# Wilson Current Mirror

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I recently came across this very cool circuit shown in Figure 1 while working on a project that needed a constant current sink. It is a well-known circuit, but as I dug into it, I was impressed with just how elegant a piece of design it really is. Before we can appreciate the Wilson current mirror, we should look at the standard two transistor current mirror as shown in Figure 2.

This circuit is called a current mirror, because the collector current through transistor Q1, set by the resistor R1, is mirrored in the collector current in Q2. Calculating ISET is easy—the voltage at Q1’s collector is fixed to VBE, or around 0.7V, thanks to the fact that the collector and base of Q1 is connected together, so the resistor sees V1—VBE across it and Ohm’s law does the rest for us.

But why is the collector current in Q2 (ILOAD) the same as ISET? Understanding this requires us to recall (or learn) a little transistor theory. I promise it won’t be too difficult.

It is common (and useful in many circumstances) to think of the transistor as a current amplifying device where IC  = βIB  but in reality, a better large-signal model of the transistor is a trans-conductance device where the collector current is a function of the base-emitter voltage. The Ebers-Moll model gives the approximation  IC = IS × e BEτ  ) where IS is the reverse saturation current of the transistor (typically  10-12 A to 10-15 A and highly temperature dependent) and Vτ is the thermal voltage (approximately 26mV at room temperature and also temperature dependent).

You don’t need to worry about these details—the key takeaway is that if two transistors of the same type at the same temperature have the same VBE, then they will have identical collector currents.

This simple current mirror is often all that is needed but it is also worth understanding one of the key limitations of this circuit. There is a phenomenon called the Early effect where a transistor’s VBE increases slightly with increasing VCE. The Early effect is caused by the widening of the depletion region at the collector-base junction with VCE. Ebers-Moll tells us that this increase in VBE will result in an increase in IC. The impact of this can be as much as a 10% or more increase in current over a few tens of VCE increase. 10% is good enough for many applications, but if you want very constant current regardless of voltage you need to look further.

Enter the Wilson current mirror, named for George R Wilson who invented this truly beautiful circuit in 1967. Q1 and Q2 are in the usual mirror configuration but switched around. The collector voltage of Q1 is fixed to 2VBE by Q3 so the programming current can be set as before. As before, Q2’s collector current will be the same as Q1’s. since their base voltages are the same. Q2 has its collector voltage fixed at VBE, so Q3 supports the balance of the supply voltage V2 not dropped across the load. The absolute magic of this circuit is that both current defining transistors, Q1 and Q2, operate at a fixed VCE, completely eliminating the Early effect. Well done George!

References:

Horowitz, Paul, and Winfield Hill. The Art of Electronics. Third edition, 11th printing, with Corrections. Cambridge New York, NY: Cambridge University Press, 2017.

“Wilson Current Mirror.” In Wikipedia, May 3, 2020. https://en.wikipedia.org/w/index.php?title=Wilson_current_mirror&oldid=954698474

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