4. (15%) Apply Miller's Theorem to \( C{gd} \) in Fig. 4. (a) Redraw the high-frequency model of a CS amplifier and (b) derive its 3-dB high-frequency of \( f{fl} \).

5. (15%) Fig. 5 shows that the common-source stage provides a voltage gain of 10 with a bias current of \( 0.5\mathrm{mA} \). Assume \( \lambda{1} = \lambda{2} = 0.1\mathrm{V}^{-1} \), \( V{\mathrm{in}} = |V{\mathrm{ip}}| = 0.4\mathrm{V} \), and \( \mu{\mathrm{e}}C{ox,n} = 2\mu{\mathrm{p}}C{ox,p} = 200\mu \mathrm{A} / \mathrm{V}^2 \) (a) Compute the required value of \( (W / L)1 \). (b) If \( (W / L)2 = 10 \), calculate required dc bias of \( V_{b} \).

6. (10%) (a) Derive the transfer function \( V{out}(s) / V{in}(s) \) and (b) find its type of response of Fig. 6. (low-pass, high-pass, or band-pass Filter)

7. (10%) Plot the \( V{in} / V{out} \) characteristic of the circuit with an ideal diode, as shown in Fig. 7. (Hint: input \( V{in} \) as \( x \)-axis and output \( V{out} \) as \( y \)-axis)

8. (15%) Draw the Bode plot gain and phase response of \( \mathrm{A(s)} = [500(\mathrm{s} + 2)] / [2\mathrm{s}(\mathrm{s} + 50)] \).

1. (10%) Derive the current \( I_{1} \) for the circuit in Fig. 1?

2. (10%) Derive the voltage \( V_{2} \) for the circuit in Fig. 2?

3. (10%) The feedback system in Fig. 3 has an open-loop amplifier \( A{2}(s) = A{0} / (1 + (s / \omega{0})) \), where \( s = j\omega \) and \( \omega \) is the frequency, \( A{0} \) and \( \omega{0} \) are the dc gain and pole frequency of the open-loop amplifier \( A{1} \), respectively. Derive the close-loop transfer function of \( Y(s) / X(s) \)?

4. (10%) Derive the transfer function \( V{\mathrm{out}} / V{\mathrm{in}} \) for the circuit in Fig. 4 with \( A_0 = \infty \).

5. (10%) Draw \( V{\text{out}} \) versus \( V{\text{in}} \) transfer curve for the circuit in Fig. 5, assuming \( D1 \) is an ideal diode with \( V{\text{ON}} = 0V \)?

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?

115年 - [無官方正解]115 國立臺北大學_碩士班一般入學考試試題_金融與合作經營學系：經濟學#147384

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