 Good morning to all of you, I am Pandur Kerr and the oldest faculty member of the department I am 29 years here, well before we start let me tell you this course, analog is a course which will actually never leave you in your whole career in case you remain a engineer irrespective what engineering branch you take. So please pay attention to analog because as the word suggests it is continuous in time and anything which is continuous in time must be important otherwise you know world will collapse, therefore anything which is continuous is analog and therefore it is very important. Before we start there are few things you should know, my name as I said already in Sandhur Kerr fixed credit course, what is this trying to do something that will try to see some of the analog circuits being implemented on bipolar as well as CMOS, it is very interesting to say that analog design appears to be much less systematic, yeah it is much less systematic whether some of those basic which make it unsympathetic are clear to you, some of the books which I will follow the first one you can see my name sitting there now, third author, I am not the author for this book so it is so happened that Cedrus asked me to revise Asia and other countries other than US it seems, so I added 150 pages to their earlier one with 1000 pages and that is why I am the third author in that book, so since I am now part of the game I will use as the textbook, however if you have a book of Milman and Gravel old book by the way this Milman person does not exist, this is like in my time I think your father or their father may be knowing the name called Thareja, you know it is your electrical engineering by Thareja, anything related to electrical electronics may be civil also he will write a book DL Thareja, you are wondering how one person can have such a width, so it apparently found that Thareja's book became popular, so every other book from the same publishing house was written in the name of Thareja, so there it tells, most well known analog circuit person in the world, he is dean of university and of course his book is unsystematic to learn but very interesting those who are really looking for very very strong physics circuits, I think Grace book is the best and the fourth book which I like normally which is written by Neiman, you may have read his other book on devices, the same author has written another book on electronic circuits and design, okay this is the syllabus which our site also gives, I do not have to talk too much about this, something they are talking about operational amplifiers, frequency response of amplifiers, this word which is border plot, border is a very famous feedback control system person and in 1948 he wrote the first book on feedback control and he actually described frequency responses and for good reason whenever I taught analog circuit, I also like the frequency response part little more than others because connected to stability of the system and therefore of course you do not say but 90s I was called Mr. Boudi really because of my fancy for this Boudi's plots, we will look into some applications of fans like comparatives, clippers and we will also see some oscillators, real operation amplifier, problems in amplifiers, normally the old books have only bipolar transistors as their basic elements but since world has changed to MOS, we will switch more on the MOS maybe 30 to 40% bipolar 60% plus MOS so that you know what is going on in the world now, so probably we will though it is not specifically written here but I may actually switch more on MOS transistors and I am told you are already been taught that officially at least, okay, whether you understood, you liked it, you do not know that is yours but I am told you know it, okay and then in the end we will see some more applications like A to D converters, D to A converters, sample holds and multiplexers time per meter. Okay, so this is something about the course, today what I am going to show you some slides which is just to tell you what is going on in the world, okay, so something I will talk today about why analog, what are the analog issues, why CMOS, we will just compare analog design with bipolar CMOS and some systems, please do not feel that is this is irrelevant or something, whatever I teach in the class throughout my semester everything can be asked in the examinations including today's talk, so I will just give you some what is VLSI, what are the technologies, what are the market needs, why analog designs are very important and what are the challenges, what VLSI has come from very large scale integrated circuits, since 16 when the semiconductor chips have started coming in the market particularly from Bell Labs and then from Texas Instruments, we started counting number of transistor per chip, so we say okay 100, small scale, 1000, maybe medium scale, 10,000 and above, large scale and maybe millions, very large scale, so that is the number we are talking, this has happened because the dimensions of the transistor started shrinking from 100 micron down to nowadays 28 nanometers, so obviously if your dimension reduces the number of transistor in the same area will increase, it is not so, the chip size itself has increased, initially I had a chip which I made in 70s was one and half mm by one and half mm, today one can have one and half centimeter to two centimeters SI, so huge chips for example Intel, recent De Leon has around 940 million transistor, it has four processor, quad processor on chip and it has a memory of 16k SRAM which is called cache and just outside another chip they are kept in the same package which is 4 GBB man, you can imagine what kind of densities we are talking, but good thing about all this, this is only for digital, analog people still talk about 1000 transistor, oh big circuit, so huge circuit, normally I prefer to have 10 transistor to 20 transistor, 50 transistor, huge analog block, the problem came because we have a technology earlier was bipolar transistors and it is very ideal for analog performance, in fact if you really want analog chip to work better, you actually go for bipolar, two reasons we did not do that or some company still market, for example some of the nationals OPAN 741 is still on bipolar, not all of them but some of them, the reason why bipolar loss because of its density limitations, that because the size could not be reduced too much and used to consume huge power, because of that slowly bipolar gave way to MOS technology and present day 99% or 98% chips are on MOS, however there is no system as far as nature is concerned which will not require analog, so a new concept appeared which is called mixed signal, analog plus digital, analog maybe 10%, 15% or even 5%, the rest will be digital, now the issue came that if you have a digital technology then I will prefer smaller diameters because then it will be faster I know, so I will go for 22 nanometers maybe 16 nanometer process, but analog says if it is a 1 micron I am very happy, larger it better for me, now that means you are trying to put analog design on a digital technology which is worse for it and now you expect that it should behave far superior, it is something asking too much, it is a paradox there, analog designers left to themselves they say okay put 1 micron length, channel length it is great, whereas digital will say put 10 nanometers if it can, 11 nanometers if it can, so there is a problem and therefore the design and integrate circuit for analog plus digital has become very, very crucial because of bad technology, circuit tricks so that it actually does lot of good things even with the digital around and that is where the challenge is there, therefore there was issues whether we should work on bipolar or CMOS and then in between someone said why not work together by CMOS, yeah there are many good things about bipolar CMOS process, one of the thing it takes some advantage of bipolar and some of MOS, but when I say some there must be lot many disadvantages both also must be coming, so you have to weigh whether this is important or that is important and then go for biasing, only 6 companies the world have biasing or technology no one else, so what is the market is asking, most of the market is saying wireless, almost every one of you I do not know if one of you do not have a mobile you should raise his hand I do not think anyone will say I do not have a mobile because that is the only past and you are constantly putting here, so wireless systems have become very important this is the market need, so whole challenge nowadays is to work for wireless system, major money is coming from wireless market, then there is another system which is coming called optical system particularly fiber communication passing a good data from say 100,000 of miles wireless does not work as good, so you want a cable where fiber was invented many years ago and now we are looking for optical systems, analog part came like this, if you have an optical system obviously you are converting some data into a photo diode into optics, you have LED and photo diodes, so you will convert one to the other from optical light to the electrical and electrical to the light and now these conversions have more problems, though the fiber will do faithful transmission, but what about the ends, so the major research right now which has much of analog components here rather optical analog components, Reynolds laws for example are re-looked into now, the other area where analog circuits are very strong are sensors, you cannot survive without sensors and will show some of them, for the digital side you are looking for a microprocessors which is around here your desktop if it runs around 1 gigahertz and a DRAM of 256 MB and you are playing a video game, oh you have to wait, now what is happening because neither there is enough memory nor there is a speed of the processor, so for this particularly game market all over the world including Sony PlayStation or Microsoft, whatever it is, there is a huge research in microsystem speeds, so you can see bad things also need something good and that is how we are looking for now around 6 gigahertz kind of processors, normal Pentium 5, Pentium which you use at least IIT has 2.1 to 3.2 gigahertz and now we are looking for 6 gigahertz, someday maybe ultimate aim is what we call as KU band 16 gigahertz, but we do not know where we will get there, I should not say we, I do not know because I may not survive the another area of interest in market right now is memories, just now I said you want memories 4 GB they are, so there is no end in requirement of memories and they will want very fast access, so there are lot of research going on in the area of memories and the most important area particularly IO input output blocks which should be of low noise, low power and very sensitive and these are the active areas of research. The word custom means in VLSI there are 2 kinds of designs we do, one is called semi-custom the other is called custom, custom essentially relate to customer, so customer says I want the specs and you meet them, so obviously you have satisfied a customer he is paying for it now, good money, but that means every spec he says you have to meet, this is very difficult because there is always what we call trade-offs, if you do this something else will be lost and to avoid that we are trying to get the best out of it, so it takes huge effort, huge amount of design time, hundreds of man years to design a good custom chip, so what we do okay, we pre-design some blocks and reuse it again, again it is called semi-custom, so essentially NL of designs individual design has to be designed every time and therefore it is called custom and as I said custom designs are costly, so it takes all hell of effort, is that clear, the major challenge in either digital analog is power and speed speed in our case of analog we call bandwidth, larger data can flow on the same line, larger bandwidth, so these are the challenges, now question arises why analog, some digital system design, by the way I have no fancy for digital or analog, I teach all sorts of courses in last 29 years I thought, last semester I was teaching a BLSR design course to post graduate students, before that I was teaching technology to post graduate, before that I was teaching digital system to second years, so I have no fancy for digital, but when I sit on this side I always abuse the other ones as if, oh I am now this side, so this so called digital designer suddenly said, oh dead, 1980 is it dead, last 10 years I find most of the research and most of the money has been now dedicated to NL, partly because of the wireless, partly because of the sensors, some answer is very simple, nature does not like digital, we are not suddenly see yesterday was no tree today some full grown tree, it takes years, ages before tree grows, nothing happens in nature which is instant, that is why when I of course I worked in data institute earlier, so I used to say Jayan Nararikar must be right, because he is suggesting steady state revolutions, because nature is normally prefers to go steady state, but the big bosses are always in big bang like a digit, one or zero, what knows, so what is important is nature being NL or even if you want to take that signal from nature which is NL or and you want to process faster, better whatever you call digital people say, I need initial input outputs as NL, so I cannot avoid NL because nature is NL, okay, what I will do, okay I will take that NL signal convert it into digital and maybe do all digital processing and then I want to display something, I will convert from digital to NL and replace it back in, but I will still require A to D and D to A converts, most of the DA speeds digital signal processors do this, here is a problem, if I have an ADC as I have a NL of signal word, NL of essentially is time varying, constantly time varying signals are called NL of, so this is NL of signal, I will convert it to digital table just to show you digital data and then I will do digital processing, the problem with this though it is shown as the same magnitudes, in real life the NL of signal from sensor from picture is extremely important, first amplify, okay, first amplify then as soon as I amplify it will get some other frequency company, so I will have to remove all those other than the signal I want, so I may need a filter and then maybe I will further go to ADC and process digitally and at the end if I want output NL of I will convert from DSP to DT, so you can see that these two parts even in otherwise digital system will be required because otherwise I cannot process it, there is a lossy cable like a copper cable or any other cable, you said an input data and this is the data you are actually sending because it is not a lossless line, actual data which is being sent is this, you can see it has a time period may be similar but its shape is how does it look like NL of, it does look like a NL of signal, so you sent a digital data but data received in the output was more like an NL of, particularly this will be dominant if the frequency builds high, okay, if you are looking at four regards above or one regard above, it is more likely that the digital data will be smeared to become NL of, so even if I am fully digital person now I will have to worry about that the data which I am seeing being NL of how do I process it so that it I still remain in digital domain, that is another problem which NL of people are now coming to the help of digital, the way we do it, we convert it by some reason four levels of digital data, so a new technique so far in digital how many levels we are looking last semester or 2, 1, 0, upper level lower level, now there is a trend going on in a very high potential domain to look for four level data and if so you will require four kinds of senses now because it should detect four levels, not that it has appeared in the market something, this is what I say going to happen now that people may look for multi-level digital data because that NL of part then can be broken into more levels instead of two only okay, so the newer research is now converting this so-called NL of looking signal into four level or even multi-level digital data, right now four is what is the method, why NL of probably I am trying to answer why NL of, most of the disk which you use hard disk, without hard disk you cannot survive 4GB, 8GB, 160GB, 320GB, it may be though come, this is your data you are storing on the disk and what you really take it out is this with the GB speeds are higher these days because you are making very high speed hard disk now and data acquisition actually smooths it and the variation can be as high as 2 millivolts to some levels, now again you will have to retrieve digital data out of this, this is called recovery, so another NL of circuit will be required to recover from this digital data, again there will be analog components, in wireless you send the data at a particular frequency for example GSM sends a data at 890 Mhz, this is your mobile communication signal, however whenever you see something like passing a signal there are two close by components which are called interferers, now they are very close to the original frequency and at times their amplitude may be larger because of the nonlinearity in the system you may get additional components which we will call later some way harmony but these are not actual harmony, noise you may see and they may have larger, so one of the major worry right now either you boost this enough so that the interfere signal is much smaller than the signal itself or shift this far away, both techniques have been tried in the wireless communication and both require a lot of NL of the system, just now I said optical this is what optical receivers are, you have a transmitter, you have a laser to convert digital data or analog data into light, you pass the fiber, you have a photo diode which receives optical light, converts into electrical, much of the processing here will be analog in the case, another area of interest as I say sensors as I said you want to measure temperature, you want to measure humidity, you want to measure all kinds of nature parameters, I will show you some other kinds of them soon, the best sensors these days available are made out of another silicon technology which is called MEMS, micro electromechanical systems, MEMS and the most sensors which are now made available which are very small, I do not know whether these days in my time you know we have a mechanical courses compulsory whether you do electronics or you do anything, so we have a applied mechanics course, we have a workshop, we have many other things also, even the surveying which I do not see anyone of, even civil people do this, I am not showing anyone theodolite and chain and everything, maybe it is there, I have not seen, so in the one of the famous gauge which mechanical people is called strain gauge and that is a huge bulky dynamometer they call, of course they measure lot of great large values of force as well as accelerations but they are very bulky, nowadays sensors have very gyroscope for example another big sensors, vibration speeds, so now we are looking for silicon sensors and one of this method is to use capacitances as their measurements because in the silicon I can make a cantilever which can under stress by acceleration or by force will vibrate or move down, the variation in this is proportional to the bending moment it has got which is proportional to the sense which it was doing and the change here can be monitored as a capacitor, if I have two plates here if it comes closer, the capacitor is larger if it goes away, the change in capacitance is the measure of the force of the, this is one more area which require lot of analog digital processing which is immense, another applications which are very, very important as I see is biomedical, I will not do all of them but just to read for you, there is a many surgical operations, there is an issue because you have, you will give an incision and lot of blood will ooze and if blood is lost too much, patient will die because of loss of blood though they keep feeding blood, so there is some medicines they give hyprion as they call and it clots, clots it but if it gives too much then they give clots in the bends itself, so blood flow will, so patient should not die is our major bacteria, so we must keep monitoring the clotting level going on, so this is essentially blood clot control which in most of the heart surgery is very important because patient may die before you think, therefore in such application I show you, analog processing is very important, so this is called in the first phase, you can put right now even there is a search going on for pancreas infections, core heart patients, everything is right now is replaceable all kinds are put here, tantalum sheets are put here, so during this implant surgery lot much of control is required which is continuous control and you need lot of analog processing, all your ECG, ZE, ZE, ZMG, ZRVs, brain any kinds of this body mapping all requires analog processors and there is a biochemical spectrograms, it takes place it does not suddenly happen, it keeps changing its pH values, so you want to know you want to see what is changing, so a spectrogram is seen, the patient is monitored when the drug is actually injected, it is such and this process is very slow, so you need a small signal which is appearing in the electrical has to be amplified noiseless because otherwise if there is a noise in that you will get something wrong, you say pH is 7.5 and it may be 2 only, so there is an issue there how to make a correct measurement of pH, another circuit which I had to Bombay has made or other product we made, I am not part of that, so it is a Sharma and my earlier Kadi Prasila Keshlal and even the madam should I am told, these days there is a worry even of course I hope you are too young and I only pray touch wood none of you will get your heart problems in your whole life, it has been now found because of so called money making business of young managers, they actually are getting heart problems at lower age than 40 which is unfortunate, now how do we know that the patient is actually having some problems, so we created a small kind of 2 probes, which is small locket which is put in gore like, then it monitors from the last ECS, if it is different than certain numbers it is actually the RF transmitted ECS circuit, the patient is running on the track in the morning jogging and he is feeling problem now, hence that it is happening to younger kids now, another problem which analog people are buying is neurons, your brain essentially works on the basis of neuron signals and as I again said all neuron processing is essentially like analog, I will show you some of time, a neural network which actually replicates a neuron behavior is like a opamp character, so you can actually think that a opamp can replace your is equivalent say model, that is why it is important that neuron theory that stood on the hard board using opamp, another area I just told you know anything you monitor inside the body is called lab inside your body, lab chip as they call, it will keep monitoring everything for you, in that the weak you have to block and sense, you need a good answer to that, at the end of the day whatever signal I get, I must reduce it is a very small signal, I must amplify it, I must filter it, I will see to it the, it is a flick of the original signal as good as possible, that is called signal condition. So these are the blocks, these are the areas where analog is used, yes I will read quickly, okay I already said the person who does this machine is called perfusionist whose role include monitoring appropriate parameters to ensure that the patient is effectively treated with anti-cogulant to avoid blood clots, okay and for at least 60 minutes this is being monitored, so okay this is more to tell you what kind of thing happen, there is a thumb brain and fibrogenic tool such parameters you keep monitoring, see what is the, but basically what elliptical people monitor, it actually changes the impedance when it changes this, so all that we do is to monitor the blood impedance and that monitoring will know whether what is the cutting level is not same, okay and then we can control it that hyperon how much we get turned not in this feedback system, okay so here is an impedance measurement system which is based on another device chip called pi 933, you can see from here there are certain digital part, there are certain analog part, this is your oscillator then there is of course multiplexer, then there is an interface, then there are digital block like registers, DFTs, but they can see there is a ADC, there is a filter, there is a gain amplifier, okay, you can see signals are analog and you are monitoring the impedance the blood clots, how it is done is this is how it is done, your blood clots are kept here, then it reacts and then it is finding the impedance and then this is done in MEMS now, the chip is outside, this is the main structure, okay and the whole processing is analog plus digital because something you have to control by this state, okay, so you can see that only giving you one example why analog cannot be ruled out, that oh everything is digital why analog, there is a requirement where analog cannot be removed, okay I just said all that, okay another thing which people say digital data transmission on a long distance needs to distraction that is noise continuous and analog kind of transceivers will be needed. Now question arises why we are not doing analog transceivers, this was known to us many years ago 60s we knew analog better than digital, so why we are not continued with analog, why we major worry came that analog signal actually died down as they move to on the line because of loss it has, so you need a repeater, if you see optical fiber every mile there is a repeater, so if you do same thing with analog yeah it can be done but then again you will have to improve it by its low noise performance filter it out, so cost involved, it is not that it cannot be done, it is just the cost involved and the power supply would have to where you have to come. So because of the cost involved in this analog receivers have lost transceivers lost to digital because digital signal can go far distance compared to analog and will require a repeater after may be 20 miles or 50 miles or 100 miles that is where our distance why are we, we have a cable why not use transceiver which are far superior in performance, so at least locally we may come back now for its own fidelity of best performance sensitivity, you may come back to analog transceiver system. For example a normal hard disk, the very little, it is the very high speeds disk have come, so you need now something to amplify that, similarly for wireless, the antenna even for not digital data, the antenna signal which you receive will depend on from how far you are away from the tower, of course towers are not good for your health that is what everyone is now saying, but I always say body is immune to everything after sometime, so probably this so called our radiation will finally become immune to that, hopefully so, maybe one angel, people ask me other day that you stay in Bombay, so much radiation from the DRC and TARAPO in it, I say our health is better now because of radiation during something, hopefully that is the way we should look, okay, I already said microcessor memory with ultra-high two clock signals across the major worry HEP is 2 centimeter, I just said now, what is the length of interconnect on Intel chip, anyone guess, what is the length of interconnect with a line taking signal from one point to the other, what is the length, it actually transfers through on a chip, typically maximum links available on chip, how much, anyone of you guess nanometers, typically Intel processor has 1 kilometer length of interconnect on chip, okay, and that is something you must understand that we always think wire or blibla, but here on a chip itself I have 1 kilometer, now if that is so, the signal will not have integrity going from one point to the other, that is our measure, it is a loss, so the clock which is running from one end to the other actually drifts away, okay, so let us say what is drift away means, at t is equal to 0, let us say 1 has to come, at some point to the t 1 0 plus point something it will come, because get delayed by them, this is called jitter, jitter is the major worry for digital data processing forget about, then the recovery of this can be done through what is called as phase lock loops which is analog lock, okay, that is why for clock recovery we will require an analog circuit, because you are running a very high speed signals on a large length of internet, this is like a transmission line, so all this memories have something what we call sense amplifier, what is sense amplifier can be, let us say memory you have read, let us say you are storing 1 as 1 volt, if the line which is coming out where you call sense, I know the cell has 1, it takes long time, because this wire is long enough, so it has a large capacitance, it takes enough time before 1 volt it reaches, I do not want to know whether it is fully 1 or not, I have already pre-charged this line will say 0.8 or 0.6, as soon as this process this charging process crosses 0.6 I will compare, if it is larger than 0.6 I say 1, I will not wait for it to go for 1, this is called sense amplifier, sense amplifier is a comparator which is an analog block, so even in the so-called hard memories the major research, excess time research is only on analog component and not so much on the cell, is that clear to you, why analog? In the case of digital, the circuit deal primarily with speed and power, I want a 4 GHz, 5 GHz data flow and I want preferably 0 watt power consumption, I mean I want 0 watt, of course I know power cannot be 0, so as low as possible, microwatts, milliwats but certainly not watts, typical chip consumes 40 to 100 watts of power, okay, micro buses of chip consumes around 40 to 100 watts of power, I want to reduce this, so the whole research right now we are looking is how to reduce the power, but there is a trade-off, as soon as I reduce the power what do I reduce essentially the current, if I reduce the current, power will go down B into I, okay, but if I reduce the current that time taken for the capacitor to charge with the lower current will be larger, Tdv by dt is smaller, so T takes longer, okay, speed there, so there is a trade-off, so now game is I want high speed but I do not want to give you power, that is the reason, thermodynamically it should not be possible, if you do not give me this I will not give the other, so how to fool thermodynamics is all over tricks, okay, if you learn my digital course some day I will tell you how I am fooling circuits and fooling others, beating as if thermodynamics is avoided, no it cannot be, somewhere else I am doing something tricks as far as you are concerned I have done I improved the speed I reduced the power, where did I spend I am not telling, okay, where I must have done, some tricks I must have done, but as far as you have come, only high speed low power, that is where the research is, in analog these are not the two parameters we are worried, this is unfortunate, we worry about speed, power, gain, precision, power supply, variation in that and many others but at least 5, 6 of them, you need large bandwidth which is called speed, you need very precise because why precise, because analog is time varying signal, any change there will be seen at the output, okay, so precision means 1.6 milliwatt means 1.6 milliwatt, 1.7 piato there will be 10 times 12 other, so I am worried that what I say I must get that, so precision is very important in analog, not so much in digital why I say so, because there is a noise margin, 1 can be recognized from VDD by 2 to VDD and 0 can be recognized from 0 to VDD by 2, anywhere is fine, here anywhere means nowhere and that is why analog means extreme precision, okay, of course there also will beat the system, do not worry everywhere like all IITNs brightest among them they feel so I do not know whether they are, hopefully they are, you beat the IIT system, not that you do good or bad, you see to it that whatever we come out with how to beat it, okay, 29 years my experience and we have lost, so I have full faith in you as well, whatever way I will try to see you should not do it, you will do it some way or the other, okay, that is the IITN, so okay, worry as I say they are very sensitive to noise, what is crosstalk, today unfortunately for me there is no crosstalk, maybe this is your first lecture you are worried about, good, keep worrying, anything you talk there if it interferes on me or my talk and it is called crosstalk, so two lines are going one data on this, one data this may interfere the next line close by because of coupling will do mutual coupling particularly inductance, mutual inductance, this is called crosstalk, particularly worst if one data is going in this direction the other is coming in this direction the crosstalk is highest both amplitude opposite, so maximum separation, so that is major worry in this interferers, crosstalks, sensitivity to noise all these worries have to be satisfied when you design analog that is why analog designs per se people they are difficult, other worry of analog is even worse, many times analog circuit books are called linear circuits, what do you understand by word linear, why they were called linear circuits, guess linear okay, word in match is y is equal to mx is a linear system, if I change x to 2x y will also get doubled if m remaining constant okay, linear system is that clear, why therefore similarly analog circuits were earlier called linear circuits because output voltage was proportional to input voltage in the meaning constant v0 by v in its constant, straight line it is called linear system, but our assumption is that the device property is always like this that is why translate input to output proportionality, but in real life you have learned bipolar devices, you have learned MOS transistors, there will be iso, so there is no real linearity in the MOS or bipolar characteristics, so there are regions where output current and input voltages are not linear or input current to input output current to input are not linearly connected, if they are not linearly related then there is a second order nonlinearity is appeared, so to say y is equal to a0x plus a1 x square no linearity, now this x square term will create let us say sin omega t was the signal, x square will create what terms sin square omega t which in terms of 1-2 sin square omega t is sin 2 omega t, that means you are now you have omega t terms and 2 omega terms also appearing is that harmonic has appeared, so part of the power has lost to second harmony, is that clear, so in the case of analog you have a very small range which is linear, as soon as you increase the amplitude even a little more you are in a nonlinear range and part of the power is anyway lost to the second or third or higher harmonics, so you have to be always worried you should remain within so called that linear range, otherwise you will immediately get into second order device problems, these are very important effects, we will see how to minimize them but not every time you can reduce to a 0 level, because of this so called smaller range so many effects it wants to do, it is very difficult for do automation like digital, in digital there are all kinds of software available, so much so nowadays there is something called silicon compilers, I give a statement I want to do this under this condition it should show me this and a chip can be designed without pure intervention, all simulators can be that, it will actually find out what you want and it will finally give a design for the automation, this is full automation, of course not the ideal we still interfere everywhere so that we remain in charge, if everything is done by computer what will be, so we keep saying no human intervention is essential, otherwise there is a possibility that automation is great in digital hardware or digital simulation, there is nothing so called fully automated analog designs or analog systems, you have to design every time because it is very problem is taken, every small problem has to individually handled and fixed, that is why analog is interesting may be difficult and much of this what is the way people do it, not essentially always by reasoning, mostly by intuition and experience, last time I saw who is Barwikar that is what I said and that is creating major problem because technology of digital particularly at 45 nanometer down is worse for analog design but we have to work with them so we have to integrate analog digital on a digital process rather than analog which would have been ideal because if I want opium only why should I put everything else, I want only this I will give very good to you but I cannot because they will say no this has to sit with microprocessor, this has something else put your block here, there is issue. So there is a difficulties in analog design therefore it is the challenge, so what is my answer to you, is analog design therefore more difficult than digital design, my experience of 29 years says yes because digital design has a large noise margin, you can have three way trade-offs only power speed and may be area whereas analog needs multi-dimensional redox, power, frequency, gain, precision, power supply and many more, okay, we are already done, sorry. There are two possible technologies which analog circuits can be implemented using bipolar current transport, they are bipolar transistors or field-based current transport which is MOS transistors, bipolar circuits have age over MOS circuits as far as performance is concerned or gain is concerned but has a drawback of large power dissipations whereas MOS technology for analog though not the best possible compared to bipolar but much more suitable for digital applications. CMOS is the best bait for digital and hence analog 2 should get implemented on CMOS not that it is better but that is just now said mostly the chips will be mixed signal both analog and digital together like a neural say and I will show you some figures, okay. This is a mixed signal neural processor, okay, this is your digital signal, neural digital signal processing, this is D28 inverter, this is analog neural network processing or neural processing, this is A2D converter and this is a processor was designed way back in 1964 or something which still works, okay. We are trying to replicate brain functions now, we are trying to see how brain works but tomorrow if you have an accident for some reasons you have a damage to your brain, can I put a chip supplement that part, this is what we are looking for, is that clear to you why this is that because there is a worry, there is a too much traumatic situation these days because the cars are too many, streets are too many, two wheelers if you are driving please take care of old person like me crossing a road at the main gate I always pray God every second because I do not know whether I will cross finally then this motorbike person will not throw me, he does not see signal, he does not see people I do not know he only sees speed, okay. So I hope some of you who have bikes we have banned and told but still the hundreds of them in case you are driving please take care of old people like us who still may want to throw at least two more years. So this is something what we are right now looking for, okay this is done quickly I show you introduction to analog circuit, you can see here this is a nonlinear system and this is a linear system, can you tell me why Vn is ground or Vdd is 1, Vout is either 1 or 0, the reason is since both are transistors and both are nonlinear components, so V0, Vn when you go for Vn from 0 to 1 both transistor will not remain in the same operating mode that means one may be in linear other may be in saturation, other may be linear, both may be saturation both may be linear. Since the characteristics in all three two zones are different there will be lot of nonlinearity in V0, Vn characters called the transfer, you have already done transfer characteristics, so that is a nonlinear device but in the case of analog circuit we only operate this is the transfer characteristics of an inverter which you just now see CMOS inverter you can see from here to here V0, Vn is nonlinear because here one is in P is in non saturation other is in saturation both saturation other opposite happens here. In the case of digital signal goes from 0 to say Vdd input goes from 0 to Vdd, analog actually works only in this zone where relatively V0, Vn is linear you can see the available input range to meet how much few millivolts you get the point because during this few millivolts only V0, Vn has relatively linearity nowhere else okay, so what does that mean the input signal in analog has to be small signal otherwise it will not remain in linear zones okay and that is why if you operate your in bias your circuit only in this range let us say this is my biasing voltage then I can apply an input signal rate which still keeps output such that V0, Vn is in linear mode okay that is where the analog differs from digital, digital I go from here to here analog I remain only here okay and therefore you can see linear circuit will always limitation of small signals it cannot have because you can see if I have this large signals which you are in non-linear areas is that clear to you therefore analog circuits normally will have very small signals limitations because of course you can go out then what will happen the power will go into other harmonics more than may be fundamental with the frequency you are 2 omega t, 3 omega t, 4 omega 5 more than non-linearity x square x cube x4 more third, fourth, fifth harmonics will start appearing plus another may appear omega 1 minus omega 2, omega 1 plus omega 2 will also start appearing which may be worse interferes and therefore analog people should normally try to operate themselves in the linear mode and therefore signals are always limited is that point clear to you that is why I say this is so you can see if you operate in this then you can remain as an amplifier and then you can see you are in linear circuits just to compare again digital so highly non-linear but very high noise immunity I just said VDD by 2 VDD 1 0 to VDD by 2 is 0 huge noise even to power supply variation if 5 if 1 word supply become 800mV or 950mV who cares that within noise margin whatever happens let it happen okay I damn clear and it only carries at a time only 1 bit of information 1 or 0 compared with linear analog circuits highly linear extremely sensitive to noise you can just see if that signal has some more noise it will transform immediate get the output any variation in power supply means bias point will very means one side may become non-linear one side may become very sensitive to power supply value and carries and bits of information in the sense the analog so it is an N bits of information is going in one go that is why it is very good essentially one more figure will come here is the advantage of digital you can see it is not very clearly visible but maybe I will read from here this is an input I have put and this center line is threshold so anything above is one anything below you can see there is a small variation is occurring below okay but it is less than we threshold now still recognize the zero but if that happens in this now you can see from here this will be visible to you as soon as it goes it also jumps so anything in digital is acceptable whereas in analog it is not acceptable okay so this is your VDD variation so you can see VDD variation will also appear at the signal outputs you can see this is my VDD variation this is over reading because that will change the bias point that will also show you the different games different outputs so very in analog is so called noise over reading every time if you do not take enough care in digital at damn okay irradiation some other day I don't know it is visible to you okay maybe just tell you there are three ways amplifier genetic will show you this later three possible way of mass realization of amplifiers okay so what we have to consider in analog is handling a positive and negative signals in digital we are only 0 to 1 is that correct 0 volt to 1 volt 2 volt 5 volt whatever supply in analog minus be hair plus be hair so dual rail hair minus VDD plus V so though power supplies are signal minus may be at a plus sign sinusoid a square hair so you need dual rail this I just now told you in the figure where do I buy us is very important because that will decide my noise I mean on linearity Khan so I must bias it correctly so biasing is most important aspect in NL of design because that may decide my all of the power delivered to the output linearity is essential because otherwise I am what is I was avoiding I immediately get you I lose power in harmonics I am I need linearity I want noise taller sorry the word is slightly made mistake I want lower noise not tolerance is essentially means it can tolerate larger noise I mean I it should not it should tolerate larger noise but doesn't happen so you must it will have a very low noise tolerance in normal system therefore you must design for it that it at least tolerate this much noise nothing should drift too much power supply should not be 1 volt and certainly pointed everything will have a score drifts the problem with design is in case of digital as I said we can have pre-designed pre-tested blocks I have a multiplier I have a multiplexer I have an adder I can once design for a given technology store it and whenever in a larger circuit I just duplicate that nothing happens in NL of that there is no standard says every block you design every time okay and difficulty in designing low voltage low power because larger the currents larger is the charging of capacitors as a faster bandwidth to make it look for four important parameters we have been looked into designs one is called transconductance what is transconductance by definition transconductance GM output current divided by inputs voltage or change in output current to the change in input voltage delta I by delta V is GM so one of the major parameter of design of NL of circuit is the GM Kipna GM and you will see later GM is proportional to I root I or some I current so if you want to gain which is GM into R you need larger GM so what does that mean larger GM will come from where larger currents larger power so gain at the cost of power no other we will see your alternate we also want to control output resistance some systems need very low output some systems connection needs very large output can be very output resistance of a system the third parameter of interest to me is called noise which is called input referred noise now this is very interesting word why it is not called output referred noise so must be something in it so we will worry about input referred noise okay and for but the north is the most important part other than the gain is the bandwidth larger the bandwidth higher frequency performance is greater or better and therefore larger bandwidths are we will see a very interesting thing will happen gain into bandwidth normally is constant what do I say gain into bandwidth is normally quotes is constant that I will see that can we beat this word normal otherwise what will happen I increase the bandwidth I lose the gain I increase the gain I lose the bandwidth okay so can I beat this system I will say I am not lost the bandwidth but I have to state gain if I had done that I have beat this so called technological constraint every technology say this is the maximum gain bandwidth possible but we will say a technology to technology on circuit do better show you how do I do it at cost we will see we stop with the night but I gain something but I will see that this so called constraint will beat what is the constraint we said in into bandwidth is constant but we will see to it can we take opposite is not possible again I repeat bandwidth increasing and gain constant is not very easy but gain increasing without losing bandwidth is possible because bandwidth is related to capacitance of the transistor that I cannot touch okay so I will say okay bandwidth do which have a head gain to my body you have which game okay okay maybe there was enough we talk today we will have some flight ladder another half an hour lecture will continue on this and will show you that little more design what is happening here than have a nice day take care