# Why is the variance of the beta value among BJTs much lower in the saturation region than in the forward active region?

In my electronics lab, we measured the beta (Ic/Ib) values of BJTs in both the active and saturation regions. While the betas measured in the forward-active region varied massively between different BJTs (even of the same model), there was virtually no variation among beta values in the saturation region. Why is this the case?

• transistor beta is a metric that only applies in forward-active mode. In saturation, it plays no role in circuit performance. – Hearth Oct 22 '19 at 1:44
• What values did you measure for beta in the saturation region? – The Photon Oct 22 '19 at 1:44
• Saturation is a gradual affair. It starts right at the point where the BC junction begins to be forward-biased (though many will argue that it starts somewhat later than that.) But there is definitely shallow and deep saturation, which will have decidedly different beta values. So spend a little time showing us the circuit and measurement techniques you used for both "active" and "saturation" modes. I think your answers will be found from a simple examination of your lab methodologies. But we'd need to see them to know for sure. – jonk Oct 22 '19 at 3:30

In active mode you give the transistor a high enough $$\V_{ce}\$$ such that the transistor can determine the collector current $$\I_c\$$ that is flowing.

Then we can apply a given base current $$\I_b\$$, let the transistor determine $$\I_c\$$ and calculate $$\\beta = I_c/I_b\$$.

In saturation mode the transistor does not get a high enough $$\V_{ce}\$$ so the transistor cannot determine the collector current $$\I_c\$$ that is flowing (for that a higher $$\V_{ce}\$$ would be needed but then we would be in active mode!).

So in saturation mode $$\I_c\$$ is determined outside the transistor. To make any current flow of course a base current $$\I_b\$$ is needed, we cannot make that $$\I_b\$$ small as that would result in a small $$\I_c\$$, maybe smaller than what we want (remember that $$\I_c\$$ is set outside the transistor) and then again we would end up in active mode.

So $$\I_b\$$ has to be fairly large. How large? Well $$\I_b\$$ needs to be more than $$\I_c/\beta\$$ because that's the current that would flow when in active mode. So if we force $$\I_b > I_c/\beta\$$ then we would have a high enough $$\I_b\$$ to be sure we're in saturation mode. Many datasheets use $$\I_c/I_b = 10\$$ when measuring in saturation mode.

So in saturation mode you cannot measure $$\\beta\$$ as it is determined by the measurement itself (both $$\I_b\$$ and $$\I_c\$$ are forced from external).

You can only measure the transistor's $$\\beta\$$ properly when it is in active mode.

The reason why $$\\beta\$$ varies a lot is due to it being a very poorly controlled property of a transistor. $$\\beta\$$ depends on doping levels and thickness of the base region, both of these are difficult to control in manufacturing. This may sound like a huge problem but it is not, the circuits in which we use transistors do not rely on the value of $$\\beta\$$ to be predictable. Instead, proper circuits are designed to work with the smallest value $$\\beta\$$ can have, then when $$\\beta\$$ is larger, the circuit will still work as designed.