 I think time for us to begin ok. As I understand you have already had two lectures and you have gone through the concepts of measurement, why measure, how to measure, what are the problems, what are the specifics. And then you have also looked at signals, you have gone through some idea about filtering of signals. As this course proceeds you will be using more and more signals. We will like you to learn and understand what are these signals, what do we do with these signals, what are the problems, what issues to address at various points. So, in this series we have also looked at one of the techniques which is analog to digital conversion, taking an analog voltage or analog signal converting to its digital representation and viewing it. Up to this point you have just an idea of this method, this technique. But why this is done and what are the issues involved with this and when you actually do put it to use what to expect, that is what we are going to look at in this lecture and also in the subsequent lab which will proceed you will be doing this. So, as this talk has been titled signal sampling and reconstruction, there are several additional terms which we will talk about like quantization, discretization, sampling, reconstruction and things like that. So, let us proceed. Now why do we discretize signals, where do we discretize signals, you do that routinely. For example, this is what you normally use. For example, what is there in a CD, music, mp3, wave files, what are these. These are nothing but digitized data which has originated probably most likely as an analog data either as an audio data or as a video data somewhere and it has gone through this process of the analog data being converted after sampling and digitizing and perhaps also encoding. It may or may not be encoded, some of the older formats like wave formats and all are not encoded, but the more efficient formats like mp3 and all, they compress information, they encode it so that a large amount of binary data can be compressed into a smaller volume and then put on to storage media. So, you are all familiar with this mp3. So, how does it originate? Now you see the sequence. The analog audio goes to a unit where there is some sampling happening, some digitizing happening, digitizing is what you do as A to D. After digitizing, encoding or perhaps not necessary and then storing on the some storage media and the vice-versa reading those binary bits which have been stored and reconstructing it back if required decoding and producing it back as an analog audio. Where is the ADC in this? Does anybody know? Can somebody tell me in which part of the sequence the ADC might be figuring? In the one where you are sampling and digitizing, the digitizing part is the ADC part and the DAC the digital to analog converter where might that be occurring? So, the ADC part comes here in the sampling digitizing and encode, the DAC parts come here in the reconstruction part. Let us continue. So, can we do like this? Take a source, take data from that as it is coming, digitize it, sample and digitize and make it into a digital bit stream. Send that bit stream to a DAC reconstruct and send it back to the receiver. Now obviously, you would say yes, such a thing would be possible when you can do this and save data and then retrieve it and then use it to reconstruct. Why not do it online continuously? Now, yes it is done and in many, many systems this is what is done. The digital bit stream here allows you the possibility of directly manipulating this data for your benefit so that you can remove if there are any noise elements or sometimes you can remove the expected noise elements which are going to interfere what we call interfering elements. For example, digital processing of data which is coming bit streams, input bit streams is the most common thing. So, what is an ADC? Where is it used? Most sensors produce an analog output and this analog output is used by the ADCs. It is converted by the ADCs into a digital equivalent or digital number what we might call a better way probably would be to say a digital representation of that analog voltage and what does that digital representation mean really? We will be looking that at that in a little more detail. So, ADCs invariably form the interface between analog signals and the digital world and then this digital data might either be directly used for online processing and then reconstructing and usage or it could be stored and used subsequently. What is this discretization? That is an important thing we keep on talking of discretization, digitization, quantization lot of words come keep on keep coming. So, let us look at it what does it really mean? Discretization is something that we do almost without realizing every day in a very everyday life we actually do it. Now, here is an example of what you might have already done. This is a meter which has got marking of 0 to 100 and it is marked there are some marks there. So, you are assuming that it is a voltmeter which is reading voltage between 0 to 100. Does it have 100 discrete steps? That is a question mark over there. Does it have 100 discrete steps? Can you actually measure voltage with a resolution of 1 volt? No, actually there are only 20 steps. So, when you measure voltage you are measuring a range of 100 volts, but discretizing this 100 volts over 20 steps. So, your resolution becomes only 5 volts. So, the discretization really means that while just look at the transfer function of such a possible volt meter that we might have. If the while the real data that you are measuring will vary continuously from 0 to 100, what you are observing here will only undergo 20 changes 20 steps. So, this is kind of a staircase transfer function. Now, this transfer function that we have is a typical transfer function of an analog to digital converter. An analog to digital converter will have linearly changing real world values on the x axis and the measured value the digital representation of that will be varying in discrete steps. It will be varying in quanta or it will be quantized. So, you will have only 20 numbers to represent this. Now, this is something which once again let me say that you many of you have probably been using without realizing. Let us go further. Here is a digital multimeter. This is my digital multimeter you have already used in the lab. A similar digital multimeter you might have used elsewhere. Now, let us look at what does it have. It has got the maximum indication of 1999 starting from 000. What it means is that it can indicate only 2000 distinct values. Now, how the multimeter is used? You can have different ranges with a 1 volt resolution up to 199 volts or with a 0.1 resolution 199.9 volts or with a 10 millivolt resolution and so on so forth. So, what is it that we are doing? We are actually saying that we take a domain which has only 2000 members and we simply keep on defining redefining the range of that. So, either it will the domain has numbers from 1 to 2000 0 to 199 volts or 10 times smaller or 10 times smaller the resolution keeps on changing. So, this really means that the ADC a typical ADC can be looked as this kind of a black box where you specify the maximum voltage range whether it is going to be 2000 volts or it is going to be 200 volts or 20 volts. So, you specify the maximum input range and you also specify how many steps will be required for quantization. In this case how many steps are there? How many steps? 2000 steps. It is customary to have two kinds of ADCs one kinds of ADCs will have steps which will be multiples of tenths in decade. For example, you will have 2000 20,000 200,000 some of these also come as 40,000 400,000 80,000 800,000 this is one kind of ADCs. The other kind of ADCs will give you conversion the output steps will be in the order of 2 to the power n this will be in binary range of typically let us say 8 bit, 10 bit, 12 bit, 14 bit, 16 bit, 18 bit it continues like that. Typical ADCs are available up to 24 bits, 24 bits ADCs are of course very high resolution use of very special applications. So, a typical ADC let us say 8 bit ADC will will be something which will have 2 to the power 8 steps which will be 256 steps. So, the maximum possible quantization that is possible in that case is 0 to 255 or 256 steps. So, an ADC is nothing, but a black box to which you give an input voltage and to that you specify what is going to be the maximum input voltage range and it gives you an output. Of course, it is a very very simplistic model it is not just this there is more to it how does it actually do this carry out this conversion. So, in the process of converting and analog voltage to a digital voltage are there some additional factors which have to be considered come into the picture. So, we will talk about that, but a little more about ADC measurement range. So, they would be typically measured in terms of bits where 2 to the power n where n would be the bit. Now, you can see an 8 bit ADC is gives you 256 steps what is the resolution of measurement in an 8 bit ADC in terms of percentage to be 100 by 256 approximately 0.4 percent little better than 0.5 percent. 12 bit ADC will be 2 to the power 12. So, 100 by 4096 much better 0.01 percent better than that and 16 bit even better. So, there would be a motivation for us to keep on increasing the width of representation digital width of representation of a analog number. So, why not keep on increasing, but the price that you have to pay when you start increasing the number comes in two ways one is the cost the price means the cost the other is what are called conversion delays. So, we will talk about conversion delays later. So, when you use a 8 bit ADC the range that you may specify could be a unipolar range 0 to 5 volts or a bipolar range minus 5 to plus 5 volts you can see that the overall range here is 5 volts while the overall range here is 10 volts. So, the same ADC for a 0 to 5 volt range will give you a resolution which is 0.196 while for a plus minus 5 volt half the resolution of that. So, you can use an ADC for any range, but you should realize that the resolution of measurement will keep on changing. Now, what are the conversion steps in the ADC? The first thing is whenever we use an ADC we have to sample the data why the data sampling is necessary will become clear a little later and if one ADC has to be used to measure multiple signals then we can multiplex data this multiplexing is nothing, but time multiplexing in real time we first measure data from first source then from second source then from third source and then keep on recycling. So, this is called time multiplexing since the ADC conversion is very fast. So, one really does not realize how with that there are missing points in between. Then there is a device which is which holds the data and the device which samples and holds the data as a single device called sample and hold because the ADC will take some time for doing the conversion. So, during that time the data will have has to be held and the sample and hold holds the data. The quantizing is done by the ADC and once that is over the data is available and then that encoding of an of the data could be just what we would have straight binary or it could be in a variety of ways. Now, what are the issues? One is the resolution that I talked about the other is the sampling rate. What is the sampling and we will look at it a little later. First of all let us look at a typical setup of measuring of converting an analog input voltage to a digital representation to its digital representation. Here we have a small box written as S stroke H. S stroke H is for sample and hold. So, a sample and hold is a device that whenever an ADC has to make a measurement it sends a signal to sample and hold that hold the analog voltage. Whatever analog voltage is existing at its input you hold it. Do not change that do not allow the analog voltage at its output of this of this S and H output change while the ADC is carrying out its conversion. So, when the ADC has finished its conversion it removes that hold input from the sample and hold and the sample and hold then goes automatically in sample mode. So, the sample and hold can work in sample mode. In the sample mode the input voltage flows to the output and in the hold mode the output voltage is held constant. So, let us look at how this would be working let us look at the a typical signal. The typical signal as a function of time will be a voltage varying in its amplitude and in time. So, look at this voltage at any time starting from the reference point 0 the voltage keeps on changing its amplitude keeps on changing. What does the sample and hold do at the output of the sample and hold? For every discrete time that it is sampling the output is held constant it is frozen then once again it is frozen once again it is frozen. So, this sample and hold what it what is it doing? It is breaking up the incoming signal into discrete points and at that specific point at the beginning of this the data is held. The ADC is taking some time to convert from the instant that the data is held to the instant that the data is converted the ADC takes some time which is called the conversion time and at the end of the conversion time the converted representation digital representation is available. So, you can see that this was what the signal originated as and this is what it will appear if I try to reconstruct it back by using this converted data. Now, one small thing that I would like to point out obviously, this signal does not exactly look like the input signal. Now, what is the factor in your opinion which will make the output signal as close to the input signal? The sampling rate the faster I sample and the faster I convert the closer is the output signal to the input that is one thing. The second thing is that the digital representation that I get depends upon what is the width of the word the digital width of the word the digital width of the word here is 12 bits. 12 bits means I get a resolution of 4096 in overall range that I am using. So, I am using 4096 quantization steps if I were using 10 bit it would be 1024 if I would be using 8 bits it will be 256. So, the accuracy of representation in the x axis is the representation of the amplitude that accuracy depends upon the resolution with which I am measuring it. And the accuracy of reproducing a dot a dot which I find here and the input back on this would depend upon two things the accuracy with which I am measuring the amplitude and also the speed with which the quickness with which I am measuring it. So, to put it back there I should have the data at that point I may not have the data at that point I may have data at a different point right. So, that is why ADC has got two important attributes the measurement resolution and the measurement speed how quickly we can make a measurement. Now, coming to this let me put a question to you you use PCs you listen to MP3 audio on your iPods from your PCs and all. So, obviously, that also would be digitized data that also would have gone through an ADC now tell me what will be the sampling speed of the ADC it is 44 kilohertz why is it 44 kilohertz. So, twice the maximum frequency is 22 kilohertz that is 44 kilohertz, but there are two channels. So, would not you have to do it at 88 kilohertz. So, when you do different types of measurements in MP3 for example, you have so many bit rates 128 bit rate 64 bit rate. So, what is what does that mean different bit rates. So, what is actually happening? So, these are interesting questions that you should you should ask yourself and try to find out supposing it were not 44 kilohertz it were 22 kilohertz or would anything be gained if I increase the sampling frequency from 44 to higher let us say 50, 60, 70, 80, 100 is there anything to be gained. So, some of these questions are all relevant they all related to your understanding of ADC and the sampling resampling rates and all. So, let us look at what happens to accuracy of reproduction of signals when you change the sampling interval sampling interval would be the sampling frequency. So, if you are sampling at 1 kilohertz your sampling interval is 1 millisecond if you are sampling at 100 kilohertz your sampling rate is accordingly 100 times faster. So, here is the signal now observe these dotted lines are the points of sampling the data is sampled here and then here and then here and then here then here and then here. Now, when it is reconstructed obviously, these are the points that are stored on the micropsacer or that are available to the micropsacer or the micro computer which it sends to the DAC and this is what is reconstructed. Now, in this reconstructed information you can see that the data is grossly different from what we sent for example, we have missed this peak. So, let us look at a little more supposing I am having a sine wave and I want to sample it each of these points of the sampling points. Analog frequency is 0.09 of sampling rate the analog frequency that we are sampling is much much smaller than the sampling rate. We are getting a large number of samples per cycle and we can reconstruct this signal very well. Let us go to a higher frequency and slower sampling rate the analog frequency is equal to 0.31 sampling rate you will observe that you are still getting sufficient samples to reconstruct at least the frequency information accurately if not the amplitude information. In this one you would have accurately got the amplitude information and also the frequency information. This one we are getting the frequency information right we may lose on the amplitude information So, sampling rate also affects when you are measuring your signals it also affects the accuracy with which you are making a measurement. Let us go further the analog frequency is 0.95 sampling rate this is the analog frequency and this is the sample points you can see that if I try to reconstruct the signal I will get a frequency of reconstructed signal which will be absolutely different from the input signal frequency which was digitized. So, this problem where the you get a signal reconstructed frequency or reconstructed signal component which was not present in the input is a big problem when we discretize signals and when we store them and this is called aliasing this what we are observing here is called aliasing and the frequency components are the aliases and there is a there is something called sampling theorem which tells you that what should be the minimum sampling rate for us to get the frequency information right. So, some of you may know some of you may not know and I am not telling you this is something that you are supposed to discover in this lab when you are going to do the experiment in the next lab you will actually be wearing the sampling frequency or you will be keeping the sampling frequency constant and you will be wearing the signal frequency. So, you should reconstruct this you will be reconstructing the digitized signal back. So, you should yourself from that infer that what is the right sampling rate at which you will get the frequency information correctly. Now, there is something about how the ADC works what is the what is a technique what is the mechanism what is the magic band the ADC how does the ADC give you the converted value. Now, in an ADC I will go further and then come back typically ADC has got many sub components and one of the type of ADC which is called successive approximation ADC the one which are going to use and also one of the more common and more popular ADCs not that just this is the only one which is largely used there are others also which are used integrating ADC is another one and sigma delta type of ADC is another one which are used quite a lot. But let us look at the successive approximation ADC which is probably still the largest or the widely most widely used. So, it consists of some components let us say a DA converter a comparator a programming a programmer is actually it is called a SAR latch successive approximation register latch it is the word written here is a programmer. There are several components which form and the successive approximation means you make an approximation you make a guess what is the actual digital representation is guessed. So, that guessed representation is given to the DA converter and the guessed analog voltage is reconstructed and that reconstructed voltage is compared with the actual voltage which you are going to convert and if they are not matching then the next guess is made then the next guess is made. So, here is the guessing method supposing this is your range entire range and you have only 8 steps in this range. So, 8 steps would mean 2 to the power 3 or 3 bit ADC 3 bit conversion the first guess that we make is always at the mid scale and at the mid scale you check whether your value is your guess is too high or too low now here is the voltage input voltage that we want to convert the first guess will be mid scale and we will realize that we are too low. And then what we do is we make the next guess which is mid scale of this upper range. So, the next guess is here and we find that this guess is too high. So, we make the next guess which is again mid scale between this one which is here and then we find that this is the last guess that we have made we report that as the value. So, obviously, this was the input at this is what we have reported and this difference is the error in representation because of the discrete width the width is just 3 bits. If I wanted a better representation then I need at least one more bit which means 16 steps if I want even better than 32 steps. So, this is basically how a successive approximation ADC works and in the microcontroller kit that we are going to use to perform this experiment. All these components are available the D2A converter is available connected to a comparator where you can compare the guessed value with the actual value and obtain the output which will say the guess is too high or the guess is too low. And the programmer here that we have shown is actually the microcontroller. On the microcontroller you can make a guess send that guessed value to the D A cut water compare it with the value which you want to measure and then make a decision whether the value was too high or too low and make the next guess make the next guess. So, in your ADC experiment that we are going to perform in the next lab we will give you this opportunity for those who would desire to do that to build what we typically called a software successive approximation ADC using a DAC. So, it uses a DAC and the microcontroller and a comparator and runs through the successive approximation algorithm in the software. So, successively makes guesses subsequent bits are tested and so if you look at this here we are testing this bit the one on the what we call most significant bit here we are testing the next bit here we are testing the last bit the least significant bit. So, you are actually doing it by testing bit by bit. So, the successive approximation ADC output is typically whatever guess was the last guess made given to the D A converter is the digital output. Now you see that we have gone through steps in this case we have gone through three steps if it is an 8 bit converter how many steps we will go through 8 steps. So, how do we go through these steps? To go through these steps we have to use one type of digital circuits which are which are synchronized where things happen synchronized with the clock with the edge. So, they are basically synchronous digital circuits and that is why though it is not shown here a clock forms of course, it is here in the programmer it forms a most important component of an ADC and this is the clock which decides how quickly the ADC is going to make a conversion. So, we keep on increasing the clock speed we can get faster and faster ADC conversion, but yes. So, now the question is that what imposes the limit to which we can keep on increasing the clock speed. There are several steps in the series. The first one is the digital circuitry inside this. So, there is a limit to which the digital circuitry can be pushed the delays inside this, but that is usually very small it is in nanoseconds that is usually not the rate limiting step. The next comes the D A converter. The D A converter is something which we will look at the D A C a little later which takes a little time to convert. Typically it has got what is called a settling delay. The output voltage that it produces takes some time to settle. So, we cannot do go faster than that. So, there is a settling delay of the D A converter and then comes the comparator. There is a the comparator is comparing this voltage with the actual analog voltage and it is producing an output the comparator itself has a settling delay. So, all these delays cascaded together is the fastest that we can clock it and that will vary from ADC to ADC that will vary from implementation the technology. So, let us get a value of the range of physical time in conversion in successive successive approximation ADCs. Typically the simplest ones may take 50 microseconds for a conversion and the fastest ones may take may not be successive approximations, but others may take around 50 nanoseconds for a conversion. Typically successive approximation ADCs large variety of these will vary from 1 microsecond to 50 microsecond. But since the number of clocks depend upon the width of the representation of the word the conversion time will also depend upon the width of the conversion. Is it 8 bits, is it 10 bits, is it 12 bits, is it 16 bits? So, 8 bits will obviously be faster than 12 bits, which will be faster than 16 bits. Typical specifications of ADCs would be the range of input voltage, the range will also decide the resolution of measurement. It will be the input impedance, it is an electrical property of the ADC and it is not something that we want to discuss here, but it is important. Typically it ranges from kilo ohms to mega ohms. The accuracy of the ADC, the nature of successive approximation is such that you will always have a half LSB error, because the last test that we made there was some error and that error in worst case would be half LSB. So, what is the accuracy in terms of what is the half LSB in terms of percentage of full scale that is the accuracy and the conversion time. The format of digital output is also important. Many times it is what we call straight binary, sometimes it is two's complement, sometimes gray code depending upon different types of ADCs. So, here we come to we have finished with the ADC and let us just go back and try to consolidate what we have learnt. And ADC is this that we have here a black box where we give an input voltage, we specify the voltage range. This specifying the voltage range is usually done by providing a analog voltage which is called reference voltage. Most often the input voltage range is of the same magnitude as a reference voltage. So, if the reference voltage would be 5 volt the input range will also be 5 volt, where is 2.5 volt will be 2.5 volt, but it is not necessary. There may be a different relation also it could be 2 input could be 2 times the reference voltage, but there is some way whereby we specify the range of the ADC. Then it is not shown here, but the clock speed the speed at which it will do the conversion the clock speed. And there are some ADCs which will have an option that you want to do a 12 bit ADC conversion or an 8 bit ADC conversion. A single ADC could be used for both purposes 8 bits or. So, if you want low precision, but you want much faster measurements the same ADC could be used for 8 bit conversion. So, there would be an option of choice of the output width. And then in an ADC you have a start conversion, you give the start conversion pulse. And when the and then ADC becomes busy it starts converting when the conversion is over it gives you what is called an end of conversion signal. And when the end of conversion happens the sample and hold knows that end of conversion has happened I should go to sampling mode. And if there is a microprocessor or a micro controller it knows that the conversion is over I should read a read a value and go ahead and ask the ADC to make the next measurement. And the other aspect in an ADC in digital measurement says that whenever we are having a real signal and we are digitizing it and we want to reconstruct it. We may be off here which is the error because of quantization and we may be off here also in the time domain in this axis because of the sampling rate. The sampling rate is finite and the sampling rate is related to the signal frequency components. And if it is not right you may end up actually reconstructing the signal with wrong frequency component which never existed at the input. The number of frequent the number of point sampling points should be typically related to the highest frequency at the input of the signal. And you can see that as you keep on reducing the sampling rate you keep on getting more and more erroneous representation. And at one point you can get absolute aliases which never existed in the input signal. Now let us go to the DAC. A digital to analog converter is converse it is just a reverse of ADC. And just like an ADC characteristic is like this that you have an input voltage and you get a digital representation. It will be a reverse the digital input would be here the x axis would be the digital input and the y axis would be the analog output. But remember it will still be a staircase kind of a transfer function it will still be steps. You will only be if the digital input is 8 bits you will get an analog value here, but analog value will vary only in 256 steps it will not be continuously varying. So, a digital input gives you a corresponding analog representation if you are using a DAC. So, digital to analog converter is used to produce an analog voltage which is related to a proportional to the digital word that we are feeding and its characteristic is inverse of that of ADC. And this is where the DAC fits in the real world computer output is digital goes to a DAC becomes analog it can be used for controlling or whatever variety of purposes. Now how does a DAC work? How is a DAC built? Now interesting part of the DAC is that it is very different from an ADC you do not have do not seem to have much of digital electronics inside you have a op amp you have some resistors the op amp has been made into a summing amplifier. I am sure you are all familiar with the op amps some point you read. So, it is a summing amplifier and they are in no is it does not matter it is really very very simple to understand. This op amp is a device which has got a very large amplification factor if you do not put it in some kind of a feedback circuit and the moment you put it into a feedback circuit it starts behaving as an elegant device where the input and output properties are represented by very simple mathematical equations. For example, in this device that we have this point that I show here is called a summing point any current which comes here gets added. So, if current is coming from here and here and here and so many input sources it will get added and it will start flowing through this resistor. So, basically this is an adder which adds currents and the voltage at this point is equal to the voltage at this point. So, if this point is at ground potential or zero potential this point is also at zero potential or ground potential and hence this is called a virtual ground. So, what current will flow into this will be governed only by the voltage at this point and the resistor. So, supposing I give at this either a voltage of 1 volt or a voltage of 0 volt the current which will flow through this will be when it is on 1 by R 1 by 2 R 1 by 4 R or 1 by 2 to the power n minus 1 R and when it is connected to zero the current which will be flowing will be zero because you have zero here and zero here. So, really speaking this produces what is called binary weighted current sources ok. The resistors here are binary weighted this is R 2 R 4 R and in a DAC if you want to produce a if you want to convert a digital value to its analog equivalent we simply give the digital word to these switches a 1 means the switches on or connected to 1 volt a 0 means the switches off or connected to 0 volt. So, if I am giving a digital representation of the minimum least significant bit then only this will be on these will be off which means current will be flowing only through this or if I am giving the digital representation of only the most significant bit high then only one of these will be on the most significant bit will be on and only current will be flowing from this. So, this is MSB this is LSB over here. So, obviously depending upon how many of these bits have been switched on the current will flow and it will get added and the output representation here that we have will be a voltage which will be directly related to all the ones and their weights. So, this will produce a output voltage which will be related to the digital representation at the input. Just like a DAC just like a ADC had a range and you had to specify a reference voltage to set the range the DAC also apparently has can have a range. So, if you have 256 bit 8 bit DAC with 256 steps you can set the range whether the 256 steps will be 0 to 5 volts or 0 to 10 volts or minus 5 to plus 5 volts that kind of set by similarly setting here a reference voltage. So, you can also decide the range of the DAC conversion. Now, one of the issues with a typical what we call weighted resistor DAC is that it requires precision of resistors over the entire range which is usually very hard to get and these such DACs are not very common. Though the DAC that you are going to use for your laboratory experiment is actually a weighted resistor DAC, but the ones which are more common are called R2R DACs we are not going into that. The specifications of the DAC are essentially its resolution which will be the bits the linearity which really says that if the input changes linearly the output should also change linearly. It should happen I mean one would one would say why it should not happen why it should not be a linear change it really is not. So, most of these systems will have some nonlinearity into it. So, DACs will typically have nonlinearity of plus minus half Lsp. The accuracy the settling time DAC will also have a settling time problem from the instant that I want to make a change the output will take some time before it settles and this how much time will it take to settle within half Lsp is called the settling time of a DAC and that may be significant. For example, the settling time of a DAC may be the DAC that you are using is 100 nanoseconds. Now, 100 nanoseconds seems very small, but when you are working with very large frequencies that 100 nanoseconds is significant and this is only an 8 bit DAC the moment you go to 12 bit DACs this becomes worse you may get a 12 bit DAC typically with a 1 microsecond settling time 1000 nanoseconds and as the accuracy of representation or as the half Lsp size becomes smaller and smaller that is for the higher resolution DACs this settling time becomes larger and larger this is an important parameter for specifying DACs. And this is also something called temperature sensitivity of a DAC that is of course, true for all digital and analog devices and the DAC is actually an analog device. So, the temperature sensitivity of an analog device will get translated to this and it will it can mar its performance. Now, after having a look at the ADC and these DACs let us put them to some use and let us look at what is going to happen in the signal digitization and requisite construction experiment. Actually you are going to do this you are going to take a input signal may not be from a microphone may be, but perhaps from a signal generator sample it in an ADC and perhaps you can also use a sampling chip sample and hold chip outside if you wish to convert to your digital bit stream you can do something with it if you wish you can do a filtering of that or you simply routed back to the DAC and reconstructed and study that if you change the clock frequency or if you change the sampling rate what happens to the reconstructed data are you really getting those problems which I have just told. Can you find out by changing the clock frequency what would be the right clock frequency for an analog signal frequency for a given analog signal let us say 1 kilo hertz is a signal frequency or 10 kilo hertz is a signal frequency and you change your clock from 5 kilo hertz to 100 kilo hertz what is the right clock frequency for you that the DAC is giving you correctly reconstructed output. So, you should perform that experiment and this is one small detail about what is a clock signal a clock signal is actually nothing but a voltage which is varying with time 0 volts to maximum 0 1 0 depending upon the technology the digital technology that you are using the 0 and 1 will be defined in terms of that for example, the TTL would have 0 as anything below 0.8 volts and 1 as anything between 2.5 and 5. So, in a clock there are 4 things which are important it could be the low part of the clock it could be the high going edge of the clock it could be the high part of the clock or it could be the low going edge of the clock. So, things may happen when the clock is low or when the clock is high or in the positive edge or in the negative edge. So, typically in digital circuits sequential digital circuits they are sensitive to the edges only. So, things happen either on the positive edge or on the negative edge most of the circuits that you will be using will probably have will be sensitive to the negative edge. You have already used timer 555. So, we will not go through the details of this just to give you a brief overview you have you have already used. So, I presume that I do not have to describe how it works this is the stable multivibrator circuit that you will be using for clock generation which you have already used. Since you are going to change the frequency remember please note there is this resistor R A and this resistor R B you know that when the capacitor charges it charges through R A and R B and when it discharges it discharges only through this transistor and hence only through R B this transistor makes this pin 7 connects this pin 7 to ground and this discharges through this right. So, and the frequency depends upon both R A and R B. So, what you might be tempted to would be to change R A as well as R B. So, you might actually end up making if you make R A large it does not matter, but if you make R A small there is a small risk which is supposing you use R A of around 1 kilo ohm 1000 ohms and you use a VCC of 5 volts then when this transistor is on that is when the capacitor is discharging there will be 2 components of current flowing in this transistor the one which is the capacitor discharge current and the other one which is flowing from the power supply through R A resistor. So, if the supply is 5 volts this will be typically and this is 1 K this will be typically 5 milliamps 5 milliamps is fine, but if you reduce it further from 1000 ohms you reduce it to 500 ohms to 200 ohms to 100 ohms this will get damaged the transistor this transistor will blow. So, what I want to caution you is you if you want to change the frequency change R B or change the capacitor of C choose a value of R A which should be the smallest acceptable value I would suggest 1 kilo ohm or 1000 ohm and change only R B and C for changing the frequency ok. And this is the frequency relation which I am sure you must have used the description of the laboratory experiment is you have to make the 5 5 based clock generator measure clock frequency during the experiment the clock frequency may be changed by altering component values. You can also observe the duty cycle and keep that check that I told you that do not change R A only change R B. The ADC circuit output can be seen on the LEDs which are available on the you are you are going to work on a kit micro controller kit which has got the ADC and DAC also on the board. And there are there is a way whereby you can observe the output converted output of the ADC on LED. So, you should observe the output also set up the DAC circuit which is for which you do not really have to do anything there are some jumpers which have to remove that will route the converted ADC output to DAC. And you can observe the reconstructed output on your scope and you should find out what is the discretization error by giving a known input to the ADC. Now give a AC waveform to ADC reconstruct using DAC and see the effect of ADC sampling frequency. This is what you are going to set up eventually the function generator which is which will be your PC scope only output going to the ADC which is getting a clock which you will be wearing the output going to the DAC observed on a PC scope and compared with the original data. The PC scope has got two channels will be comparing these two right. So, that is about all if you have questions let us have them yes. I do not know the resolution of the ADC DAC inside the PC scope, but I presume that this will be at least 1 megabits I do not know somebody we can find out you can ask the TAs they will tell you. I think it will be probably at least 1 megabit maybe more no no no only successive approximation ADCs have a DAC as a part of them others like sigma delta they are based on a totally different technique and the integrating ADC is also on a totally different technique integrating ADC is made of like a DAC it is made of some integrators basically there are there are op amps inside. Any more questions regarding what is it that? So, you are all clear about what is going to be performed in the lab ok.