Settling Time Analysis

The time-domain trajectory of the instantaneous carrier frequency as it converges to its target after activation. This profile directly exposes the loop filter characteristics of the phase-locked loop (PLL), including its order, bandwidth, and component tolerances. A critically damped loop will settle monotonically, while an underdamped loop exhibits a decaying oscillatory approach. The precise shape of this curve—including any inflection points—is a unique hardware signature.

A direct indicator of the PLL's damping factor. During lock acquisition, the frequency often exceeds the target before settling. Key metrics include:

• Peak Overshoot: The maximum frequency excursion beyond the steady-state value, expressed as a percentage.
• Ringing Artifact: A damped sinusoidal oscillation superimposed on the frequency trajectory, caused by parasitic inductance and capacitance in the loop filter resonating.
• Decay Time Constant (τ): The exponential rate at which the ringing amplitude diminishes, revealing the energy dissipation characteristics of the circuit.

The total duration required for the PLL to synchronize with the reference signal and stabilize within a specified tolerance (e.g., ±1 ppm). This interval is a critical transient window that exposes the dynamic response of the entire synthesis chain. Lock time is influenced by the initial frequency error, loop bandwidth, and charge pump current. Variations in lock time across multiple power-up cycles form a statistical signature unique to the device's component tolerances.

The path traced by the instantaneous phase of the signal in the complex (I/Q) plane during settling. Unlike steady-state analysis, this trajectory reveals the non-linear dynamics of the oscillator and modulator as they stabilize. Key features include:

• Phase Discontinuity: An abrupt, unintended phase jump at the moment of turn-on.
• Spiral Convergence: The characteristic inward spiral path as the phase error is driven to zero by the PLL control loop.
• Phase Noise Burst: A temporary elevation in phase noise during the locking period, creating a unique noise signature.

The amplitude envelope often settles concurrently with the frequency, and the two are coupled through power supply modulation. The inrush current during turn-on causes a momentary voltage sag on the supply rail, which amplitude-modulates the output. This reveals:

• Transient Voltage Sag: The depth and duration of the supply dip, indicating the equivalent series resistance (ESR) of decoupling capacitors.
• Amplitude Ramp Profile: The detailed shape of the power envelope's rising edge, including any non-linearities reflecting the specific biasing network and transistor physics of the power amplifier.

The rapid frequency change during settling generates broadband spectral noise, known as transient spectral splatter or key-click analysis. This momentary interference in adjacent channels reveals the switching speed and linearity of the hardware. The spectral centroid and kurtosis of this short-time Fourier transform (STFT) spectrum serve as robust features, indicating whether the transient energy is biased toward higher or lower frequencies and quantifying its impulsive, non-Gaussian nature.

The total duration required for a phase-locked loop (PLL) to synchronize its output frequency with a reference signal after power-up or a channel change. This interval is a critical transient period that exposes the loop's dynamic characteristics, including the loop bandwidth and damping factor. The lock time is heavily influenced by component tolerances in the loop filter, making it a highly device-specific metric for RF fingerprinting.

The complete time-domain trajectory of the instantaneous carrier frequency as it converges to its steady-state value. This profile reveals the loop filter characteristics of the PLL, including any underdamped oscillations or overdamped sluggishness. Key features include:

• PLL Overshoot: The peak frequency excursion beyond the target lock frequency.
• Settling Time: The time to remain within a defined tolerance (e.g., ±1 kHz).
• Phase Error Convergence: The rate at which the phase detector's error voltage stabilizes.

The dynamic behavior of the voltage-controlled oscillator (VCO) during the start-up period. This includes frequency pushing (a shift caused by power supply voltage changes during inrush current) and frequency pulling (a shift caused by a changing load impedance from the power amplifier turning on). These effects imprint a unique, non-linear signature on the carrier frequency trajectory before the PLL fully corrects the error.

A temporary, significant elevation in the phase noise spectrum of the local oscillator during the transient locking period. Before the loop stabilizes, the VCO's control voltage fluctuates, creating a unique noise signature. This burst is characterized by:

• Elevated Noise Floor: A temporary increase in broadband noise.
• Spectral Spurs: Momentary discrete tones from reference feedthrough.
• Duration: The time until the loop suppresses the noise to its steady-state specification.

The time-dependent path of the instantaneous frequency deviation from the nominal carrier. This trajectory visualizes the complete frequency settling behavior of the transmitter's synthesis chain. Analysis often uses zero-crossing analysis or the derivative of the instantaneous phase to map the precise curve from the initial transient frequency error to the final locked state, highlighting any non-linearities in the VCO's tuning sensitivity.

The total energy contained in a momentary, unintended frequency hop or spurious output generated by the frequency synthesizer during a power-up event. This glitch is a direct result of digital switching noise coupling into the VCO control line or divider circuits. The glitch's amplitude, duration, and spectral content form a repeatable, hardware-dependent artifact that is highly useful for transient fingerprinting.