Operational Amplifiers

& Op Amp Circuits

The name “operational amplifier” comes from the

fact that they were originally used to perform
mathematical operations such as addition of signals,
subtraction, integration and differentiation.

Ref Book: Electric circuits Nilsson Riedel 9th Edition.

 The Operational Amplifier
• Usually Called Op Amps
• An amplifier is a device that accepts a varying input signal and
produces a similar output signal with a larger amplitude.

• Usually connected so part of the output is fed back to the input.

(Feedback Loop)

• Most Op Amps behave like voltage amplifiers. They take an input

voltage and output a scaled version.

• They are the basic components used to build analog circuits.

• Integrated circuit fabrication techniques have made high-performance

operational amplifiers very inexpensive.
Operational Amplifiers
The op amp is built using VLSI techniques. The circuit
diagram of an LM 741 from National Semiconductor is
shown below.
V+

Vin(-)

Vo
Vin(+)

Taken from National Semiconductor

V-
data sheet as shown on the web.
Operational Amplifiers
The circuit in the previous slide is usually encapsulated into
a dual in-line pack (DIP). For a single LM741, the pin
connections for the chip are shown below.

Pin connection, LM741.

 IC Product OUTPUT A 1 8 V+

OFFSET
1 8 N.C.
-IN A 2  7 OUTPUT B
NULL
+
-IN 2 7 V+
+IN A 3  6 -IN B

V 4 + 5 +IN B
+IN 3 + 6 OUTPUT

OFFSET
V 4 5 NULL
Dual op-amp 1458 device
DIP-741

• An op amp is an active circuit

element designed to perform
mathematical Operations of
addition, subtraction,
multiplication, division,
741 general purpose op-amp differentiation, and
integration.
 Symbol and Terminals

• The op-amp is a circuit of components integrated into one chip. We

will study the op-amp as a singular device.
• A typical op-amp is powered by two dc voltages and has an
inverting(-) and a noninverting input (+) and an output.
• Note that for simplicity the power terminals are not shown but
understood to exist.
Operational Amplifiers
A model of the op amp, with respect to the symbol, is
shown below.

V1
Op Amp Model.
_
Ro Vo
Vd Ri
+
AVd
V2

The model above is at times shown

as follows:
Ri
V1
+
_

Vd Ri AVd Vo
+
V2 _
 The Ideal Op-Amp
• The ideal op-amp has
• Infinite voltage gain
• Infinite bandwidth
• Infinite input impedance
• Zero output impedance

The Practical Op-Amp

• The practical op-amp has:
• high voltage gain
• wide bandwidth
• high input impedance
• low output impedance

8
 Ideal Op Amp:

i1 = 0
_ _
+ i2 = 0 Vi
+ + +
V1 +
Vo
V2 = V1
_ _ _

(a) i1 = i2 = 0: Due to infinite input resistance.

(b) Vi is negligibly small; V1 = V2.

 Internal Block Diagram of an Op-Amp
A typical op-amp is made up of three types of amplifier circuit: a
differential amplifier, a voltage amplifier, and a push-pull amplifier, as
shown in Figure. A differential amplifier is the input stage for the op-amp
(has two inputs and provides amplification of the difference voltage
between the two inputs). The voltage amplifier provides additional op-amp
gain. Some op-amps may have more than one voltage amplifier stage.

Accumulates a very high gain by multiple stages

 The Four Amplifier Types
Gain Transfer
Description Symbol Function

Voltage Amplifier Av vo/vin

Current Amplifier Ai io/iin

gm
Transconductance Amplifier io/vin
(siemens)

rm
Transresistance Amplifier vo/iin
(ohms)
Op-amp signal input modes & parameters

A) Single-Ended Input
Operation mode;
• One input is grounded.
• The signal voltage is applied only to the other input.

 When the signal voltage is applied to the inverting input,

• an inverted amplified signal voltage appears at the
output. (figure below)

Vin .

Vout

+
.
• When the signal voltage is applied to the non-inverting
input with the inverting input grounded,
• a noninverted amplified signal voltage appears at the
output.

Vout
Vin
+
.
B) Differential Input
Operation mode;
• Two opposite-polarity (out-of-phase) signals are
applied to the inputs
• This type of operation is also referred to as double-ended.
• The amplified difference between the two inputs
appears on the output.

Vin1 .
_

Vout
Vin2
+
.

Vout = A(Vin1 – Vin2)

C) Common-Mode Input
Operation mode
• Two signal voltages of the same phase, frequency and
amplitude are applied to the two inputs.
• When equal input signals are applied to both inputs, they
cancel, resulting in a zero output voltage.

• This action is called common-mode rejection.

• Means that this unwanted signal will not appear on the
output and distort the desired signal.

Vin .

Vout
Vin
+
.
Identify the type of input mode for each op-amp in Figure.

(a) Single-ended input (b) Differential input (c) Common-mode

 Common-Mode Rejection Ratio
• Desired signals can appear on only
• one input or
• with opposite polarities on both input lines.

• These desired signals are amplified and appear on the output.

• Unwanted signals (noise) appearing with same polarity on both

input lines are
• cancelled by the op-amp and don’t appear on the output.

• The measure of an amplifier’s ability to reject common-mode

signal is called CMRR (common-mode rejection ratio).

• Ideally, op-amp provides

• a very high gain for desired signal (single-ended or
differential)
• zero gain for common-mode signal.
• The higher the open-loop gain with respect to the common-
mode gain, the better the performance of the op-amp in terms
of rejection of common-mode signals.

• Therefore; CMRR  Aol

Acm
where Aol = open-loop voltage gain
Acm = common-mode gain

• The higher the CMRR, the better.

• A very high value of CMRR means that
• the open-loop gain, Aol is high and
• the common-mode gain, Acm is low.
 Aol 
• The CMRR expressed in decibels (dB) is CMRR  20 log  
 cm 
A
 Open-Loop Voltage Gain

• Open-loop voltage gain, Aol of an op-amp

• is the internal voltage gain of the device
• represents the ratio of output voltage to input voltage
when there are no external components.
• The open-loop voltage gain is set entirely by the internal
design.

• Data sheets often refer to the open-loop voltage gain as

• the large-signal voltage gain.
Q. A certain op-amp has an open-loop voltage gain of 100,000 and a common-mode
gain of 0.2. Determine the CMRR and express it in decibel.

Aol = 100,000, and Acm = 0.2. Therefore,

Aol 100,000
CMRR    500,000
Acm 0.2
Expressed in decibels,
CMRR  20 log(500,000)  114dB

Q. An op-amp data sheet specifies a CMRR of 300,000 and an Aol of 90,000.

What is the common-mode gain?

Aol 90,000
Acm    0.3
CMRR 300,000
 Example 1
A certain op-amp has an open-loop voltage gain
of 40,000 and a common-mode gain of 0.2.

i) Determine the CMRR

ii) Express the CMRR in decibels.
Input Bias Current
I1

V1 _

I2 Vout
+
V2

• Input bias current is the average of the two op-

amp input currents.
• The input bias current is
• the dc current required by the inputs of the amplifier
to properly operate the first stage.
• By definition, the input bias current is
• the average of both input currents and is calculated
as;
I1  I 2
I BIAS 
2
Input Impedance
• Two basic ways of specifying the input impedance of an
op-amp are
• Differential.
• Common-mode.

• Differential input impedance is

• the total resistance between the inverting and the non-
inverting input.
• Measured by determining the change in bias current for
a given change in differential input voltage.
_

ZIN(d) .

Differential input impedance

• Common-mode input impedance is
• the resistance between each input and ground.
• Measured by determining the change in bias
current for a given change in common-mode input
voltage.
_

ZIN(cm)
.

Common-mode impedance
 Output Impedance

• The output impedance is

• the resistance viewed from the output terminal of
the op-amp as indicated in figure below

Zout
.

+
Op-amps with Negative Feedback
• Negative feedback is a process where a portion of the
output voltage is returned to the input with a phase
angle opposed the input signal.

• Advantages:
• Higher input impedance
• More stable gain
• Improved frequency response
• Lower output impedance
• More linear operation

Negative Feedback is the process of “feeding back” a fraction of the output

signal back to the input, but to make the feedback negative, we must feed
it back to the negative or “inverting input” terminal of the op-amp using an
external Feedback Resistor called Rƒ.
 Gain in negative feedback
• Negative feedback sounds bad, & positive good—but in
electronics positive feedback means runaway or oscillation, and
negative feedback leads to stability.

• Hooking the output to the inverting terminal:

• If the output is less than Vin, it shoots positive
• If the output is greater than Vin, it shoots negative
• result is that output quickly forces itself to be exactly Vin

negative feedback loop

Vin

+
Positive feedback pathology
• In the configuration below, if the + input is even a smidge
higher than Vin, the output goes way positive.

• This makes the + terminal even more positive than Vin, making
the situation worse.


Vin positive feedback: BAD
+
Negative vs. Positive Feedback

Familiar examples of negative feedback:

• Thermostat controlling room temperature Fundamentally
• Driver controlling direction of automobile pushes toward
• Pupil diameter adjustment to light intensity
stability

Familiar examples of positive feedback:

• Microphone “squawk” in sound system Fundamentally
• Mechanical bi-stability in light switches pushes toward
instability or
bi-stability
Closed-Loop Voltage Gain, Acl
• The closed-loop voltage gain is
• the voltage gain of an op-amp with external
feedback.

• The amplifier configuration consists of

• the op-amp
• an external negative feedback circuit that
connects the output to the inverting input.

• The closed-loop voltage gain is determined by

• the external component values and can be
precisely controlled by them.
 Noninverting Amplifier
+
Vout
_
Vin Rf
. Feedback
network
Vf
Ri

• Noninverting amplifier is
• an op-amp connected in a closed-loop with a controlled
amount of voltage gain is shown in figure above.

• The input signal is applied to

• the noninverting (+) input.
Rf
Acl ( NI )  1 
Ri
• The output is applied back to
• the inverting (-) input through the feedback circuit (closed
loop) formed by the input resistor Ri and the feedback
resistor Rf.
 Example
Determine the gain of the amplifier in figure below. The
open-loop voltage gain of the op-amp is 100,000.

Vin +
Vout
_
Rf
100kΩ

Ri
Rf 4.7kΩ

Acl ( NI )  1 
Ri

Answer: 22.3
Inverting Amplifier
Rf

Ri
_
Vout
Vin Aol
+

• Inverting amplifier
• An op-amp connected with a controlled amount of
voltage gain.
• The input signal is applied through a series input resistor Ri
to the inverting (-) input.
• The output is fed back through Rf to the same input.
• The noninverting (+) input is grounded.
• What is an Inverting Amplifier?

• An inverting amplifier (also known as an inverting

operational amplifier or an inverting op-amp) is a type
of operational amplifier circuit which produces an
output which is out of phase with respect to its input by
180o.
• This means that if the input pulse is positive, the output
pulse will be negative and vice versa.
• The figure below shows an inverting operational
amplifier built by using an op-amp and two resistors.
• The voltage gain of the inverting operational amplifier
is,

• This indicates that the voltage gain of the inverting

amplifier is decided by the ratio of the feedback resistor
to the input resistor with the minus sign indicating the
phase-reversal.
Summing Amplifier
Aside from amplification, the op-amp can be made to do addition
very readily
• If one takes the inverting
amplifier and combines
several inputs each via their
own resistor.
• The current from each input
will be proportional to the
applied voltage and the input
resistance

i1 
 v1  va 
i2 
 v2  va 
i3 
 v3  va 
R1 R2 R3
• At the inverting terminal, these current will combine to equal the current
through the feedback resistor

ia 
 va  vo 
Rf
• This results in the following relationship:
 Rf Rf Rf 
vo    v1  v2  v3 
 R1 R2 R3 
• Note that the output is a weighted sum of the inputs

• The number of inputs need not be limited to three.

Example: Ideal Operational Amplifier
The difference amplifier in the circuit below has been modeled as
an ideal op amp. Use node equations to analyze this circuit and
determine vo in terms of the two source voltages va and vb.
Solution

• It is convenient to use node equations to analyze circuits

containing ideal op amps.
• There are three things to remember.
1. The node voltages at the input nodes of ideal operational amplifiers
are equal. Thus, one of these two node voltages can be eliminated
from the node equations
2. The currents in the input leads of an ideal operational amplifier are
zero.
3. The output current of the operational amplifier is not zero.
Solution
Questions

Questions are for Groups 8 to 13.

Presentations shall be on Tuesday 28th Feb 2023

Each group has 10 minutes.

This shall be graded out of 10.

41
Group 8
Consider the circuit shown in Figure below.
Find the value of the voltage measured by the
voltmeter.
 Group 9
The op amps in the circuit below operate from ±12V power
supplies, but are ideal otherwise.
i) Classify each of the amplifier stages as inverting or non-
inverting.
ii) What are the voltage gain, input resistance, and output
resistance of the overall amplifier?

Hint: Apply the inverting and noninverting amplifier formulas to the individual
stages. The gain will be the product of the gains. AV-1320 The input resistance
will be the input resistance of the first stage. The output resistance will equal
43
that of the last amplifier 20k//100k.
Group 10
With clear examples, discuss the importance of operational
amplifiers in signal filtration.

44
Group 11
Find io in the circuit below given that the op amp is ideal.

45
Group 12

a) What circuit configuration is shown below?

b) Find Vo if Va = 1V, Vb = 1.5V and Vc = -4V.

46
Group 13

For the circuit below, calculate Vo when Vg

equals 4V.

47