An Early Model of Transistors and Circuits

Abstract

Bipolar junction transistors (BJTs) have been at the core of linear electronics from its beginnings. Although their properties can be well represented transport model equations, design and analysis approaches have, to a good extent, been limited to using current-equispaced horizontal and parallel isolines of the characteristic surface. Here, we resort to the geometrical structure imposed on BJTs behavior by the Early effect and voltage as a means to derive a simple, intuitive and more complete respective model that, though excluding cut-off and saturation regimes, can simplify the design and characterization of BJTs and respective circuits, including integrated devices. The approach involves using a beam of isolines converging at the Early voltage as the model of a BJT. The angles of the isolines, another important aspect of BJTs, are experimentally verified often to vary almost in linear fashion with the base current, endowing the proposed Early model with an intrinsic geometric nature. An experimental-numerical methodology is suggested for the Early model estimation, and applied to 12 real-world small signal NPN BJTs. Interesting results are obtained, including the identification of diverse Early voltage values for different BJT types and the observation, for the considered BJTs, of the almost linear variation of the isoline angles with the input current. A case example of transfer function estimation, as well as total harmonic distortion analysis, are also provided in order to illustrate the potential of the proposed methodology for approximating, under certain circumstances, the operation of the common emitter configuration. The proposed model also has good potential as a didactic aid in physics and electronics programs, complementing the currently adopted modeling approaches.