Phase Noise Analysis

Phase noise captures the short‑term randomness in the phase of an otherwise periodic signal. Put simply, it is the tiny, fast wobble of a signal’s phase, like a metronome that does not click at exactly the same instant every time. On a spectrum analyzer, it appears as faint sidebands (“skirts”) around the carrier frequency as a small power leaks away from the main tone. Phase noise is commonly given as single‑sideband (SSB) power distribution, $L(f)$, in dBc/Hz at a given offset from the carrier frequency. In the time domain, the same phenomenon is represented as timing jitter ¹.

At the component level, phase-noise analysis is central to oscillator engineering: measuring $L(f)$ across offsets reveals intrinsic device noise and turns design choices into tangible metrics such as timing jitter and short-term stability ^{2 3}. At the system level, the same analysis underpins synchronization technologies: disciplining oscillators to a cleaner standard, validating master-slave distribution links, and maintaining phase coherence across distributed nodes. More broadly, because clocks, synthesizers, and optical/RF oscillators anchor communications, radar, navigation, coherent optics, and precision timing, controlling phase noise is directly tied to overall signal quality and short-term frequency stability. Real sources are never perfectly clean; thermal and flicker noise, device physics, and phase-locked loop (PLL) dynamics perturb instantaneous phase and frequency ³. Characterizing these fluctuations enables like-for-like comparison of oscillators, synthesizers, and the links that distribute them, rigorous jitter budgets, well-chosen loop bandwidths, and reliable in-band performance predictions across the offset ranges that matter.

Phase‑noise characterization has traditionally relied on spectrum‑analyzer methods, mixer/PLL detectors, or delay‑line discriminators. Cross‑correlation is often used to push the instrument noise floor lower ⁴. An alternative software‑based approach timestamps signal edges with picosecond precision and estimates the phase‑noise power spectral density (PSD) from the time‑tag stream. This unifies phase‑noise, jitter, and frequency stability analysis from a single acquisition while covering offsets from close‑in to far‑from‑carrier with consistent processing.

Building on this approach, Swabian Instruments integrates phase‑noise analysis into the Time Tagger software. The PhaseNoise measurement class computes SSB phase‑noise spectra from time tags using a windowed, overlapped Welch method and quasi‑logarithmic offset spacing. It also reports integrated jitter over user‑defined bands and can reference an external standard via a software-based PLL when required. As a result, laboratory‑grade phase‑noise characterization lives side‑by‑side with frequency‑stability, jitter, and 1 Pulse Per Second (PPS) tools, simplifying setups and accelerating development.

A standard phase-noise measurement compares the device under test (DUT) with a clean reference oscillator at the same effective frequency, using a phase detector, analog (mixer/sampler) or digital (I/Q), inside a locked loop. The two paths are brought to the same frequency (directly or after division/multiplication/mixing), the loop holds them in quadrature, and the detector’s baseband phase-error signal is processed to obtain the single-sideband spectrum L(f). When a clearly superior reference is not available, engineers and researchers use two-source or three-oscillator (three-cornered-hat) methods and often apply dual-channel cross-correlation to suppress instrument noise.

As an alternative front end, delay-line or resonator discriminators convert phase fluctuations to voltage without requiring a same-frequency reference. For link/distribution tests, a primary (master) node’s frequency (e.g., the standard 10 MHz) and a remote node’s recovered frequency are measured simultaneously so the link’s added phase noise can be quantified.

Common challenges in Phase Noise analysis include:

As an alternative to classical mixer/phase-locked loop or discriminator-based analyzers, Swabian Instruments’ Time Tagger offers a software-centric route: it timestamps zero crossings with picosecond precision, locks the time-tag stream to an external standard via a software PLL, and computes the SSB spectrum L(f) directly from the tags (windowed, overlapped Welch processing with quasi-log offset spacing). With all inputs on a common time base, multiple DUTs or link endpoints (e.g., a primary 10 MHz and a remote recovered 10 MHz) can be analyzed simultaneously, and integrated jitter over user-defined bands is derived from the same dataset. Key advantages of Swabian Instruments’ Time Tagger for phase-noise analysis include:

To showcase the PhaseNoise measurement class, three 10 MHz references (a rubidium standard, a quartz OCXO, and a MEMS OCXO) are measured and their single-sideband spectra $L(f)$ plotted. Across much of the band, the quartz and MEMS traces are broadly similar, while at high offset frequencies, the rubidium unit shows higher phase noise. This behavior is expected: a rubidium standard disciplines an internal quartz oscillator with a narrow loop bandwidth, so beyond the servo bandwidth, the synthesis chain and free-running quartz dominate, yielding higher wideband (far-out) noise than a good standalone OCXO.

At the highest offsets, the quartz and MEMS curves track the dashed measurement floor, indicating that the instrument limit constrains the observed noise there. Spectra were computed via windowed, overlapped Welch PSD on a quasi-log grid (512 points per octave) over a 1-hour acquisition; the floor was obtained by splitting a single 10 MHz into two inputs and software-locking one channel to the other. The dataset supports like-for-like comparisons and integrated-jitter estimates over user-defined bands.