阶梯型正弦波相角量化误差的周期性与对称性&mdash;&mdash;阶梯波研究之五

陆祖良

doi:10.3969/j.issn.1000-1158.2021.07.13

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计量学报 ›› 2021, Vol. 42 ›› Issue (7) : 913-922. DOI: 10.3969/j.issn.1000-1158.2021.07.13

电磁学计量

阶梯型正弦波相角量化误差的周期性与对称性——阶梯波研究之五

陆祖良

作者信息 +

Periodicity and Symmetry in Quantization Error of Phase Angle of Sinusoidal Waveform Generated by Digital-to-Analog Converter

LU Zu-liang

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文章历史 +

摘要

一般数模转换器产生的正弦波实际上是阶梯波的基波,提出了这类正弦波相角量化误差的概念,描述并证明了它的固有特性诸如周期性、对称性,推导了相角量化误差的零点分布,讨论了这些特性在高准确度相角建立中的应用。这种零点分布是量化的,其宽度为0.5H(H=2π/N),当N为奇数时则为0.25H。为了克服相角量化误差,可使相角成为该宽度的整数(p)倍。在规定的不确定度内任意指定的相角差原则上可通过调节参数p和N得以实现。

Abstract

A sinusoidal waveform generated by digital-to-analog converter is actually a fundamental of staircase waveform. The quantization error of phase angle of this kind of the sinusoidal waveform is defined. Its intrinsic characteristics such as periodicity and symmetry are described and proved. The relative zero-point distribution is derived. The application of these characteristics in building of phase angle with higher accuracy is discussed. This zero-point distribution is quantization too with a width of 0.5H (H=2π/N) or 0.25H for odd numbers of N. In order to overcome the quantization error of phase angle, it is advised to the phase angler become an integer multiple, p, of this width, where parameters of p and N can be adjusted to such that an arbitrarily phase angle difference demand can be realized in principle within a specified uncertainty.

导出引用

陆祖良. 阶梯型正弦波相角量化误差的周期性与对称性——阶梯波研究之五[J]. 计量学报. 2021, 42(7): 913-922 https://doi.org/10.3969/j.issn.1000-1158.2021.07.13

LU Zu-liang. Periodicity and Symmetry in Quantization Error of Phase Angle of Sinusoidal Waveform Generated by Digital-to-Analog Converter[J]. Acta Metrologica Sinica. 2021, 42(7): 913-922 https://doi.org/10.3969/j.issn.1000-1158.2021.07.13

中图分类号： TB971

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