ET-Induced AM/PM Distortion

The fundamental mechanism where the PA's insertion phase varies as a function of the instantaneous drain voltage. As the supply modulator adjusts Vdd to track the envelope, the transistor's parasitic capacitances—particularly Cgd and Cds—change nonlinearly, causing a voltage-dependent phase rotation of the RF output. This creates a direct mapping between the envelope signal amplitude and the output phase error, requiring the DPD to apply a complex gain correction that varies with both input power and supply voltage.

In ET systems, amplitude and phase distortions are not independent. The dynamic supply modulation creates a cross-coupled nonlinearity where:

• Changes in drain voltage simultaneously affect gain (AM-AM) and phase (AM-PM)
• The shaping function that maps envelope to supply voltage directly influences the phase trajectory
• Aggressive efficiency optimization often exacerbates AM-PM by pushing the PA into regions of rapid phase variation This coupling demands joint AM-AM/AM-PM correction rather than independent compensation paths.

ET-induced AM-PM exhibits significant memory effects beyond static nonlinearity. Short-term memory arises from the supply modulator's finite bandwidth and slew rate, causing the actual Vdd to lag behind the ideal envelope. Long-term thermal memory occurs because dynamic supply changes alter instantaneous power dissipation, creating temperature-dependent phase shifts that persist across multiple symbol periods. These effects require DPD models with memory depth—typically 3-5 taps for short-term and dedicated thermal state tracking for long-term compensation.

The iso-gain contour-based shaping function directly determines the severity of AM-PM distortion. Key relationships include:

• Deep tracking (aggressive Vdd modulation) maximizes efficiency but traverses regions of steep phase gradient
• Iso-gain shaping minimizes AM-AM variation but may still produce significant AM-PM if the constant-gain contours have inherent phase curvature
• Phase-aware shaping adds a constraint to avoid operating points with rapid phase variation, trading some efficiency for improved linearity The shaping function is effectively a phase distortion control parameter.

As signal bandwidth increases, ET-induced AM-PM becomes more severe due to:

• Envelope-bandwidth mismatch: The supply modulator cannot track the fastest envelope variations, creating phase errors at high envelope frequencies
• Slew-rate limitations: The modulator's finite dV/dt causes the actual Vdd to deviate from the ideal, introducing dynamic phase errors that correlate with envelope derivative
• Frequency dispersion: The PA's phase response to supply variation is itself frequency-dependent, creating a 2D memory effect across both modulation frequency and RF carrier frequency Wideband 5G NR signals (100+ MHz) are particularly susceptible.

Characterizing ET-induced AM-PM requires specialized measurement techniques:

• Dual-input vector network analysis captures S21 phase vs. both input power and supply voltage
• Dynamic AM-PM extraction uses modulated test signals with synchronized Vdd and RF envelope capture
• 3D phase surfaces plot output phase as a function of instantaneous |Vin| and Vdd, revealing the full nonlinear memoryless behavior
• Residual phase error after static correction quantifies the memory component requiring dynamic DPD These measurements feed directly into augmented Volterra or neural network model training.

The nonlinear variation in a PA's gain as a function of its instantaneous drain voltage. As the supply modulator reduces the drain voltage to save power during low-envelope periods, the transistor operates closer to its knee region, causing both gain compression (AM-AM) and a significant phase shift (AM-PM). Characterizing this supply-dependent complex gain is the first step in building an ET-aware DPD model.

A modeling framework that treats the PA as a system with two independent inputs: the RF input signal and the dynamic supply voltage. Unlike single-input models, this structure can natively capture the interaction between the RF envelope and the supply modulation that produces ET-specific AM/PM distortion. Common implementations include augmented Volterra series and dual-input memory polynomials.

The precise time-synchronization between the RF signal path and the envelope tracking supply voltage path at the transistor's drain. A timing mismatch as small as a fraction of a nanosecond can cause the supply voltage to be misaligned with the RF envelope, producing severe transient phase distortion that appears as a dramatic increase in AM/PM conversion. This is often the dominant source of residual distortion in ET systems.

A deterministic mapping function, often implemented as a look-up table (LUT), that translates the instantaneous baseband signal magnitude into a target supply voltage. The shaping function directly determines the PA's operating trajectory across its characteristic plane. A poorly designed shaping function can push the PA into regions of extreme phase nonlinearity, exacerbating AM/PM distortion and making linearization more difficult.

A unified behavioral model that simultaneously captures the nonlinear dynamics of both the power amplifier and the supply modulator. Since the modulator itself introduces nonlinearities—such as slew-rate limiting and switching ripple—that corrupt the intended supply waveform, a joint model is essential for accurately predicting and inverting the complete chain of AM/PM distortion sources in a single predistorter.