EbersMoll

The Ebers–Moll model is a foundational mathematical model for bipolar junction transistors (BJTs) that expresses the transistor currents as functions of the base–emitter and base–collector voltages. It was introduced by John J. Ebers and James L. Moll in 1954 and became a standard tool for understanding and analyzing BJT behavior in DC and analog circuits. The model captures both diode junction behavior and the transistor action that couples the two junctions.

The core of the Ebers–Moll model consists of two exponential diode currents, governed by the thermal voltage Vt = kT/q. It uses two junction saturation currents, I_Es for the emitter–base path and I_CS for the collector–base path, together with forward and reverse transport factors α_F and α_R. The conventional form of the equations is:

I_E = I_Es (exp(V_BE / Vt) − 1) − α_R I_CS (exp(V_BC / Vt) − 1)

I_C = α_F I_Es (exp(V_BE / Vt) − 1) − I_CS (exp(V_BC / Vt) − 1)

I_B = I_E − I_C

where V_BE is the base–emitter voltage and V_BC is the base–collector voltage.

The model describes forward active, reverse active, and saturation regions by allowing both junctions to be forward- or reverse-biased and by coupling the diode currents through the transport factors. It provided a physically motivated alternative to simple current gain approximations and laid the groundwork for later transistor models used in circuit simulators.

In practice, the Ebers–Moll model has largely been superseded by more comprehensive models (such as Gummel–Poon) that include parasitics and temperature effects, but it remains a historically important and conceptually clear representation of BJT operation.