Influence Mechanism of Truncation on Low-Frequency Phase Measurement

TL;DR

This paper analyzes how truncation affects low-frequency phase measurement in digital phasemeters, revealing noise characteristics and proposing dither addition to mitigate phase noise for high-precision applications.

Contribution

It provides a detailed analysis of truncation-induced noise in digital phasemeters and demonstrates that Gaussian dither effectively reduces low-frequency phase noise.

Findings

Truncation noise can be modeled as white noise under certain conditions.

Non-white noise occurs when signal and sampling frequencies are near integer multiples.

Adding Gaussian dither significantly reduces low-frequency phase noise.

Abstract

Driven by advances in electronic technology, modern digital phasemeters have significantly improved in integration and functionality, enabling real-time measurement and analysis of dynamic signals. High-precision phase measurement is closely associated with the quantization process. This paper specifically analyzes the white and non-white noise characteristics associated with the quantization errors of phase truncation in digital phasemeters. The error can be considered white noise under specific conditions, which power correlates with the resolution of quantizer and is uniformly distributed within the Nyquist frequency. However, when the signal frequency and sampling frequency are close to an integer multiple, the non-white noise caused by truncation can result in low-frequency phase noise. Additionally, artifacts may induce nonlinear phase errors. Introducing Gaussian dither synthesized by LFSRs can smooth the truncation process, thereby mitigating its impacts on phase measurement. The results indicate that for a 10 MHz signal under test, the noise floor of the phasemeter exceeds the requirement from 2 mHz to 0.1 Hz due to the integer multiple. After adding dither, the phase noise was optimized by 9.5 dB at 10 mHz, achieving the requirement of 1.3 $\rm{\upmu rad/Hz^{1/2}} \cdot \rm{NSF}$ from 0.1 mHz to 1 Hz in space gravitational wave detection. This demonstrates that adding dither can effectively suppress the low-frequency phase noise caused by truncation.