20EC402-LIC -Introduction and Unit-I - 28-01-2023.pptx

Linear Integrated Circuits
(20EC402)

Introduction
Integrated Circuit (or) IC
– Low cost electronic circuit consisting of active
and passive components that are irreparably
joined together on a single crystal chip of
silicon.
18-Aug-23 (Unit-I: Basics of Operational Amplifiers) 2
 Active Components – are the parts of a circuit that rely on an external power source to
control or modify electrical signals. (transistors and SCRs) use electricity to control
electricity.
 Passive components – are an electronic component which can only receive energy,
which it can either dissipate, absorb or store it in an electric field or a magnetic field.
 Passive elements do not need any form of electrical power to operate.

Introduction
Advantage
• Advantage over the “interconnecting discrete
components”
Miniaturization - increase equipment density
Cost reduction - due to batch processing
Increased system reliability
- due to elimination of soldered joints
Improved functional performance
Matched devices
Increased operating speed
Reduction in power consumption
Discrete Components - a component with just one circuit element, either passive (resistor, capacitor,
inductor) or active (transistor..).

Introduction - Classification
• Classification
– Digital ICs
– Linear ICs
• IC Technology
– Monolithic Technology
– Hybrid Technology
• Monolithic IC
– All circuit components and interconnections are manufacture into (or) on top of a
single chip of silicon.
– Suitable for the identical circuit required in large nos. (∴ Low cost, high reliability)
• Hybrid ICs
– Separate components parts attached to a ceramic substrates interconnection by
metallization pattern (or) wire bonds
– Suitable for small quantity, custom circuits

Introduction - Classification of ICs
• Based on active devices used ICs can be classified as
– Bipolar (Using BJT)
– Unipolar (Using FET)
• Can be further classified depends on isolation
technology
Integrated Circuits
Monolithic Circuits Hybrid Circuits
Bipolar Unipolar
PN Junction
Isolation
Dielectric
Isolation
MOSFET JFET

Introduction
Fundamentals of Monolithic IC Technology
– A circuit fabricated from a single stone (or) crystal
– From Greek Mono – single, Lithic – stone
• Example: 10cm diameter wafer – divided into 8000, 1mm
thickness, if 10 such wafers processed on one batch 80,000 ICs.
– Normally 20% fault free chips can be produced / batch
– Fabrication of discrete devices such as Transistor, Diode
(or) IC in the same technology
– Various processes usually take place thro a single plane
(Technology) referred to “Planar Technology”

Introduction - A Brief Chronology
Invention of
Transistor
1947
First IC – Small
Scale Integration
(SSI)
Gates/Chip - 3 to 30 approx. (or)
100 Transistors/Chip
(Logic gates, Flip-Flops)
1960-1965
Medium Scale
Integration (MSI)
100 to 1000 Transistors/Chip
1965-1970
Large Scale
Integration (LSI)
1K-20K Transistors/Chip
(Processor, RAM, ROM)
1970-1980
Very Large Scale
Integration (VLSI)
Gates/Chip - >3000. (or)
20K-10L Transistors/Chip
1980-1990
Ultra Large Scale
Integration (ULSI)
106-107 Transistors/Chip
(Logic gates, Flip-Flops)
1990-2000
Chronology - the order in which a series of past events took place

Introduction - Integrated Chips

Introduction
Fundamentals of Monolithic IC

Syllabus - Objectives
• The student should be made to:
– Learn the basic building blocks of Linear Integrated Circuits.
– Understand the Linear and Non-Linear applications of Operational
Amplifiers.
– Acquire the concept and applications of Analog Multipliers and
PLL.
– Analyze ADC and DAC using Op-Amp.
– Study the concepts of waveform generation using Op-Amp and
some special function ICs.

Syllabus - Unit I
Basics of Operational Amplifiers
• Basic information about Op-amps:
• Symbol,
• Power Supply Connection
• Ideal Operational Amplifier
• Inverting Amplifier
• Non-Inverting Amplifier
• Voltage Follower
• Differential Amplifier
• Op-amp: Block Diagram
• DC characteristics
• AC characteristics:
• Frequency response,
• Frequency Compensation
• Slew rate
Syllabus - Unit II
Applications of Operational Amplifiers
• Basic Op-amp Applications
– Scale Changer
– Summing Amplifier
– Subtractor
• Instrumentation amplifier
• V-to-I and I-to-V converters
• Precision Rectifier
• Peak detector
• Clipper and Clamper
• Sample and Hold circuit
• Log amplifier
• Antilog amplifier
• Differentiator
• Integrator
• Comparators
• Schmitt trigger
• Filters:
– Low pass filters
– High pass filters
– Band pass filters
– Butterworth filters.

Syllabus - Unit III
Analog Multiplier and PLL
• Analog Multiplier using Emitter
Coupled Transistor Pair
• Gilbert Multiplier Cell
• Variable transconductance
technique
• Analog multiplier ICs and their
Applications – PLL:
– Basic principles
– Analysis
• Voltage controlled oscillator
• Monolithic PLL IC 565
• Application of PLL:
– Frequency Multiplication
– Division
– Frequency translation
– FM demodulation
– FSK demodulator.
Syllabus - Unit IV –
Analog to Digital and
Digital to Analog Converters
• Basic DAC techniques
– Weighted resistor type
– R-2R Ladder type
– Inverted R-2R Ladder DAC
• A/D Converter
– Flash type
– Counter Type A/D converter,
– Successive Approximation type
– Single Slope type
– Dual Slope type
• DAC/ADC Specifications.

Syllabus - Unit V
Waveform Generators and Special Function ICs
• Sine-wave generators
– Multivibrators
• Triangular wave generator using op-
amp
• Function generator
• Timer IC 555
– Functional Description
– Monostable operation
– Astable operation
• IC Voltage regulators:
– Fixed voltage series regulator
– IC 723 general purpose regulator
– Switching regulator
• Frequency to Voltage converter
• Voltage to Frequency converter
• Audio Power amplifier
• Video Amplifier
• Opto-couplers
• Fibre optic IC.

Syllabus - Outcomes
• On successful completion of this course, the students will be able to,
– Understand the basic building blocks and characteristics of Linear
Integrated Circuits.
– Recognize the Linear and Non-Linear applications of Operational
Amplifiers.
– Know the concept of Analog Multipliers and PLL and their
Applications.
– Realize A/D Converter and D/A Converter using Op-amp.
– Acquire the concept of waveform generators using op-amp and
special function ICs.

• TEXT BOOKS:
– Roy Choudhry D and Shail Jain, “ Linear Integrated
Circuits”, New Age International Pvt. Ltd., 4th Edition,
2018.
• REFERENCES:
– Salivahanan S and Kanchana Bhaskaran V S, “Linear Integrated
Circuits”, Tata McGraw Hill, 2nd Edition, 6th Reprint, 2010.
– Serigo Franco, “Design with Operational Amplifiers and Analog
Integrated Circuits”, Tata McGraw-Hill, 4th Edition, 2016.
– Ramakant A Gayakward, “Op-amp and Linear ICs”, Prentice Hall /
Pearson Education, 4th Edition, 2015.
– Gray and Meyer, “Analysis and Design of Analog Integrated Circuits”,
Wiley International, 5th Edition, 2009.
– William D Stanely, “Operational Amplifiers with Linear Integrated
Circuits”, Pearson Education, 4th Edition, 2001.

Syllabus - Unit I
Basics of Operational Amplifiers
• Basic information about Op-amps:
• Symbol,
• Power Supply Connection
• Ideal Operational Amplifier
• Non-Inverting Amplifier
• Voltage Follower
• Differential Amplifier
• Op-amp: Block Diagram
• DC characteristics
• AC characteristics:
• Frequency response,
• Frequency Compensation
• Slew rate

Operational Amplifier
• Basic information of op-amp
– Is an important linear IC
– Commonly referred to as op-amp
– Internally quite complex
– Performance can completely described by terminal
characteristics
• Schematic of an op-amp is
Schematic Diagram is a drawing that defines the logical connections between
components on a circuit board

Packages
1. Metal can (TO) Package
2. The dual-in-line package (DIP)
3. The flat package (or) Flat pack
Op-amp package may contain
• Single – 8 terminals (DIP (or) mini DIP)
• Two (or) dual – 10 terminals (flat pack (or) CAN)
• Four (or) Quad
Popular op-amp is μA741

Various IC Packages of 741 op-amp

Power Supply Connections
• V+ & V- are the power supply terminals, connected to two DC voltage
sources
• Two sources 15V batteries each
• Power supply may range from ±5V to 22V
• The common terminal of the V+ and V- sources is connected to a reference
point or ground.
• The common point of the two supplies must be grounded, otherwise twice
the supply voltage will get applied and it may damage the op-amp.

Power Supply Connections
• Instead of using two power supplies, single power supply can be used
to obtain V+ and V- as shown in circuits.
R should be >10KΩ & C=0.01
to 10μF, does not draw more
current from VS
• Zener diodes are used for
symmetrical supply
• RS chosen such that it supplies
sufficient current to Zener
Diode.
• Potentiometer is used
to generate equal
values of V+ & V-
• D1, D2 protect the IC if
supply reversed

Manufacturers Designation for Linear ICs
Manufacturer Codes Example
Farchild μA, μAF
National Semiconductor LM, LN, LF,TBA LM741
Motorola MC, MFC MC1741
RCA CA, CD CA3741
Texas Instruments SN SN52741
Signetics NIS, NE/SE N5741
Classes such as A,C,E,S,SC
741 Military grade (operating temp -550 to 1250C)
741C Commercial grade (operating temperature 00 to 700 / 750C)
741A Improved version of 741(Better electrical specifications)
741E Improved version of 741C (Better electrical specifications)
741S Military grade with higher slew-rate
741SC Commercial grade with higher slew-rate

Ideal Op-Amp
• Schematic op-amp symbol is
• When V1 = 0, V0 is 1800 out of phase with V2
• if V2 = 0, V0 is in phase with V1

Ideal Op-Amp Characteristics
• Open loop voltage gain AOL = ∞
• Input impedance Ri = ∞
• Output Impedance Ro = 0
• Bandwidth BW = ∞
• Zero effect (ie V0=0) when V1 = V2 = 0
• It can be seen that
1. If ideal op-amp 𝒊𝟏 = 𝒊𝟐 = 𝟎, because of 𝑹𝒊 = ∞ ie
there is no loading in input side.
2. Because of 𝒈𝒂𝒊𝒏 = ∞ , 𝑽𝒅 = 𝑽𝟏 − 𝑽𝟐 = 𝟎
3. V0 is independent of Io as R0 = 0, so it can run
infinite number of other devices.

Ideal Op-Amp characteristics
• Where 𝑨𝑶𝑳 ≠ ∞, 𝑹𝒊 ≠ ∞ , 𝑹𝟎 ≠ 𝟎
• Op-amp is “voltage controlled voltage source”
• AOLVd = equivalent Thevenine Voltage source
• R0 = Thevenine equivalent resistance
• ∴ 𝑽𝟎 = 𝑨𝑶𝑳𝑽𝒅 = 𝑨𝑶𝑳 𝑽𝟏 − 𝑽𝟐
• Op-amp amplifies the difference between input voltages
• This ideal op-amp characteristics used in mathematical modelling

Open Loop Operation of Op-Amp
• Simplest way to use an op-amp is in the open loop
• Since gain is (AOL =) ∞
𝑽𝟎 = 𝑽𝑺𝒂𝒕 𝑾𝒉𝒆𝒏 𝑽𝟏 > 𝑽𝟐
(or)
𝑽𝟎 = −𝑽𝑺𝒂𝒕 𝑾𝒉𝒆𝒏 𝑽𝟐 > 𝑽𝟏 VSat → Saturation voltage
• So, amplifier acts as a switch only.
• Application
– Comparator
– Zero crossing detector etc,.

Feedback in ideal Op-Amp
• Utility can be increased by providing “negative feedback”.
• The output not saturated, it works under “Linear manner”.
• Negative Feedback circuits
• Assumptions:
1. Current drawn either input terminals is negligible
2. Vd is essentially zero.
– Most widely used
– V0 is fed back to the inverter
input thro Rf, R1

Inverting Amplifier - Analysis
• Assume an ideal op-amp
as Vd=0, a is at ground potential
Current 𝒊𝟏 =
𝑽𝒊
𝑹𝟏
• Op-amp draws no current
⟹ 𝑽𝟎 = −𝒊𝟏𝑹𝑭 = −
𝑽𝒊
𝑹𝟏
𝑹𝑭
∴ 𝒈𝒂𝒊𝒏 𝑨𝑪𝑳 =
𝑽𝟎
𝑽𝒊
= −
𝑹𝑭
𝑹𝟏
(or)
• Also, By KCL at ‘a’
𝑽𝒂 − 𝑽𝒊
𝑹𝟏
+
𝑽𝒂 − 𝑽𝟎
𝑹𝑭
= 𝟎
Since Va = 0
−
𝑽𝒊
𝑹𝟏
=
𝑽𝟎
𝑹𝑭
⟹
𝑽𝟎
𝑽𝒊
= −
𝑹𝑭
𝑹𝟏
= 𝑨𝑪𝑳
•-ve indicates phase shift 1800 between Vi
& V0 avoid loading effect, limits the gain
•RL → Load resistor
(can be the oscilloscope etc,. acts as a load
Load current 𝒊𝑳 =
𝑽𝟎
𝑹𝑳
𝒊𝒇 𝑹𝟏 = 𝒁𝟏, 𝑹𝒇 = 𝒁𝒇 ⟹ 𝑨𝑪𝑳 = −
𝒁𝑭
𝒁𝒊
• Used in op-amp applications like
Integrator, Differntiator, etc,.

Practical Inverting Amplifier
• 𝑨𝑪𝑳 =
𝑽𝟎
𝑽𝒊
=
𝑹𝑭
𝑹𝟏
Valid for ideal op-amp
• For practical op-amp, it should be calculated fro low frequency model ie.
• Analyzed for expressions ACL, Rif
Usually
𝑹𝒊 ≫ 𝑹𝟏 ⟹ 𝑽𝒆𝒒 ≅ 𝑽𝒊 & 𝑹𝒆𝒒 ≅ 𝑹𝒊
From figure
𝑽𝟎 = 𝒊𝑹𝟎 + 𝑨𝑶𝑳𝑽𝒅
⟹ 𝑽𝒅 = −𝒊𝑹𝟎 + 𝑽𝟎 𝑨𝑶𝑳
also 𝑽𝒅 + 𝒊𝑹𝒇 + 𝑽𝟎 = 𝟎
⟹
𝑽𝟎
𝑨𝑶𝑳
−
𝒊𝑹𝟎
𝑨𝑶𝑳
+ 𝒊𝑹𝒇 + 𝑽𝟎 = 𝟎
⟹ 𝑽𝟎
𝟏 + 𝑨𝑶𝑳
𝑨𝑶𝑳
= 𝒊
𝑹𝟎 − 𝑹𝒇𝑨𝑶𝑳
𝑨𝑶𝑳
⟹ 𝑽𝟎 𝟏 + 𝑨𝑶𝑳 = 𝒊 𝑹𝟎 − 𝑨𝑶𝑳𝑹𝒇 ⟹ 𝒊
=
𝑽𝟎 𝟏 + 𝑨𝑶𝑳
𝑹𝟎 − 𝑨𝑶𝑳𝑹𝒇

Practical Inverting Amplifier
• Also by KVL
𝑽𝒊 = 𝒊 𝑹𝟏 + 𝑹𝒇 + 𝑽𝟎 ⟹ 𝑽𝒊 =
𝑽𝟎 𝟏+𝑨𝑶𝑳
𝑹𝟎−𝑨𝑶𝑳𝑹𝒇
𝑹𝟏 + 𝑹𝒇 + 𝑽𝟎
𝑨𝑪𝑳 =
𝑽𝟎
𝑽𝒊
=
𝑹𝟎 − 𝑨𝑶𝑳𝑹𝒇 + 𝑹𝟏 + 𝑹𝒇 + 𝑨𝑶𝑳𝑹𝟏 + 𝑨𝑶𝑳𝑹𝒇
𝑨𝑪𝑳 =
𝑽𝟎
𝑽𝒊
=
𝑹𝟎 + 𝑹𝒇 + 𝑹𝟏 𝟏 + 𝑨𝑶𝑳
𝒊𝒇 𝑨𝑶𝑳 ≫ 𝟏 ⟹ 𝑨𝑶𝑳𝑹𝟏 ≫ 𝑹𝟎 + 𝑹𝒇 ⟹ 𝑨𝑪𝑳 =
𝑹𝒇
𝑹𝟏

Input Resistance (Rif)
From figure 𝑹𝒊𝒇 =
𝑽𝒅
𝒊
⟹ 𝑽𝒅 = 𝑹𝒊𝒇𝒊
• by loop equation
𝑽𝒅 + 𝒊 𝑹𝒇 + 𝑹𝟎 + 𝑨𝑶𝑳𝑽𝒅 = 𝟎
⟹ 𝟏 + 𝑨𝑶𝑳 𝑽𝒅 + 𝒊 𝑹𝒇 + 𝑹𝟎 = 𝟎
⟹ 𝟏 + 𝑨𝑶𝑳 𝑹𝒊𝒇𝒊 + 𝒊 𝑹𝒇 + 𝑹𝟎 = 𝟎
⟹ 𝑹𝒊𝒇 =
𝑹𝒇+𝑹𝟎
𝟏+𝑨𝑶𝑳

Output Resistance (Rof)
Rof (without RL) can be calculated from Voc & Isc
Figure can modified as
• Under short circuit
𝒊𝑨 =
𝑽𝒊 − 𝟎
𝑹𝟏 + 𝑹𝒇
, 𝒊𝑩 =
𝑨𝑶𝑳𝑽𝒅
𝑹𝟎
𝒂𝒍𝒔𝒐 𝑽𝒅 = −𝑹𝒇𝒊𝑨 ⟹ 𝒊𝑩 = −
𝑨𝑶𝑳
𝑹𝟎
𝑹𝒇𝒊𝑨
𝒇𝒓𝒐𝒎 𝑭𝒊𝒈𝒖𝒓𝒆 𝒊𝒔𝒄 = 𝒊𝑨 + 𝒊𝑩
=
𝑽𝒊
𝑹𝟏 + 𝑹𝒇
−
𝑨𝑶𝑳𝑹𝒇𝒊𝑨
𝑹𝟎
⟹ 𝒊𝒔𝒄 = 𝒊𝑨 + 𝒊𝑩 =
𝑽𝒊
𝑹𝟏 + 𝑹𝒇
−
𝑨𝑶𝑳𝑹𝒇
𝑽𝒊
𝑹𝟏 + 𝑹𝒇
𝑹𝟎
⟹ 𝒊𝒔𝒄 =
𝑽𝒊
𝑹𝟏 + 𝑹𝒇
𝑹𝟎
= 𝑽𝒊
𝑹𝟎 𝑹𝟏 + 𝑹𝒇
𝒘𝒌𝒕 𝑹𝒐𝒇 =
𝑽𝒐𝒄
𝒊𝒔𝒄
, 𝑨𝑪𝑳 =
𝑽𝒐𝒄
𝑽𝒊
⟹ 𝑽𝒐𝒄 = 𝑨𝑪𝑳𝑽𝒊
⟹ 𝑹𝒐𝒇 =
𝑨𝑪𝑳𝑽𝒊
𝑽𝒊
=
𝑨𝑪𝑳

Non-Inverting Amplifier
• For the circuit, Vi given to non-inv,
with feedback, the circuit amplifier
without inverting input signal
• It is the negative feedback system
As 𝑽𝒅 = 𝟎, ⟹ 𝑽 𝒂𝒕 𝒂 𝒊𝒔 𝑽𝒊
• Rf, R1 forms as potential divider
∴ 𝑽𝒊 =
𝑽𝟎
𝑹𝟏 + 𝑹𝒇
𝑹𝟏
⟹
𝑽𝟎
𝑽𝒊
=
𝑹𝟏+𝑹𝒇
𝑹𝟏
= 𝟏 +
𝑹𝒇
𝑹𝟏
⟹ 𝑨𝑪𝑳 =
𝑽𝟎
𝑽𝒊
= 𝟏 +
𝑹𝒇
𝑹𝟏
• for unity gain Rf, R1 are adjusted.

Practical Non-Inverting Amplifier
by KCL at input node
𝑽𝒊 − 𝑽𝒅 𝒀𝟏 + 𝑽𝒅𝒀𝒊 + 𝑽𝒊 − 𝑽𝒅 − 𝑽𝟎 𝒀𝒇 = 𝟎
⟹ − 𝒀𝟏 + 𝒀𝒊 + 𝒀𝒇 𝑽𝒅 + 𝒀𝟏 + 𝒀𝒇 𝑽𝒊 = 𝑽𝟎𝒀𝒇 → (𝟏)
similarly at output node KCL gives
𝑽𝒊 − 𝑽𝒅 − 𝑽𝟎 𝒀𝒇 + 𝑨𝑶𝑳𝑽𝒅 − 𝑽𝟎 𝒀𝟎 = 𝟎
− 𝒀𝒇 − 𝑨𝑶𝑳𝒀𝟎 𝑽𝒅 + 𝑽𝒊𝒀𝒇 = 𝒀𝒇 + 𝒀𝟎 𝑽𝟎 → 𝟐
𝟐 ⟹ 𝑽𝒅 =
𝑽𝒊𝒀𝒇− 𝒀𝒇+𝒀𝟎 𝑽𝟎
𝒀𝒇−𝑨𝑶𝑳𝒀𝟎
→ 𝟑
𝟑 𝒊𝒏 𝟏 ⟹ − 𝒀𝟏 + 𝒀𝒊 + 𝒀𝒇
𝑽𝒊𝒀𝒇− 𝒀𝒇+𝒀𝟎 𝑽𝟎
𝒀𝒇−𝑨𝑶𝑳𝒀𝟎
+ 𝒀𝟏 + 𝒀𝒇 𝑽𝒊 = 𝑽𝟎𝒀𝒇
⟹
𝑽𝟎
𝑽𝒊
=
−𝒀𝒊𝒀𝒇−𝑨𝑶𝑳𝒀𝟎 𝒀𝟏+𝒀𝒇
− 𝒀𝟏𝒀𝒇+𝒀𝟏𝒀𝟎+𝒀𝒊𝒀𝒇+𝒀𝒊𝒀𝟎+𝒀𝒇𝒀𝟎+𝑨𝑶𝑳𝒀𝟎𝒀𝒇
Practical non-inverting amplifier
by creating the equivalent circuit

The Non-Inverting Amplifier
⟹
𝑽𝟎
𝑽𝒊
=
−𝒀𝒊𝒀𝒇−𝑨𝑶𝑳𝒀𝟎 𝒀𝟏+𝒀𝒇
− 𝒀𝟏𝒀𝒇+𝒀𝟏𝒀𝟎+𝒀𝒊𝒀𝒇+𝒀𝒊𝒀𝟎+𝒀𝒇𝒀𝟎+𝑨𝑶𝑳𝒀𝟎𝒀𝒇
⟹
𝑽𝟎
𝑽𝒊
=
𝑨𝑶𝑳𝒀𝟎 𝒀𝟏 + 𝒀𝒇 + 𝒀𝒊𝒀𝒇
𝑨𝑶𝑳 + 𝟏 𝒀𝟎𝒀𝒇 + 𝒀𝒇 𝒀𝟏 + 𝒀𝒊 + 𝒀𝟎 𝒀𝟏 + 𝒀𝒊
⟹
𝑽𝟎
𝑽𝒊
=
𝑨𝑶𝑳𝒀𝟎 𝒀𝟏+𝒀𝒇 +𝒀𝒊𝒀𝒇
𝑨𝑶𝑳+𝟏 𝒀𝟎𝒀𝒇+ 𝒀𝟏+𝒀𝒊 + 𝒀𝒇+𝒀𝟎
𝒊𝒇 𝑨𝑶𝑳 → ∞ ⟹ 𝑨𝟎𝑳 =
𝑽𝟎
𝑽𝒊
=
𝑨𝑶𝑳𝒀𝟎 𝒀𝟏+𝒀𝒇
𝑨𝑶𝑳𝒀𝟎𝒀𝒇
= 𝟏 +
𝒀𝟏
𝒀𝒇
𝑨𝟎𝑳 =
𝑽𝟎
𝑽𝒊
= 𝟏 +
𝑹𝑭
𝑹𝟏

Voltage Follower
• Substitute 𝑹𝟏 = ∞, 𝑹𝒇 = 𝟎 in Non-Inverting Amplifier, the modified circuit is
𝒘𝒌𝒕 𝑨𝑪𝑳 =
𝑽𝟎
𝑽𝒊
= 𝟏 +
𝑹𝑭
𝑹𝟏
⟹ 𝑨𝑪𝑳 =
𝑽𝟎
𝑽𝒊
= 𝟏 ⟹ 𝑽𝟎 = 𝑽𝒊
• Then O/P Voltage = I/P Voltage (in magnitude and phase)
• Output follows input exactly, it is called as voltage follower
• For unity gain, I/P impedance is very high, O/P impedance is zero, so draws
negligible current from the source.

Differential Amplifier
• The circuit amplifies the difference between two signals is called difference (or)
differential amplifier.
• Useful in instrumentation circuits
• a,b are at same potential ‘V3’
• KCL at node ‘a’ & ‘b’
𝑽𝟑−𝑽𝟐
𝑹𝟏
+
𝑽𝟑−𝑽𝟎
𝑹𝟐
= 𝟎,
𝑽𝟑−𝑽𝟏
𝑹𝟏
+
𝑽𝟑
𝑹𝟐
= 𝟎
⟹ 𝑽𝟑
𝟏
𝑹𝟏
+
𝟏
𝑹𝟐
− 𝑽𝟐
𝟏
𝑹𝟏
=
𝑽𝟎
𝑹𝟐
, 𝑽𝟑
𝟏
𝑹𝟏
+
𝟏
𝑹𝟐
− 𝑽𝟏
𝟏
𝑹𝟏
= 𝟎
⟹ 𝑽𝟎 =
𝑹𝟐
𝑹𝟏
𝑽𝟏 − 𝑽𝟐
• Useful for detecting very small differences in signals.

Difference Mode and Common Mode Gains
𝑽𝟎 =
𝑹𝟐
𝑹𝟏
𝑽𝟏 − 𝑽𝟐
• If 𝑽𝟏 = 𝑽𝟐 ⟹ 𝑽𝟎 = 𝟎 for ideal case
• In practical some small amount exist called common mode component.
• The V0 not only depends on Vd also depends on average voltage of
input called common mode signals VCM ⟹ 𝑽𝑪𝑴 =
𝑽𝟏+𝑽𝟐
𝟐
• Gain at the output wrt +ve terminal is slightly different in magnitude
to that of the –ve terminal
𝑽𝟎 = 𝑨𝟏𝑽𝟏 + 𝑨𝟐𝑽𝟐
– A1 & A2 are the voltage amplification for input 1 & 2, with input (opposite/
remaining) is grouded

Difference Mode and Common Mode Gains
Since 𝑽𝑪𝑴 =
𝑽𝟏+𝑽𝟐
𝟐
, 𝑽𝒅 = 𝑽𝟏 − 𝑽𝟐
𝑽𝟏 = 𝑽𝑪𝑴 +
𝟏
𝟐
𝑽𝒅, 𝑽𝟐 = 𝑽𝑪𝑴 −
𝟏
𝟐
𝑽𝒅
𝑽𝟎 = 𝑨𝟏𝑽𝟏 + 𝑨𝟐𝑽𝟐 = 𝑨𝟏 𝑽𝑪𝑴 +
𝟏
𝟐
𝑽𝒅 + 𝑨𝟐 𝑽𝑪𝑴 −
𝟏
𝟐
𝑽𝒅
𝑽𝟎 = 𝑽𝑪𝑴 𝑨𝟏 + 𝑨𝟐 +
𝑽𝒅
𝟐
𝑨𝟏 − 𝑨𝟐 ⟹ 𝑽𝟎 = 𝑽𝑪𝑴𝑨𝑪𝑴 + 𝑽𝒅𝑨𝑫𝑴
⟹ 𝑨𝑪𝑴 = 𝑨𝟏 + 𝑨𝟐, 𝑨𝑫𝑴 =
𝑨𝟏 − 𝑨𝟐
𝟐
• Voltage gain for the difference mode signal is ADM
• Voltage gain for the common mode signal is ACM

Common Mode Rejection Ratio
• The relative sensitivity of an op-amp to a
difference signal as compared to a common
mode signal is called “Common Mode
Rejection Ratio”(CMRR)
𝝆 =
𝑨𝑫𝑴
𝑨𝑪𝑴
𝒅𝑩
• Higher the value of CMRR better is the op-
amp

DC Characteristics
• Op-amp responds equally well to both ac and dc input voltage
(but practically not)
• ideal op-amp draws no current from source also Vo (independent
of temperature)
• Practically two inputs responds differently due to mismatch in
transistors
• the non-ideal dc characteristics that add error components to
the dc output voltage are
1. Input bias current
2. Input Offset current
3. Input Offset voltage
4. Thermal Drift

Input Bias Current
• Op-Amp’s input is differential amplifier made up of BJT (or)
FET, input transistors have to be biased, ie., current to base by
external circuit
• Practically small value of dc current is made to bias the input
transistors
• IB
+ & IB
- are base currents entering to inv, noninv terminals and
IB
- ≠ IB
+ due to internal imbalances
• manufacturers specify 𝑰𝑩 =
𝑰𝑩
+
+𝑰𝑩
−
𝟐
• Consider

Input Bias Current
• Input Vi=0; VO=0;
• We find the output voltage is offset by 𝑽𝟎 = 𝑰𝑩
−
𝑹𝒇
– Example: 741 opamp with Rf = 1MΩ, IB = 500nA (for BJT), V0=500nA
X 1MΩ = 500mV
• But signal levels are measured in mV
• Can be compensated by RComp has been added between
non-Inv input to ground
Offset voltage - the voltage
that must be applied to the input
to cause the output to be zero

Input Bias Current
• By KVL −𝑽𝟏 + 𝟎 + 𝑽𝟐 − 𝑽𝟎 = 𝟎 ⟹ 𝑽𝟎 = 𝑽𝟐 − 𝑽𝟏
• By selecting Rcomp → V2 can be cancelled with V1 then
V0=0;
𝑽𝟏 = 𝑰𝑩
+
𝑹𝑪𝒐𝒎𝒑 ⟹ 𝑰𝑩
+
=
𝑽𝟏
𝑹𝑪𝒐𝒎𝒑
⟶ (𝟏)
• at node ‘a’ Vi = 0, Va = -V1
𝑰𝟏 =
𝑽𝟏
𝑹𝟏
& 𝑰𝟐 =
𝑽𝟐
𝑹𝒇
• for compensation V0=0 (When Vi = 0)
∴ 𝑽𝟐 = 𝑽𝟏 ⟹ 𝑰𝟐 =
𝑽𝟏
𝑹𝒇
• KCL at node ‘a’
𝑰𝑩
−
= 𝑰𝟐 + 𝑰𝟏 =
𝑽𝟏
𝑹𝒇
+
𝑽𝟏
𝑹𝟏
= 𝑽𝟏
𝑹𝟏 + 𝑹𝒇
𝑹𝟏𝑹𝒇
⟶ 𝟐
• Assume, 𝑰𝑩
−
= 𝑰𝑩
+
⟹ 𝑽𝟏
𝑹𝟏+𝑹𝒇
𝑹𝟏𝑹𝒇
=
𝑽𝟏
⟹ 𝑹𝑪𝒐𝒎𝒑 =
𝑹𝟏𝑹𝒇
𝑹𝟏 + 𝑹𝒇
= 𝑹𝟏 𝑹𝒇
• To compensate bias current 𝑹𝑪𝒐𝒎𝒑 = 𝑹𝟏 𝑹𝒇

Input Offset Current
𝒘𝒌𝒕 𝑽𝟏 = 𝑰𝑩
+
𝑹𝑪𝒐𝒎𝒑 & 𝑰𝟏 =
𝑽𝟏
𝑹𝟏
KCL at ‘a’
𝑰𝟐 = 𝑰𝑩
−
− 𝑰𝟏 = 𝑰𝑩
−
−
𝑰𝑩
+
𝑹𝟏
𝑽𝟎 = 𝑰𝟐𝑹𝒇 − 𝑽𝟏 = 𝑰𝟐𝑹𝒇 − 𝑰𝑩
+
𝑽𝟎 = 𝑰𝑩
−
−
𝑰𝑩
+
𝑹𝟏
𝑹𝒇 − 𝑰𝑩
+
𝑹𝑪𝒐𝒎𝒑 = 𝑹𝒇 𝑰𝑩
−
+ 𝑰𝑩
+
𝑽𝟎 = 𝑹𝒇𝑰𝑶𝑺
• Bias current compensation will work when 𝑰𝑩
+
= 𝑰𝑩
−
• Due to transistors are not identical, there is always small difference between
IB
+ & IB
- , This is called “Offset Current IOS” 𝑰𝑶𝑺 = 𝑰𝑩
+
− 𝑰𝑩
−
• for BJT , IOS = 200nA; for FET, IOS = 10PA
• even for bias current compensation offset current produces output voltages

Input Offset Current
even with “bias current Compensation”
• When Rf = 1MΩ, IOS 200nA (for BJT), output offset voltage V0 = 1MΩ X
200nA = 200mV.
• The effect of offset current ‘IOS’ can be minimized by keeping Rf small
• For good gain R1 & Rf should be too high
• Solution is using T – feedback network (This allow large Rf by keeping R1
as low)
• By T to π conversion
𝑹𝒇 =
𝑹𝒕
𝟐
+ 𝟐𝑹𝒕𝑹𝒔
𝑹𝒔
• To design ‘T’ network first select 𝑹𝒕 ≪
𝑹𝒇
𝟐
then 𝑹𝒔 =
𝑹𝒕
𝟐
𝑹𝒇−𝟐𝑹𝒕

Input Offset Voltage
• Inspite of the above compensation, it is found that VO is still not be zero with Vi
= 0.
• One may have to apply a small voltage at the input terminals to make V0 = 0
• This is called “Input offset voltage VOS”
∴ 𝑉2 =
𝑅1
𝑅1 + 𝑅𝑓
𝑉0
⟹ 𝑉0 =
𝑅1 + 𝑅𝑓
𝑅1
𝑉2 = 1 +
𝑅𝑓
𝑅1
𝑉2
𝑉0𝑆 = 𝑉𝑖 − 𝑉2 & 𝑉𝑖 = 0
𝑉0 = 1 +
𝑅𝑓
𝑅1
𝑉𝑂𝑆

Total output offset voltage (VOT)
• VOT is less than the VOS by Input bias current or
input bias voltage, because VOS, IB counld be either
+ve (or) –ve WRT ground
• VOT of any inver and noninv amplifier without any
compensation technique is
𝑽𝟎𝑻 = 𝟏 +
𝑹𝒇
𝑹𝟏
𝑽𝑶𝑺 + 𝑹𝒇𝑰𝑩
• offset null pin connection
• manufacturers recommendation
based on datasheets
• If null off set pins are not available external
balancing technique

Total output offset voltage (VOT)
• But due to RComp
𝑽𝟎𝑻 = 𝟏 +
𝑹𝒇
𝑹𝟏
𝑽𝑶𝑺 + 𝑹𝒇𝑰𝑶𝑺

Thermal Drift
• IB, IOS, VOS are change with temperature
• A circuit carefully nulled at 250C may not remain, when
temperature rise to 350C, is called drift.
• Offset current drift expressed in nA/0C, offset voltage drift
expressed in mV/0C
1). IC have to be away from heat
2). Forced air cooling can be used.

AC Characteristics
Frequency Response
• ideally op-amp will have infinite
bandwidth, ie., open loop gain is 90dB
• Practically it decreases at high frequency
• There must be a capacitive component in
equivalent circuit due to physical
characteristics of device (BJT/FET)
• Op-amp with one break frequency all
capacitances can be represented by a
single C as
DC characteristics will affect SS DC response
For small signal sinusoidal (ac) application has to know the ac characteristics as
the frequency response and slew rate.

Frequency Response
Where, 𝒇𝟏 =
𝟏
𝟐𝝅𝑹𝟎𝑪
corner frequency (or)
upper 3dB frequency
𝑨 =
𝑨𝑶𝑳
𝟏 +
𝒇
𝒇𝟏
𝟐
, 𝝋 = − 𝒕𝒂𝒏−𝟏
𝒇
𝒇𝟏
𝑨 , 𝝋 is function of frequency
• High frequency model with single corner frequency
• For one pole RoC, One -20dB decade comes into effect
• Open loop voltage gain is
𝑽𝑶 =
−𝒋𝑿𝑪
𝑹𝟎−𝒋𝑿𝑪
𝑨𝑶𝑳𝑽𝒅 ⟹ 𝑨 =
𝑽𝑶
𝑽𝒅
=
𝑨𝑶𝑳
𝟏+𝟐𝝅𝒇𝑹𝟎𝑪
⟹ 𝑨 =
𝑨𝑶𝑳
𝟏+𝒋
𝒇
𝒇𝟏

Frequency Response
• It is seen that
𝟏). 𝒇𝒐𝒓 𝒇 ≪ 𝒇𝟏 𝑨 = 𝟐𝟎 𝒍𝒐𝒈 𝑨𝑶𝑳
𝟐). 𝒂𝒕 𝒇 = 𝒇𝟏, 𝑨 = 𝟑𝒅𝑩 𝒅𝒐𝒘𝒏 𝒇𝒓𝒐𝒎 𝒅𝒄 𝒗𝒂𝒍𝒖𝒆 𝑨𝑶𝑳
f1 – is called corner frequency
𝟑). 𝒂𝒕 𝒇
≫ 𝒇𝟏 𝒈𝒂𝒊𝒏 𝒓𝒐𝒍𝒍𝒔 𝒐𝒇𝒇 𝒂𝒕 𝒓𝒂𝒕𝒆 𝒐𝒇 − 𝟐𝟎𝒅𝑩/𝒅𝒆𝒄𝒂𝒅𝒆
 at corner frequency f1 the phase angle is -450
 at infinite frequency the phase angle is -900
 Maximum 900 phase change in op-amp with single capacitor
• In ‘S’ Domain
𝑨 =
𝑨𝑶𝑳
𝟏 + 𝒋
𝒇
𝒇𝟏
=
𝑨𝑶𝑳
𝟏 + 𝒋
𝝎
𝝎𝟏
=
𝑨𝑶𝑳𝝎𝟏
𝝎𝟏 + 𝒋𝝎
=
𝑨𝑶𝑳𝝎𝟏
𝒔 + 𝝎𝟏

Frequency Response
• A practical op-amp, has number of stages and each produces a capacitive
component
• Number of RC pole equal to number os break frequency (Example: 3break
frequency)
𝑨 =
𝑨𝑶𝑳𝝎𝟏𝝎𝟐𝝎𝟑
𝒔 + 𝝎𝟏 𝒔 + 𝝎𝟐 𝒔 + 𝝎𝟑

Stability of an Op-Amp
• Let us consider the effect of feedback on op-amp frequency response
• Consider an op-amp
• for inv amplifier V1=0
• for –ve feedback the closed loop transfer
function as
𝑨𝑪𝑳 =
𝑨
𝟏 + 𝑨𝜷
A → open loop voltage gain
β → feedback ratio
• Characteristics equation (1+Aβ) =0 then the circuit is stable
𝟏 + 𝑨𝜷 = 𝟎 ⟹ 𝟏 − −𝑨𝜷 = 𝟎 ⟹ −𝑨𝜷 = 𝟏 ⟹ 𝑨𝜷 = 𝟏
∠ −𝑨𝜷 = 𝟎 (𝒐𝒓 𝒎𝒖𝒍𝒕𝒊𝒑𝒍𝒆 𝒐𝒇 𝟐𝝅)
∠ 𝑨𝜷 = 𝝅 (𝒐𝒓 𝒐𝒅𝒅 𝒎𝒖𝒍𝒕𝒊𝒑𝒍𝒆 𝒐𝒇 𝝅)

• Circuit is resistive feedback, does not produce any phase shift
• In inversion mode phase shift → 1800 (at low frequency)
– One RC pair Phase shift → -900 (at high frequency)
– For two RC pair phase shift → -1800
– Total phase shift =0 at high frequency
• Oscillation begins → instability
– Instability means 𝟏 + 𝑨𝜷 < 𝟏 ⟹ 𝑨𝜷 < 𝟎 ⟹ 𝑨𝑪𝑳 > 𝑨
• The phase contribution at R in feedback network is zero
– at low frequency
𝑨 = 𝟎 ⟹ 𝑨𝜷 > 𝟎 ⟹ 𝑨𝑪𝑳 < 𝑨 system is stable
– at high frequency
• A have 3 corner frequency (or RC pair),
• open loop gain A → -2700 phase shift,
• Aβ → -ve → instability.

Closed Loop
Gain
Decade Rate Phase Shift Stable Unstable
Point A 10,000(or) 80dB -20dB -900 Stable
Point B 1000 (or) 60dB -40dB -1800 Unstable
Point C 20dB -60dB -2700 Unstable
• for stable operation rate of closure between ACL & open loop curve
should be -20dB/decade

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