Analysis and modeling of small-signal bipolar transistor operation at arbitrary injection levels

In this paper a study of small-signal operation of bipolar transistors is presented. Firstly, we derive the governing equations and the associated boundary conditions which describe the small-signal minority carrier transport in the quasi-neutral base region at arbitrary injection levels. Analytical solutions of the transport equations are then discussed. A consequence of the linearity of the transport equations is that the minority carrier currents at the device terminals can be expressed in terms of infinite polynomials of the complex variable. It is then shown that all the hitherto proposed non-quasi-static (NQS) models can be simply obtained by different approximations of the general current expressions. As a consequence, the differences between the various models are clarified, and models previously developed for the low-injection regime are extended to high-injection conditions. The dependence of fundamental model parameters such as the transit time, the partitioning factor, etc., on the injection level is analyzed in detail, and a simple analytical formulation is proposed. Limitations of previous approaches are outlined. Finally, selected NQS models are compared.