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GATE 2016 EE - SET 2 - Question 2

An ideal integrator is an inverting amplifier that has a capacitor in the feedback path. 

\frac{V_{out}}{V_{in}}=\frac{-Z_{2}}{Z_{1}}=\frac{\frac{-1}{SC}}{R}=\frac{-1}{SCR}

V_{out} = \frac{-1}{SCR}V_{in}\Rightarrow -SCR\ast V_{out}=V_{in}

This can be further written as, \dot{V_{out}}=\frac{-1}{RC}\ast V_{in}

Integrating both sides will give the expression, V_{out}=\int \frac{-1}{RC}\ast V_{in}

The equation above proves that the figure shown in the question is an integrator amplifier, therefore implies that it is a low pass filter. 

 

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