Key-Click Analysis

The instantaneous bandwidth of the broadband noise generated during the switching transient. The splatter bandwidth is inversely proportional to the rise/fall time of the keying envelope—faster transitions produce wider spectral contamination. Key metrics include:

• Occupied Bandwidth: The frequency range containing 99% of the transient energy
• Adjacent Channel Power Ratio: The ratio of splatter power in neighboring channels to the main carrier power
• -40 dBc Bandwidth: The spectral width at which the splatter amplitude drops 40 dB below the carrier

A transmitter with a slew-rate-limited power amplifier will exhibit a narrower, more controlled splatter profile than one with an underdamped switching circuit.

The 10%-90% rise time and 90%-10% fall time of the keying envelope are rarely symmetric due to differing charge and discharge paths in the transmitter hardware. This asymmetry creates a unique temporal signature:

• Rise time is dominated by the power amplifier's gate biasing network and current sourcing capability
• Fall time reflects the discharge rate of decoupling capacitors and the power supply's sink impedance
• Asymmetry ratio (rise time / fall time) serves as a robust, unit-specific identifier

Variations in parasitic inductance and equivalent series resistance of the power distribution network directly shape this temporal profile.

The damped sinusoidal oscillation superimposed on the keying envelope immediately after the switching edge, caused by the resonant interaction of parasitic inductance and capacitance in the transmitter's output matching network. Characteristic parameters include:

• Resonant frequency: Typically in the 10-500 MHz range, determined by the LC tank formed by bond wires and transistor parasitics
• Damping factor: The exponential decay rate of the oscillation envelope, reflecting the effective series resistance
• Peak overshoot amplitude: The maximum excursion above the steady-state level, often 5-20% of nominal

These parameters form a passive component fingerprint that is extremely difficult to clone or emulate.

An abrupt, unintended shift in the instantaneous phase of the carrier signal at the moment of key-down or key-up. This discontinuity arises from:

• PLL phase perturbation caused by the sudden impedance change when the power amplifier is switched
• VCO pulling due to load variation during the current inrush event
• Modulator imbalance during the transient settling of the IQ baseband circuits

The magnitude and direction of the phase jump, typically measured in degrees of carrier cycle, is a deterministic function of the transmitter's component tolerances and layout parasitics. Phase-coherent receivers can extract this feature with high precision.

The time-domain trajectory of the instantaneous carrier frequency as it converges to its steady-state value after the key-down event. This profile reveals the dynamic behavior of the phase-locked loop and voltage-controlled oscillator:

• Lock time: The duration from key-down to frequency stabilization within a specified tolerance
• Frequency overshoot: The peak deviation beyond the target frequency during acquisition
• Settling envelope shape: Underdamped, critically damped, or overdamped—determined by the PLL loop filter component values

The settling profile is highly sensitive to component aging and temperature variations, making it a valuable indicator of hardware condition over time.

The center of mass of the short-time Fourier transform spectrum during the key-click event shifts dynamically as different frequency components dominate at different phases of the transient. This shift trajectory encodes:

• High-frequency emphasis during the initial fast-edge portion of the transient
• Low-frequency convergence as the envelope settles toward steady-state
• Resonant peaks corresponding to ringing frequencies in the output network

The centroid trajectory in the time-frequency plane provides a compact, translation-invariant feature vector for device classification. It is particularly robust against multipath channel distortion because the centroid is a relative, not absolute, spectral measure.