An Integral Charge Control Model of Bipolar Transistors

Since its formulation in 1954, the Ebers-Moll model 1 has been the major large-signal model for bipolar transistors. It is based directly on device physics and covers all operating regimes, that is, active, saturated, and cut-off operation. But various approximations limit the accuracy of the model. In the original paper the frequency dependence was described in terms of frequency-dependent current generators. For time-domain analysis, this required use of Laplace transforms. In 1957 Beaufoy and Sparkes" analyzed the bipolar transistor from a charge control point of view. T h e charge control model 2 or the equivalent 3,4 charge control form of the Ebers-Moll model, is directly useful for transient analysis. It is this model, in various forms, that is presently used in all the major general purpose network analysis programs. M o r e elaborate models 5-7 are useful for detailed device studies, but they have not found widespread use in analysis programs due to their complexity. As device technology evolved over the years making possible devices of reproducible characteristics, and as deeper understanding was gained in device-theoretical studies, many new effects were identified that are not represented by the basic Ebers-Moll model. Among these are a finite, collector-current-dependent output conductance due to basewidth modulation 8 (Early effect), space-charge-layer generation and recombi827