Objective
To design Integrator using operational amplifier and verify its functionality.
Components
Components
Operational amplifier 741 IC
Fixed DC power supply (14 volts)
Resistor ( 10Ω , ±1% tolerance carbon type )
Capacitor ( 0.2µF )
Resistor ( 100K Ω, 10 KΩ(2) )
Hook up wires
Bread board
Fixed DC power supply (14 volts)
Function generator
CRO
Fixed DC power supply (14 volts)
Resistor ( 10Ω , ±1% tolerance carbon type )
Capacitor ( 0.2µF )
Resistor ( 100K Ω, 10 KΩ(2) )
Hook up wires
Bread board
Fixed DC power supply (14 volts)
Function generator
CRO
Theory
INTEGRATOR
A circuit in which the output voltage is the internal of the input voltage waveform is the integrator or the integration amplifier. the expression output voltage Vo can be obtained by writing KCL equation at node V2
................................................i1 = IB + iF
Since IB is negligible
................................................i1 = if = iC
As the relationship between current through and voltage across the capacitor is,
A circuit in which the output voltage is the internal of the input voltage waveform is the integrator or the integration amplifier. the expression output voltage Vo can be obtained by writing KCL equation at node V2
................................................i1 = IB + iF
Since IB is negligible
................................................i1 = if = iC
As the relationship between current through and voltage across the capacitor is,
..............................................Ic = Cd/dtVc
Therefore ,..........................(Vin-v2)/r1 = Cfd/dt(V2-V0)
Therefore ,..........................(Vin-v2)/r1 = Cfd/dt(V2-V0)
Therefore ...........................V1 = V2 = 0 because gain A is very large
Therefore............................Vin/R1 = Cf d(-V0) dt
The output voltage can be obtained by integrating both sides with respect to time
Therefore............................Vin/R1 = Cf d(-V0) dt
The output voltage can be obtained by integrating both sides with respect to time
...........................................ʃVin/R1 dt = ʃCfd/dt(-Vo) dt
..........................................= CF (-Vo) + Vot=0
Therefore, Vo = -1/(R1C1) ʃ Vin dt + C
Where C is the integration constant and is proportional to the value of the output voltage is directly proportional to the negative inversely proportional to the time constant R1CF for example , if the input is a since wave ,the output will be a cosine wave, or if the input is square wave ,the output will be a triangular wave , if R1CF = 1 and is given by ,
Therefore, Vo = -1/(R1C1) ʃ Vin dt + C
Where C is the integration constant and is proportional to the value of the output voltage is directly proportional to the negative inversely proportional to the time constant R1CF for example , if the input is a since wave ,the output will be a cosine wave, or if the input is square wave ,the output will be a triangular wave , if R1CF = 1 and is given by ,
..................................fb = 1/(2ӆR1CF)
The gain limiting frequency fa is given by,
The gain limiting frequency fa is given by,
.................................fa = 1/2ӆ RFCF
Generally, the value of fa and in two R1Cf and values should be selected
Generally, the value of fa and in two R1Cf and values should be selected
................................fa
Procedure
1. Connect the circuit as shown in figure 2 for integrator circuit
2. Calculate time period from the function generator to the CRO which should be much greater than RC
2. Calculate time period from the function generator to the CRO which should be much greater than RC
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