In the Common-Source Amplifier Shown in Fig $V_{t}=1 \mathrm{~V}$ And $k_{n}=16 \mathrm{~mA} / \mathrm{V}^{2}$

In the common-source amplifier shown in Fig. 10.10.1, the signal source has a zero average and provides de continuity to ground. The MOSFET has $V_{t}=1 \mathrm{~V}$ and $k_{n}=16 \mathrm{~mA} / \mathrm{V}^{2}$ .
(a) Find the value of $g_{m}$ at which the device is operating.
(b) Find the midband gain $V_{o} / V_{\text {sig }}$ in $\mathrm{V} / \mathrm{V}$ and in dB.
(c) Find the value of $C_{S}$ that places the lower 3-dB frequency $\omega_{L}$ at $100 \mathrm{rad} / \mathrm{s}$ .
(d) If $C_{g s}=1 \mathrm{pF}$ and $C_{g d}=0.2 \mathrm{pF}$ , find the value of the upper $3-\mathrm{dB}$ frequency, $\omega_{H}$ .
(e) It is desired to double $\omega_{H}$ by changing the value of $g_{m}$ (through changing the bias current $I$ ), find the required value of $I$ , the new value of the midband gain (in $\mathrm{V} / \mathrm{V}$ and in $\mathrm{dB}$ ), and the new value of $\omega_{L}$ .