Inverting differentiator amplifier realized with op-amp is given in figure bellow.
Op-amp voltage differentiator is the circuit that differentiates input voltage over time. Input impedance is equal to
and feedback is resistive (resistor R1).
Output voltage can be calculated as function of input voltage by equaling currents. V– is on the virtual ground, so input current for smooth periodical signals is:
The same current flows into resistor R1, so output voltage, is:
For smooth periodical signals, complex operator jÏ‰ is equal to voltage over time differential operator
so output voltage is
In order to change amount of energy stored in capacitor (decreasing or increasing energy amount alike), some non-zero time has to be consumed. Voltage on capacitor canâ€™t change in time instant. So, if one of the capacitor electrode change it potential suddenly, another electrode changes self potential for the same amount. This feature of capacitor makes it impropriate for differentiating input pulses, since V– will be shifted from virtual ground.
Op-amp differentiator amplifier is not so close to ideal differentiator, as voltage integrator is close to ideal integrator. Voltage integrator behaves as integrator for both smooth and pulse inputs.