Fundamental Problems of the Theory of Transistor Charge Control.

In order to determine dynamic currents and voltages of a circuitry containing transistors, dynamic transistor characteristics must be known. This paper shows how to derive dynamic transistor characteristics for a charge-controlled transistor model by a synthesis of Ebers and Moll's static and Beaufoy and Sparkes' dynamic transistor relations. Dynamic transistor quantities may then be determined by two methods: one may solve the related system of dynamic circuit equations directly, and another may solve the system of corresponding ' adjoined static ' circuit equations leading to 'adjoined static' quantities from which dynamic quantities may then be computed. Adjoined static quantities are time-dependent quantities which would be observed if all base-charging currents were supplied from wells inside the transistor base, whereas in reality they are supplied by sources outside the base, leading to the observation of corresponding dynamic quantities. The possibility of deriving dynamic from adjoined static quantities follows from the basic assumptions of charge-control theory.
If switching times or, more generally, durations of dynamic transistor processes in terms of base charge only are required, then, given current or voltage control, the respective control quantity being known as a function of time, it is not necessary to formulate and solve the complete system of circuit equations. In the case of current control, one may solve Sparkes' equation, assuming different values for the switching time constant corresponding to the various operating regions. In the case of voltage control, an analogue equation may be solved, derived from a generalization of Sparkes' equation, which obviates the need for regional time constants. Both methods do not lend themselves well to the determination of dynamic transistor currents and voltages generally, except in the active region where base charge and output current are approximately proportional. [ABSTRACT FROM AUTHOR]