6. (10%) Considering the channel length modulation, draw the low-frequency small-signal model and derive the low-frequency gain of the circuit in Fig. 6?

7. (10%) For the circuit in Fig. 7, \( V{\text{in}} \) and \( V{\text{out}} \) are input and output voltages, respectively, \( V{\text{b1}} \) is a dc bias voltage. (a) Is \( M1 \) a current course, common-source, common-drain, or common-gate amplifier? (b) Is \( M_2 \) a current source, common-source, common-drain, or common-gate amplifier? (You must explain.)

8. (10%) Determine the change of \( V{\text{out}} \) in Fig. 8 if the input is changed by \( \Delta V{\text{in}} \)?

9. (10%) Explain the operational principle of an n-channel MOSFET from the effect that is induced by electrical field. (a) How does \( V{GS} \) control \( I{DS} \)? (b) How does \( V{DS} \) control \( I{DS} \)?

10. (10%) (a) For an npn bipolar transistor, which terminal (emitter, base or collector) requires a high doping concentration, explain why? (b) Should the base-collector junction \( V_{BC} \) be forward biased or reverse biased, explain why?

1. (10%) For the circuit shown in Fig. 1, specify the resistance \( R \) that will cause current \( i_{\mathrm{b}} \) to be \( 1.33\mathrm{mA} \) by the method of Thévenin theorem.

2. (15%) For the \( 2^{\text{nd}} \) order circuit shown in Fig. 2, find the complete response \( v(t) \), including both the components of natural response and forced response, of the circuit for \( t > 0 \) when \( v(0) = 9\mathrm{V} \) and \( i_{\mathrm{L}}(0) = 0\mathrm{A} \).

3. (10%) Wheatstone bridge based circuits are often applied in sensor devices and offer possible ways to transfer resistive sensor measurements into electrical signals. A Wheatstone bridge based Op-amp circuit, shown as Fig. 3, was devised to transfer the resistive sensor \( R{1} \) to the output voltage \( v{0} \). Determine the value of \( v{0} \) when \( R{1} = 10\mathrm{k}\Omega \).

4. (15%) While \( V{C} \) denotes the DC component of the output voltage, \( v{0} \) and \( v{1} \) denote the AC components of the output and input voltages. Determine the small-signal voltage gain \( A{\nu} = v{0} / v{1} \) of the BJT amplifier shown in Fig. 4. Assume the thermal voltage \( V{\mathrm{T}} = 25\mathrm{mV} \), \( V{\mathrm{BE}} = 0.7\mathrm{V} \), \( \beta = 100 \).

5. (10%) Determine the output voltage \( v{0} \) of the circuit shown in Fig. 5. Assume the threshold voltage of the NMOS transistor \( V{\mathrm{TH}} = 1\mathrm{V} \), its transconductance parameter \( k{n} = \mu{n}C_{\mathrm{ox}}(W / L) = 1\mathrm{mA} / \mathrm{V}^{2} \), and neglect the channel-length modulation effect \( \lambda = 0 \).

6. (20%) Determine the small-signal voltage gain \( A{s} \) of the MOS amplifier shown in Fig. 6. The transistor has \( V{\mathrm{TH}} = 3\mathrm{V} \), \( k{n} = \mu{n}C{\mathrm{ox}}(W / L) = 0.25\mathrm{mA} / \mathrm{V}^{2} \) and \( \lambda = 0.02\mathrm{V}^{-1} \), and assume that the coupling capacitors \( C1 \) and \( C2 \) are sufficiently large to shorten the AC signals at their frequencies of interest, and \( A{s} \equiv -g{m}R{L} \), where \( R_{L} \) is AC equivalent resistance.

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