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)}
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 .
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 .
