Where does each of the FET equations apply? (saturation vs. linear regime)

• The saturation voltage is given by $V_{ds({\rm sat})}=V_{gs}-V_t$, where $V_t$ is the threshold voltage for turn-on of current $I_d$. This is independent of regime; it specifies the saturation voltage.

• In the linear regime where $V_{ds} < V_{ds({\rm sat})}$, $I_d = K(2 V_{ds({\rm sat})}-V_{ds}) V_{ds}$, where $K$ is a constant.

• In the saturation regime where $V_{ds} > V_{ds({\rm sat})}$, we have $I_d = K V_{ds({\rm sat})}^2$.