Question

Differentiation amplifier produces

(a) Output waveform as integration of input waveform

(b) Input waveform as integration of output waveform

(c) Output waveform as derivative of input waveform

(d) Input waveform as derivative of output waveform

The question was posed to me in class test.

My question comes from Differentiator in division Operational Amplifier Applications of Linear Integrated Circuits

Answer 1

The correct answer is:

(c) Output waveform as derivative of input waveform

Explanation:

A differentiation amplifier (or differentiator circuit) produces an output that is the derivative of the input waveform. The differentiator amplifies the rate of change (slope) of the input signal.

For example:

• If the input is a sinusoidal wave, the output will be a cosine wave that is phase-shifted by 90°.
• If the input is a square wave, the output will be a series of spikes corresponding to the transitions of the square wave.

In mathematical terms, if the input is vin(t)v_{\text{in}}(t)vin​(t), the output vout(t)v_{\text{out}}(t)vout​(t) of a differentiator circuit is:

vout(t)=−RCddtvin(t)v_{\text{out}}(t) = -RC \frac{d}{dt} v_{\text{in}}(t)vout​(t)=−RCdtd​vin​(t)

Thus, the output waveform is the derivative of the input waveform, which makes (c) the correct option.