Power Supply Rejection Ratio (PSRR)

PSRR is the ratio of the change in supply voltage to the resulting change in the output signal, expressed in decibels (dB). A low PSRR means a significant portion of power supply noise couples directly into the signal path. This coupling occurs through finite output impedance of current sources and incomplete isolation in amplifier stages. The specific frequency response of PSRR is a device-unique trait, varying due to on-chip decoupling capacitance and parasitic inductances.

A device's PSRR is not a perfect, flat line; it degrades at higher frequencies. This frequency-dependent attenuation curve is shaped by the physical layout and component values of the voltage regulation and bias networks. An attacker or authenticator can inject a known, low-amplitude pilot tone onto the power rail and measure its modulated remnant at the RF output. The amplitude and phase of this remnant, relative to the injected tone, form a unique hardware signature.

Unlike static non-linearity, PSRR-based fingerprints are environmentally reactive. A device's power supply noise is a function of its activity (e.g., CPU load, transmit power) and external factors (e.g., battery voltage droop, temperature). This creates a dynamic signature that reflects the device's instantaneous operating state. While this complicates authentication, it also provides a rich, multi-dimensional feature space that is extremely difficult to clone or replay.

Characterizing PSRR for fingerprinting requires more than a single dB value. Critical metrics include:

• PSRR vs. Frequency: The signature is the entire curve, not a single point.
• Supply-Induced Jitter: Noise on the supply modulates the zero-crossings of clock buffers, creating a unique phase noise profile.
• Intermodulation with Signal: The mixing of supply noise with the intentional signal creates deterministic sidebands that are a direct product of the PSRR non-linearity.

PSRR is distinct from static non-linearity (INL/DNL) because it is a dynamic, stimulus-dependent impairment. While INL is a fixed deviation from an ideal transfer curve, PSRR dictates how a time-varying disturbance on the power rail maps to the output. It is also distinct from thermal noise, as PSRR-related artifacts are deterministic given a known supply fluctuation. This makes it a complementary feature for multi-modal fingerprinting systems.

In a Digital-to-Analog Converter (DAC), poor PSRR on the reference voltage or output buffer supply directly amplitude-modulates the reconstructed waveform. In an Analog-to-Digital Converter (ADC), supply noise couples into the comparator and sample-and-hold circuits, causing gain errors and aperture jitter that are supply-dependent. Time-interleaved ADCs are particularly susceptible, as supply noise modulates the already-present interleaving mismatch spurs, creating a complex, coupled signature.

The collective impact of manufacturing process shifts, supply voltage fluctuations, and operating temperature changes on circuit performance. PVT defines the statistical distribution of hardware impairments that make each device unique.

• Process: Microscopic variations in doping and lithography
• Voltage: IR drops and supply ripple coupling (directly linked to PSRR)
• Temperature: Thermal gradients affecting carrier mobility and threshold voltages

PSRR is itself a PVT-sensitive parameter, varying across the operational envelope and contributing to a dynamic, environmentally-coupled fingerprint.

A measure of a data converter's static linearity, defined as the maximum deviation of the actual transfer function from an ideal straight line. INL creates a unique, process-dependent signature in the output waveform.

• Measured in Least Significant Bits (LSBs)
• Arises from component mismatch in DAC resistor ladders and ADC comparators
• A smooth, low-frequency INL profile is a strong, persistent identifier

When power supply ripple modulates the converter's reference voltage, the effective INL profile shifts dynamically, creating a supply-dependent distortion signature.

The deviation between an actual step width and the ideal 1 Least Significant Bit (LSB) step in a data converter. Large DNL errors can lead to missing codes—a permanent, highly distinctive gap in the transfer function.

• A DNL of -1 LSB indicates a missing code
• Caused by random comparator offsets and capacitor mismatch
• Missing codes are a binary, unclonable feature for device identification

Poor PSRR on internal bias generators can cause DNL to vary with supply ripple, making the missing code pattern a function of the power rail noise spectrum.

The sample-to-sample variation in the precise instant a sample-and-hold circuit captures a signal. This timing uncertainty modulates the phase of the digitized waveform and creates a unique, clock-related fingerprint.

• Measured in femtoseconds or picoseconds RMS
• Translates directly to increased noise floor at higher input frequencies
• Jitter spectrum often contains deterministic spurs from coupled supply noise

A switching power supply with poor PSRR in the clock generation circuitry directly injects periodic jitter, creating supply-synchronous phase modulation sidebands that are highly identifiable.

The frequency-domain representation of rapid, random fluctuations in a signal's phase, often originating from oscillator instabilities. Phase noise manifests as a unique spectral skirt around the carrier.

• Characterized by dBc/Hz at specific offset frequencies
• Close-in phase noise is dominated by flicker noise upconversion
• Far-out phase noise floor is set by thermal noise and supply-induced interference

Power supply ripple at the oscillator's voltage regulator input is directly converted to phase noise via the supply pushing mechanism, imprinting the PSRR profile onto the carrier's spectral purity.

Non-linear distortion products generated when two or more signals at different frequencies are applied to a non-linear system. IMD reveals the specific polynomial transfer function of the transmitter chain.

• Second-order (IM2) and third-order (IM3) products are most significant
• The amplitude and phase of IMD products are device-specific
• Power supply ripple can intermodulate with the signal, creating supply-borne IMD spurs

A power amplifier with poor PSRR will exhibit IMD products whose frequencies are the sum and difference of the signal and the power supply ripple frequency, a telltale signature of the power delivery network.