The document discusses operational amplifiers (op-amps) and their use in integrator and differentiator circuits. It defines an op-amp as an integrated circuit that amplifies input signals through high gain. An integrator circuit uses an op-amp with a capacitor in feedback, resulting in an output voltage that is inversely proportional to time. A differentiator circuit contains a capacitor in the signal path, producing an output equal to the derivative of the input voltage. Practical implementations of these circuits are also described, along with their applications in areas like analog computing and signal processing.

1. Seminar Topic :-
Integrator And Differentiator
Op-Amp
Presented By:-
Danish Iqbal
Batch:-EN-14
Roll No:-1401421019

2. What is Op-Amp ?
• An Operational Amplifier (Op-Amp) is an
integrated circuit that uses external voltage to
amplify the input through a very high gain .
• Operation Amplifier circuit designed to boost
the power of low level signal

3. Op-Amp Integrator:-
• If feedback component used is a capacitor ,the
resulting connection is called integrator.
• The circuit diagram of ideal op-amp integrator

4. • The output voltage is negative of input voltage
and inversely proportional to time constant R
and C .
Vo(s)= -Vin(s) %SRC
• The gain A, A=Vo(s)%Vin(s) = - 1/(jwCR)
• Taking magnitude of A
A= 1/(wCR) = W/Wa
Where Wa=1/CR

5. • The integrator work as a low pass filter circuit
when time constant is very large .
• At w=0, the gain A is infinite for an ideal op-
amp .
• At dc , the capacitor C behaves as an open
circuit and there is no negative feedback.
• But in practice output never becomes infinite .

6. Practical Op-Amp Integrator:-
• The gain of an integrator at low frequency (dc)
can be limited to avoid saturation by
introducing a feedback resistance(Rf) in shunt
with feedback capacitance(Cf) .
• The resistor Rf limits the low frequency gain to
–Rf/R( generally Rf=10R) .

7. Circuit diagram of Practical
Integrator :-
• Vo(s)= -Vin(s)/{sR1Cf+(R1/Rf)}

8. Differentiator Op-Amp:-
• The op-amp circuits that contain capacitor is
the differentiating amplifier .

9. • The output voltage Vo is a constant (-RC)
times the derivative of the input voltage V1 .
• In Laplace form ,s=jw
Vo(s)= -sCRVin(s)
• The gain is ,A=Vo(s)/Vin(s)
A=-sCR = -jwCR
• The magnitude of A=wCR
• A=W/Wa = f/fa
where Wa=1/CR

10. • At high frequency a differentiator may become
unstable and break into oscillation .
• The input impedence (Xc=1/wc) decrease with
increase in frequency ,therewise making the
circuitsensitive to high frequency noise .
• To overcome through the problem of
unstability and high frequency noise we use
the practical differentiator .

11. Circuit Diagram of Practical
Differentiator:-

12. Output Equation:-
• Vo(s)/Vin(s) = - sRfC1/{(1+sCfRf)(1+sC1R1)}
• If CfRf=C1R1 and s=jw
• Vo(s)/Vin(s) = jwRfC1/{(1+jwCfRf)^2}
• The magnitude of A,
A= wRfC1/{(1+jf/fb)^2}
where

13. Applications of Op-amp Differentiator
and Integrator:-
• Differentiating amplifiers are most commonly
designed to operate on triangular and
rectangular signals.
• Differentiators also find application as wave
shaping circuits, to detect high frequency
components in the input signal.
• The integrator circuit is mostly used in analog
computers, analog-to-digital converters and
wave-shaping circuits .

14. Any Query ….?
Thank You