The current mirror is a type of circuit used in electrical engineering for biasing analog circuits, and replacing load resistors in operational and differential amplifiers. Transistors (when constructed as part of an integrated circuit) are much smaller than resistors, so many integrated circuits employ circuits such as this in order to save space. Current mirrors can be constructed using MOSFETs or bipolar transistors (BJTs).

If you've read this far, you are probably saying to yourself, "That's just great, but what does the circuit actually DO? What is its purpose in life?" I will attempt to explain that the best I can. In basic terms, a current mirror's output current should match its reference current - and does in the ideal model. This circuit can provide a reliable current reference. For simplicity, I will restrict this discussion to the ideal current mirror.

In the ideal current mirror, input impedance is low, output impedance is high, and the output current is independent of the output voltage. βf is assumed to be large, and effects of the Early voltage are neglected.

```
Vb --|                    |-- Vcc
|                    |
> R                  |
>                    |
| |            |     |
| v Iref       v Ic2 |
|                    |
Ic1 |----------|         |
|          |         |
-\  <- Ib1 | Ib2 -> /-
Q1    |--------o-------|    Q2
</         +        \>
|         Vbe        |
|          -         |
|__________o_________|
GND

Figure 1: BJT Current Mirror
```

Figure 1 shows a current mirror constructed with two BJTs. These BJTs are assumed to be matched; that is, characteristics such as forward and reverse gain are identical. In practice, this is generally a good assumption as long as the transistors are part of the same die. The purpose of the lone resistor R in this circuit is to develop the reference current, Iref.

This current mirror is connected in a common emitter configuration. Note that Q1 uses a diode connection; that is, the collector is tied to the base.

Before starting analysis, it is useful to define the terms that will be used in the equations.

Vb - The voltage that, in conjunction with R, creates the source for Iref
Vcc - Source voltage, equal to Vb in this case
Vbe - Base-emitter voltage for both transistors
Iref - Reference current
Ib1 - Base current for Q1
Ib2 - Base current for Q2
Ic1 - Collector current for Q1
Ic2 - Collector current for Q2 (also the output current of the circuit)
βf - Forward transistor gain, equal in Q1 and Q2

Using Kirchhoff's Current Law at the collector of Q1 gives us the following expressions for Iref:

1.) Iref = (Vb - Vbe)/R

2.) Iref = Ic1 + Ib1 + Ib2

Since Vbe is assumed to be equal for both transistors, we can write:

3.) Iref = (βf +2)Ib2

4.) Ic2 = βf * Ib2 = (βf)*Iref/(βf + 2) = Iref/{1 + (2/βf)}

βf is assumed to be >> 2, so:

5.) Ic2 ~= Iref, which means that indeed the output current is approximately equal to the reference current.

Current mirrors can be found in many textbook examples of circuits; for instance, most operational amplifiers employ a current mirror in their input stage. If you are seriously interested in building a current mirror, it would be smart to consult an engineering text, so that you may take real-world variables into consideration.

References:

Jaeger, Richard C. Microelectronic Circuit Design. Boston: McGraw-Hill Co. 1996
Franco, Sergio. Design with Operational Amplifiers and Analog Integrated Circuits 2nd Ed. Boston: McGraw-Hill Co. 1998