Transient Phase Noise

During the phase-locked loop (PLL) lock time, the phase noise floor is significantly higher than the specified steady-state value. This temporary elevation occurs because the loop has not yet suppressed the voltage-controlled oscillator (VCO) free-running noise. The duration and profile of this elevated noise floor directly reflect the loop filter bandwidth and damping factor, providing a unique hardware fingerprint that cannot be cloned or mimicked by a digital synthesizer.

Unlike steady-state phase noise, which is wide-sense stationary, transient phase noise is inherently non-stationary. Its statistical moments—mean, variance, and higher-order cumulants—evolve rapidly over microseconds. Key features include:

• Time-varying power spectral density that converges toward the steady-state profile
• Frequency-dependent settling where close-in phase noise stabilizes before far-out noise
• Stochastic jitter accumulation that differs on every power-up cycle

This non-stationarity provides a rich, multi-dimensional feature space for transient fingerprint extraction.

During the transient, the VCO experiences frequency pushing (supply voltage fluctuations) and frequency pulling (load impedance changes) that imprint unique signatures on the carrier. The transient current inrush to the power amplifier causes a momentary supply sag, which modulates the VCO frequency. Simultaneously, the changing impedance of the PA as it ramps up pulls the oscillator. These coupled effects create a deterministic yet device-specific transient frequency trajectory that serves as a robust identifying feature.

The PLL settling transient is dominated by the loop filter's component values. Microscopic manufacturing variances in resistors and capacitors—often 1-5% tolerance—produce measurable differences in:

• Settling time to within 1 kHz of the target frequency
• PLL overshoot magnitude and ringing frequency
• Phase margin degradation visible as underdamped oscillations

These analog component tolerances are physically unclonable, making the transient phase noise profile a hardware-intrinsic security primitive.

The instantaneous self-heating of the transistor junction during the high-current turn-on event causes a rapid, minute shift in the semiconductor's carrier mobility and threshold voltage. This thermal transient modulates the oscillator's phase through:

• Thermally-induced capacitance changes in varactor diodes
• Propagation delay shifts in digital divider circuits
• Bias point drift in the VCO active devices

The thermal time constant, typically in the microsecond range, creates a characteristic transient phase trajectory that is unique to each device's die-attach and packaging quality.

When a frequency synthesizer switches channels or powers up, it generates momentary spurious outputs known as glitch energy. These unintended frequency hops contain:

• Broadband spectral splatter from divider reset transients
• Charge pump imbalance pulses during phase acquisition
• Fractional-N spur transients that settle over multiple reference cycles

The total glitch energy and its spectral distribution form a repeatable signature of the synthesizer's digital logic and charge pump design, providing a distinct marker for transient phase noise fingerprinting.