Current mirror
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A current mirror is a circuit designed to copy a current flowing through one active device by controlling the current in another active device of a circuit, keeping the output current constant regardless of loading. The current being 'copied' can be, and sometimes is, a varying signal current.
BJT Current Mirror
Operation
Transistor Q1 is connected such that it has a constant current flowing through it (due to R1 and Vs) and behaves as a forward-biased diode, and the current is determined mainly by the resistance R1. It is important to have Q1 in the circuit, instead of a regular diode, because the two transistors can 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. [According to the Ebers-Moll transistor model, the collector current through a given transistor is directly related to the natural exponent of the base-emitter voltage. In other words, Ic is proportional to e raised to the power of the base-emitter voltage. For a given transistor type, this characteristic will match closely, regardless of the beta (current gain) of the transistor.] The second transistor, Q2, which then has the same base-emitter voltage, will match its collector current to Q1's. This current will be maintained over a wide range of voltages, as long as Q2 stays out of saturation, and does not dissipate enough power to heat up too much relative to Q1. (In addition to matching transistor types, it is important to keep their temperatures closely matched. In integrated circuits and transistor arrays where both transistors are on the same die, this is easy to achieve. But if the two transistors are widely separated and are at different temperatures, the currents will not match.)The constant current flowing through R1 can be varied by altering the value of R1 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 a current regulator. It can also be thought of as a constant current source, (or, more accurately, a constant current sink) due to the way it is used in integrated circuits.
Additional matched transistors can be connected to the same base and will supply the same collector current. In other words, the right half of the circuit can be duplicated several times with differing values of R2 on each. Note, however, that each additional right-half transistor "steals" a bit of collector current from Q1 due to the non-zero base currents of the right-half transistors. This will result in a small reduction in the programmed current.)
Circuit analysis
The current through R1 is given by:
[I_ = I_ + I_ + I_]
Where [I_] is the collector current of Q1, [I_] is the base current of Q1, [I_] is the base current of Q2.
The collector current of Q1 is given by:
[I_ = \beta I_]
Where [\beta] is the DC current gain of Q1. If Q1 and Q2 are perfectly matched, [\beta] of Q2 will be that same as that of Q1. Similarly, the base currents of Q1 and Q2 will be the same. (Note: [\beta] is also commonly denoted as hFE)
After substituting and rewriting, one finds that the collector current of Q2 is given by:
[I_ = \frac}]
If [\beta >> 1], then
[I_ \approx I_]
Typical values of [\beta] will yield a current match of 1% or better. Even better matching can be achieved with more sophisticated current mirrors, such as the Widlar current source, Cascoded current sources and Wilson current source.
MOSFET Current Mirror
Operation
Transistor T1 is operating in the saturation region, and so is T2. In this setup, the output current Iout will be directly related to Iref. Id is a function of the gate source voltage of a transistor given by Id = f(Vgs). This is a relationship derived from the functionality of MOSFET technology. In the case of a current mirror, Id = Iref. Thus if Iref is a function of Vgs. Iref is known and normally provided by a band-gap reference circuit. By this same relationship we find Iout. Iout = Id is also a function of Vgs. As we are able to derive Vgs from Iref based on properties of the transistor, this same Vgs applies to transistor T2 in the diagram. This principle works because both transistors T1 & T2 have good matching of their properties such as channel length and doping concentrations. The source terminals of both transistors are also biased to the same voltage so that the Vgs property can be applied. At this point the relationship of f(Vgs) = Iout is applied thus finding that Iout = Iref. Is can also be shown that Vds (drain-source voltage) of each transistor is the same. The Id equation that describes this principle is –[I_ = \fracK_\left(\frac\right)(V_ - V_)^2 (1 + \lambda.V_)]
where,
[K_ = \mu C]
µ and C are constants associated with the transitor, W/L is the width to length ratio of the transistor, Vgs is the gate-source voltage, Vt is the threshold voltage, λ is the channel length modulation constant, and Vds is the drain source voltage.
References
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