Lumped Models of Transistors and Diodes

Lumped models are shown which can be used to approximate the properties of transistors and diodes over a wide range of conditions and applications. Two analytical procedures lead to a lumped model approximating a distributed system. In the familiar one, a differential analysis of the distributed system is made, subsequently a rational approximation is made to the transcendental functions resulting from the differential analysis. In the other, one makes a lumped model at the outset to approximate the distributed system and analyzes it. The lumping approximation at the outset generally simplifies the analysis and permits consideration of phenomena which would be prohibitive to analyze on a differential basis. Throughout, it provides a close tie of analysis to the physical phenomena involved. A lumped model for diffusion transistors is shown here which is analogous in end result to the Ebers-Moll model. The simple model is subsequently amended to account for the drift phenomenon, photo effects and avalanche multiplication.