Transient Thermal Response

The dynamic relationship between power dissipation and junction temperature rise over time. Unlike static thermal resistance, Zth(t) captures the transient heating curve as heat propagates through distinct material layers.

• Defined as: Zth(t) = ΔT(t) / P_diss
• Extracted from cooling curve measurements after power step removal
• Governs the duration and magnitude of thermal memory effects in GaN/GaAs PAs
• Critical for constructing accurate Foster and Cauer thermal models

The characteristic times required for junction temperature to reach ~63.2% of steady-state after a power step. Multiple time constants exist due to the distributed thermal capacitance of die, attach, package, and heatsink layers.

• Die-level: Microsecond-scale, governed by semiconductor thermal mass
• Package-level: Millisecond-scale, dominated by die attach and substrate
• Heatsink-level: Second-scale, controlled by external cooling interface
• Each time constant creates a distinct memory duration in the distortion envelope

Dynamic temperature fluctuation driven by the low-frequency components of the modulated signal envelope. When the envelope bandwidth falls within the device's thermal bandwidth, junction temperature tracks the instantaneous power envelope.

• Creates history-dependent gain and phase variations
• Most pronounced with signals having high PAPR (e.g., OFDM)
• Thermal filtering effect: high-frequency envelope components are attenuated
• Results in thermal-induced spectral asymmetry that memoryless DPD cannot correct

Mathematical representation of junction temperature as the convolution of instantaneous power dissipation with the device's thermal impulse response. This linear time-invariant framework enables compact behavioral modeling.

• T_j(t) = T_amb + P_diss(t) ∗ h_th(t)
• h_th(t) derived from cooling curve differentiation
• Enables extraction of thermal resistance networks from measurements
• Forms the basis for thermal-induced memory polynomial augmentation in DPD

Two canonical representations for fitting transient thermal response data. Foster networks provide behavioral fits with no physical correspondence, while Cauer networks map directly to material layers.

• Foster: Series RC stages, mathematically convenient, non-physical node voltages
• Cauer: Ladder with capacitors to ground, each stage represents a physical layer
• Foster parameters are non-unique; Cauer parameters reflect actual thermal resistances
• Both used in electro-thermal co-simulation for DPD algorithm verification

A phase shift nonlinearity that varies with the signal envelope history due to temperature-dependent transistor capacitances. Unlike instantaneous AM-PM, thermal AM-PM exhibits long-duration memory.

• Caused by temperature sensitivity of Cgs, Cgd, and Cds
• Creates dispersive phase response across the modulation bandwidth
• Cannot be compensated by memoryless LUT-based predistortion
• Requires thermal-aware DPD with temperature-indexed correction coefficients

The fundamental metric defining the dynamic relationship between power dissipation and junction temperature rise. Unlike static thermal resistance, thermal impedance captures the time-dependent heat flow through multiple material layers.

• Measured in °C/W and represented as a complex frequency-dependent function
• Extracted from the transient thermal response cooling curve using deconvolution
• Governs the magnitude and duration of thermal memory effects in GaN and GaAs PAs

Two canonical network topologies for representing extracted thermal impedance as lumped-element equivalent circuits.

• Foster model: Series-connected parallel RC stages providing a mathematical fit to the transient heating curve; no direct physical correspondence to material layers
• Cauer model: Ladder network with capacitors connected to thermal ground; each stage maps to a physical material layer (die, attach, package)
• Foster models are easier to extract; Cauer models are preferred for electro-thermal co-simulation

Characteristic times governing how quickly a device junction responds to changes in power dissipation. Extracted from the transient thermal response curve using the method of time-constant spectrum analysis.

• Short time constants (μs–ms): Die-level heating within the semiconductor itself
• Long time constants (ms–seconds): Heat propagation through die attach, package, and heat sink
• These time constants directly determine the thermal memory duration that DPD must compensate

The mechanism by which the low-frequency components of a modulated signal's envelope cause dynamic junction temperature fluctuations.

• The envelope bandwidth of modern signals (e.g., OFDM) falls within the thermal bandwidth of the device
• This creates a direct coupling between signal statistics and temperature-induced gain/phase variations
• Thermal AM-AM and thermal AM-PM distortion arise specifically from this envelope-temperature interaction

The mathematical operation that computes instantaneous junction temperature as the convolution of the power dissipation waveform with the device's thermal impulse response.

• T_j(t) = P_diss(t) ∗ Z_th(t) + T_ambient
• This convolution captures the full history-dependent temperature evolution
• Forms the basis for thermal-aware predistortion algorithms that incorporate temperature prediction into coefficient calculation

A co-simulation methodology that couples semiconductor device physics with dynamic thermal analysis to predict temperature-dependent nonlinearities.

• Combines finite element thermal analysis with compact transistor models
• Captures the bidirectional feedback: electrical losses heat the device, and temperature changes alter electrical behavior
• Essential for predicting thermal-induced spectral asymmetry and validating DPD performance before hardware prototyping