# How to analyse Darlington pair?

Is the LEFT circuit of darlington pair, equivallent to the RIGHT transistor circuit?

Is my asumption true? I replaced the two transistors in darlington pair with one; having beta equal to the product of betas of the two transistors, and the voltage from of 1.4 (0.7+0.7) across Base and Emitter.

Then I am calculating the Ib and hence the Ic. In practical experiments, I found that my calculations are not very exact, but close enough.

For example, for the circuit to the right I found:

• Ib = 63 nano Ampere

• Ie = 4.5 mA

In measurements, I am finding the Ie about 5.5 mA.

An important Darlington property that is not accounted for in your right circuit is the increased collector-emitter saturation voltage $U_{CE,SAT}$.

Allow me two random examples of fairly general purpose transistors where Ic=100mA:

• BC547 (regular): $U_{CE,SAT,max}=600mV$
• BC517 (Darlington): $U_{CE,SAT,max}=1000mV$

Notice that these values are maxima, the typical value for the Darlington isn't mentioned, but in practice the difference between thesaturation voltages will be much larger.

This is caused by the fact that the Q1 (output stage) can never reach full saturation. If $U_{C,B1} = 0\text{V}$ (ideally), there will always be the $U_{B1,E} = 0.7\text{V}$ voltage drop in Q1.

simulate this circuit – Schematic created using CircuitLab

As a result, a Darlington transistor will dissipate more power than a regular one at a given collector current.

The presence of Rc in the left schematic makes things complicated. In a true darlington, the two collectors are directly tied together. You can't just project Rc from the collector of the first transistor to the combined transistor on the right. That would only be true if the two collectors were tied together, then Rc connected from there to the positive supply.

In this case, Rc only matters if it drops enough voltage to limit the current to the collector of the first transistor. If it doesn't, then you can eliminate it.

• Yes - as mentioned by Olin Lathrop - the shown transistor combination is NOT a Darlington pair. – LvW Jul 15 '14 at 7:34