The transient integral charge control relation—A novel formulation of the currents in a bipolar transistor

The present paper describes the transient integral charge control (TICC) relation. This term designates a formula describing the emitter, base, and collector terminal currents of a bipolar junction transistor (BJT) for a one-dimensional current flow. The relation holds for dc as well as for transient bias conditions, and basically can be regarded as a more general formulation of Gummel's charge control relation [1], whose validity is restricted to dc conditions and to situations where recombination and generation effects are negligible. The structure of the TICC relation resembles Gummel's formulation extended by some additional terms. We shall use this relation in order to derive a formula for the high-frequency behavior of the transconductance. The expression obtained via the TICC relation allows for physical interpretation and simple calculation. The validity of the derived formulas is carefully checked by numerical means. This yields a validity range of our approach far beyond the Start of the high-current regime.