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### Op-amp Integrator, Operational Amplifier Integrator

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ToggleAn 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 V_{IN} is applied, the capacitor charges via the resistor R_{1}. The voltage V_{c} or V_{OUT} 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 V_{C} or V_{OUT}. The integrator shows a low-pass behavior.

Calculating OP-Amp as an Integrator:

Regarding frequency dependence: As the frequency increases, the capacitive reactance of the capacitor decreases and with it the voltage V_{C} and therefor U_{OUT }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: