Transient Thermal Signature

The fundamental physics driving the transient thermal signature. During the turn-on transient, a high inrush current flows through the resistive channel of the power amplifier transistor. This current density causes instantaneous I²R power dissipation within the semiconductor lattice. Unlike steady-state heating, this energy is deposited in microseconds, creating a rapid, localized temperature spike at the transistor junction before thermal diffusion can distribute the heat to the surrounding die and packaging.

The thermal response is governed by multiple RC-equivalent time constants representing different physical layers:

• Junction-to-case: Microsecond-scale heating at the transistor channel
• Case-to-heat-sink: Millisecond-scale diffusion through the die substrate
• Heat-sink-to-ambient: Second-scale convection to the environment The transient thermal signature exploits the junction-level time constant, which is highly sensitive to microscopic variations in doping profiles, gate oxide thickness, and localized defect density.

The instantaneous temperature rise directly modulates key transistor parameters, imprinting a thermal signature onto the RF waveform:

• Threshold voltage (Vth): Decreases with temperature, altering the turn-on bias point
• Transconductance (gm): Degrades as lattice scattering increases, reducing gain during the ramp
• Electron mobility: Decreases due to increased phonon scattering, slowing the rise time
• Drain-source resistance (Rds_on): Increases, modifying the envelope shape These shifts create a unique, repeatable distortion pattern in the transient amplitude and phase trajectory.

The transient thermal signature exhibits hysteresis and history dependence due to thermal memory effects in the semiconductor material. The junction temperature at the start of a burst depends on the prior duty cycle and cooling interval. This creates a state-dependent fingerprint where:

• A burst following a long idle period has a cold-start thermal profile
• A burst in a high-duty-cycle sequence starts from an elevated baseline temperature
• Charge trapping in gate oxides and buffer layers adds a field-dependent thermal component These memory effects provide an additional dimension for device discrimination beyond the static hardware impairment.

The rapid temperature change generates a characteristic broadband spectral splatter distinct from steady-state phase noise. As the junction heats, the instantaneous frequency drifts due to:

• Thermal expansion of the oscillator's resonant cavity or crystal
• Dielectric constant variation in frequency-determining components
• VCO pushing from supply current modulation This produces a chirp-like frequency trajectory during the first microseconds, visible in a short-time Fourier transform as a curved spectral feature that is highly individual to each transmitter's thermal path impedance.

The transient thermal signature manifests most visibly as a non-linear distortion in the amplitude ramp profile. As the junction temperature rises, the power amplifier gain compresses slightly, causing:

• A deviation from the ideal linear ramp slope
• A characteristic inflection point where thermal gain sag overcomes the input drive increase
• An overshoot correction as the bias network compensates This thermal gain sag is distinct from electrical slew-rate limitations and provides a unique, unclonable feature extractable via high-resolution envelope analysis.