(a) For the circuit shown in figure 1(a), find the following [20] i. V

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(a) For the circuit shown in figure 1(a), find the following [20] i. Vi(s)/Vs(s) ii. Vo(s)/Vi(s) iii. Vo(s)/Vs(s) iv. Draw the magnitude plot for |T(jω)| in dBvs. frequency v. Lower 3 dB cut-off frequency fL vi. Upper 3 dB cut-off frequency fH vii. Bandwidth (b) Consider the n-channel MOSFET amplifier in figure 1(b). ID = 12 kn′W L(VGS − Vt)2, VDD = 5 V, RL = 2 kΩ, kn′WL = 1 mA/V2, Vt = 1 V. You can ignore channel length modulation. CC is the input coupling capacitor. You can assume it is infinitely large. [10] i. Determine the required ratio RA/RB such that the MOSFET gm = 1 mA/V. Remember that gm is defined as ∂ID/∂VGS ii. Draw the small-signal π model for the amplifier iii. Calculate the gain Vout/Vin (for gm = 1 mA/V ) (a) Figure for question 1 (a) (b) Figure for question 1 (b)

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(a) For the circuit shown in figure 1(a), find the following $[20]$ i. $V_{i} (s) / V_{s} (s)$ ii. $V_{o} (s) / V_{i} (s)$ iii. $V_{o} (s) / V_{s} (s)$ iv. Draw the magnitude plot for $| T (j ω) |$ in $d B v s$ . frequency v. Lower $3 d B$ cut-off frequency $f_{L}$ vi. Upper $3 d B$ cut-off frequency $f_{H}$ vii. Bandwidth (b) Consider the n-channel MOSFET amplifier in figure 1(b). $I_{D} = \frac{1}{2} k_{n}^{'} \frac{W}{L} {(V_{G S} - V_{t})}^{2}, V_{D D} = 5 V, R_{L} = 2$ $k Ω, k_{n}^{'} \frac{W}{L} = 1 m A / V^{2}, V_{t} = 1 V$ . You can ignore channel length modulation. $C_{C}$ is the input coupling capacitor. You can assume it is infinitely large. $[10]$ i. Determine the required ratio $R_{A} / R_{B}$ such that the MOSFET $g_{m} = 1 m A / V$ . Remember that $g_{m}$ is defined as $\partial I_{D} / \partial V_{G S}$ ii. Draw the small-signal $π$ model for the amplifier iii. Calculate the gain $V_{out} / V_{in}$ (for $g_{m} = 1 m A / V$ ) (a) Figure for question 1 (a) (b) Figure for question 1 (b)