# Operational Amplifiers

 Question 1
The $\frac{V_{\text {OUT }}}{V_{\text {IN }}}$ of the circuit shown below is

 A $-\frac{R_{4}}{R_{3}}$ B $\frac{R_{4}}{R_{3}}$ C $1+\frac{R_{4}}{R_{3}}$ D $1-\frac{R_{4}}{R_{3}}$
GATE EC 2023   Analog Circuits
Question 1 Explanation:

Here, $A_{1}$ is an inverting amplifier and $A_{2}$ is a non-inverting amplifier.
\begin{aligned} V_{01}&=\frac{-R_{2}}{R_{1}} V_{i n} \\ V_{02}&=\left(1+\frac{R_{2}}{R_{1}}\right) V_{i n} \end{aligned}

Also, $A_{3}$ is an inverting summing amplifier,
\begin{aligned} V_{\text {out }} & =\frac{-R_{4}}{R_{3}} V_{01}-\frac{R_{4}}{R_{3}} V_{02}=\frac{-R_{4}}{R_{3}}\left[\frac{R_{2}}{R_{1}} V_{\text {in }}+\left(1+\frac{R_{2}}{R_{1}}\right) V_{\text {in }}\right] \\ V_{\text {out }} & =\frac{-R_{4}}{R_{3}} V_{\text {in }} \\ \text { Gain, } \frac{V_{\text {out }}}{V_{\text {in }}} & =\frac{-R_{4}}{R_{3}} \end{aligned}
 Question 2
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   Analog Circuits
Question 2 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 3
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   Analog Circuits
Question 3 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 4
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   Analog Circuits
Question 4 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 5
Consider the circuit with an ideal OPAMP shown in the figure.

Assuming $\left | V_{\text{IN}} \right |\ll \left | V_{\text{CC}} \right |$ and $\left | V_{\text{REF}} \right |\ll \left | V_{\text{CC}} \right |$ , the condition at which $V_{\text{OUT}}$ equals to zero is
 A $V_{\text{IN}}\:=\:V_{\text{REF}}$ B $V_{\text{IN}}\:=\:0.5\:V_{\text{REF}}$ C $V_{\text{IN}}\:=\:2\:V_{\text{REF}}$ D $V_{\text{IN}}\:=\:2\:+\:V_{\text{REF}}$
GATE EC 2021   Analog Circuits
Question 5 Explanation:
For ideal op-amp, $V^{\prime}=V^{+}=0$
KCL at node $\mathrm{V}^{-}:$
\begin{aligned} \frac{V_{\text {IN}}-0}{R}+\frac{\left(-V_{\text {REF }}-0\right)}{R}+\frac{V_{\text {OUT }}-0}{R_{F}} &=0 \\ \frac{V_{\text {OUT }}}{R_{F}} &=\frac{1}{R}\left(V_{\text {REF }}-V_{\text {IN }}\right) \\ V_{\text {OUT }} &=\frac{R_{F}}{R}\left(V_{\text {REF }}-V_{\text {IN }}\right)\\ \text { We want, }\qquad V_{\text {OUT }}&=0 \\ \Rightarrow\qquad V_{\text {REF }}-V_{\text {IN }}&=0 \\ \Rightarrow\qquad V_{\text {IN }}&=V_{\text {REF }} \end{aligned}

There are 5 questions to complete.