(Solved): Consider an NMOS transistor operating in the triode region with \( \mathrm{V}_{\mathrm{GS}}=3 \mat ...

Consider an NMOS transistor operating in the triode region with \( \mathrm{V}_{\mathrm{GS}}=3 \mathrm{~V}, \mathrm{~V}_{\mathrm{tn}}=0.7 \mathrm{~V} \), and \( k_{n}=2.5 \frac{\mathrm{mA}}{\mathrm{V}^{2}} \). a) Find an expression for the incremental resistance. \( r_{d s} \equiv 1 /\left.\frac{\partial i_{D}}{\partial v_{D S}}\right|_{v_{D S}=V_{D S}} \) \[ \text { Hint }) i_{D}=k_{n}\left(v_{G S}-V_{t n}-\frac{v_{D S}}{2}\right) v_{D S}=k_{n}\left[\left(v_{G S}-V_{t n}\right) v_{D S}-\frac{v_{D S^{2}}^{2}}{2}\right] \] b) Give the values of \( r_{A c} \) for \( V_{D S}=0,0.46\left(=20 \%\right. \) of \( \left.\left(v_{f c}-V_{+n}\right)\right), 1.15,1.84 \mathrm{~V} \), and \( 2.3 \mathrm{~V} \). LUIINdIE (A) diu (D) IUI LIE GIVUII VDS.