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A current mirror is a circuit designed to copy a current 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. Conceptually, an ideal current mirror is simply an ideal current amplifier with unity current gain.

BJT Current Mirror

Operation

Transistor Q₁ is connected such that it behaves as a forward-biased diode. The constant current through it (due to R1 and Vs) is determined mainly by the series resistance R1 as long as Vs is significantly larger than 0.7V, the typical forward V_BE voltage for a silicon BJT. It is important to have Q₁ in the circuit instead of a regular diode because, assuming the two transistors are closely matched, the base current for each transistor should be nearly identical since V_BE for each transistor is identical. With nearly identical base currents, the matched transistors should then have nearly identical collector currents as long as V_CE2 is not significantly larger than V_BE. If V_CE2 is much larger than V_BE, the collector current in Q₂ will be somewhat larger than for Q₁ due to the Early effect and further, Q₂ may get substantially hotter that Q₁ due to the associated higher power dissipation. When this occurs, the transistors will no longer be matched. To maintain matching, the temperature of the transistors must be nearly the same. 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, the precision of the current mirror will not be stable.

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:

${\displaystyle I_{R1}=I_{C1}+I_{B1}+I_{B2}}$

Where ${\displaystyle I_{C1}}$ is the collector current of Q1, ${\displaystyle I_{B1}}$ is the base current of Q1, ${\displaystyle I_{B2}}$ is the base current of Q2.

The collector current of Q1 is given by:

${\displaystyle I_{C1}=\beta _{0}I_{B1}}$

Where ${\displaystyle \beta _{0}}$ is the DC current gain of Q1. If Q1 and Q2 are perfectly matched, ${\displaystyle \beta }$ of Q2 will be:

${\displaystyle \beta _{2}=\beta _{0}\ (1+{\frac {V_{CB2}}{V_{A}}})}$

where V_A is the Early voltage.

Because V_BE1 = V_BE2 and Q1 and Q2 are matched, I_B1 = I_B2.

After substituting and rewriting, the collector current in Q2 is given by:

${\displaystyle I_{C2}={\frac {I_{R1}}{1+{\frac {2}{\beta _{0}}}}}\ (1+{\frac {V_{CB2}}{V_{A}}})}$

If ${\displaystyle \beta _{0}>>1}$, then

${\displaystyle I_{C2}\approx I_{R1}\ (1+{\frac {V_{CB2}}{V_{A}}})}$

Typical values of ${\displaystyle \beta }$ will yield a current match of 1% or better. Even better accuracy and precision 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 I_out will be directly related to I_ref. I_d is a function of the gate source voltage of a transistor given by I_d = f(V_gs). This is a relationship derived from the functionality of MOSFET technology. In the case of a current mirror, I_d = I_ref. Thus I_ref is a function of V_gs. I_ref is known and normally provided by a band-gap reference circuit. By this same relationship we find I_out. I_out = I_d is also a function of V_gs. As we are able to derive V_gs from I_ref based on properties of the transistor, this same V_gs 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 V_gs property can be applied. At this point the relationship of f(V_gs) = I_out is applied thus finding that I_out = I_ref. I_s can also be shown that V_ds (drain-source voltage) of each transistor is the same. The I_d equation that describes this principle is –

${\displaystyle I_{d}={\frac {1}{2}}K_{p}\left({\frac {W}{L}}\right)(V_{gs}-V_{t})^{2}(1+\lambda .V_{ds})}$

where,

${\displaystyle K_{p}=\mu C}$

µ and C are constants associated with the transitor, W/L is the width to length ratio of the transistor, V_gs is the gate-source voltage, V_t is the threshold voltage, λ is the channel length modulation constant, and V_ds is the drain source voltage.

It must be recognized that these equations are accurate only for rather dated technology, although they often are used for mathematical convenience even today. Any quantitative design based upon new technology uses computer models for the devices that account for the changed current-voltage characteristics in new technology. Among the differences that must be accounted for in an accurate design is the failure of the square law in V_gs for voltage dependence and the very poor modeling of V_ds drain voltage dependence provided by λV_ds.

See also

• Current source
• Widlar current source
• Wilson current source

References

• Gray, Paul (2001). Analysis and Design of Analog Integrated Circuits. Wiley. ISBN 0-471-32168-0. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)

• Analog circuits