# BJT Collector Current dependance by Temperature

Discussion in 'General Electronics Chat' started by Georacer, Jun 13, 2010.

1. ### Georacer Thread Starter Moderator

Nov 25, 2009
5,142
1,266
We all know that in a BJT, a rise in temperature causes a drop in Vbe and an increase in collector current, when working in the active region. We can verify that in most transistor layouts using Kirchoff's laws. But what about the actual collector current equation: $I_c=I_s\cdot({e^{\frac{V_{\tiny{BE}}}{nV_{\tiny{T}}}})$ ? Having in mind that $V_{\tiny{BE}}$ drops when temperature increases, shouldn't Ic drop too? I know some other variable in the equation must be affected by the temperature, but I don't know which one and how it affects the whole situation. I examined V$_{\tiny{T}}$ but it doesn't seem to affect Ic enough to compensate for the change of $V_{\tiny{BE}}$.

Last edited: Jun 13, 2010
2. ### Ron H AAC Fanatic!

Apr 14, 2005
7,050
657
If $\small{T}$ is the variable, you can either:
1. Hold $\small{V_{BE}}$ constant and examine what happens to $Ic$ as $\small{T}$ changes:

$I_c=I_s\cdot(e^{\frac{qV_{BE}}{{\eta}kT})$

2. Hold $I_c$ constant and examine what happens to $\small{V_{BE}}$ as $\small{T}$ changes:

$V_{BE}=\frac{{\eta}kT}{q}\cdot(ln\frac{I_c}{I_s})$

All this assumes $I_s$ is constant, but unfortunately, it is also a function of temperature.

Last edited: Jun 13, 2010
3. ### Georacer Thread Starter Moderator

Nov 25, 2009
5,142
1,266
It seems I did a little mistake, and for the worse:
As the exponent of e increases, Ic increases and vice versa (not proportionaly, but exponentialy). Now, both reduction of Vbe and increase of T (and consequently Vt) decrease the exponent. As a result, both reduce Ic. Things are not looking good for our model, as none of the parameters mirror reality.
This is really confusing...

4. ### Ron H AAC Fanatic!

Apr 14, 2005
7,050
657
I think this excerpt from Art of Electronics (2nd edition, p.81) explains the source of our confusion, and makes my previous post invalid (or irrelevant).
Also see http://www.cmi.ac.in/~ravitej/lab/10-boltz.pdf

• ###### Vbe vs temp.PNG
File size:
70.4 KB
Views:
219
Georacer likes this.
5. ### jonnylazer New Member

Jan 12, 2010
17
0
Is rises very quickly with temperature and dominates the shrinking exponential.

6. ### Georacer Thread Starter Moderator

Nov 25, 2009
5,142
1,266
Well, I think that is the best answer we are going to get. Thank you for your effort and patience, leafing that book to find the right page. That link was also helpful. I feel a little dissapointed though, since such a common phenomenon has no clear explanation in any reknowned electronics book (I have also searched in Sedra/Smith).
Thanks again, and have a nice day!

Vasanthkini likes this.