ELECTRONIC DEVICES AND
CIRCUITS
LECTURE 19
Dated: 17th May 2016
Instructor :Kashif Mehmood
CHAPTER 2
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OP-AMP
(Operational Amplifiers)
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From Microelectronic Circuit by Sedra Smith 6th Edition
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2.5 INTEGRATORS AND DIFFERENTIATORS

By implementing op-amp using RC circuits two basic applications,
namely, integrators and differentiators are formed

Consider the inverting closed-loop configuration with impedances Z1(s)
and Z2(s) replacing resistors R1 and R2, respectively
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2.5.1 The Inverting Configuration with
General Impedances
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
The closed loop gain G=
3
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See class notes for Solution
2.5.2 THE INVERTING INTEGRATOR

By placing a capacitor in the feedback path (i.e., in place of Z2 in Fig.
2.22) and a resistor at the input (in place of Z1), we obtain the circuit of
Fig. 2.24(a). We shall now show that this circuit realizes the
mathematical operation of integration.
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Kashif Mehmood
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

Let input be the time varying voltage v1(t) as shown ,then the current
flows through capacitor is also time varying i1(t) as shown in the Fig.
Let the initial voltage across capacitor is Vc .the voltage at any time t is
found by
5
2.

Also 0-vo(t)= vc(t) which implies

The expression in the previous slides become
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
Thus the circuit provides an output voltage that is proportional to the
time integral of the input, with Vc being the initial condition of
integration and CR the integrator time constant.
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
The negative output shows that this integrator is an inverting
integrator. It is also known as a Miller integrator
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The integrator behaves as a low-pass filter, Observe also that at ω = 0, the
magnitude of the integrator transfer function is infinite.
This problem of the integrator circuit can be alleviated by connecting a
resistor RF across the integrator capacitor C, as shown in Fig. 2.25
The integration is no longer ideal, and the lower the value of RF, the less
ideal the integrator circuit becomes
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.
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See class notes for Solution
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See class notes for Solution
2.5.3 THE OP-AMP DIFFERENTIATOR


Interchanging the location of the capacitor and the resistor of the
integrator circuit
results in the circuit in Fig. 2.27(a), which performs the mathematical
function of differentiation.
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CR is the differentiator time-constant
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See class notes for Solution
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See class notes for Solution
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ANNOUNCEMENTS REGARDING EDC-B


MCQs Type Quiz from whole Syllabus (Weightage
10% ,Time 1 Hr) will be held on 6th January 2016 in
room 602 at 11am
5% Lab project and Project Report Due date is 30th
December 2015 in my office at 11am
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
Quiz 2 (weightage 8% ,Time 2Hrs) will be held on 4th
Jan 2016 in class.(Syllabus Ch 5 and Ch 2)
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
Assignment
4
of
Ch2
is
uploaded
in
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2016 (Monday) in class
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