Analysis
Figure 1 is an example Widlar current source using bipolar transistors, where the emitter resistor R2 is connected to the output transistor Q2, and has the effect of reducing the current in Q2 relative to Q1. The key to this circuit is that the voltage drop across the resistor R2 subtracts from the base-emitter voltage of transistor Q2, thereby turning this transistor off compared to transistor Q1. This observation is expressed by equating the base voltage expressions found on either side of the circuit in Figure 1 as:
where β2 is the beta-value of the output transistor, which is not the same as that of the input transistor, in part because the currents in the two transistors are very different. The variable IB2 is the base current of the output transistor, VBE refers to base-emitter voltage. This equation implies (using the Shockley diode law):
Eq. 1
where VT is the thermal voltage.
This equation makes the approximation that the currents are both much larger than the scale currents IS1, IS2, an approximation valid except for current levels near cut off. In the following the distinction between the two scale currents is dropped, although the difference can be important, for example, if the two transistors are chosen with different areas.
Read more about this topic: Widlar Current Source
Famous quotes containing the word analysis:
“Whatever else American thinkers do, they psychologize, often brilliantly. The trouble is that psychology only takes us so far. The new interest in families has its merits, but it will have done us all a disservice if it turns us away from public issues to private matters. A vision of things that has no room for the inner life is bankrupt, but a psychology without social analysis or politics is both powerless and very lonely.”
—Joseph Featherstone (20th century)