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].

1 Circuit Analysis
2 Advantages over other configurations
3 References
4 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.