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.