Thermal Memory Effect

The instantaneous power dissipation within the transistor channel causes a local temperature rise that modifies carrier mobility and threshold voltage. GaN HEMTs are particularly susceptible due to their high power density. The thermal time constant ranges from microseconds to milliseconds, creating a low-frequency memory envelope that tracks the average signal power over time. This manifests as slow gain compression and phase drift that cannot be corrected by memoryless predistorters.

In multi-channel and MIMO arrays, heat generated by one power amplifier diffuses through the shared substrate and alters the operating point of adjacent amplifiers. This thermal crosstalk creates spatially correlated memory effects that vary with the beamforming configuration and per-channel activity. The effect is exacerbated in mmWave phased arrays where element spacing is tight and thermal resistance paths overlap.

Thermal memory is driven by the envelope power history, not the instantaneous RF carrier. Key characteristics include:

• Long-term average power determines the baseline junction temperature
• Envelope peaks cause transient heating spikes with exponential decay
• Modulation format (OFDM vs. single-carrier) changes the thermal profile
• Duty cycle in TDD systems introduces periodic cooling intervals This makes thermal memory highly waveform-dependent and challenging to model with static coefficients.

Thermal memory effects must be separated from trapping effects and bias circuit memory for accurate modeling:

• Thermal: Time constants of 10 µs to 1 ms, driven by dissipated power
• Trapping: Time constants of 1 µs to 100 µs, driven by electric field and charge capture
• Bias circuit: Time constants of 1 ns to 1 µs, driven by video bandwidth limitations GaN devices exhibit all three simultaneously, requiring models that capture multiple memory timescales for effective linearization.

Uncompensated thermal memory degrades ACLR improvement by 3-10 dB in wideband systems. As the power amplifier heats up during transmission bursts, the optimal predistorter coefficients drift, causing:

• Residual spectral regrowth that increases over burst duration
• EVM floor that rises with sustained high-power operation
• Coefficient staleness in static DPD look-up tables Adaptive DPD with thermal-aware coefficient tracking is essential for maintaining linearity over extended operation.

Several techniques capture thermal memory in behavioral models:

• Augmented memory polynomial with low-frequency envelope filtering terms
• Two-box models separating static nonlinearity from a thermal filter cascade
• LSTM neural networks that inherently learn long-timescale dependencies
• Temperature-injection models that use measured or estimated junction temperature as an auxiliary input Accurate thermal modeling requires wideband modulated stimuli that exercise the full envelope bandwidth of the target signal.

Power amplifier memory effects are categorized by their time constants relative to the signal envelope period. Thermal memory is classified as a long-term memory effect with time constants typically in the microsecond to millisecond range.

• Short-term memory: Caused by bias circuit impedance and matching network frequency response. Time constants are on the order of the RF carrier period (nanoseconds).
• Long-term memory: Caused by thermal dynamics, trapping effects, and bias circuit charging. Time constants range from microseconds to seconds.
• Quasi-memoryless: When memory effects are negligible, the PA output depends only on the instantaneous input envelope.

Distinguishing between these categories is crucial for selecting appropriate behavioral models. Volterra series capture both types, while memory polynomials primarily address short-term effects unless augmented with thermal terms.

The standard memory polynomial model can be augmented with thermal memory terms to capture slowly varying gain and phase shifts. This approach adds envelope-dependent terms with longer time delays to the conventional polynomial structure.

• Standard memory polynomial: Models short-term memory with delays of 1-3 samples
• Thermal augmentation: Adds terms with delays corresponding to the thermal time constant (e.g., 100-1000 samples at typical DPD sampling rates)
• Envelope thermal model: Includes a low-pass filtered version of the instantaneous power as an additional input to represent the thermal state
• Two-stage approach: Separate short-term and long-term memory models combined in cascade

This augmentation significantly improves ACLR performance for signals with varying average power levels.

Power-Added Efficiency (PAE) quantifies a power amplifier's ability to convert DC supply power into added RF output power. It directly influences thermal memory effects because dissipated power (PDC + PRF_in - PRF_out) becomes heat.

• Formula: PAE = (PRF_out - PRF_in) / PDC × 100%
• Typical values: 30-50% for GaN mmWave PAs at back-off
• Dissipated power: P_diss = PDC - (PRF_out - PRF_in)
• Impact on thermal memory: Higher dissipation causes larger temperature swings and more pronounced thermal memory

Improving PAE through techniques like envelope tracking and Doherty architectures reduces both energy consumption and the severity of thermal memory effects requiring DPD compensation.