Chapter 2 of 'Microelectronic Circuits' by Sedra and Smith focuses on operational amplifiers (op-amps), covering their ideal characteristics, configurations (inverting, non-inverting, and difference amplifiers), and the impact of negative feedback on signal processing. The text details the fundamentals of op-amp design including terminal functionalities, gain calculations, and the use of negative feedback to enhance amplifier stability and accuracy. Applications and problem sets are also included to reinforce the theoretical concepts presented.

1. Oxford University Publishing
Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)
Chapter #2: Operational Amplifier
from Microelectronic Circuits Text
by Sedra and Smith
Oxford Publishing
Karama Jeribi Friha

2. Oxford University Publishing
Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)
Introduction
 IN THIS CHAPTER YOU WILL LEARN
 The terminal characteristics of the ideal op-amp.
 How to analyze circuits containing op-amps, resistors,
and capacitors.
 How to use op-amps to design amplifiers having
precise characteristics.

3.  1. Introduction
 2. The Ideal Op Amp
 3. The Inverting Configuration
 4. The Noninverting Configuration
 5. Difference Amplifiers
 Problem set
3 Outline

4. Introduction
The Operational Amplifiers
4
 Invented in 1941 by Bell Labs engineer Karl D. Swartzel Jr. using
vacuum tubes.
 First monolithic IC op-amp was designed by Bob Widlar at
Fairchild Semiconductor.
 The 741 op-amp is perhaps the best known op-amp in the world.
Many other op-amps use the same pin configuration as the 741.
 It is an active circuit element designed to perform amplification
and mathematical operations of addition, subtraction,
multiplication, division, differentiation and integration.
 Op-amps are ubiquitous low cost components used in countless
applications for analog signal processing (gain, filtering, signal
conditioning).

5. The 741 op-amp
741
5
pin configuration circuit symbol
A typical op amp

6. Classic 741 Schematic
6
The op amp is an electronic device consisting of a complex arrangement of resistors, transistors, capacitors,

7. Oxford University Publishing
Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)
The Op Amp Terminals
 terminal #1
 inverting input
 terminal #2
 non-inverting input
 terminal #3
 output
 terminal #4
 positive supply VCC
 terminal #5
 negative supply VEE

8. Function and
Characteristics
of the Ideal Op Amp
 The op amp is designed to:
1. sense the difference between the voltage signals applied
at its two input terminals (i.e., the quantity V2 – V1),
2. multiply this by a number A, and cause the resulting
voltage A( V2 – V1) to appear at output terminal 3 .
3. input terminal 1 is called the inverting input terminal and
is distinguished by a "-" sign,
4. input terminal 2 is called the noninverting input terminal
and is distinguished by a "+" sign
8

9. Cont’d
9
A is called the differential gain = open-loop gain

10.  The op amp responds only to the difference signal v2 − v1 and
hence ignores any signal common to both inputs.
 That is, if v1 = v2 = 1 V, then the output will (ideally) be zero.
This property is called common-mode rejection
  we conclude that an ideal op amp has zero common-mode
gain or, equivalently, infinite common-mode rejection
 An important characteristic of op amps is that they are direct-
coupled or dc amplifiers, where dc stands for direct-coupled (it
could equally well stand for direct current, since a direct-
coupled amplifier is one that amplifies signals whose frequency
is as low as zero).
10 Characteristic of Op Amps

11. Oxford University Publishing
Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)
Differential &
Common-Mode
Signals
 Q: How is common-mode input (vIcm) defined in
terms of v1 and v2?
𝑣𝐼𝑐𝑚 =
1
2
(𝑣1 + 𝑣2)
common−mode input
but also...
𝑣1 = 𝑣𝐼𝑐𝑚 − 𝑣𝐼𝑑
diff
/2
inverting input
𝑣2 = 𝑣𝑐𝑚𝑖 + 𝑣𝐼𝑑/2
non−inverting input
𝑣𝐼𝑑= 𝑣2 − 𝑣1

12. 2.1.3. Differential &
Common-Mode
Signals
𝑣𝐼𝑐𝑚 =
1
2
(𝑣1 + 𝑣2)
common−mode input
but also...
Representation of the signal sources 𝑣1and 𝑣2 in terms of their differential and common mode

13.  1. Infinite input impedance (Due to this almost any
source can drive it)
 2. Zero output impedance (So that there is no change in
output due to change in load current)
 3. Zero common-mode gain or, equivalently, infinite
common-mode rejection
 4. Infinite open-loop gain A (Huge Gain!!!!!)
 5. Infinite bandwidth
13 Characteristics of the Ideal Op Amps

14. Typical Op Amp Parameters
Parameter Variable Typical Ranges Ideal Values
Open-Loop
Voltage Gain
A 105 to 108
∞
Input Resistance Ri 105 to 1013 W
∞W
Output Resistance Ro 10 to 100 W 0 W
Supply Voltage Vcc/V+
-Vcc/V-
5 to 30 V
-30V to 0V
N/A
N/A

15. 2. For close loop configuration, the OP-AMP tries to
keep the inputs the same voltage
Two Rules to remember !!!
1. No Current flows In or Out of the Inputs
15

16. Example 1
16

17. Oxford University Publishing
Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)
The Inverting
Configuration
 Q: What are two basic closed-loop op-amp
configurations which employ op-amp and resistors
alone?
 A: 1) inverting and 2) non-inverting op amp

18. The Inverting Configuration
 It consists of one op amp and two resistors 𝑅1and 𝑅2.
 Resistor 𝑅2 closes the loop around the op amp
18
negative
feedback

19. Oxford University Publishing
Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)
The Inverting
Configuration
 question: what are two basic closed-loop op amp configurations which
employ op-amp and resistors alone?
 answer: inverting and non-inverting op amp
 note: here we examine the inverting type
source is applied to
inverting input
non-inverting input is
grounded
R2 facilitates “negative
feedback”
R1 regulates level of
this feedback
Figure 2.5: The inverting closed-loop configuration.

20. The Closed-Loop Gain
 Aim: to determine the closed-loop gain G
 Assumption: the op amp to be ideal
 the equivalent circuit 
20

21. Oxford University Publishing
Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)
The Inverting
Configuration
 question: what are two basic closed-loop op amp configurations which
employ op-amp and resistors alone?
 answer: inverting and non-inverting op-amp
 note: here we examine the inverting type
Figure 2.5: The inverting closed-loop configuration.
i1 i = 0
i1

22. Con’t…
22
2 Rules!

23. Result:
 We started out with an amplifier having very large gain
A, and through applying negative feedback we have
obtained a closed-loop gain R2/R1 that is much smaller
than A but is stable and predictable.
 That is, we are trading gain for accuracy.
23

24. Effect of Finite Open-Loop Gain
 Assumption: the op-amp open-loop gain A is
finite.
24
The current 𝑖1 through 𝑅1 can now be found from

25. Con’t…
 The infinite input impedance of the op amp forces the current
𝑖1 to flow entirely through 𝑅2.
 The output voltage Vo can thus be determined from
 the closed-loop gain G
25

26. Oxford University Publishing
Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)
Effect of Finite
Open-Loop Gain
 Q: How does the gain expression change if open loop
gain (A) is not assumed to be infinite?
if then the previous
gain expression is
2 1
2
yielded
2
1
1
/
1 ( / )
1
A
G
A
Out
A
In
v R R
G
R R
v
A
R
R




 

 
 

 

ideal gain
non-ideal gain

27. Oxford University Publishing
Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)
2.2.1. Effect of
Finite
Open-Loop Gain
 Q: Under what condition can G = -R2 / R1 be
employed over the more complex expression?
 A: If 1 + (R2/R1) << A, then simpler expression may
be used.
2 2 2 1
2 1
1 1
if then el
/
1
1 ( /
1
se
)
A A
R R R R
A G G
R R
R R
A
 

    

 
 
 
ideal gain non-ideal gain

28. The Non-inverting
Configuration
 The second closed-loop configuration we shall
study is
28

29. Oxford University Publishing
Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)
The Non-Inverting
Configuration
source is applied to
non-inverting input
inverting input is
grounded
through R1
R1 and R2 act as voltage divider,
regulating negative feedback to the
inverting input
node #1
node #2

30. Con’t…
30

31. Example 2:
31

32. Example 3
 2.9 Use the superposition principle to find the output
voltage of the circuit
32

33. The Voltage Follower = Buffer amplifier
 We will explore the property of high input impedance
 to connect a source with a high impedance to a low-impedance load.
 It is used mainly as an impedance transformer or a power amplifier.
 voltage follower, since the output “follows” the input. In the ideal case,
Vo = Vi, Rin = ∞, Rout = 0,
33

34. Oxford University Publishing
Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)
Difference
Amplifiers
 difference amplifier – is a closed-loop configuration
which responds to the difference between two
signals applied at its input and ideally rejects signals
that are common to the two.
 Ideally, the amp will amplify only the differential
signal (vId) and reject completely the common-
mode input signal (vIcm). However, a practical
circuit will behave as below…
𝑣𝑂𝑢𝑡 = 𝐴𝑑𝑣𝐼𝑑 + 𝐴𝑐𝑚𝑣𝐼𝑐𝑚

35. Oxford University Publishing
Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)
Difference
Amplifiers
differential gain
differential input
common-mode input
common-mode gain
𝑣𝑂𝑢𝑡 = 𝐴𝑑𝑣𝐼𝑑 + 𝐴𝑐𝑚𝑣𝐼𝑐𝑚

36. Oxford University Publishing
Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)
Difference
Amplifiers
 The efficacy of a differential amplifier is measured by
the degree of its rejection of common-mode signals
in preference to differential signals.
 common-mode rejection ratio (CMRR) – is the
degree to which a differential amplifier “rejects” the
common-mode input.
 Ideally, CMRR = infinity…
𝐶𝑀𝑅𝑅 = 20 𝐥𝐨𝐠10
𝐴𝑑
𝐴𝐶𝑚

37. Oxford University Publishing
Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)
2.4. Difference
Amplifiers
 10
20 Di
Cm
A
CMMR
A
log
Figure : Representing the input signals to a differential amplifier in
terms of their differential and common-mode components.

38. Single-Op-Amp Difference Amplifier
 The gain of the noninverting amplifier configuration is
positive, (1+R2/R1) while that of the inverting
configuration is negative, (-R2/R1)
 Combine the two configurations together
 we have to make the two gain magnitudes equal in
order to reject common-mode signals
38

39. Oxford University Publishing
Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)
A Single
Op-Amp
Difference Amp
 Q: What are the characteristics of the difference
amplifier?
 A: Refer to following equations…
 
2 1 4 2
2 1
4 3 1 1
1 3 2
2 1
2 4 1
but i
(
f
)
( )
then
Out In In
Out In In
R R R R
v v v
R R R R
R R R
v v v
R R R

 


 
 
 

 

40. A Superior Circuit—The
Instrumentation Amplifier
40

41. Oxford University Publishing
Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)
2.4.2. The
Instrumentation
Amplifier
 question: however, can we get “more” from these amps than simply
impedance matching?
 answer: yes, maybe additional voltage gain???
A popular circuit for an instrumentation amplifier.
stage #1
non-inverting
op amp (A1)
non-inverting
op amp (A2)
stage #2
difference op
amp (A3)
vOut = (1 + R2/R1)vIn
vOut = (R4/R3)vId

42. Oxford University Publishing
Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)
2.4.2. The
Instrumentation
Amplifier
A popular circuit for an instrumentation amplifier. (b) The circuit in
(a) with the connection between node X and ground removed and
the two resistors R1 and R1 lumped together. This simple wiring
change dramatically improves performance.

43. Oxford University Publishing
Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)
The
Instrumentation
Amplifier
 Q: How can one analyze this circuit?

44. Con’t…
44

45. Oxford University Publishing
Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)
Conclusion
 The IC op-amp is a versatile circuit building block. It is
easy to apply, and the performance of op-amp circuits
closely matches theoretical predictions.
 The op-amp terminals are the inverting terminal (1), the
non-inverting input terminal (2), the output terminal (3),
the positive-supply terminal (4) to be connected to the
positive power supply (VCC), and the negative-supply
terminal (5) to be connected to the negative supply (-
VEE).

46. Oxford University Publishing
Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)
Conclusion (2)
 The ideal op-amp responds only to the difference input
signal, that is (v2 - v1). It yields an output between
terminals 3 and ground of A(v2 - v1). The open-loop gain
(A) is assumed to be infinite. The input resistance (Rin) is
infinite. The output resistance (Rout) is assumed to be
zero.
 Negative feedback is applied to an op-amp by
connecting a passive component between its output
terminal and its inverting (negative) input terminal.

47. Oxford University Publishing
Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)
Conclusion (3)
 Negative feedback causes the voltage between the two
input terminals to become very small, and ideally zero.
Correspondingly, a virtual short is said to exist between
the two input terminals. If the positive input terminal is
connected to ground, a virtual ground appears on the
negative terminal.

48. Oxford University Publishing
Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)
Conclusion (4)
 The two most important assumptions in the analysis of
op-amp circuits, assuming negative feedback exists, are:
 the two input terminals of the op-amp are at the
same voltage potential.
 zero current flows into the op-amp input terminals.
 With negative feedback applied and the loop closed, the
gain is almost entirely determined by external
components: Vo/Vi = -R2/R1 or 1+R2/R1.

49. Oxford University Publishing
Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)
Conclusion (5)
 The non-inverting closed-loop
configuration features a very high input
resistance. A special case is the unity-
gain follower, frequently employed as
a buffer amplifier to connect a high-
resistance source to a low-resistance
load.
 The difference amplifier of the Figure is
designed with R4/R3 = R2/R1, resulting
in vo = (R2/R1)(vI2 - vI1).

50. Oxford University Publishing
Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)
Conclusion (6)
 The instrumentation amplifier of the
Figure is a very popular circuit. It
provides vo = (1+R2/R1)(R4/R3)(vI2 - vI1).
It is usually designed with R3 = R4 and
R1 and R2 selected to provide the
required gain. If an adjustable gain is
needed, part of R1 can be made
variable.

51. Oxford University Publishing
Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)
Problem Set
 Exercise 1
Give the expression of V0.

52. Oxford University Publishing
Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)
Problem Set
 Exercise 2
Determine the voltage gain of the op-amp circuit below.

53. Oxford University Publishing
Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)
Problem Set
 Exercise 3
Determine V0 in the following configurations.
Configuration (a) Configuration (b)