Q. What is a differentiator circuit?

By introducing electrical reactance into the feedback loops of op-amp amplifier circuits, we can cause the output to respond to changes in the input voltage over time. The differentiator produces a voltage output proportional to the input voltage's rate of change. A differentiator circuit produces a constant output voltage for a steadily changing input voltage. The circuit must place the full transition voltage across its output at the instant of the transient (instantaneous, or very fast, voltage change). Since a capacitor operates as a short circuit (zero resistance) for the first transient instant, it transfers all the transient voltage to the resistor. Over time the capacitor charges, which results in its effective resistance (reactance) increasing exponentially thereby reducing the current exponentially. By using the capacitor's charging current to develop the output voltage across the resistor the RC differentiator produces the correct output across its output terminals for differentiation.