[Paper Review] 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 Standards0 citations

TL;DR

The paper argues for SI-consistent quantities and terminology in phase and amplitude noise, critiques the use of L(f) and dBc/Hz, and proposes SI-aligned measurement units and vocabulary.

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.

Motivation & Objective

• Clarify physical quantities and units used in phase and amplitude noise measurements.
• Promote adoption of SI-consistent terminology across laboratories and instruments.
• Identify and critique non-SI quantities and terms commonly used (e.g., L(f), dBc/Hz).
• Propose measurement practices and units that align with SI for phase and amplitude noise measurements.

Proposed 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.

Experimental results

Research questions

• 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?

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.