New formulation of the collector current and current gain relations for design purposes of power transistor switches

New, compact analytical formulas for the collector current and current gain of bipolar power transistors are derived for operation in quasisaturation and saturation regions. The derivation is based on a regional approach taking into consideration current gain dependency on collector minority carrier lifetime and effective surface recombination velocity at the low-high (n^-n⁺) junction. The paper represents an attempt to apply the theory of low-high junction (LHJ) to a bipolar power transistor operated in the saturation region. The current-voltage characteristics predicted by the proposed formulation are compared with the experimental results available in the literature to demonstrate the validity and usefulness of the new formulation. The new set of equations can be used as the basis of the design framework for the evaluation of optimal parameters of bipolar power transistor switches