Analysis and Exact Solutions of Relaxation-Time Differential Equations Describing Non Quasi-Static Large Signal FET Models

A relaxation-time differential equation for a non quasi-static large-signal FET model is analyzed and solved exactly in closed form for the first time. It is proved that for certain large-signal excitations, when the stimulation frequency is large compared to the inverse relaxation time, the mathematical solution of the transient analysis problem for the drain current is nonphysical unless the model´s nonlinear constitutive relations satisfy an integrability (conservation) condition. This is true despite the fact that the model can exactly reproduce the measured dc i-v curves and bias-dependent small-signal parameters.