This paper studies the causes and distribution of reconstruction errors in subtractive dither structure and provides solution to minimize these errors. We present the generation of reconstruction errors in two types of quantization, namely mid-riser and mid-tread, with their corresponding distributions. We then construct a 12-bit pipeline analog to digital converters (ADC) simulation model and use a 16-bit digital to analog converter (DAC) to convert the dither sequence into analog signals. We perform statistical analysis on the resulting data, verify the accuracy of the distribution, and find that reconstruction error only occurs when the dither signal accuracy surpasses that of the ADC. Additionally, we find that mid-tread quantization has the lowest probability of reconstruction error. Finally, we analyze the impact of reconstruction error on the signal to noise ratio (SNR) and spurious free dynamic range (SFDR) at various input frequencies. Our findings show that the reconstruction errors' effect on the SFDR and SNR of the input signal is less than 1 dB.

中文翻译：

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减法抖动结构中重构误差的影响

本文研究了减色抖动结构中重建误差的原因和分布，并提供了最小化这些误差的解决方案。我们提出了两种类型的量化（即中立板和中胎面）中重建误差的产生及其相应的分布。然后，我们构建了一个 12 位流水线模数转换器 (ADC) 仿真模型，并使用 16 位数模转换器 (DAC) 将抖动序列转换为模拟信号。我们对所得数据进行统计分析，验证分布的准确性，发现只有当抖动信号精度超过ADC时才会出现重构误差。此外，我们发现中间量化具有最低的重建错误概率。最后，我们分析了不同输入频率下重构误差对信噪比（SNR）和无杂散动态范围（SFDR）的影响。我们的研究结果表明，重构误差对输入信号 SFDR 和 SNR 的影响小于 1 dB。