[论文解读] Vocabulary, Physical Quantities and Units for the Measurement of Amplitude Noise and Phase Noise

Enrico Rubiola, Jacques Millo+4 more|arXiv (Cornell University)|Mar 9, 2026

Advanced Frequency and Time Standards被引用 0

一句话总结

本文主张在相位与幅度噪声中使用与SI一致的量纲与术语，批评使用 L(f) 与 dBc/Hz，并提出与SI对齐的测量单位与词汇。

ABSTRACT

The widespread use of non-SI quantities and units, together with improper and misleading terminology, generates confusion in the domain of phase and amplitude noise. We discuss such physical quantities, units and terms with the purpose of stimulating a discussion between labs, and to agree for the full adoption of the International System of Units (SI) and clear, unambiguous terminology.

研究动机与目标

• 澄清在相位与幅度噪声测量中使用的物理量与单位。
• 推动实验室与仪器普及SI一致的术语。
• 识别并批评常用的非SI量和术语（如 L(f)、dBc/Hz）。
• 提出符合SI的测量做法与单位，用于相位与幅度噪声测量。」,
• method
• Define the random phase varphi(t) and amplitude modulation alpha(t) and their spectral representations.
• Derive the single-sided PSD S_phi(f) and its SI-compatible unit rad^2/Hz.
• Argue for using rad^2/Hz (or dB rad^2/Hz) for phase noise and dB/Hz (or dB 1/Hz) for amplitude noise.
• Explain the issues with the L(f) quantity and its relation to S_phi(f) (including the 1 Hz noise interpretation).
• Discuss the limitations of the SSB noise concept and the applicability to real oscillators where varphi(t) diverges.
• research_questions
• What SI-consistent quantities and units should be used for phase and amplitude noise measurements?
• How should phase noise (and AM noise) be represented to reflect the underlying physics and measurement processes?
• Why is the common L(f) (dBc/Hz) representation misleading or inconsistent with SI?
• key_findings
• S_phi(f) has SI dimension of time with unit rad^2/Hz; the natural choice is rad^2/Hz or dB rad^2/Hz.
• Amplitude noise lacks an intrinsic unit and naturally uses dB/Hz or dB 1/Hz, with potential V/V-based expressions in EE contexts.
• L(f) is misnamed as SSB noise and is inconsistent with SI, partly because it mixes AM/PM interpretations and is tied to energy conservation assumptions not valid for all oscillators.
• The declared equivalence L(f) = 1/2 S_phi(f) is problematic and leads to unit inconsistencies when converting to dB units.
• The current reliance on L(f) and dBc/Hz in calibration and metrology contexts is problematic and warrants rewriting toward SI-consistent practice.
• table_headers: []
• table_rows: []

提出的方法

• Define the random phase varphi(t) and amplitude modulation alpha(t) and their spectral representations.
• Derive the single-sided PSD S_phi(f) and its SI-compatible unit rad^2/Hz.
• Argue for using rad^2/Hz (or dB rad^2/Hz) for phase noise and dB/Hz (or dB 1/Hz) for amplitude noise.
• Explain the issues with the L(f) quantity and its relation to S_phi(f) (including the 1 Hz noise interpretation).
• Discuss the limitations of the SSB noise concept and the applicability to real oscillators where varphi(t) diverges.

实验结果

研究问题

• RQ1 What SI-consistent quantities and units should be used for phase and amplitude noise measurements?
• RQ2 How should phase noise (and AM noise) be represented to reflect the underlying physics and measurement processes?
• RQ3 Why is the common L(f) (dBc/Hz) representation misleading or inconsistent with SI?

主要发现

• S_phi(f) has SI dimension of time with unit rad^2/Hz; the natural choice is rad^2/Hz or dB rad^2/Hz.
• Amplitude noise lacks an intrinsic unit and naturally uses dB/Hz or dB 1/Hz, with potential V/V-based expressions in EE contexts.
• L(f) is misnamed as SSB noise and is inconsistent with SI, partly because it mixes AM/PM interpretations and is tied to energy conservation assumptions not valid for all oscillators.
• The declared equivalence L(f) = 1/2 S_phi(f) is problematic and leads to unit inconsistencies when converting to dB units.
• The current reliance on L(f) and dBc/Hz in calibration and metrology contexts is problematic and warrants rewriting toward SI-consistent practice.