Electro-thermal theory of intermodulation distortion in lossy microwave components

An analytic formulation of dynamic electro-thermally induced nonlinearity is developed for a general resistive element, yielding a self-heating circuit model based on a fractional derivative. The model explains the 10 dB/decade slope of the intermodulation products observed in two-tone testing. Two-tone testing at 400 MHz of attenuators, microwave chip terminations, and coaxial terminations is reported with tone spacing ranging from 1 to 100 Hz. Index Terms--Compact modeling, electrothermal, fractional calculus, fractional derivative, heat transfer, intermodulation distortion, multiphysics modeling, nonlinear computer-aided design (CAD), passive intermodulation distortion (PIM), thermal model, transient.