Undershoot Characterization

The peak negative deviation below the steady-state baseline, typically measured in dB or as a percentage of nominal amplitude. This magnitude directly correlates with the reverse recovery charge of power supply rectifier diodes and the equivalent series resistance (ESR) of filter capacitors. A transmitter with degraded capacitors will exhibit a deeper undershoot due to reduced holdup capacity. Typical values range from 0.5% to 5% of nominal amplitude in well-regulated designs.

The exponential time constant (τ) governing the return from the undershoot minimum to the steady-state level. This parameter reflects the RC discharge-recharge cycle of the power supply decoupling network. Key contributors include:

• Bulk capacitance value and dielectric absorption
• Voltage regulator loop bandwidth and transient response
• Load current step magnitude at turn-off

A slower recovery (larger τ) often indicates aging electrolytic capacitors or a regulator with insufficient phase margin.

The undershoot is frequently followed by a ringback—a damped overshoot as the control loop compensates. The undershoot-to-ringback ratio and the zero-crossing interval between them form a compound signature. This interaction reveals the damping factor (ζ) of the power supply's closed-loop transfer function. Underdamped systems (ζ < 0.7) produce pronounced ringback; critically damped systems (ζ ≈ 1) exhibit a monotonic recovery without overshoot.

The undershoot event generates a broadband spectral signature distinct from the steady-state carrier. Short-time Fourier transform (STFT) analysis reveals:

• Low-frequency energy concentration (typically 1-100 kHz) corresponding to the power supply loop bandwidth
• Harmonic content from any non-linear recovery behavior, such as diode snap-off
• Phase discontinuity at the undershoot minimum, visible as a momentary spectral spreading

This spectral fingerprint is separable from the intentional modulation and serves as a robust identifier.

Undershoot characteristics are sensitive to junction temperature and load impedance. Key effects include:

• Increased undershoot depth at elevated temperatures due to higher diode reverse recovery time
• Faster recovery at higher load currents as the regulator's output stage enters a different operating region
• Capacitance derating with DC bias voltage, altering the recovery time constant

These dependencies create a multi-dimensional signature space that can be modeled for robust, environment-invariant identification.

The undershoot profile exhibits high intra-device repeatability (typically < 0.1 dB variation across bursts) while maintaining strong inter-device discrimination. This is because the signature is rooted in manufacturing tolerances of passive components and semiconductor parameters that are stable over short timeframes. Statistical metrics such as undershoot depth variance and recovery time jitter serve as secondary discriminators, with genuine devices showing tightly clustered values and counterfeit or degraded units displaying outlier distributions.

The characteristic decay profile of a signal burst's trailing edge, revealing the discharge behavior of capacitive elements and power supply regulation within the transmitter. The ramp-down signature provides the immediate context for the undershoot event, as the amplitude's descent toward the noise floor is what triggers the reverse recovery response. Analyzing the slope and linearity of this decay is essential for isolating the subsequent undershoot artifact from the intentional power-down sequence.

The short-duration signal anomaly generated during the power-down sequence of a transmitter, characterized by unique phase discontinuities and amplitude collapse profiles. The turn-off transient is the parent category that encompasses the entire shutdown event, including the ramp-down, the undershoot, and any associated ringing. Characterizing the complete turn-off transient provides a holistic hardware fingerprint, of which the undershoot is a critical, energy-storage-revealing component.

The final portion of the transient envelope where the signal energy falls from its steady-state level to zero, characterized by its exponential or linear decay constant. The transient decay profile is the broader temporal window that contains the undershoot. By modeling the decay constant of the return to baseline after the undershoot's negative peak, analysts can extract the time constant of the transmitter's power supply holdup capacitance and discharge path impedance.

The statistical variation in the 90% to 10% fall time of a signal burst, providing a unique metric derived from the discharge path impedances and power supply holdup capacitance. Fall-time variance is directly influenced by the same component tolerances that dictate the depth and duration of the undershoot. A transmitter with a highly variable fall time will also exhibit a statistically variable undershoot profile, making this a correlated and reinforcing feature for device authentication.

The momentary fluctuation in the transmitter's supply voltage caused by the inrush current during turn-on, which amplitude-modulates the output signal and reveals the power supply's impedance. While often discussed for turn-on, transient power supply modulation is the root cause of the turn-off undershoot. The sudden cessation of current draw causes an inductive kickback and a voltage sag on the supply rail, which directly amplitude-modulates the output envelope below the nominal level.

The characteristic exponential decay envelope of a ringing artifact, whose time constant and resonant frequency serve as a distinct hardware signature of the transmitter's reactive components. The damped oscillation profile often immediately follows the undershoot, as the power supply network's parasitic inductance and capacitance resonate after the voltage sag. The transition from the undershoot's negative peak into this damped ringing is a highly unique, unclonable signature of the specific printed circuit board layout and component selection.