Which circuit or mechanism outputs a signal directly related to the rate of change of its input?

Which circuit or mechanism outputs a signal directly related to the rate of change of its input?

• A. Differentiator
• B. Integrator
• C. Amplifier
• D. Filter

Answer: (A)

The rate at which a signal changes over time is its derivative, and a differentiator is built to produce an output that is proportional to that derivative. In other words, the output tracks dv_in/dt, so it responds to how quickly the input is changing rather than just how large it is. Think through some examples: if the input is constant, its rate of change is zero, so the output sits at zero (apart from offsets). If the input is a ramp, the slope is constant, and the differentiator yields a steady output corresponding to that slope. If the input is a sine wave, the derivative is a cosine wave with amplitude proportional to the frequency, illustrating that the output reflects the instantaneous rate of change. In contrast, an integrator outputs the accumulated value of the input over time, an amplifier simply scales the input, and a filter shapes the spectrum without inherently producing a signal tied to the instantaneous rate of change.

The rate at which a signal changes over time is its derivative, and a differentiator is built to produce an output that is proportional to that derivative. In other words, the output tracks dv_in/dt, so it responds to how quickly the input is changing rather than just how large it is.

Think through some examples: if the input is constant, its rate of change is zero, so the output sits at zero (apart from offsets). If the input is a ramp, the slope is constant, and the differentiator yields a steady output corresponding to that slope. If the input is a sine wave, the derivative is a cosine wave with amplitude proportional to the frequency, illustrating that the output reflects the instantaneous rate of change.

In contrast, an integrator outputs the accumulated value of the input over time, an amplifier simply scales the input, and a filter shapes the spectrum without inherently producing a signal tied to the instantaneous rate of change.