112 年 國立中山大學通訊工程研究所乙組《電子學》

1. (15%) A fourth-order filter has zero transmission at $\omega = 0$, $\omega = 2$ rad/s, and at $\omega = \infty$. The natural modes are $-0.1 \pm j0.5$ and $-0.1 \pm j1.5$. Find the transfer function $T(s)$. (Hint: The natural modes are the time functions corresponding to the poles.) (15%)

2. (35%) Consider the common-emitter amplifier of Fig. 1 under the following conditions: $R_S = 5$ k$\Omega$, $R_1 = 33$ k$\Omega$, $R_2 = 22$ k$\Omega$, $R_E = 3.9$ k$\Omega$, $R_C = 4.7$ k$\Omega$, $R_L = 5.6$ k$\Omega$, $V_{CC} = 5$ V. The dc emitter current can be shown to be $I_E \approx 0.33$ mA, at which $\beta_0 = 120$, $r_o = 300$ k$\Omega$, and $r_x = 50 \, \Omega$.
   (a) Find the input resistance, $R_{in}$. (Hint: $R_{in} = R_1 \parallel R_2 \parallel (r_x + r_{\pi})$) (10%)
   (b) Find the midband gain, $A_M$. (10%)
   (c) For $C_{C1} = C_{C2} = 1 \, \mu F$ and $C_E = 10 \, \mu F$, estimate the low-frequency 3-dB frequency. Also find the frequency of the zero introduced by $C_E$. (15%)

🖼️【此處有附圖，請對照原卷】
Figure 1. (a) common-emitter amplifier stage; (b) Equivalent circuit for the amplifier of Fig. 1(a) in the low-frequency band.

3. (20%) Design the circuit of Fig. 2 so that the transistor operates at $I_D = 0.4$ mA and $V_D = +1$ V. The NMOS transistor has $V_T = 2$ V, $\mu_n C_{OX} = 20 \, \mu A/V^2$, $L = 10 \, \mu m$, and $W = 400 \, \mu m$. Neglect the channel-length modulation effect (i.e., assume that $\lambda= 0$).
   (a) Find $R_S$. (10%)
   (b) Find $R_D$. (10%)

🖼️【此處有附圖，請對照原卷】
Figure 2.

4. (30%) For the circuit shown in Fig. 3, find the values of the labeled node voltages for:
   (a) $\beta = \infty$. (15%)
   (b) $\beta = 100$. (15%)

🖼️【此處有附圖，請對照原卷】
Figure 3.