# Ebers–Moll model aF? Where does it come from?

I am just getting back into electronics after a long while. For the life of me I can't figure where the $\alpha_F$ variable in the Ebers–Moll model comes from when you are calculating $I_C$ or $I_B$ using the formulas given under the Ebers–Moll section on the BJT Wiki Page. My first instinct is that it is $h_{fe}$ , if I am to take the meaning of 'common base forward short-circuit current gain' literally, since $h_{fe}$ was the closest rating I could find in any datasheet.

So what I am asking is: Where do you get $\alpha_F$ when you are using the Ebers–Moll model of a BJT?

## 2 Answers

αF is not the Hfe of the transistor. Per the model, αF of the emitter current reaches the collector.

This means that αF of the diode current passing through the base-emitter junction contributes to the current flowing through the base-collector junction.

Typically, αF has a value of between 0.98 and 0.99. the forward beta (~hfe) is αF/(1-αF).

• I did not think it was hfe! So what would I put into the equation then? – Zack Frost Feb 15 '17 at 20:48
• Use hfe on the datasheet and the relation in the answer to estimate αF: aF = hfe/(1+hfe). – John D Feb 15 '17 at 20:52
• Ok! That makes sense now. I missed that part at the end for whatever reason. – Zack Frost Feb 15 '17 at 20:56

It is defined as function of collector and emitter current. More specifically a ratio of the exponential functions which describe the current at the emitter and collector. You should find that the forward ratio is near unity.