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The Buffered Current Mirror

Base Current Compensation

A basic current mirror. A current mirror with base current compensation.

As we mentioned on the page discussing errors in current mirrors, the basic current mirror circuit shown to the left has, among other problems, a mismatch between IREF and IO caused by the unavoidable presence of base current for the two transistors flowing through R. With high-gain transistors the difference is small and sometimes negligible, but sometimes it must be recognized and minimized.

A simple way to reduce the base current flowing through R is to add a third transistor, Q3, to the circuit as shown to the right. Now the base current for Q1 and Q2 is also the emitter current of Q3, and only the base current for Q3 must still flow through R. This effectively reduces the base current error by a factor of (β + 1).

Adding Q3 to the circuit does change IREF slightly, since Q1 no longer has its collector and base connected together. Instead, we have an extra VBE to account for. For this circuit, IREF = (+V - 2VBE)/R. This is not normally a problem, but it can be in low-voltage circuits.

The Math

Assuming Q3 has the same parameters as Q1 and Q2, the base current for Q3 will be 2IB/(β + 1). Applying this change, the mathematical expression that relates IO to IREF becomes:

IREF  =  IC1  +  2IB

β + 1
IREF  =  IC1  +  2IC1

β(β + 1)
IREF  =  IC1  +  2IC1

β² + β
IREF  =  (β² + β)IC1  +  2IC1

β² + β β² + β
IREF  =  β² + β + 2  IC1

β² + β
IO = IC2 = IC1  =  β² + β  IREF

β² + β + 2

For transistors with a gain of 100, the ratio is 10,100/10,102 = 0.9998. This is a much smaller error than the percentage variation between the transistors themselves, even within an IC. Older transistors with a gain as low as 30 will produce a ratio of just under 0.9979, which is still only about 0.2% and can usually be neglected.

If multiple mirror transistors are driven from a single reference, the only part of the equation that changes is the "+ 2" constant. As with the basic mirror circuit, that number simply reflects the number of transistors whose base current will flow through Q3. In almost all cases, this change can be neglected.

Output Resistance Unchanged

Because the output transistor is not affected in any way by the addition of Q3, its output resistance is likewise unaffected. Thus, the problems associated with this output resistance and its changes as VCE changes will remain exactly as they were in the basic current mirror circuit.

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