Thermal AM-AM Distortion

Unlike memoryless AM-AM distortion, thermal AM-AM causes the amplifier's gain compression or expansion to shift dynamically as junction temperature fluctuates. Key mechanisms include:

• Threshold voltage drift: As temperature rises, the transistor threshold voltage decreases, altering the conduction angle and small-signal gain
• Carrier mobility degradation: Increased lattice vibrations at higher temperatures reduce electron mobility, lowering transconductance and saturated output power
• Quiescent bias shift: Self-heating changes the DC operating point, moving the amplifier along its load line and modifying the instantaneous gain profile

The result is a history-dependent gain curve where identical instantaneous input amplitudes produce different output amplitudes depending on prior signal envelope history.

Thermal AM-AM distortion is driven by envelope frequency heating, where the low-frequency components of the modulated signal's amplitude envelope fall within the thermal bandwidth of the device:

• The instantaneous power dissipation waveform is proportional to the squared envelope of the RF signal
• When envelope frequency components are slower than the thermal cutoff frequency, the junction temperature tracks these variations
• This creates a thermal convolution effect: the instantaneous junction temperature equals the convolution of dissipated power with the device's thermal impulse response
• Modern wideband signals (e.g., 5G NR with 100 MHz bandwidth) have envelope components spanning DC to hundreds of MHz, ensuring significant spectral content within the thermal response bandwidth

A defining characteristic of thermal AM-AM distortion is spectral asymmetry in the output spectrum that cannot be corrected by memoryless linearization:

• The thermal memory effect introduces a frequency-dependent phase shift between the envelope and the resulting gain modulation
• This dispersive behavior causes unequal spectral regrowth on the upper and lower sidebands of the modulated signal
• Unlike electrical memory effects (which operate at megahertz rates), thermal asymmetry appears at kilohertz to low-megahertz offset frequencies from the carrier
• The asymmetry pattern is temperature-history dependent: a long high-power burst creates a different asymmetry profile than a short peak with the same average power
• This signature distinguishes thermal AM-AM from other nonlinear mechanisms and requires thermal-aware predistortion for effective compensation

Thermal AM-AM does not occur in isolation—it interacts with and exacerbates other nonlinear memory mechanisms:

• Bias network modulation: Temperature-induced changes in quiescent current alter the impedance seen by the baseband bias network, coupling thermal and electrical memory
• GaN trapping synergy: In GaN HEMTs, thermally activated electron trapping in buffer layers and surface states creates a compound memory effect where temperature accelerates charge capture and emission rates
• AM-AM/AM-PM coupling: Thermal gain compression simultaneously modifies the device's nonlinear capacitances, inducing correlated thermal AM-PM distortion that rotates the constellation diagram
• Multi-stage interaction: In multi-stage power amplifiers, driver-stage thermal AM-AM creates a time-varying input signal for the final stage, compounding the overall distortion

This coupling necessitates electro-thermal modeling that jointly captures both thermal and electrical memory for accurate behavioral prediction.

Thermal AM-AM distortion exhibits memory durations orders of magnitude longer than electrical memory effects, governed by the device's thermal time constants:

• Die-level time constants: The semiconductor die itself has thermal time constants in the microsecond to millisecond range due to its small thermal mass
• Package-level time constants: The package substrate, die attach, and heat spreader introduce time constants from milliseconds to seconds
• Heat sink time constants: The external cooling solution can have time constants of seconds to minutes, though these typically affect only the average operating point
• The distributed nature of thermal capacitance creates a multi-time-constant response that cannot be captured by a single exponential decay
• This long memory span requires predistorter models with deep memory taps or recurrent neural network architectures that can track state over extended time horizons

Isolating thermal AM-AM from other distortion mechanisms requires specialized pulsed and modulated measurement techniques:

• Pulsed I-V characterization: Applying short-duration pulses with varying quiescent temperatures separates thermal effects from trapping by controlling the thermal state independently
• Two-tone envelope modulation: Using a low-frequency envelope modulation on an RF carrier creates controlled thermal excitation at known frequencies, enabling extraction of the thermal transfer function
• Step-response thermometry: Measuring gain changes following a step in average power reveals the thermal impulse response through the time-dependent gain recovery
• Infrared thermography: Direct spatial temperature measurement across the transistor channel provides validation data for thermal models and confirms the temperature distribution causing AM-AM distortion
• Load-pull with thermal control: Combining active load-pull with precise baseplate temperature control isolates the thermal contribution to dynamic gain compression

A distortion mechanism where the device's temperature history, caused by signal envelope variations, alters its instantaneous electrical behavior. This creates a long-term nonlinear memory that cannot be corrected by memoryless linearization. The effect manifests when the signal's envelope bandwidth falls within the thermal bandwidth of the device, typically in the kilohertz to megahertz range.

The process by which power dissipation within the transistor channel increases its own junction temperature. This dynamic heating leads to shifts in:

• Carrier mobility (degrading drain current)
• Threshold voltage (altering turn-on characteristics)
• Transconductance (modifying gain profile)

The resulting gain compression or expansion is the physical root cause of thermal AM-AM distortion.

A measure of a material's resistance to heat flow, defining the dynamic relationship between power dissipation and temperature rise. Represented as Zth(t), it captures both:

• Static thermal resistance (Rth, steady-state)
• Transient thermal response (dictated by thermal capacitance)

This impedance function is the transfer function that converts the instantaneous power envelope into the junction temperature waveform driving AM-AM distortion.

The characteristic time required for a device's junction temperature to reach approximately 63.2% of its steady-state value following a step change in power dissipation. Multiple time constants exist in a real device:

• Die-level: nanoseconds to microseconds
• Package-level: milliseconds
• Heat sink: seconds to minutes

The slowest time constants dictate the memory duration that predistorters must compensate for.

A co-simulation technique that couples semiconductor device physics with dynamic heat generation and dissipation equations. This approach simultaneously solves:

• Electrical equations (carrier transport, current-voltage relationships)
• Thermal equations (heat diffusion, Fourier's law)

The result is a unified prediction of temperature-dependent nonlinearities including thermal AM-AM and AM-PM distortion under realistic modulated signal conditions.

A behavioral model structure that augments standard memory polynomials with additional terms specifically designed to capture low-frequency, long-duration thermal lag effects. Key characteristics:

• Standard terms: model short-term electrical memory
• Thermal terms: use heavily decimated samples or integrated power history
• Cross-terms: capture interaction between instantaneous amplitude and thermal state

This structure enables accurate predistortion without requiring explicit temperature sensing.