Base spreading resistance of square-emitter transistors and its dependence on current crowding

The internal DC and small-signal low-frequency base-spreading resistances of a square-emitter transistor have been calculated analytically as a function of base current. Simplifying assumptions result in a nonlinear differential equation with a simple explicit solution. The validity of the assumptions has been checked by exact numerical device simulation. The error of the analytical approximation has a maximum of only 11% at negligible current crowding (r_Bi-r_Bi,0=r_s /32 instead of the exact value r_s/28.6). In the total operating range of interest, the error of the analytical expression for r_Bi can be dropped to negligible values if the exact value of r_Bi,0 is inserted