GATE Papers >> EEE >> 2015 >> Question No 121

Question No. 121

The operational amplifier shown in the figure is ideal. The input voltage (in Volt) is . The amplitude of the output voltage ${V}_{0}$ (in Volt) is ________.

Solution of Question No 121 of GATE 2015 EEE Paper

${\mathrm V}_\mathrm i=2\sin\left(2\mathrm\pi\times200\mathrm t\right)$

The transfer function of the system is

$\begin{array}{l}\mathrm H(\mathrm s)=\frac{1000}{(1000\times0.1\times10^{-6}\mathrm s+1)1000}\\\mathrm H(\mathrm s)=\frac1{(10^{-4}\mathrm s+1)}\end{array}$

The input is $2\sin\left(2\mathrm\pi\times2000\;\mathrm t\right)$

$\mathrm\omega=4000\mathrm\pi$

Output will be $2\;\mathrm H\left(\mathrm{jω}\right)\vert_{\mathrm\omega=4000\mathrm\pi}.\sin\left(4000\mathrm{πt}\right)$

Output $=1.245\;\sin\left(4000\mathrm{πt}-51.46^\circ\right)$

So, amplitude of output is 1.245.