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Errors in Current Mirrors

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Errors in Current Mirrors 

There are three main sources of error in the operation of any current mirror. The obvious first problem is that no two transistors are absolutely identical in all respects. There will always be at least small variations. We can match transistors to within a few percentage points in an integrated circuit, but they will still be slightly different.
The second problem is the base current required by any bipolar junction transistor (BJT). This base current is small for highgain transistors, but it is still present and is still a source of error.
The third problem is a little more subtle. When the collectorbase voltage of a BJT changes, the width of the electric field and corresponding depletion region within the transistor also changes. This in turn changes the effective width of the base region, and actually changes the current gain (β) of the transistor. This is equivalent to a parameter mismatch between transistors, and hence an error in mirrored output current. This can also be modeled as a highvalued resistance, designated r_{o}, in parallel with the output terminals but still inside the transistor. This resistance passes some current through itself, and thus reduces the amout of ouitput current available to the external circuit.
We can't do anything about the variations between transistors, other than to allow for those differences and, in extreme cases, make provision for manual adjustments to the circuit. However, we can do a number of things to reduce (but not eliminate) the other two problems. First, however, we must understand what they are and how much effect they will have.
When we set the reference current, I_{REF}, we normally calculate it as (+V  V_{BE})/R, in accordance with Ohm's Law. However, this does not take into account the fact that both transistors draw a certain amount of base current (I_{B}), and the current for both bases also flows through R. Thus, with matched transistors, the correct equation is I_{REF} = I_{C1} + 2I_{B}. Since it is still true that I_{O} = I_{C2} = I_{C1}, it follows that I_{O} will necessarily be slightly less than I_{REF}.
The commonemitter current gain, I_{C}/I_{B}, of a transistor is commonly designated by the Greek letter β (beta). Using this relationship, we can restate our equation for the current mirror:
I_{REF}  =  I_{C1}  +  2I_{B} 
I_{REF}  =  I_{C1}  +  2I_{C1} 


β  
I_{REF}  =  βI_{C1}  +  2I_{C1} 



β  β  
I_{REF}  =  (β + 2)  I_{C1}  


β  
I_{O} = I_{C2} = I_{C1}  =  β  I_{REF}  


β + 2 
If there are multiple mirror transistors, that "β + 2" term will change according to the number of transistors in the entire mirror circuit. For example, in the circuit shown to the right, there are four transistors. Therefore, there are four bases that must be supplied with current, and the term becomes "β + 4."
Since modern transistors have a β of 100 or more, the difference is not very large, but it does still exist and does constitute a discrepancy. For the greatest possible accuracy, this amounts to an error that must be minimized.
The issue of the change in gain of a BJT as V_{CB} changes is a bit more complicated. It is caused by the Early effect, and applies to any BJT. Here, Q1 has a fixed V_{CB} of zero, since its collector and base are hard wired together. This means that for Q1, V_{CE} = V_{BE}. However, Q2 does not have this condition. Now, remember that the BJT output includes an internal resistance, as shown to the right.
That output resistance, r_{O}, will divert some of I_{O} through itself, depending on the collector voltage, V_{C}, of Q2. Of course, the higher the value of r_{O}, the less effect it will have on circuit operation. Therefore we want this resistance to be as high as possible. However, it is always present, and must generally be taken into account.
There are a number of ways to increase the effective value of r_{O}, and some of them also help to reduce the effect of base current as well. We'll look at a number of typical methods in the remainder of the pages in this group, and discuss the tradeoffs involved with each of them.


 
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