# Analog Circuits

 Question 1
Consider the circuit shown with an ideal long channel nMOSFET (enhancementmode, substrate is connected to the source). The transistor is appropriately biased in the saturation region with $V_{GG}$ and $V_{DD}$ such that it acts as a linear amplifier. $v_i$ is the small-signal ac input voltage. $v_A$ and $v_B$ represent the small-signal voltages at the nodes A and B, respectively. The value of $\frac{v_A}{v_B}$ is ________ (rounded off to one decimal place).

 A -2 B 2 C -1 D 1
GATE EC 2022      FET and MOSFET Analysis
Question 1 Explanation:
For ac analysis

\begin{aligned} V_A &=-i_d\cdot 4k \\ V_B&=i_d\cdot 2k \\ \frac{V_A}{V_B}&=\frac{-4}{2} \\ \frac{V_A}{V_B}&=-2 \end{aligned}
 Question 2
A circuit and the characteristics of the diode (D) in it are shown. The ratio of the minimum to the maximum small signal voltage gain $\frac{\partial V_{out}}{\partial V_{in}}$ is ________ (rounded off to two decimal places)

 A 0.25 B 0.55 C 0.75 D 0.95
GATE EC 2022      Diodes Applications
Question 2 Explanation:
Replacing the given circuit with small signal equivalent.

Case-I when diode is ON
As $r_d(ON)=0,$ the $2k\Omega$ resistor in parallel to the diode becomes open circuit.
$\therefore \; V_{out}=V_{IN}\times \frac{2}{4}=\frac{V_{in}}{2}$
$\therefore \; \frac{\partial V_{out}}{\partial V_{in}}|_{max}=\frac{1}{2}\;\;\;...(i)$
Case-I: When diode is off:
$r_d(off)=\infty \Rightarrow total \; R_{eq}=2+2+2=6k\Omega$
$\therefore \; V_{out}=\frac{V_{in} \times 4}{6}=\frac{2}{3}V_{in}\Rightarrow \frac{\partial V_{out}}{\partial V_{in}}|_{min}=\frac{2}{3}\;\;\;...(ii)$
From (i) and (ii)
$\frac{\left (\frac{\partial V_{out}}{\partial V_{in}}\right )_{min}}{\left (\frac{\partial V_{out}}{\partial V_{in}}\right )_{max}}=\frac{1/2}{2/3}=0.75$
 Question 3
A circuit with an ideal OPAMP is shown. The Bode plot for the magnitude (in dB) of the gain transfer function $(A_V(j\omega )=V_{out}(j\omega )/V_{in}(j\omega ))$ of the circuit is also provided (here, $\omega$ is the angular frequency in rad/s). The values of $R$ and $C$ are

 A $R=3k\Omega ,C=1\mu F$ B $R=1k\Omega ,C=3\mu F$ C $R=4k\Omega ,C=1\mu F$ D $R=3k\Omega ,C=2\mu F$
GATE EC 2022      Operational Amplifiers
Question 3 Explanation:

\begin{aligned} \text{maximum gain}&=12dB\\ 20 \times \log A_{max}&=12\\ A_{max}&=4\\ 1+\frac{R_2}{R_1}&=4\\ R_2&=3R_1\\ R&=3 \times 1=3k\Omega \\ \log _{10}\omega _c&=3\\ omega _c&=1000rad/sec\\ omega _c&=\frac{1}{R_3C}\\ C&=\frac{1}{R_3 \times \omega _c}\\ C&=\frac{1}{1000 \times 1000}=1\mu F \end{aligned}
 Question 4
For the following circuit with an ideal OPAMP, the difference between the maximum and the minimum values of the capacitor voltage ($V_c$) is __________.

 A 15 V B 27 V C 13 V D 14 V
GATE EC 2022      Multivibrators and 555 Timer
Question 4 Explanation:

When,
\begin{aligned} V_0&=+15V\\ V^+&=\frac{R}{3R} \times 15=5V\\ V_{cmax}&=5V \end{aligned}

When,
\begin{aligned} V_0&=-12V\\ V^+&=\frac{2R}{3R} \times (-12)=5V\\ V_{cmin}&=-8V \end{aligned}

$V_{cmax}=V_{cmin}=5-(-8)=13V$
 Question 5
Consider an ideal long channel nMOSFET (enhancement-mode) with gate length $10\mu m$ and width $100\mu m$. The product of electron mobility ($\mu _n$) and oxide capacitance per unit area ($C_{OX}$) is $\mu _n C_{OX}=1mA/V^2$. The threshold voltage of the transistor is 1 V. For a gate-to-source voltage $V_{GS}=[2-\sin (2t)]V$ and drain-tosource voltage $V_{DS}=1V$ (substrate connected to the source), the maximum value of the drain-to-source current is ________.
 A 40 mA B 20 mA C 15 mA D 5 mA
GATE EC 2022      FET and MOSFET Analysis
Question 5 Explanation:
$\mu _n Co_x=1mA/V^2; W=100\mu m;L=10\mu m$
$V_T= \perp V; V_{GS}=[2-\sin 2t]V;V_{DS}=1V$

Let,
\begin{aligned} V_{GS} &=3V(max)\\ \Rightarrow V_{DS} &\lt V_{GS}-V_t\\ \because \; 1 &\lt (3-1) \end{aligned}
MOSFET in triode region
\begin{aligned} I_{Dmax}&=\mu _CO_x\left ( \frac{\omega }{L} \right )\left \{ \left ( V_{as \; max}-V_t \right )V_{DS}-\frac{1}{2}V_{DS}^2 \right \}\\ &=1 \times \left ( \frac{100}{10} \right )\left \{ (3-1) \times 1-\frac{1}{2} \times 1^2 \right \}mA\\ &=10(2-1/2)\\ &=15mA \end{aligned}
 Question 6
An ideal OPAMP circuit with a sinusoidal input is shown in the figure. The 3 dB frequency is the frequency at which the magnitude of the voltage gain decreases by 3 dB from the maximum value. Which of the options is/are correct?

 A The circuit is a low pass filter. B The circuit is a high pass filter. C The 3 dB frequency is 1000 rad/s. D The 3 dB frequency is (1000/3) rad/s.
GATE EC 2022      Operational Amplifiers
Question 6 Explanation:
\begin{aligned} \frac{V_{out}}{V_{in}}&=\frac{-2000}{1000+\frac{1}{j\omega \times 10^{-6}}}\\ Gain&=\frac{V_{out}}{V_{in}}\frac{-2}{1+\frac{1}{\left (\frac{j\omega }{1000} \right ) }} \end{aligned}
$\omega \rightarrow \infty \Rightarrow gain=-2$
$\omega \rightarrow 0 \Rightarrow gain=0$
$\omega _c=1000$ rad/sec = cutoff frequency
Hence, it is HPF.
 Question 7
The ideal long channel nMOSFET and pMOSFET devices shown in the circuits have threshold voltages of 1 V and -1 V, respectively. The MOSFET substrates are connected to their respective sources. Ignore leakage currents and assume that the capacitors are initially discharged. For the applied voltages as shown, the steady state voltages are ______

 A $V_1=5 V, V_2=5 V$ B $V_1=5 V, V_2=4 V$ C $V_1=4 V, V_2=5 V$ D $V_1=4V, V_2=-5 V$
GATE EC 2022      FET and MOSFET Analysis
Question 7 Explanation:

 Question 8
Consider the CMOS circuit shown in the figure (substrates are connected to their respective sources). The gate width ($W$) to gate length ($L$) ratios $\frac{W}{L}$ of the transistors are as shown. Both the transistors have the same gate oxide capacitance per unit area. For the pMOSFET, the threshold voltage is -1 V and the mobility of holes is $40\frac{cm^2}{V.s}$. For the nMOSFET, the threshold voltage is 1 V and the mobility of electrons is $300\frac{cm^2}{V.s}$. The steady state output voltage $V_o$ is ________.

 A equal to 0 V B more than 2 V C less than 2 V D equal to 2 V
GATE EC 2022      FET and MOSFET Analysis
Question 8 Explanation:

\begin{aligned} \mu _PCO_x\left ( \frac{\omega }{L} \right )_1[4-V_0-1]^2&=\mu _nCO_x\left ( \frac{\omega }{L} \right )_2[V_0-0-1]^2\\ \Rightarrow \frac{300}{40}\times \frac{1}{5}(V_0-1)^2&=(3-V_0)^2\\ \Rightarrow \sqrt{1.5} (V_0-1)&=3-V_0\\ \Rightarrow V_0&=\frac{3+\sqrt{1.5}}{\sqrt{1.5}+1} \lt 2V \end{aligned}
 Question 9
A circuit with an ideal $\text{OPAMP}$ is shown in the figure. A pulse $V_{\text{IN}}$ of $20\:ms$ duration is applied to the input. The capacitors are initially uncharged.

The output voltage $V_{\text{OUT}}$ of this circuit at $t=0^{+}$ (in integer) is _______ V.
 A 15 B -15 C 12 D -12
GATE EC 2021      Operational Amplifiers
Question 9 Explanation:
At, $t=0^{+}:$ Capacitor is short circuit
\begin{aligned} \therefore\quad V^{-}=V_{\text {in }}=5 \mathrm{~V} \\ V^{+}=0 \mathrm{~V} \end{aligned}

\begin{aligned} \text{If}\qquad V^- &>V^{+} \\ V_{\text {out }} &=-V_{\text {sat }}=-12 \mathrm{~V} \end{aligned}
 Question 10
An asymmetrical periodic pulse train $v_{in}$ of $10\:V$ amplitude with on-time $T_{\text{ON}}=1\:ms$ and off-time $T_{\text{OFF}}=1\:\mu s$ is applied to the circuit shown in the figure. The diode $D_{1}$ is ideal.

The difference between the maximum voltage and minimum voltage of the output waveform $v_{o}$ (in integer) is ______________ V.
 A 7 B 5 C 12 D 10
GATE EC 2021      Diodes Applications
Question 10 Explanation:
$V_{\text{in}} = 10 V:$ Diode is ON

$\therefore$Capacitor charges upto $10 \mathrm{~V},$
\begin{aligned} \therefore \qquad V_{C}&=10 \mathrm{~V} \\ V_{\text {in }}&=0 ; \text { Diode is OFF } \end{aligned}

Discharging time constant $=R \times C$
\begin{aligned} &=10 \mathrm{~m} \mathrm{sec} \\ \tau_{\text {discharging }} &>>\tau_{\mathrm{OFF}} \end{aligned}
Capacitor discharges negligibly
\begin{aligned} \therefore\qquad V_{C}&=10 \mathrm{~V}\\ \text{In steady state},\qquad V_{C} &=10 \mathrm{~V} \\ V_{\text {out }} &=V_{\text {in }}-V_{C}=V_{\text {in }}-10 \mathrm{~V}\\ \text{When }\qquad V_{\text {in }}&=10 \mathrm{~V}\\ \Rightarrow\qquad V_{\text {out }} &=10-10=0 \mathrm{~V} \\ V_{\text {in }} &=10 \mathrm{~V} \\ \mathrm{~V}_{\text {out }} &=0-10=-10 \mathrm{~V}\\ \Rightarrow\qquad V_{\text {out(max) }}-V_{\text {out(min) }}&=0-(-10)=10 \mathrm{~V} \end{aligned}

There are 10 questions to complete.