GATE 2016 EC (EC3) – Question 50

Analog Circuits · Op-amp Circuits · 2 marks · Numerical answer

In the shown circuit $R_1=R_2=R_3=1\ \Omega$, L=1 μH and C=1 μF. For $V_{in}=\cos(10^6t)$, the overall voltage gain $V_{out}/V_{in}$ is ________.

Show answer and explanation

Correct answer: -1.0 to -1.0

Explanation

The first stage is noninverting with $A_1=1+R_1/(j\omega L)$. At ω=$10^6$, the inductor impedance is j Ω, giving $A_1=1-j$.

The second stage is inverting with input impedance $R_2+1/(j\omega C)=1-j$ Ω and feedback resistance 1 Ω. Thus $A_2=-1/(1-j)$.

The product is **$A_1A_2=-1$**, a unity-magnitude inversion.

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