109 年 國立成功大學電機工程學系碩士班乙組《電子學》

Consider the folded-cascode amplifier of Fig. 1 for the following case: $V_{DD}=1.8 \text{ V}$, $\mu_pC_{ox} = \frac{1}{4}\mu_nC_{ox}$, and $V_{tn}=-V_{tp}=0.5 \text{ V}$, To operate $Q_1$ and $Q_2$ at equal bias currents $I$, $I_1=2I$ and $I_2=I$. While current source $I_1$ is implemented using the simple circuit and current source $I_2$ is realized using a cascoded circuit. The transistor $W/L$ ratios are selected so that each operates at an overdrive voltage of $0.2 \text{ V}$. (20%)

(a) What must the relationship of $(W/L)_2$ to $(W/L)_1$ be? (4%)
(b) What is the minimum dc voltage required across current source $I_1$ for proper operation? If a $0.1\text{-V}$ peak-to-peak signal swing is to be allowed at the drain of $Q_1$, what is the highest dc bias voltage that can be used at that node? (4%)
(c) What is the value of $V_{SG}$ of $Q_2$, and hence what is the largest value to which $V_{G2}$ can be set? (4%)
(d) What is the minimum dc voltage required across current-source $I_2$ for proper operation? (4%)
(e) Given the results of (c) and (d), what is the allowable range of signal swing at the output? (4%)
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Consider the integrated-circuit CS amplifier in Fig. 2 for the case $I_{BIAS}=100 \text{ μA}$, $Q_2$ and $Q_3$ are matched, and $R_{sig}= 200 \text{ kΩ}$. For $Q_1$: $\mu_nCox=90 \text{ μA/V}^2$, $|V_A|=12.8 \text{ V}$, $W/L=100 \text{ μm}/1.0 \text{ μm}$. For $Q_2$: $|V_A|=19.2 \text{ V}$. Neglecting the effect of the capacitance inevitably present at the output node.

(a) Find the low-frequency gain (5%)
(b) Find the 3-dB frequency $f_H$ (5%)
(c) Find the frequency of the zero $f_Z$ (4%)
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Fig. 3 shows the feedback circuit with the case $g_{m1}=g_{m2}=2 \text{ mA/V}$, $R_{sig}=200 \text{ kΩ}$, $R_{D1}=R_{D2}=10 \text{ kΩ}$, $R_1=1 \text{ kΩ}$, and $R_2=9 \text{ kΩ}$. For simplicity, neglect $r_o$ of each of $Q_1$ and $Q_2$.

(a) Find the loop gain $\beta A$ (4%)
(b) Find the voltage gain $V_o/V_s$ (4%)
(c) Find the input resistance $R_{in}$ (4%)
(d) Find the output resistance $R_{out}$ (4%)
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For the Class AB output stage shown in Fig. 4, we know that $Q_3$ and $Q_4$ are the major power BJTs which deliver current to load resistance $R_L$. Please give your answer and brief explanation for the following questions: (15%)

(a) In addition to provide two $V_{BE}$ voltage drop for biasing the $Q_3$ and $Q_4$ like the conventional diode-connected biasing circuit does, what is the major advantage of the input stage which consists of $Q_1, Q_2, R_1$ and $R_2$? (5%)
(b) What is the major purpose of the last stage which consists of $Q_5, Q_6, R_3$ and $R_4$? (5%)
(c) What is the major purpose of the resistors $R_5$ and $R_6$? (5%)
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Fig. 5 shows a three-stage feedback amplifier: (20%)
$A_1$ has an $82-\text{kΩ}$ differential input resistance, a $20-\text{V/V}$ open-circuit differential voltage gain, and a $3.2-\text{kΩ}$ output resistance.
$A_2$ has a $5-\text{kΩ}$ input resistance, a $20-\text{mA/V}$ short-circuit transconductance, and a $20-\text{kΩ}$ output resistance.
$A_3$ has an $20-\text{kΩ}$ input resistance, unity open-circuit voltage gain, and a $1-\text{kΩ}$ output resistance.
The feedback amplifier feeds a $1-\text{kΩ}$ load resistance and is fed by a signal source with a $9-\text{kΩ}$ resistance.

(a) If $R_1 = 20 \text{ kΩ}$, find the value of $R_2$ that results in a closed-loop gain $V_o/V_s$ that is ideally $5\text{ V/V}$. (4%)
(b) Find the feedback amplifier's input resistance $R_{in}$. (4%)
(c) Find the feedback amplifier's output resistance $R_{out}$. (4%)
(d) If the high-frequency response if the open-loop gain $A$ is dominated by a pole at $100\text{ Hz}$, what is the upper $3-\text{dB}$ frequency of the closed-loop gain? (4%)
(e) If for some reason, $A_1$ drops to half its nominal value, what is the percentage change in the closed-loop gain $A_f$? (4%)
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Please analysis and design an oscillator which uses a bistable circuit. (15%)
(a) Fig. 6. shows a square waveform generator. The positive and negative saturation levels of the op-amp used in the bistable circuit are $L_+$ and $L_-$, respectively. The trigger levels are $V_+$ and $V_-$. If $V_\pm = \beta L_\pm$, derive a relationship between the oscillator period and the time-constant $\tau = RC$. (5%)
(b) Follow 6(a), how to modify the circuit of Fig. 6 to generate a triangular waveform. You are allowed to use one more op amp. (5%)
(c) Based on the conditions of 6(a), please derive a relationship between the oscillator period and the RC for the circuit you design in 6(b). (5%)

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