# Constant current source

#### yifei87

Joined Sep 7, 2008
16
hey guy,
i have a question on following circuit. GIven I_o= 10uA. Determine the value of R1, assuming Vbe=0.7V at a current of 1mA. How to solve this question? anyone can show me by steps?
thanks

#### Ron H

Joined Apr 14, 2005
7,014
I think there is something wrong with your problem statement. If Iref is 1mA and I_o is 10uA, Q1 has to have an emitter area 100 times that of Q2.

#### steveb

Joined Jul 3, 2008
2,436
Yes, the Io can not be correct as written. There must have been a misinterpretation. My guess is that Io refers to the reverse saturation current. If so, you can use the Schockley diode equation:

Id= Io * (exp(Vd/(n*Vt)) - 1)

This circuit is a current mirror. The basic assumption is that the two transistors have nearly the same characteristics and should be at the same temperature. The left transistor is wired as a diode. If you force current through the diode, the diode voltage drives the transistor base directly, so the transistor emitter current "mirrors" the diode current.

You can figure out the steps if you recast the Schockly diode equation as follows:

Vd=n*Vt * ln(Id/Io+1)

n*Vt is typically 30 mV at room temperature and ln refers to the natural logarithm.

To get the exact relation, you must be careful to account for the base current and the fact that the transitor current gain is not infinite.

There is a very quick approximation you can use for this circuit.

R1 = (Vsupply - 0.7 V) / Iref or in this case R1= (9.3 V) / Iref

This approximation works well if the supply voltage is much larger than the diode voltage.

However, if the problem has given you the reverse saturation current, you need to be much more exact.

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