Op-amp Differentiator

It behaves as a voltage differentiator.


Recall the two rules:

  1. No Current Flows into the Input Terminals
  2. The Differential Input Voltage is Zero i.e. $V_+ = V_- $



Current through Capacitor = Current through resistor
$ \Rightarrow C \frac{d(V_{in} - 0)}{dt} = \frac{0-V_{out}}{R}$
$ \Rightarrow C \frac{dV_{in}}{dt} = \frac{-V_{out}}{R}$
$ \Rightarrow V_{out} = -RC \frac{dV_{in}}{dt}$