Q.Determine the value of $I_D$ given $I_{DSS} = 4$ mA, $V_{GS} = -2$ V and $V_P = -5$ V.

Shockley's equation is the fundamental relation that gives the drain current of a JFET in its pinch-off (saturation) region:

Here $I_{DSS}$ is the drain-source saturation current (the maximum drain current, flowing when $V_{GS}=0$), $V_{GS}$ is the gate-to-source voltage, and $V_P$ is the pinch-off voltage. The squared bracket is why the transfer characteristic is a curve rather than a straight line.

The equation captures the two limiting cases neatly: when $V_{GS}=0$ the bracket equals 1, so $I_D = I_{DSS}$ (maximum current); and when $V_{GS}=V_P$ the bracket is zero, so $I_D = 0$ (pinch-off). For any bias in between, it predicts the drain current.

It is highly useful for numerical problems. Rearranged, it also lets you find any one quantity from the others — for example $I_{DSS} = \dfrac{I_D}{\left(1 - V_{GS}/V_P\right)^2}$, or $V_P$ from a measured $I_D$. When substituting, keep the signs of $V_{GS}$ and $V_P$ consistent (both are negative for an n-channel device), so that the ratio $V_{GS}/V_P$ is positive.

Differentiating this equation with respect to $V_{GS}$ leads directly to the expression for transconductance, which is why Shockley's equation underpins both the transfer characteristic and the small-signal parameter $g_m$.