被最小化。问题的约束是根据重建滤波器的设计幅度响应与 SDM 的 STF 的理想幅度响应之间的最大绝对差的规范来定义的。在本文中，遗传算法被用来寻找制定的优化问题的近似全局解。为了减少所需的计算能力，应用了矩阵求逆引理。

更新日期：2022-07-28

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