(10pt) In the following NMOS inverter circuit, $V_{DD}$ = 5 V, the pull-up resistor, $R_D$ = 10 k$\Omega$, the device threshold voltage, $V_m$ = 1 V, and K of the MOSFET is equal to 0.1 mA/V$^2$.
(a) (1.0pt) Sketch the transfer characteristics of the inverter, i.e. $V_o$ versus $V_i$ curve;
(b) (2.0pt) Find the regions of the input voltage within which the NMOS is in cut-off, saturation, and triode, respectively;
(c) (2.0pt) Find the input voltages at which the slope of the $V_o$ versus $V_i$ curve is -1 and their corresponding output voltages.
(d) (1.0pt) What is the output voltage when the input voltage is at half of $V_{DD}$?
(e) (1.5pt) What are the powers consumed by $R_D$ and by the NMOS device, respectively, when the input voltage is at half of $V_{DD}$?
(f) (1.0pt) What is $R_{on}$ of the device when the input voltage is at $V_{DD}$?
(g) (1.5pt) What are the powers consumed by $R_D$ and by the NMOS device, respectively, when the input voltage is $V_{DD}$?
