Turn-Off Transient

The ramp-down signature is the amplitude-versus-time envelope of the signal's trailing edge. Unlike the turn-on ramp, this profile is dominated by the discharge of capacitive elements and the power supply's holdup time.

• Fall-Time Variance: The statistical distribution of the 90% to 10% fall time reveals the stochastic nature of the discharge path.
• Undershoot Characterization: The amplitude dip below the noise floor immediately after ramp-down reflects the reverse recovery of power supply components.
• Burst Trailing Edge Slope: The maximum negative rate of amplitude change indicates how quickly energy storage elements can be depleted.

An abrupt, unintended shift in the instantaneous phase of the carrier signal occurs during the turn-off transient. This is caused by the non-ideal switching of frequency synthesis components as bias voltages collapse.

• Transient Phase Trajectory: The path traced by the instantaneous phase in the complex plane reveals the underlying dynamics of the oscillator's power-down sequence.
• Phase Noise Burst: A temporary elevation in the phase noise spectrum often occurs as the phase-locked loop (PLL) loses lock, creating a unique noise signature before the signal ceases.
• Zero-Crossing Analysis: Measuring intervals between final zero-voltage crossing points provides a precise time-domain extraction of the instantaneous frequency drift during shutdown.

As the transmitter powers down, the carrier frequency does not simply stop; it drifts. The instantaneous frequency drift is caused by thermal transients and voltage-controlled oscillator (VCO) pulling effects as the supply voltage sags.

• Transient Frequency Trajectory: Visualizes the complete frequency deviation path from steady-state to zero, revealing the VCO's sensitivity to voltage collapse.
• Transient VCO Pulling: The undesired frequency shift caused by the sudden impedance change of the load presented by the power amplifier as it turns off.
• Settling Time Analysis: In this context, it measures the duration for the frequency to decay to an undetectable level, exposing the PLL's hold-in range characteristics.

A ringing artifact is a damped sinusoidal oscillation superimposed on the transient envelope, caused by parasitic inductance and capacitance resonating in the output matching network as the driving signal is removed.

• Damped Oscillation Profile: The exponential decay envelope of the ringing has a specific time constant and resonant frequency that serves as a distinct hardware signature.
• Transient Spectral Splatter: The rapid switching generates broadband noise, with the adjacent channel splatter component revealing the filtering effectiveness during the burst offset.
• Key-Click Analysis: A historical term for spectral sidebands generated by abrupt signal cessation, now applied to modern transient-induced spectral artifacts.

The turn-off transient is heavily influenced by the immediate electrical history of the device. Transient memory effects arise from thermal trapping and charge storage in semiconductor materials.

• Transient Voltage Sag: The specific drop in the regulated supply voltage rail during the final current draw indicates the equivalent series resistance (ESR) of the decoupling network.
• Transient Thermal Signature: The minute, rapid change in electrical behavior caused by the instantaneous cooling of the transistor junction as current flow ceases.
• Transient Ground Bounce: A voltage spike on the internal ground reference caused by the collapsing magnetic field in parasitic bond wire inductances, creating a final identifying artifact.

Robust fingerprinting relies on statistical measures that are blind to Gaussian noise. Transient higher-order statistics isolate the deterministic non-linear signatures of the hardware.

• Transient Kurtosis: Quantifies the 'peakedness' of the amplitude distribution during the decay, detecting impulsive, non-Gaussian artifacts from switching events.
• Transient Skewness: Measures the asymmetry of the amplitude probability density function, revealing directional biases in the hardware's non-linear power-down response.
• Transient Bispectrum: A higher-order spectral analysis that reveals quadratic phase coupling, effectively suppressing noise and highlighting non-linear interactions unique to the transmitter's components.