Memory Effects

Dynamic variations in amplifier gain and phase caused by transient temperature changes in the transistor channel. As instantaneous dissipated power fluctuates with the signal envelope, the junction temperature rises and falls with time constants ranging from microseconds to milliseconds.

• Self-heating: Power dissipation heats the channel, reducing carrier mobility and gain
• Bias circuit interaction: Temperature-dependent quiescent current shifts alter the operating point
• Long time constants: Thermal capacitance of the die and package creates low-frequency memory

GaN HEMT devices exhibit particularly complex thermal memory due to high power density and multi-finger thermal coupling.

Nonlinear distortion arising from frequency-dependent impedance interactions between the transistor and its surrounding bias and matching networks. The envelope-frequency impedance seen by the device's intrinsic current source modulates the output waveform.

• Bias network resonance: Inductive bias lines and capacitive bypass networks create envelope-frequency resonances
• Baseband impedance: The impedance presented to the low-frequency difference-frequency components generated by the nonlinearity directly controls memory depth
• Harmonic terminations: Improper harmonic impedances reflect energy back to the device, mixing with the fundamental

Minimizing electrical memory requires careful baseband impedance engineering across the entire modulation bandwidth.

Slow charge capture and release at deep-level traps in the semiconductor material, particularly in GaN HEMTs and GaAs devices. Trapped charge modulates the channel's electric field, causing gate lag and drain lag phenomena.

• Gate lag: Trapping under the gate edge reduces drain current after a high-voltage pulse
• Drain lag: Trapping in the buffer or surface states alters the channel's conductivity
• Time constants: Ranging from nanoseconds (surface traps) to seconds (buffer traps)
• Bias dependence: Trap occupancy is a function of the instantaneous and recent drain voltage history

Trap effects introduce complex, history-dependent nonlinearities that are difficult to distinguish from thermal memory without specialized characterization.

A simplified Volterra series derivative that captures memory effects using a diagonal kernel structure. The model expresses the current output as a sum of nonlinear functions of delayed input samples, dramatically reducing the coefficient count compared to the full Volterra series.

• Structure: y(n) = Σ_k Σ_m a_{km} · x(n-m) · |x(n-m)|^{k-1}
• Diagonal-only: Only terms where all delays are equal are retained, eliminating cross-memory products
• Generalized Memory Polynomial (GMP): Extends the model by adding cross-terms between the current sample and lagging envelope values
• Implementation: Highly efficient for FPGA and ASIC DPD implementations due to its regular, parallelizable structure

The memory polynomial is the most widely adopted model for commercial digital predistortion systems.

A classification of memory effects based on their time constant relative to the modulation envelope period. This distinction determines the required memory depth in the predistorter model.

Short-Term Memory:

• Time constants comparable to the inverse modulation bandwidth
• Caused by matching network dispersion and harmonic terminations
• Captured by memory taps spanning 1–5 symbol periods

Long-Term Memory:

• Time constants much longer than the symbol period
• Caused by thermal dynamics, trap effects, and bias circuit charge/discharge
• Requires extended memory depth or specialized long-memory kernels
• Often exhibits a frequency response below 1 MHz

Accurate DPD must span both regimes, often requiring hybrid model structures that separately address short-term and long-term dynamics.

A two-dimensional characterization technique that separates the nonlinear behavior of a power amplifier into the carrier-frequency domain and the envelope-frequency domain. This reveals how memory effects manifest as asymmetry in the intermodulation distortion spectrum.

• Envelope domain: Represents the dynamic variation of the complex gain as a function of the modulation frequency
• Asymmetric IMD: Memory effects cause upper and lower intermodulation sidebands to have unequal amplitudes and phases
• Measurement: Extracted using two-tone or multi-tone tests with swept tone spacing to map the envelope-frequency response
• Visualization: Envelope-frequency gain surfaces directly show the memory depth required for linearization

This analysis is essential for diagnosing whether memory effects originate from electrical, thermal, or trapping mechanisms.