# Op-amp Integrator

Home  ⇒  Overview Courses   ⇒  ElectronicsOperational amplifier ⇒ Op-Amp as Integrator

### Op-amp Integrator, Operational Amplifier Integrator

Operational Amplifier as Integrator

An operational amplifier as an integrator has a capacitor as negative feedback. This results in a certain time and frequency behavior. If a constant input voltage VIN is applied, the capacitor charges via the resistor R1. The voltage Vc or VOUT thus increases steadily.

If the input voltage is sinusoidal, a phase shift of approx. 90 degrees can be seen at the output. This is due to the fact that the phase shift between current and voltage is 90 degrees for the capacitor.

Regarding frequency dependence: With increasing frequency, the capacitive reactance of the capacitor decreases and thus the voltage drop VC or VOUT. The integrator shows a low-pass behavior.

Calculating OP-Amp as an Integrator:

Op-Amp as an integrator - calculation

Regarding frequency dependence: As the frequency increases, the capacitive reactance of the capacitor decreases and with it the voltage VC and therefor UOUT drop . The integrator shows its low-pass behavior.

If the input voltage is sinusoidal, a phase shift of approximately 90 degrees can be seen at the output. The reason for this is that the phase shift between current and voltage in the capacitor is 90 degrees.

#### Exercises - Op-Amp as Integrator

An Op-Amp  as an inverting integrator is given with the following input voltage. Specify the corresponding output voltage:

Exercises Op-Amp as Integrator