Amplitude Ramp Profile

The statistical distribution of the measured 10% to 90% rise time across multiple burst transmissions from the same device. This variance reflects the stochastic nature of the power-up sequence, including thermal noise in the bias network and minor fluctuations in the supply rail. A consistent rise-time variance is a unique identifier, as it is determined by the specific slew rate of the power amplifier and the charging time of its input capacitance.

The amplitude ramp is rarely a perfectly linear slope. Inflection points—where the rate of amplitude change itself changes—reveal the transition between different circuit domains activating. For example, an initial slow rise may correspond to the phase-locked loop (PLL) acquiring lock, followed by a sharp increase as the power amplifier's final stage saturates. These non-linearities are direct reflections of the transmitter's specific component values and parasitic elements.

The quantification of the transient amplitude excursion beyond the steady-state level. An underdamped response in the power amplifier's automatic level control (ALC) loop causes a peak that overshoots the target power. Key metrics include:

• Peak Overshoot Ratio: The percentage of the peak amplitude above the steady-state value.
• Settling Time: The duration required for the amplitude to stabilize within a specified tolerance (e.g., ±1 dB) after the overshoot. This ringing is a direct consequence of the loop filter's damping factor.

The momentary fluctuation in the transmitter's supply voltage caused by the inrush current during turn-on. This sag amplitude-modulates the output signal, creating a unique dip or ripple on the ramp profile. The artifact's shape reveals the equivalent series resistance (ESR) of the power supply decoupling capacitors and the impedance of the power distribution network (PDN), which are highly specific to the physical layout and component aging.

A momentary, unintended voltage spike at the output of the digital-to-analog converter (DAC) caused by timing skews between internal switches during the major code transition at the start of a burst. This glitch energy appears as a sharp, narrow pulse superimposed on the early part of the amplitude ramp. Its magnitude and duration are unique to the silicon process and layout of the specific DAC chip used in the transmitter.

The minute, rapid change in the amplitude ramp shape caused by the instantaneous self-heating of the transistor junction during the high-current turn-on event. As the die temperature rises within microseconds, the transistor's gain and threshold voltage shift, subtly altering the ramp's slope. This creates a history-dependent signature, as the profile will differ slightly for a 'cold start' versus a 'warm re-key,' revealing the device's thermal time constant.

The statistical distribution of the measured 10% to 90% rise time across multiple burst transmissions. While the Amplitude Ramp Profile defines the shape, rise-time variance quantifies the stochastic stability of that shape. A tight variance indicates a highly deterministic biasing network, whereas a wide variance suggests thermal noise or jitter in the power-up sequence. This metric is critical for distinguishing between identical hardware models that have identical nominal ramp shapes but different noise signatures.

The quantification of the transient amplitude excursion beyond the steady-state level during the ramp-up phase. This is a direct distortion of the ideal Amplitude Ramp Profile caused by an underdamped response in the power amplifier's control loop. The percentage of overshoot and the decay rate of the subsequent ringing are highly specific to the damping factor of the bias network, providing a unique hardware fingerprint that is difficult to clone.

The measurement of the duration required for the amplitude to stabilize within a specified tolerance band (e.g., ±1%) after the initial turn-on event. This metric defines the temporal endpoint of the Amplitude Ramp Profile. A long settling time often indicates a slow-slewing biasing network or high capacitance in the power supply decoupling, directly reflecting the specific passive component values selected during manufacturing.

The extraction of the instantaneous magnitude contour of a signal using the Hilbert Transform. This is the primary mathematical tool used to isolate the Amplitude Ramp Profile from the carrier frequency. By computing the analytic signal, engineers can visualize the pure power envelope's attack, decay, sustain, and release (ADSR) characteristics without the distortion caused by the rapid oscillations of the RF carrier wave.

The composite transient profile specifically attributed to the power amplifier's gate or base biasing network. The Amplitude Ramp Profile is often dominated by this signature, as the PA is the primary consumer of inrush current. The specific curvature of the ramp—whether it is exponential, linear, or has inflection points—reveals the physics of the transistor's channel formation and the reactive components in the bias tee.

The dependence of the current Amplitude Ramp Profile on the transmitter's previous operating state. Caused by thermal trapping and charge storage in semiconductor materials, this effect means the ramp shape may differ slightly if the device was recently transmitting versus idle for a long period. This history-dependent signature adds a layer of complexity to fingerprinting, requiring models that account for temporal context.