In this Article, we will learn about the Op Amp Integrator and how Integrator is used as a op amp . Also we will learn more about its applications and its advantages. Also we will check about the reasons for how is the integrator became as practical integrator.

Op Amp Integrator :-

Definition :

A circuit in which the output voltage waveform is the integrator or the integration amplifier. The integrator circuit is obtained by using a basic inverting amplifier Configuration if the feedback resistor Rf is replaced by Capacitor Cf.

Also Read : Differentiator using operational amplifier

Op Amp Integrator Circuit Diagram :

The circuit will work by passing a current that charges or discharges the capacitor Cf during the time under consideration. The input current doesn't vary with Capacitor charge and a linear integration of output is acheived.

The Circuit can be analysed by applying kirchoff's current law at node V1.

i1 = ib + if ------ (1) [ Since, Sum of incoming currents is equal to the sum of outgoing currents ] .

ib << if

ib ~= 0 [ Since, For Ideal Op Amp ]

So neglect ib in equation (1)

Therefore, i1 = if ------ ( 2 )

Formula for current passing through capacitor is ic = C * d/dt (Vc) -------- (3)

In the Circuit, the current passing through capacitor Cf is the feedback current if , Therefore if = iCf.

Voltage across the capacitor Vc = VCf .

From the circuit Vcf = ( V2 - V0 )

Therefore, iCf = Cf * d/dt ( Vcf ) = if

if = Cf * d/dt ( V2- V0 ) -------- (4)

From the Circuit, i1 = ( Vin - V2 ) / R1 ---------(5)

i1 = if

Therefore, ( Vin - V2 ) / R1 = Cf * d/dt (V2 - V0 ) ---------(6) [ From equation 4 & 5 ]

From the circuit ,

vid = 0

Vid = V1 - V2 => V1 - V2 = 0 => V1 = V2 .

In the circuit, non inverting terminals are connected to ground i.e, V1 = 0.

Therefore, V2 = 0. [ Since, V2 node acts as virtual ground ]

Substitute V1 = 0, V2 = 0 in equation ( 6 )

Therefore, Vin / R1 = Cf * d/dt (-V0 )

Integrate on both sides with respect to time " t " .

Here " K " is the integration constant. It is the proportional to the value of

output voltage Vo at t = 0 Sec.

Therefore, the integrator output V0 is proportional to the integration of input signal Vin.

Here, R1*Cf is the time constant.

Op Amp Integrator Waveform :

Drawbacks of basic integrator :

1. The gain of the integrator can be limited at low frequency.

2. For Dc Signals Capacitor Cf acts as an open loop So integrator can't show integrator action.

To overcome the effects, the Capacitor is shunted with a resistor ( Rf ).

The Practical Integrator :

Op Amp Integrator Frequency Response :

The Frequency of basic integrator is fb = 1 / (2*pi*R1*Cf)

Here R1Cf is the time constant.

The frequency of practical integrator is fa = 1 / (2*pi*Rf*Cf)

Here RfCf is the Time Constant.

Applications :

Integrator is most commonly used analog computers.
Integrator is used in Analog to digital convertors.
Integrator is used in Signal wave Shaping circuits is sine to cosine, cosine to sine, Square to triangular form, triangular to sawtooth form.