New formulation of the current and charge relations in bipolar transistor modeling for CACD purposes

New, compact analytical formulas for the current and stored charge in a vertical bipolar transistor are derived. The derivation is not based on the charge control concept, but shows how current and charge depend on minority carrier concentrations, which in turn are functions of junction voltages. In this way the influence of the built-in field, the bias-dependent transit times, and the Early effect are incorporated quite naturally. The new set of equations is the framework of a complete transistor model for computer-aided circuit design purposes.