The MOSFET in the amplifier circuit of Fig. P7.123 has Vt = 0.6 V, kn = 5 mA/V2 , and VA

QUESTION:

The MOSFET in the amplifier circuit of Fig. P7.123 has \(V_{t}=0.6 \mathrm{~V}\), \(k_{n}=5 \mathrm{~mA} / \mathrm{V}^{2}\), and \(V_{A}=60 \mathrm{~V}\). The signal \(v_{\text {sig }}\) has a zero average.

(a) It is required to bias the transistor to operate at an overdrive voltage \(V_{O V}=0.2 \mathrm{~V}\). What must the dc voltage at the drain be? Calculate the dc drain current \(I_{D}\) taking into account \(V_{A}\). Now, what value must the drain resistance \(R_{D}\) have?

(b) Calculate the values of \(g_{m}\) and \(r_{o}\) at the bias point established in (a).

(c) Using the small-signal equivalent circuit of the amplifier, show that the voltage gain is by

\(\frac{v_{o}}{v_{\text {sig }}}=-\frac{R_{2} / R_{1}}{1+\frac{1+R_{2} / R_{1}}{g_{m}\left(R_{D}\left\|r_{o}\right\| R_{2}\right)\left(1-1 / g_{m} R_{2}\right)}}\)

and find the value of the gain.

P.S. This feedback amplifier and the gain expression should remind you of an op amp utilized in the inverting configuration. We shall study feedback formally in Chapter 11.