109 年 國立中山大學電機工程學系碩士班甲組《電子學》

Please note that all calculation answers must include the unit and calculation process.

The NMOS transistor in the CS amplifier shown in Fig. 1 has $V_t = 0.7\text{ V}$, $V_A = 50\text{ V}$, $R_{\text{sig}} = 120\text{ k}\Omega$, $R_{G1} = 300\text{ k}\Omega$, $R_{G2} = 200\text{ k}\Omega$, $R_D = 5\text{ k}\Omega$, $R_S = 2\text{ k}\Omega$, $R_L = 5\text{ k}\Omega$, and $V_{DD} = 5\text{ V}$.

(a) Neglecting the channel length modulation effect, the MOSFET is operating in saturation with $I_D = 0.5\text{ mA}$ and $V_{OV} = 0.3\text{ V}$. What must the MOSFET's $\mu_n C_{ox} (W/L)$ be? What is the dc voltage at the drain?

(b) Find the input resistance $R_{\text{in}}$ and overall gain $v_o / v_{\text{sig}}$ ($V_A$ effect needs to be considered).

(c) If $v_{\text{sig}}$ is a sinusoid with a peak amplitude $v_s$, find the maximum allowable value of $v_s$ for which the transistor remains in saturation. What is the corresponding amplitude of the output voltage?

(d) What is the value of resistance $R_3$ that needs to be inserted in series with capacitor $C_{C3}$ as shown in Fig. 2 in order to allow us to double the input signal peak amplitude $v_s$? What output voltage now results?

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For the follower circuit in Fig. 3, let transistor $Q_1$ has $\beta = 50$ and transistor $Q_2$ has $\beta = 100$, $V_{CC} = 5\text{ V}$, $R_{B1} = R_{B2} = 1\text{ M}\Omega$, $I_1 = 50\text{ }\mu\text{A}$, $I_2 = 5\text{ mA}$ and neglect the Early effect. Use constant voltage drop model of $V_{BE} = 0.7\text{ V}$. Thermal voltage $V_T = 25\text{ mV}$.

(a) Find the dc emitter current and the dc base voltage of $Q_1$ transistor.

(b) If a load resistance $R_L = 1\text{ k}\Omega$ is connected to the output terminal, find the voltage gain from the base to the emitter of $Q_2$ and the input resistance $R_{\text{ib2}}$ looking into the base of $Q_2$.

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A current-mirror-loaded MOS differential amplifier of the type shown in Fig. 4 is specified as follows: $(W/L)_n = 100$, $(W/L)_p = 200$, $\mu_n C_{ox} = 2\mu_p C_{ox} = 0.2\text{ mA/V}^2$, $V_{An} = |V_{Ap}| = 20\text{ V}$, and $I = 0.8\text{ mA}$.

(a) Calculate the differential gain $A_d$.

(b) Let the output resistance of current source is $25\text{ k}\Omega$. Calculate common-mode gain $|A_{\text{cm}}|$ and CMRR (in dB).

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Consider a CC-CE amplifier such as that in Fig. 5 with the following specifications: $I_1 = I_2 = 1\text{ mA}$ and identical transistors with $\beta = 100$, $f_T = 400\text{ MHz}$, and $C_\pi = 2\text{ pF}$. Thermal voltage $V_T = 25\text{ mV}$. Let the amplifier be fed with a source $v_{\text{sig}}$ having a resistance $R_{\text{sig}} = 4\text{ k}\Omega$, and assume a load resistance $R_L = 4\text{ k}\Omega$. Find the midband voltage gain $v_o / v_{\text{sig}}$ and estimate the 3-db frequency $f_H$ by the method of open-circuit time constants (please show the value of each time constant).

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