MOSFET current sources are also called as current mirrors.

The figure shows a basic two transistor NMOS current mirror. The drain and source terminals of the enhancement mode transistor M1 are connected, which means that M1 is always biased in the saturation region. Assuming $\lambda = 0$ we can write the reference current as

$I_{REF}=K_{nl}(V_{GS}-V_{TNV})^2$ - (1)

Solving for Vgs yields,

$V_{GS}=V_{TNL}+\sqrt{\frac{I_{REF}}{K_{NL}}}$

For the drain current to be independent of the drain-to-source vollage (for $\lambda = 0$), transistor M2 should always be biased in the saturation region. The load current is then

$I_0 = K_{N2}(V_{GS} - V_{TN2})^2$

substituting equation (1), we get

$I_O=K_{n2}\left[\sqrt{\frac{I_{REF}}{K_{a1}}} + V_{TN1} - V_{TN2}\right]^2 $ - (2)

If M1 and M2 are identical transistors, then Vtn1 = Vtn2 and Kn1 = Kn2 and equation (2) becomes

Io = Iref

Since there are no gate currents in MOSFETs, the induced load current is identical to the reference current. provided the two transistors are matched. The relationship between the load current and the reference current changes if the width-to-length ratios, or aspect ratios, or the two transistors change.

If the transistors are matched except for the aspect ratios. we find

$I_O=\frac{(W/L)_2}{(W/L)_1}.I_{REF}$

The ratio between the load and reference currents is directly proportional to the aspect ratios and gives designers versatility in their circuit designs.