Integrator and Integrator Circuit
Table of Contents
Integrator and Integrator Circuit
Integrator
The Integrator, also known as an Integrator op amp, is a circuit in which the output voltage Waveform is the Integral of the input voltage Waveform. If the Feedback Resistor is swapped out for a Capacitor, a basic Inverting Amplifier Configuration can be used to create the desired circuit.
So The expression for the output voltage V0 can be Obtained by KVL eqn at node V2.
where C Integration constant A
So eqn (3) Indicates that the output is directly Proportional to the negative Integral of the input volts and Inversely Proportional to the time constant R1 CF .
Ex: If the input is sine wave -> output is cosine wave.
If the input is square wave -> output is triangular wave.
These waveform with assumption of R1Cf = 1, Vout =0V (i.e) C =0.
Because the capacitor CF acts as an open circuit to the input offset voltage Vio when Vin = 0, the integrator functions as an open loop amplifier.
Or
The error voltage at the integrator’s output is created by the input offset voltage Vio and the portion of the input that charges the capacitor CF.
Integrator Circuit
Practical Integrator
A resistor RF is connected across the feedback capacitor CF of the practical integrator in order to lower the error voltage at the output. Thus, RF restricts the low frequency gain and lessens output voltage variations. A resistor RF can be added to the practical integrator to address the stability and low frequency roll-off issues. So The frequency response of the basic integrator is shown from this fb and is the frequency at which the gain is dB.
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.
So 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.
Generally, the value of fa and in turn R1 CF and RF CF values should be selected such that fa<fb. In fact, the input signal will be integrated properly if the time period T of the signal is larger than
or
equal to RF CF, (i.e) T >= RF CF @@@@ 6
Uses:
Most commonly used in analog computers.
ADC
Signal wave shaping circuits.