Modeling of three terminal devices: A black box approach

A unified black box approach is presented for synthesizing nonlinear dc circuit models of 3-terminal devices characterized by two families of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\upsilon-i</tex> curves in piecewise-linear form. In order to model arbitrary curves with nonuniform spacings and slopes, three simple but versatile building blocks-a controlled linear resistance, a controlled concave resistor, and a controlled convex resistor-are introduced and shown to be essential ingredients. The circuit parameters and functions characterizing each element in the black box model can be determined easily from the slopes and breakpoints associated with the segments of the prescribed characteristic curves. The paper concludes with the presentation of several nonlinear dc circuit models for four widely used devices; namely, bipolar transistors, field-effect transistors (FET's), unijunction transistors, and triacs.