# Current mirror

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Currentmirror.png
A current mirror

A current mirror is a circuit designed to regulate a current; to keep it constant regardless of loading.

Transistor Q1 is connected such that it has a constant current flowing through it; it actually behaves like a forward-biased diode, and the current is determined by the resistance R1. It is important to have Q1 in the circuit, instead of a regular diode, because the two transistors will be matched, and thus the two branches of the circuit will have similar characteristics. The voltage at the base of Q1 will necessarily be the exact voltage that sustains the collector current. The second transistor, Q2, which then has the same base voltage, changes its own resistance so that the total resistance in the second branch of the circuit is the same as the total resistance in the first branch, regardless of the load resistor, R2. Since the total resistance in each branch is the same, and they are connected to the same supply, VS+, the amount of current in each branch is the same.

The value of R1 can be varied to change the amount of current going through R2. Since R2 can change dynamically, and the current through it will stay the same, the current mirror is not only a current regulator, but also can be thought of as a constant current source, which is the way it is used in integrated circuits.

More matched transistors can be connected to the same base and will supply the same current. In other words, the right half of the circuit can be duplicated several times with several different loads on each.

## Analysis

The current through R1 is given by:

[itex]I_{r1} = I_{c1} + I_{b1} + I_{b2}[itex]

Where [itex]I_{c1}[itex] is the collector current of Q1, [itex]I_{b1}[itex] is the base current of Q1, [itex]I_{b2}[itex] is the base current of Q2.

The collector current of Q1 is given by:

[itex]I_{c1} = \beta I_{b1}[itex]

Where [itex]\beta[itex] is the DC gain of Q1. If Q1 and Q2 are perfectly matched, [itex]\beta[itex] of Q2 will be that same as that of Q1. Similarly, the base currents of Q1 and Q2 will be the same.

After substituting and rewriting, one finds that the collector current of Q2 is given by:

[itex]I_{c2} = \frac{\beta I_{r1}}{\beta + 2}[itex]

If [itex]\beta >> 1[itex], then

[itex]I_{c2} \approx I_{r1}[itex]

Typical values of [itex]\beta[itex] will yield a current match of 1% or less. Even better matching can be achieved with more sophisticated current mirrors, such as the Widlar current source and Wilson current source.de:Stromspiegel

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