Wilson current mirror:

A Wilson current mirror or 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. 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.

Circuit Analysis:

Assumptions:

1.All transistors have the same current gain β.

2.Q1 and Q2 are matched, so their collector currents are equal.

Therefore, IC1 = IC2 (= IC) and IB1 = IB2 (= IB) ... (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 IE3 = IC2 + IB1 + IB2 ... (4)

substituting for IC2, IB1 and IB2 from (1) in (4),

IE3 = IC + 2.IB ... (5)

so,

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

substituting for IE3 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,

IR1 = IC1 + IB3 ... (8)

But, IC1 = IC2 = IC

Substituting for IC from (7) in (8) and since 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 IR1 which in turn is dependent on VCC and R1. If VCC 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.

Wilson current source

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 IC3 is almost

equal to the reference or input current IR1. It also has a very high output impedance.

Further improvement:

Improved Wilson current mirrorAdding a fourth transistor to the Wilson current mirror improves its linearity at higher current levels. It accomplishes this by equalizing

the collector voltages of Q1 and Q2 at 1 Vbe. This leaves the finite beta and voltage differences of each of Q1 and Q2 as the remaining unbalancing influences in the

mirror.