Wilson current source

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A Wilson current source is a circuit configuration designed to provide a constant current source or sink. The circuit is shown in the image. It is named after George Wilson, an integrated circuit design engineer working for Tektronix.^[1] Rumour has it that Wilson came up with this configuration after being challenged to come up with a useful new circuit that used three active devices.^{[citation needed]}

1 Circuit Analysis
2 Advantages over other configurations
3 Further improvement
4 References
5 See also

[edit] Circuit Analysis

Wilson current source

Assumptions:

All transistors have the same current gain β.
Q1 and Q2 are matched, so their collector currents are equal.

Therefore, I_C1 = I_C2 (= I_C) and I_B1 = I_B2 (= I_B) ... (1)

Base current of Q3 is given by,

$I_{B3} = \frac{I_{C3}}{\beta}$ ... (2)

and emitter current by,

$I_{E3} = \left(\frac{\beta + 1}{\beta}\right)I_{C3}$ ... (3)

From the schematic, it is evident that I_E3 = I_C2 + I_B1 + I_B2 ... (4)

substituting for I_C2, I_B1 and I_B2 from (1) in (4),

I_E3 = I_C + 2.I_B ... (5)

so,

$I_{E3} = I_C\left(1 + \frac{2}{\beta}\right)$ ... (6)

substituting for I_E3 from (3),

$\left(\frac{\beta + 1}{\beta}\right)I_{C3} = I_C\left(1 + \frac{2}{\beta}\right)$

rearranging,

$I_C = \left(\frac{\beta + 1}{\beta + 2}\right)I_{C3}$ ... (7)

Current through R1 is given by,

I_R1 = I_C1 + I_B3 ... (8)

But, I_C1 = I_C2 = I_C

Substituting for I_C from (7) in (8) and since $I_{B3} = \frac{I_{C3}}{\beta}$ we get,

$I_{R1} = \left(\frac{\beta + 1}{\beta + 2}\right)I_{C3} + \frac{I_{C3}}{\beta}$ ... (9)

Therefore, $I_{R1} = \left(\frac{\beta + 1}{\beta + 2} + \frac{1}{\beta}\right)I_{C3}$ ... (10)

And finally,

$I_{C3} = \frac{I_{R1}}{1 + \frac{2}{\beta(\beta + 2)}}$ ... (11)

From the above equation we can see that if $\frac{2}{\beta(\beta + 2)} << 1, I_{C3} \approx I_{R1}$

And the output current (assuming the base-emitter voltage of all transistors to be 0.7 V) is calculated as,

$I_{C3} \approx I_{R1} = \frac{V_{CC} - 1.4}{R1}$

Note that the output current is equal to the input current I_R1 which in turn is dependent on V_CC and R1. If V_CC is not stable, the output current will not be stable. Thus the circuit does not act as a constant current source.

In order for it to work as a constant current source, R1 must be replaced with a constant current source.

[edit] Advantages over other configurations

This circuit has the advantage of virtually eliminating the base current mis-match of the conventional current mirror thereby ensuring that the output current I_C3 is almost equal to the reference or input current I_R1. It also has a very high output impedance.

[edit] Further improvement

Improved Wilson current mirror

Adding a fourth transistor to the Wilson current mirror (as shown in the diagram to the right) improves its linearity at higher current levels. It accomplishes this by equalizing the collector voltages of Q1 and Q2 at 1 V_be. This leaves the finite beta and voltage differences of each of Q1 and Q2 as the remaining unbalancing influences in the mirror.^[2]

[edit] References

^ Sedra, A.S. & Smith, K.C.: "Microelectronic Circuits, 5th Ed.", page 651. OUP, 2006
^ B. Wilson, Current mirrors, amplifiers and dumpers, Wireless World, December, 1981 p. 47, at p. 48. The author was, at the time of the article, a Ph.D. in the Department of Instrumentation and Analytical Science, University of Manchester Institute of Science and Technology.