Operational Amplifier differentiator & Integrator

Operational Amplifier differentiator

The operational amplifier is an amplifier which is directly coupled between the output and input, having a very high gain. It is used to perform a wide variety of mathematical operations like summation, subtraction, multiplication, differentiation and integration etc. in analogue computers.

An operation amplifier can be used as a differentiator as shown in Fig. 1. This circuit produces an output voltage that is proportional to the time derivative input voltage. Hence this circuit is called differentiator.

Operational Amplifier Differentiator
Figure 1: Operational Amplifier Differentiator

Assuming that G is virtually ground. Since the current flowing in to the virtual ground is equal to current flowing out of it we can write.

i1= if= i-1
i_ = 0
i1 = if -=0
i1 = if

Operational Amplifier Differentiator Equation

from the definition of capacitance, the

charge on the capacitor is

q = CV

the charging current i is the time rate of change of charge.

Hence, output voltage V0 is equal to a constant —RC times the derivative of the input voltage Vi.

Operational Amplifier Integrator

An operational amplifier can also be used as a integrator by changing the position of R and C as shown in Fig. 2. this circuit produces an output voltage that is proportional to the time integral of the input voltage. Hence, this circuit is called an integrator.

Operational Amplifier Integrator
Figure 2: Operational Amplifier Integrator

Assuming that G is virtually ground. Since the current flowing in to the virtual ground is equal to the current flowing out of it we can write.

i1+ if  =i_
i_ = 0
i1+ if = 0
i1 = –if

Operational Amplifier Integrator Equation

Hence, output voltage V, is equal to a constant -1/RC times the integral of the input voltage Vi.