# Op-Amp Integrator

## Integrator

• A circuit in which the output voltage waveform is the integral of the input voltage waveform is the integrator or Integration Amplifier. Such a circuit is obtained by using a basic inverting amplifier configuration if the feedback resistor RF is replaced by a capacitor CF. Integrator Circuit

• The expression for the output voltage V0 can be obtained by KVL eqn. at node V2. ## i1 = I B + if

Since I B is negligible small, i1 = if
Relation between current through and voltage across the capacitor is V1=0 because A is very large,
The output voltage can be obtained by integrating both sides with respect to time Indicates that the output is directly proportional to the negative integral of the input volts and inversely proportional to the time constant R1 CF.

## Waveforms from Integrator Waveforms Integrator

## Practical Integrator

• Practical Integrator to reduce the error voltage at the output, a resistor RF is connected across the feedback capacitor CF.
• Thus RF limits the low frequency gain and hence minimizes the variations in the output voltages.
• The frequency response of the basic integrator, shown from this fb is the frequency at which the gain is dB and is given by  • Both the stability and low frequency roll-off problems can be corrected by the addition of a resistor RF in the practical integrator.
• Stability refers to a constant gain as frequency of an input signal is varied over a certain range.
• Low frequency -> refers to the rate of decrease in gain roll off at lower frequencies.
• From the fig of practical Integrators, f is some relative operating frequency and for frequencies f to fa to gain RF / R1 is constant. After fa the gain decreases at a rate of 20dB/decade or between fa and fb the circuit act as an integrator.
• The gain limiting frequency fa is given by
• • The value of fa and R1CF and RF CF values should be selected such that fa<fb.
• The input signal will be integrated property if the time period T of the signal is larger than or equal to RF CF, ## Practical Integrator Uses: Practical Integrator Uses