PLL Phase Noise Burst

The loop filter is the primary determinant of the phase noise burst profile. Its topology (passive vs. active) and component values dictate the damping factor and natural frequency of the PLL's transient response.

• An underdamped loop creates a pronounced noise overshoot with ringing artifacts.
• An overdamped loop exhibits a slow, monotonic settling with a prolonged elevated noise floor.
• The filter's time constant directly sets the duration of the noise burst, typically ranging from microseconds to milliseconds.

The voltage-controlled oscillator (VCO) converts the loop filter's control voltage into a frequency. Its tuning sensitivity (Kvco), measured in Hz/V, acts as a gain factor that amplifies any noise present on the control line during the transient.

• A high Kvco magnifies the noise burst, making the signature more prominent and easier to fingerprint.
• VCO pushing—frequency shift due to power supply ripple during the inrush current—adds a deterministic, device-specific modulation component to the burst.
• Thermal transients within the VCO's resonator cause a characteristic instantaneous frequency drift during the burst.

The phase-frequency detector (PFD) and charge pump inject short, high-current pulses into the loop filter at the reference frequency rate. During the locking transient, these pulses are highly irregular, creating a distinct spectral signature.

• Charge pump mismatch (sourcing vs. sinking current imbalance) generates reference spurs that are elevated during the transient.
• Dead-zone elimination circuitry in the PFD creates a characteristic noise pedestal when the loop is near lock.
• The reference frequency and its harmonics appear as discrete spectral lines within the burst, their amplitude modulated by the loop's settling behavior.

The phase noise burst creates a three-dimensional signature across time, frequency, and amplitude that is unique to each transmitter due to component tolerances.

• The transient spectral centroid shifts predictably as the loop settles, tracing a unique trajectory in the time-frequency plane.
• Higher-order statistics like kurtosis and bispectrum analysis reveal non-Gaussian artifacts caused by discrete spurious signals within the burst.
• Unlike steady-state phase noise, the burst contains cyclostationary features linked to the reference clock, providing a robust fingerprint that is resistant to Gaussian channel noise.

Steady-state phase noise is a continuous, low-level random process. The PLL phase noise burst is a deterministic, time-limited event governed by the loop's initial conditions and component values.

• The burst is non-stationary; its statistical properties evolve rapidly over time, requiring time-frequency analysis (wavelets, short-time Fourier transform) rather than simple spectral averaging.
• Settling time—the interval until the phase noise variance falls within a specified tolerance of the steady-state value—is a key metric that varies between devices due to PLL bandwidth tolerances.
• The burst's peak phase noise density (dBc/Hz at a given offset) during the transient is often 10–30 dB higher than the manufacturer's specified steady-state performance.

Capturing the PLL phase noise burst requires high-dynamic-range equipment and precise triggering to isolate the transient from the steady-state transmission.

• A real-time spectrum analyzer (RTSA) with digital phosphor technology can capture the spectrogram of the burst without gaps.
• Zero-crossing analysis on the raw IQ data provides a high-resolution estimate of instantaneous frequency deviation during the burst.
• Transient wavelet decomposition isolates the burst's multi-scale features, separating the rapid initial overshoot from the slower thermal settling components.
• A transient matched filter, correlated with a known device template, maximizes the signal-to-noise ratio for fingerprint extraction in low-SNR environments.

The duration required for a phase-locked loop to synchronize with a reference signal after power-up. This period defines the temporal window during which the PLL phase noise burst is observable. The lock time is a direct function of the loop filter bandwidth and damping factor, and its precise duration serves as a coarse, high-level identifier of the PLL design. A shorter lock time generally indicates a wider loop bandwidth, which changes the spectral profile of the noise burst.

The dynamic behavior of the voltage-controlled oscillator during start-up, including frequency pushing and pulling effects. The VCO is the primary source of the elevated phase noise during the burst. Its transient response is highly sensitive to power supply rail noise and load impedance changes, imprinting a unique, device-specific signature onto the carrier's instantaneous frequency trajectory before the PLL loop establishes control.

The complete time-domain response of the PLL as it acquires lock, encompassing frequency overshoot, phase error convergence, and the phase noise burst itself. This transient is a rich source of fingerprinting features because its exact shape is determined by passive component tolerances in the loop filter. Key features include:

The short-term, elevated random frequency fluctuations of the local oscillator specifically during the start-up period. Unlike steady-state phase noise, transient phase noise is non-stationary and typically 10–30 dB higher. This burst is caused by the combined effects of thermal transients in the VCO, power supply inrush current, and the PLL's initial out-of-lock condition, creating a unique, unrepeatable noise signature for each power cycle.

The trajectory of the instantaneous carrier frequency as it converges to its steady-state value after activation. This profile directly reveals the loop filter characteristics of the PLL. Analysis involves extracting the instantaneous frequency via Hilbert transform or zero-crossing detection. The profile's shape—including any underdamped ringing or overdamped exponential decay—is a deterministic hardware signature of the specific resistor and capacitor values in the loop filter.

The center of mass of the transient's short-time Fourier transform (STFT) spectrum. This single-value feature indicates whether the PLL phase noise burst energy is biased toward higher or lower frequencies. A higher centroid suggests a faster, more underdamped loop response with greater high-frequency spectral splatter, while a lower centroid indicates a slower, overdamped design. It serves as a robust, low-dimensional feature for coarse emitter classification.