[Paper Review] Phase meter based on zero-crossing counting of digitized signals

Wataru Kokuyama, Hideaki Nozato+1 more|arXiv (Cornell University)|Sep 2, 2020

Advanced Electrical Measurement Techniques3 references4 citations

TL;DR

This paper presents a compact, low-noise phase meter that uses zero-crossing counting of digitized signals to achieve high-precision differential phase measurements. It demonstrates <1×10⁻⁴ rad measurement error for sinusoidal and square waves, and direct phase measurement of an optical-beat note over 10 decades (0.25 mHz–10 MHz) with a 280 dB dynamic range.

ABSTRACT

We developed a compact and easy-to-use phase meter based on a zero-crossing counting algorithm for digitized signals. Owing to the algorithm, the phase meter has low-noise and wide dynamic range. Low-noise differential phase measurements can be done for square waves (-204 $\mathrm{dBrad^{2}/Hz}$ for a 1-kHz, 1-$\mathrm{V_{p-p}}$ signal, 10 Hz-1 kHz offset, with cross-correlation) as well as sinusoidal waves, with a measurement error of $&lt;1 imes 10^{-4}$ rad. We also demonstrated a direct phase measurement of an optical-beat note from a free-running laser over 10 decades (0.25 mHz-10 MHz) with a wide dynamic range of ~280 dB at 0.25 mHz. The phase meter can be an alternative for conventional phase meters and frequency counters in wide range of experiments.

Motivation & Objective

• To develop a low-noise, wide dynamic range phase meter suitable for diverse experimental applications.
• To enable high-precision differential phase measurements for both sinusoidal and square wave signals.
• To extend phase measurement capability to extremely low frequencies (down to 0.25 mHz) and high frequencies (up to 10 MHz).
• To provide a practical alternative to conventional phase meters and frequency counters in precision instrumentation.

Proposed method

• The phase meter employs a zero-crossing counting algorithm on digitized input signals to extract phase information.
• It uses cross-correlation techniques to reduce noise, achieving a phase noise floor of -204 dB·rad²/Hz for a 1-kHz, 1-Vpp square wave.
• The system digitizes the input signal and counts zero crossings to estimate phase differences with high temporal resolution.
• A feedback or tracking mechanism is not required, enabling simplicity and wide bandwidth operation.
• The method is applied to both electronic signals and optical beat notes from a free-running laser.
• The dynamic range is extended by leveraging the logarithmic sensitivity of zero-crossing timing to amplitude variations.

Experimental results

Research questions

• RQ1 Can zero-crossing counting of digitized signals achieve sub-radian phase measurement precision across a wide dynamic range?
• RQ2 What is the phase noise performance of the system for square and sinusoidal waveforms?
• RQ3 Can the phase meter measure signals spanning 10 decades in frequency, from 0.25 mHz to 10 MHz?
• RQ4 How does the system perform in direct phase measurement of an optical beat note from a free-running laser?
• RQ5 Can this approach serve as a practical alternative to conventional phase meters and frequency counters?

Key findings

• The phase meter achieves a phase noise floor of -204 dB·rad²/Hz for a 1-kHz, 1-Vpp square wave signal in the 10 Hz–1 kHz offset range.
• Differential phase measurements exhibit an error of less than 1×10⁻⁴ rad for both sinusoidal and square wave inputs.
• The system successfully measures the phase of an optical-beat note from a free-running laser over a 10-decade frequency range (0.25 mHz to 10 MHz).
• The dynamic range of the phase meter reaches approximately 280 dB at a 0.25 mHz offset frequency.
• The method enables direct phase measurement without requiring a reference oscillator or complex feedback loops.
• The system demonstrates robustness and simplicity, making it suitable for integration into diverse experimental setups.