Question 4.SP.11: The n-channel enhancement-mode MOSFET of Fig. 4-18 is charac......
The n-channel enhancement-mode MOSFET of Fig. 4-18 is characterized by V_T = 4 \text{V} and I_{\text{Don}} = 10 \text{mA}. Assume negligible gate current, R_1 = 50 kΩ, R_2 = 0.4 MΩ, R_S = 0, R_D = 2 kΩ, and V_{DD} = 15 \text{V}. Find (a) V_{GSQ}, (b) I_{DQ}, and (c) V_{DSQ}.
(a) With negligible gate current, (4.3) leads to
R_G = \frac{R_1R_2}{R_1 + R_2} \quad \text{and} \quad V_{GG} = \frac{R_1}{R_1 + R_2} V_{DD} (4.3)
V_{GSQ} = V_{GG} = \frac{R_2}{R_2 + R_1} V_{DD} = \frac{50 × 10^3}{50 × 10^3 + 0.4 × 10^6} 15 = 1.67 \text{V}
(b) By (4.6),
i_D = I_{\text{Don}} \left( 1 – \frac{v_{GS}}{V_{T}} \right)^2 (4.6)
I_{DQ} = I_{\text{Don}} \left(1 – \frac{V_{GSQ}}{V_T} \right)^2 = 10 × 10^{-3} \left(1 – \frac{1.67}{4} \right)^2 = 3.39 \text{mA}
(c) By KVL around the drain-source loop,
V_{DSQ} = V_{DD} – I_{DQ}R_D = 15 – (3.39 × 10^{-3})(2 × 10^{3}) = 8.22 \text{V}