Op-Amp Integrator
Applications of Operational Amplifiers in Tamil
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](https://cdn.wikitechy.com/tutorials/linear-integrated-circuits/integrator-circuit.gif)
Integrator Circuit
- The expression for the output voltage V0 can be obtained by KVL eqn. at node V2.
![Integrator](https://cdn.wikitechy.com/tutorials/linear-integrated-circuits/integrator.png)
i1 = I B + if
Since I B is negligible small, i1 = if
Relation between current through and voltage across the capacitor is
![Integrator](https://cdn.wikitechy.com/tutorials/linear-integrated-circuits/integrator-equation.png)
V1=0 because A is very large,
The output voltage can be obtained by integrating both sides with respect to time
![op amp Integrator](https://cdn.wikitechy.com/tutorials/linear-integrated-circuits/op-amp-integrator.png)
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](https://cdn.wikitechy.com/tutorials/linear-integrated-circuits/waveforms-integrator.gif)
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
![practical Integrator](https://cdn.wikitechy.com/tutorials/linear-integrated-circuits/practical-integrator.png)
![Integrator](https://cdn.wikitechy.com/tutorials/linear-integrated-circuits/practical-integrator-circuit.png)
- 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,
![Gain Limiting Frequency](https://cdn.wikitechy.com/tutorials/linear-integrated-circuits/gain-limiting-frequency.png)
![Gain Limiting Frequency](https://cdn.wikitechy.com/tutorials/linear-integrated-circuits/practical-integrator-equation.png)
Practical Integrator Uses:
![Practical Integrator Uses](https://cdn.wikitechy.com/tutorials/linear-integrated-circuits/practical-integrator-uses.gif)
Practical Integrator Uses
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