Motivation for Analog IC Design

7/26/2019 Motivation for Analog IC Design

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Analog Integrated Circuit Design

Prof. Dr. Nagendra Krishnapura

Department of Electrical Engineering

Indian Institute of Technology, Madras

ecture ! "Course Introduction# Negati$e %eed&ac' Control

Hello everyone. Welcome to the course analog integrated circuit design. It is a video course

under the national program for technology enhanced learning. To introduce myself, I am

Nagendra Krishnapura, I am from the department of the electrical engineering at IIT Madras.

I have been woring here for ! years. "ou can find my website here and also, my email here.

The website has some reference material, problem sets from other analog courses which you

may find useful and other resources. Now, I will #ust give $uic introduction to this course.

This course is entitled analog integrated circuit design.

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'o, first we need to understand why analog integrated circuit design- Why we study these

things at all- 'o, if you loo at any modern signal processing system, it loos something lie

this. onceptually it can be depicted this way. It typically has core of digital signal

processing, and digital signal processing is used because digital storage is easy and digital

processing is very easy. To interface with the real world, for instance, with the voice signal,

as I am speaing or with the radio signals, you have to interface with the analog world. /ll

the real world signals are analog signals lie the voice or the radio signal.


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'o, you receive the audio or the radio signals through what are nown as sensors, and convert

them to the electrical signals and convert them to do some analog signal processing, and

convert them to the digital domain. 'imilarly, on the other side, you tae the digital signals2

convert them to analog, do some analog signal processing and actuate the natural world

signals. This could be for instance, the signal coming out of your loudspeaers when you are

hearing my lectures.

'o, in this entire system which is rather comple3, every system today can be represented lie

this. It could be a music player, and then the digital signal processing consists of the storage

and the processing inside the player. It could be a mobile phone. In a system lie this, "ou

will have an outer layer of an analog signal processing and a inner digital core, and it is in the

interface electronics that you will use analog circuits. "ou will use analog circuits for signal

conditioning. "ou also use analog circuits for analog to digital and digital to analog

conversion. 'o, the circuit that we will be studying in this course will be related to this circuit

that you will be using in this interface blocs.

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'o, lie I mentioned where do we use analog circuits in modern system 6n 78'I chips- "ou

have an analog to digital conversion that is done by an analog circuit. We have digital to

analog conversion. 'imilarly, that is an analog bloc, and you have amplification which for

instance could be an audio amplifier. "ou have a small audio signal, you amplified to the

level that it can be driven by a loudspeaer, and that is done by analog circuits and you also

have signal processing circuit at high fre$uencies, where it is more convenient to do it using

analog than digital2 and these two are common to a lot of circuits. "ou have power

management which means that you have voltage references, voltage regulators.

I am sure all of you have used the power supplies in the lab at some point. They give you

precisely ad#ustable 9 voltages and they are generated using voltage references, and voltage

regulators and finally, you have oscillators which for instance in a digital system also, you

need a cloc and that is given by the oscillators and you use a phase loc loop to precisely

ad#ust the fre$uency of oscillators. If you loo at the last two which I have highlighted here,

they are found even on many so:called digital I'. ;or instance, you will have power

management blocs, voltage references and regulators and oscillators and


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'o, we will be studying these circuits as well in this course. =ust to give you some $uic

e3amples, I have taen a photograph of a chip which was published in a conference, few

years bac. The chip itself is an image sensor, but you see that you have the image sensing

area in the middle, you have voltage regulator on top, which is an analog circuit. "ou have

what are nown as sensing circuit on the top which are also analog circuit. 'imilarly, you

have timing generators which has oscillators and other clocs which is an analog circuit and

you have analog to digital converter which is also an analog circuit.

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=ust to tae another e3ample, here is a wireless 8/N transceiver. This is what would be in

your wireless 8/N chips inside your laptop.


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'o, in this also, you see that there are number of blocs, and each of these blocs denotes a

different analog circuit. "ou have high:fre$uency power amplifiers here and here, and you

have a fre$uency synthesi>er which generates the carrierfre$uency very precisely in this part,

and you have a bias circuitry over here and yet another e3ample is a 9 &/M which we

mostly thin of as a completely digital blocs, but there are I?6 circuits and there are

decoders etc. which form and sense amplifier, which form analog circuitry inside a 9 &/M.

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'o, these are some e3ample where analog circuits are used in a modern 78'I chips. with that

bacground 8et us move onto the ne3t thing. and one of the other thing is what can you do

after you learn analog ic design. If you loo at analog ic design in India, there is a number of

companies which are starting analog circuit design activity which includes multinationals and

Indian start:ups. 'o, there is a big demand for silled designers in the area of analog

integrated circuit design.

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'o, it is not only interesting, it is also a profitable activity for many of you. 'o, with that

bacground, we now now why it might be interesting to learn analog ic design. 'o, let us

loo at what are we going to do in this course. 'o, here is the list of the course goals. @asic

goals can be summari>ed in the first line which says that you learn to design negative

feedbac circuits on M6' integrated circuits.

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'o, what is negative feedbac- "ou use negative feedbac for controlling the output in some

way. We will come to the details of this as we go along. /nd using that, you will learn to

mae amplifiers, voltage references, voltage regulators, other biasing circuit. We will also seehow to mae phrase loc loops and then, we will see some application circuit such as filters.


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/s we go through the course, we will learn about the details of all of these blocs, and these

are the prere$uisites for the course, that is, these are the things that you need to now if you

want to understand what is going on in this course.

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'o, first of all, we need to now circuit analysis in both small signal and large signal

domains. I am sure you have learned these things in your basic circuit course, and you willneed to be fluent with laplace transforms which is used for fre$uency response, analysis of

circuits, sinusoidal steady states response, bode plots and some nowledge of differential

e$uations. These are re$uired for analy>ing circuits which have capacitors and inductors. In

addition to this, you need to now something about ideal opamp circuits. @asically you need

to now how to analy>e ideal opamp circuits, and have some idea of the non:idealities of the

opamp.

We will be discussing these in detail in this course and you will need to now single transistor

amplifiers blocs lie common source, common emitter, common collector, and common

base. 'imilarly, common gate and common drain amplifiers and also differential pairs

because we will be using these basic amplifier blocs to mae our more complicated circuits.

'o, here is a slightly more detailed overview of the course contents. The first part of the

course we will deal with negative feedbac amplifiers.

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'o, this means, first we will see how to mae an amplifier using negative feedbac in the first

place. When you use negative feedbac, as you are familiar from control system courses, you

will run into constants with stability and you will have to fre$uency compensates the negative

feedbac loop. Those things we will go through and will see how to mae negative feedbac

circuits using opamps. We will also see various levels of opamps models. 6ne of the things

that you will learn in this course is that you do not use a single model for every occasion. "ou

will use models with varying degrees of sophistication for different occasions. 'o, we will see

opamp models of various levels.

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Then, after we are learning about opamps at bloc level, we will go to how to mae the

opamps at the transistor level. 'o, in particular we will be looing at how to mae opamps on

a M6' integrated circuit. ;or this we will first loo at what components are available on

M6' integrated circuits, so that we can mae opamps with it and we also loo at concepts

lie device model that is small signal 9 models of the components of the M6' I.

'imilarly, 9 large signal model, / small signal models and two thins perhaps unfamiliar

to you mismatch and noise models, and using these components, we will mae a single stage

opamp what are nown as cascode opamps as well as multi stage opamp with fre$uency

compensation.

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We will also loo at what are nown as fully differential circuits. These are the circuits where

every signal are represented by a pair of signal e$ual and opposite to each other, and studying

this, we will come across differential and common mode half circuit, common mode feedbac

circuits and we will mae fully differential miller compensated opamp, and a fully

differential feed forward compensated opamp. These are #ust varieties of the opamps which

are suitable for use in different applications.


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Then, we will also loo at the phase loced loop which is really important building bloc of

analog integrated circuit. ;irst, we will try to mae fre$uency multiplication circuit using

negative feedbac #ust lie we mae an amplifier using negative feedbac. That will lead us

to a phase loced loop, and it turns out there are two types of phase loced loop. The type II

loop is of practical importance. Then, we loo at the components of the phase loced loop

which is the oscillator and then, we also loo at the basics of phase noise and also, loo at

different noise transfer function inside a phase loc loop.

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'o, as I mentioned earlier, we will also be going through designs of different opamps which

are listed here. 'ingle stage opamp, folded and telescopic cascade opamps, two stage opamp,

and fully differential opamp and common mode feedbac and we will loo at some

application circuits such as bandgap reference and constant gm bias generation.

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This lists the applications and some more details. These are the applications we will belooing at. / bandgap reference is a ind of circuit that maintains a constant voltage

regardless of the temperature at which it is operating. We will see later that most circuits are

sensitive to the temperature, but this band gap reference circuits put out a voltage which is

$uite insensitive to temperature. We will loo at how to mae constant current and constant

gm bias. This is for biasing transistors.

We will loo at continuous time filters and then, switched capacitor filters also. 'o, that is

about what is going to be in this course. 6f course, all of that will be covered in great detail in

the rest of the classes. Now, if you loo at the title, it says analog integrated circuit design.

Now, what is designed and how do I learn it- Many of you perhaps asing this $uestion to

yourselves.


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Here is a $uic distinction between design and analysis. Cssentially, design is creating

something that does not e3ist here whereas, analysis relates to studying something that

already e3ists. 'o, because of this there is some difference between the ways you approach

design and analysis, and typically analysis is easier.

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Dsually what happens is you study some method of analysis and then, you apply it. There is a

se$uence of steps you apply that and you will be able to analy>e the circuit or system or

whatever that is you are analy>ing. Now, to be able to design, you have to now a little more


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than that. of course you have to now analysis that is prere$uisites. It is necessary, but not

sufficient, but in addition to this, to be able to design something, you will need to have

multiple ways of looing at building blocs because you do not now e3actly in what

combination you have to put things together to be able to design. "ou have to be comfortable

with trial and error approaches. It is not a fi3 se$uence of steps lie analysis, but maybe

sometimes you try some combinations if it does not wor, you try some other combinations

and it should be guided by the nowledge that you have already ac$uired with analysis. "ou

should also be comfortable with appro3imations, and we will see down this course that we

will use appro3imation a lot because in many real world situations, if you try to calculate the

e3act answer, the answer loo very complicated and more importantly does not lead to any

insight. Now, for design what is needed is insight. "ou may not need to now the e3act

answer, but you need to now which way the answer is going if you change a particular

variable. ;or that appro3imation are crucial.

Now, it loos as though the appro3imation is the shortcut to a solution. It is not. /ctually

maing a #udicious appro3imation is more difficult than doing e3act analysis using the fi3

se$uence of steps. This is because you do not now e3actly what appro3imation is good and

what appro3imation is valid in a particular situation. That you have to #udge based on the

situation, you are analy>ing. /nd you also have to be able to thin about situation intuitively.

Intuitively means that you have to be able to get an idea of the answer without going through

the complete analysis of the situations and of course, last three are e3tremely important for

creativity.

"ou have to be curious about what you are studying and then, you have to have an open mind

when you coming up with your solution and of course, you have to be through. That is, you

cannot design something that meet one particular aspect and then, ignore everything else.

That will be a very bad design. ;or a good design, you have to thoroughly investigate every

possible implication of the design.

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I will #ust give a $uic word about intuition. Now, sometimes intuitive thining is confused

with sloppy thining. That is, you do not thin through the problem thoroughly that is not

what it means. What it means is basically when you loo at a new problem, you try to lets I

guess or analy>e the problem without actually going through every step of the analysis. Now,

how do you do this- "ou can relate the problem to the other problem which you have already

solved.

This is the very common thing that we do. "ou loo at a problem and then, you say this is

e3actly what the other problem that I solved yesterday and then, you analy>e it using the

same method, and sometimes you use some boundary condition, dimensions checs to get an

idea of what the answer should loo lie, but without calculating the e3act answer. /nd

intuition is something you can build up.

'o, the way to do that is you solve many problems. When you solve a lot of problems, you

will start to get an idea of what the solution would loo lie. What is to be done here is not

mindless solving of hundreds of problem, but every time you solve a problem, you need to

thin about why the answer came out the way it is, it did. That is you get an answer and then,

you should thin about the answer and see how it came about. 'imilarly, when you solve

another circuit, you do the same. /fter you do this for a number of problems what happens is,

you will start recogni>ing the nature of the solution even before doing the analysis. That is

what I mean by intuition. /t least you should be able to guess the form of the solution before

applying full blown analysis. 'o, intuition and analysis complement each other.


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'o, after you get sufficiently e3perience, you will be able to intuitively tell the solution to

many things and there will be many situations where your intuition is not up to arriving at the

solution, but that is o and then you use your analytical sills to come up with the solution

and then, build up your intuition based on that one. 'o, that is about the contents of the course

and also, some insides into the design. Now, one $uic word on using these lectures that lot

of you will be using these on your computer, that is watching the lecture and it is somewhat

different from sitting in a classroom from where you interact with the professor directly.

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'o, one of the most important thing is #ust lie you do in class, you tae notes as you watch

because watching me solve the problem or do an analysis will not help you get the same sill.

"ou have to do it yourself because when you are watching the lecture, you may thin that I

understand this, I understand this, and so on, but the whole point of an analog I design

course is that you have to be able to go bac and do the design yourself, and the only way

you will be able to do that is if you do the analysis also as I do it or maybe pause the lecture

and do the analysis yourselves. The second important thing is you have to wor out all steps

in solving a problem. I mean you do not #ust watch me or somebody else solving it. "ou have

to wor out every step of it and then, more importantly thin about the answer you get in

every step.

'o, that is the way to build up your sill and doing all this, you can e3pect to spend about

three hours to understand one hour of this lecture. 'o, you have to be able to devote the time


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to be able to fully understand it. 'o, a lot of you will be watching this on the computer. 'o,

there will be facility to pause and repeat and so on.


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This is the general form of nodal analysis, that is the sum of current flowing out of every

branch e$ual the current source which is connected to that branch and in general, this current

can be non:linear functions of voltages, but the situation we are most familiar with and we

will be using the most, is linear circuit analysis, where each of these currents is a linear

function of voltage.

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'o, this type of set of e$uations can be solved by matri3 inversion. Here g lstands for the

conductance between node and l and gstands for the conductance between node and

ground. This depicts a situation where you have a number of conductance and current sourcesonly. as you now there are some special cases.


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If you have an independent voltage source, you cannot use the nodal $uestion, and that node

you have to use the e$uation for the voltage source. 'imilarly, for the voltage controlled

voltage source, you cannot use the node e$uation because you do not now what current is

flowing through the controlled source. Instead of that you use the e$uation for the controlled

voltage source. if you have a current controlled voltage source.

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'imilarly, you replace the e$uation of the node with something that relates to the current

controlled voltage source. ;inally, the situation that we will see that very often in integrated

circuit design because all transistors are voltage controlled current sources. The e$uation at

the node which has a voltage controlled current source will have an e3tra term which has to

be absorbed into the left:hand side. /s I mentioned, this is not meant to be a detailed

treatment of circuit analysis. This is #ust a refresher of what you have learnt earlier, and what

you should be fluent with, so that you can follow this course effectively.

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6ne last element which needs a special treatment is ideal opamp. If you have an ideal opamp,

again you cannot use the KirchhoffEs current law to usefully analy>e the output of the opamp

because again you do not now what current is flowing through output of the opamp. "ou

substitute that with an e$uation at the input of the opamp which says that the input terminal

of the ideal opamp are at the same voltage. , and l are input terminal and v:vle$ual to ) at

the input of the ideal opamp. 'o, with this you will get n e$uations in n unnowns and you

will be able to solve for all the variables in the circuit.

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How do you actually solve this system of e$uations- "ou have to invert the matri3, this g

matri3, to be able to get the solution.

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/gain, this is a $uic reminder that one of the ways of doing this is ramerEs rule where you

substitute the right hand side vector into the appropriate column of the matri3, and tae the

ratio of determinants.

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C3actly the same scheme holds when you have capacitors and inductors. The earlier situation

implied that we had only conductances or resistances. when you have capacitors and

inductors, e3actly the same situation arises e3cept that instead of conductance, they are

taling about admittances and you have to invert admittances matri3 to get the solution.

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Now, another thing that you need to refresh yourself on is 8aplace transform analysis for

linear systems. 'o, it is a very convenient tool for analysis. "ou now that a linear system,

linear time invariant system can be described by its transfer function H%s. In that case, if the

input is F%s, the output will be H%sF%s, and also, you now that if the input in the timedomain is est,the output will be H%sest. /nd this is most commonly used with sinusoidal


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steady:state. substituting sG# implies a sinusoid of fre$uency is applied to the input to the

linear time invariant system. 'o, if you have an input of F%#,the output will be

H%#F%#.

'o, if you apply an input e#twhich basically corresponds to the sinusoid of fre$uency , the

output will be H%#%which is a comple3 numbere#t. Now what happens in practice is you

apply a real sinusoid cos%t to the system. If you apply cos%t to a linear time invariant

system which has a transfer function H%s, the output will have a magnitude H%#, that is

the magnitude of transfer function at the fre$uency of the sinusoid and it will also be phase

shifted. It is cos%tJH%#, that is there is a phase shift and the amount of phase shift

e$uals the phase angle of the comple3 number H%# at the fre$uency of the sinusoid.

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Now, this is what is nown as a steady state solution. What it means, letEs say you apply

cos%t to the stable linear time invariant system, and wait for some time until all the

transients settle. The output that you get will be a sinusoid at the same fre$uency, and its

amplitude and phase will be changed by the transfer function of the linear time invariant

system. 'o, again please refresh your basics of sinusoidal, steady state solution, 8aplace

transform because again we will be using that widely in through this course.

'o, the transfer function H%s of any linear time invariant system can be put in this form,

where /dc is the dc gain and you have a numerator polynomial and a denominator

polynomial, and instead of describing it as a polynomial lie this, it can also be represented as


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a product of terms where each terms has the corresponding roots which are >eros for the

numerator and poles for the denominators.

I have taen a special case, where there is a single pole at the origin because this is a case that

we will be using $uite heavily with our negative feedbac system. 'o, in this case H can be

represented as a term u?s. This is a dimensional term and it has a pole at the origin that is s G

) and then, there can be a product of >eros at numerator and product of terms containing

poles in the denominator, and as we now for stability, all of the poles


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Now, one of the other things about time domain analysis is that it can be more intuitive.

Many times you can figure out what is happening in the time domain more intuitively than

what is happening in the fre$uency domain. 'o, for intuition, lot of times we use time domain

e3amples and for the e3act analysis fre$uency domain e3amples, sometimes also time

domain analysis. 'o, it is important to be fluent with both fre$uency and time domain

analysis to be able to understand circuits very well.

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/nother concept that we use widely is bode plots. @ode plots are nothing, but sinusoidal

steady state response of linear time invariant circuits. /s we now the sinusoidal steady:state

response is characteri>ed by a single comple3 number H%#. This H%# has a magnitude and

also a phase. The magnitude and the phase are plotted separately and these plots are nown as

bode plots.

@asically, you plot the logarithm of the magnitude and the angle of the transfer function

versus logarithm of the fre$uency and more importantly, you appro3imated by straight:line

segments. Now, these things, these appro3imated plots can be $uite good. It is a good

appro3imation when you have only real poles and >eros. 8ot of the situations that we analy>e,

we will have real poles and >eros and for that bode plots will be e3tremely useful. It is a

$uic way of looing at the response of the circuit.

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;inally, you can use simulator to verify some of the results that we obtain in this course

because as circuits becomes more complicated, It becomes more and more difficult to analy>e

and you will have to resort to simulators, but before we use the simulators, we should really

understand what you are doing because the simulators are powerful tools and they are also

indispensable for comple3 circuits, but as you now with any computer analysis, garbage in

and garbage out.

'o, in the initial stages whenever you simulate any circuit, you mae sure that you analy>ed it

by hand before. "ou tae simple circuit, you analy>e it by hand and mae sure that you now

the answer that you are going to get and then, simulate and verify it. /s you go on, you will

be able to use the simulator in the appropriate way and then, you can use it to analy>e more

and more comple3 circuits.

'imulators are also very powerful because finally everything has to be done with an

e3periment, but in many cases, there are many things that cannot be measured with the

e3periments, but that can be measured using simulators for instant e3tremely small currents

and then, currents in any branch of the circuit, these are all things that are very difficult to

measure in a real e3periment, but $uite easy to do in a simulator. 'o, simulator can be a good

learning tool as well, but you have to use it appropriately and there are different levels of

simulations.

'o, we can use tools lie Matlab and 6ctave for system level simulations, that is analysis for

fre$uency response, pole:>eroes and transfer functions and you can use spice for circuit


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analysis at the transistor level including non:linear circuit, and sometimes, you may be in the

middle of a very complicated calculations, and you may want to use a symbolic manipulator

to mae sure that the comple3ity of algebra does not lead you to a wrong solution. When you

have too many terms, you may end up maing mistaes. In those situations, you use a tool

lie Ma3ima for symbolic analysis.

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These are some references that can be used for this course. 'o, the first one refers to the video

lectures from our website and rests are the reference boos. This course does not follow a

particular reference boo in the same order, but there are lots of e3amples.


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analog circuit design is interesting and it is useful for designing present day integrated

circuits.

'o, what will we do here onwards is to do the actual integrated design, we will get into the

course itself and start. /s I mentioned earlier, we will start by analy>ing negative feedbac

amplifiers. Throughout most of this course, I will be using the tablet in this mode that is I will

be writing on it as a whiteboard and I mentioned this earlier as well. 'o, through the course I

will be posing certain problems and then, I will do the analysis. It will be very beneficial for

you if you pause the video at that point and do the analysis yourself and then, compare it to

what I do because the thing that you remember best is the thing that you do yourself and not

the thing that you watch somebody else doing.

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'o, what we will start off with is negative feedbac amplifiers, that is, letEs say, I am

interested in amplifier. That means, that I have an input 7 iand I lie output to be E times 7 i

and for now assume that 7 iis a dc that is to say it is constant with time. That means we are

assuming that 7iis constant with time, it is not varying with time. Now, I would lie to mae

a circuit that gives me an output voltage 7) G 7iand what is E is the gain that I desire.

'o, let us say it could be ! or 0) or whatever value that you want and also, I would lie to

reali>e this using negative feedbac. How do I do this is the first part of the problem.

'o, first we have to understand what I mean by using negative feedbac. What is meant by

using negative feedbac- I am sure all of you have an intuitive idea of what negative


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feedbac is because we use all the time if not mae amplifiers for other things. 'o, using

negative feedbac simply means that you loo at what the output is. This is the actual output

and you compare it to the desired output and based on the result of the comparison, you

control the output. 'o, this is what is meant by feedbac system where you loo at the output

and then, you compare with desire output and you control the output, so that it becomes the

appropriate value. This is negative feedbac system in general.

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We can tae a lot of obvious e3ample that you use in everyday life. ;or instance, let us say

you are driving a car or motorcycle and you want to ad#ust the speed to a certain value. 'o,

letEs say you want to reach the speed of !) m?hr. ;or this system, the desire speed is !)

m?hr, and let us says how you actually do this. What you do is you loo at the actual speed

and you sense it. Here, sensing the actual speed simply means you loo at the speedometer.

'o, you sense the actual speed, you compare it to the desired speed and then, you do

something to control the actual speed. What is this something that you do- That is the most

important bloc here and that lead directly to our negative feedbac amplifier. 'o, before we

go there, what do I mean by compare- Cssentially by compare I mean that you tae the

difference between the desired speed and the actual speed. 'o, when you are looing at the

speedometer, letEs say the desired value is !) and the needle is showing *), essentially you

are acting on a difference between *) and !) that is what you do, right.

%&efer 'lide Time( *)(*B


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'o, in other words, a negative feedbac system for speed controls. Here I am taling about

your manually controlling the speed of the motorcycle, the way most people drive. 'o, if you

want to go to a certain desired speed, you tae the difference between the desired speed and

the actual speed. 6f course when you are driving, you do not do this computation. "ou simply

loo at the speedometer whether it is at the right level or not and based on this difference

which is the error, you do something in a way that finally the actual speed reaches the desired

speed.

%&efer 'lide Time( *4(*A


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'o, what is that something that you do- This is something that we use all the time. I am sure,

some of you would drive a motorcycle everyday and then, you do this. "ou want to go to a

certain speed and then, you are able to reach the desired speed, but what is the action that you

tae so that you reach the desired speed. What we have to do is to find out the nature of this

bloc because this system is very effective. if I tell you to go out !) ilometers in an hour,

you will reach !).

&efer 'lide Time( **(0+

If I tell you to go at *) ilometers an hour, you will go out *). 'o, it loos lie the system

wors. We #ust have to find out how this system wors and replicate the same thing with

circuits, so that amplifier does the same thing. The amplifier output has to be times 7 i. 'o,

it has to reach times 7istarting from any value, it has to mimic the action that you carry out

on a motorcycle or your car.

'o, we have to find out the nature of the bloc which is mared by $uestion mar, this one.

How do we do that- The way to do that is by looing at what happens if the sensing fails.

Why is this easy to do- @ecause if the sensing fails, there is no feedbac and this error will be

constant. What I mean by this is for instant let us say you have a stuc speedometer. 'o, let us

say the desired speed is !) ilometers an hour and the speedometer is stuc at B) ilometers

an hour. If this is the case, you will always thin that the error is 4) ilometers an hour.

That is to say you will thin that you are going 4) ilometers an hour less than where you

should be going. "ou will thin that you are going at 4) ilometers less than the speed at


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which you should be going. Then, what happens to the actual speed2 because you thin that

you are constantly going at B) ilometers an hour, what happens is that you go on

accelerating and the actual speed will go on increasing with time.

%&efer 'lide Time( *1()A

This is e3actly what happens, right. 8et us say you have no idea what speed you are going at,

that is you have no sensors, no other vehicles or no other reference point you have, only yourspeedometer to loo at.'o, if your speedometer is stuc at the fi3ed speed, what you will do is

you will accelerate continuously and the actual speed will go on increasing continuously with

time. 'o, this curve gives you a clue of the behavior of this bloc which I have mared by

$uestion mar. What is the speed- What is this bloc- "ou can get another clue to this by

assuming that instead of being stuc at B) ilometers an hour that side, letEs say it is stuc at

*5 ilometers an hour.

'o, in this case again the speedometer is stuc, but you thin that you are going very close to

the desired speed. "ou are only #ust 0 ilometer below the desired speed. 'o, what you do

again is you will accelerate, but this time you will do so very gently. 'o, what will happen is

the speed will again go on increasing with time, but it will do so at a much lower rate.

'o, the behavior of the system mared in $uestion mars is this red curve when the error is

only 0 ilometer an hour, and it is the blac curve when the error is 4) ilometers an hour.

;rom this we can you tell what the nature of the system is-. It loos pretty obvious that the

actual speed is an integrated version of the error. That is why the error eeps increasing


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monotonically with time. 'o, we will use this principle to derive the negative feedbac

amplifier in the ne3t class.

Documents

Motivation for Analog IC Design