Power Amplifier Non-Linearity

Amplitude-to-Amplitude (AM-AM) conversion characterizes how the PA's output amplitude deviates from an ideal linear relationship with the input amplitude. Near the 1 dB compression point (P1dB) , gain begins to compress, causing constellation points to shrink toward the origin. This compression curve is unique to each amplifier due to transistor-level manufacturing variances in the semiconductor die, creating a distinctive, measurable signature in the steady-state portion of a transmission.

Amplitude-to-Phase (AM-PM) conversion is a non-ideal effect where the phase shift introduced by the amplifier varies as a function of the instantaneous input signal amplitude. As the PA approaches saturation, the input capacitance of the transistor changes non-linearly, causing a power-dependent phase rotation. This results in a constellation-dependent phase distortion that is highly specific to the individual amplifier's biasing network and transistor characteristics.

When a modulated signal with a non-constant envelope passes through a non-linear PA, intermodulation products are generated, causing energy to spill into adjacent frequency channels. This out-of-band emissions profile, known as spectral regrowth, is a direct consequence of third-order and higher non-linearities. The shape and magnitude of the regrowth shoulders are unique to each device, providing a fingerprint that can be captured without demodulating the signal.

Memory effects occur when the PA's output depends not only on the current input sample but also on previous samples, caused by thermal dynamics, bias circuit impedance, and trapping effects in the transistor. These effects manifest as an asymmetrical distortion pattern around the carrier frequency. The time constants of these memory effects—governed by the specific thermal impedance and decoupling capacitor values of the circuit—are highly individual to each physical device.

Non-linear amplification generates energy at integer multiples of the fundamental carrier frequency. While these second and third harmonics are often filtered, the internal generation mechanism reflects the specific transfer function of the amplifier. The relative power ratios between harmonics, and the way they interact with the fundamental through harmonic mixing, provide a rich feature set for fingerprinting that is independent of the modulation scheme being used.

The knee voltage is the point on the transistor's I-V curve where it transitions from the linear region to saturation. Manufacturing variations in the drain-source on-resistance (RDS(on)) and pinch-off voltage cause each PA to enter compression at a slightly different point. This creates a unique soft-clipping profile at the waveform peaks, which can be extracted as a fingerprint feature using higher-order statistics that are sensitive to the shape of the probability density function of the signal.

The two fundamental mechanisms of PA non-linearity. AM-AM conversion describes the non-linear relationship between input and output amplitude, causing gain compression at saturation. AM-PM conversion is the unintended phase shift that varies with the instantaneous signal envelope power.

• Gain Compression: As input power increases, gain drops from its linear small-signal value, typically quantified by the 1 dB compression point (P1dB).
• Phase Distortion: AM-PM effects rotate constellation points differently based on their distance from the origin, creating a signal-dependent phase error that is highly device-specific.

The spillover of modulated signal energy into adjacent frequency channels, directly caused by the intermodulation products generated when a non-linear amplifier processes a varying-envelope signal. This out-of-band emission creates a unique spectral mask.

• ACPR/ACLR: Adjacent Channel Power/Leakage Ratio quantifies the severity of regrowth, a critical regulatory compliance metric.
• Fingerprinting Utility: The specific shape and amplitude of spectral regrowth shoulders are a rich, unique identifier because they are a direct product of the individual PA's non-linear transfer function.

A comprehensive, single-number metric that aggregates all in-band impairments—including PA non-linearity, I/Q imbalance, and phase noise—into a measure of the Euclidean distance between measured and ideal constellation points.

• In-Band Distortion: While spectral regrowth measures out-of-band effects, EVM captures the in-band signal degradation that reduces demodulation margin.
• Composite Metric: EVM alone cannot isolate PA non-linearity from other impairments, but a high EVM near peak power strongly indicates amplifier compression.

A theoretical figure of merit used to characterize a PA's third-order non-linearity. A higher OIP3 (Output Third-Order Intercept Point) indicates better linearity and lower intermodulation distortion.

• Two-Tone Test: IP3 is extrapolated from a test where two closely spaced tones are applied, and the resulting third-order intermodulation products are measured.
• Cascaded Linearity: In a receiver chain, the IP3 of each stage, including the LNA and mixer, is critical for calculating overall system linearity using the Friis formula for intercept points.

A distinct hardware impairment where a portion of the unmodulated carrier signal leaks through the mixer to the output, creating a DC offset in the baseband constellation. This is often confused with PA non-linearity effects.

• Origin Offset: LO leakage manifests as a fixed displacement of the entire constellation from the origin, independent of signal amplitude.
• Distinction from PA Effects: Unlike AM-AM compression, which scales with envelope power, LO leakage is a constant additive term, making it a separable and highly stable fingerprinting feature.