Electrothermal X-Parameters for Dynamic Modeling of RF and Microwave Power Transistors

For the first time, this paper presents and validates a novel extension of the X-parameter behavioral modeling paradigm to include dynamic electro-thermal phenomena, a key source of long-term memory affecting transistors. The dynamic thermal X-parameter model (DTXM) adds a novel but straightforward method to implement envelope domain sub-circuit in a feedback loop around a conventional static X-parameter model, enabling the simulation of modulated waveform-dependent dynamic self-heating effects. The extended model is identified from conventional CW or pulsed X-parameter measurements, over a range of ambient temperatures. A re-referencing of the extracted X-parameter data to the junction temperature is performed, based on estimated or a calculated thermal resistance and thermal capacitance. The model can also be generated in the simulation environment starting from a dynamic electro-thermal compact time-domain model. The DTXM accounts for thermally-induced asymmetry of intermodulation distortion products and temperature hysteresis depending on the signal bandwidth.