| 数模变换量化误差固有特性再讨论 |
| Revisiting Discussion for Inherent Characteristics of Quantization Error from Digital-to-Analogue Conversion |
| 投稿时间：2025-06-25 修订日期：2025-07-28 |
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| 中文摘要: |
| 为了在数模转换中准确实现预设相角，一般采用增加转换分辨力的方法，这实质上是在幅值轴方向上进行精细分割以接近原始信号，存在成本高、速度慢、功耗大等不足。针对该问题，进一步提出在时间轴方向上进行适当分割以接近原始信号的方法。为此论述量化误差包括相角量化误差（Phase Angle Quantization Error, PQE）和幅值量化误差（Amplitude Quantization Error, AQE）的定义，阐述所研究的量化过程应满足的4个一般性条件，分析量化误差随相角变化而变化的固有特性，并开展模拟实验和真实实验进行验证，结果表明：量化误差呈现周期性分布，误差周期是信号周期的1 / N（N为一个信号周期内的采样个数）；在误差周期内，量化误差的分布是对称的；相角量化误差的零点具有独立性，这些零点与转换分辨力、信号幅值无关。指出调节N值使这些零点与预设相角相联系具有重要应用价值，有望推动相角标准研制和阻抗电桥技术发展，并扩展高速、低功耗、低成本数模转换器（Digital-to-Analogue Converter, DAC）的应用。 |
| 英文摘要: |
| To accurately achieve the desired phase angle during digital-to-analog conversion, a commonly used approach is to increase the conversion resolution. This method relies on finer amplitude-axis discretization to better approximate the original waveform. However, it comes with several disadvantages, such as high cost, slow conversion speed, and considerable power consumption. To address these limitations, this paper further explores a novel method—time-axis segmentation. A definition of quantization error is introduced, which includes both phase angle quantization error (PQE) and amplitude quantization error (AQE). Four essential conditions for the quantization process are presented. The paper also analyzes how the quantization error inherently varies with the phase angle. Simulation and experimental results are provided to validate the theoretical conclusions. The results show that the quantization errors exhibit a periodic distribution, with the error period being 1/N of the signal cycle, where N denotes the number of samples per signal cycle. Within each error period, the quantization errors are symmetrically distributed. Moreover, a series of zero-points of the phase angle quantization error is derived, which are independent of both the conversion resolution and the signal amplitude. By adjusting N to align these zero-points with the desired phase angle, new application opportunities arise. This study is expected to contribute to the advancement of phase angle standards and impedance bridge technology, and promote the use of high-speed, low-power, and cost-effective digital-to-analog converters. |
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| 中文关键词: 相角 量化误差 幅值 数模转换 误差 |
| 英文关键词:phase angle quantization error amplitude digital-analog conversion error |
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