 So, let us pp to that next problem, next problem I had one s above that, I am going to solve only a piece of this, not the full thing where the process is going to be same. Now, there is a s term s in the numerator, I said transfer function that it will not be there. So, some term with some gain may be you continue with 6, it does not matter. So, there are two ways again of doing it, the first way is very simple again do by t of s is a s plus 2 s has disappeared. No, anybody has any doubt, if the order of the denominator is more than the order of the numerator, there is nothing in the numerator a b c d etcetera, like this people keep asking. So, method 2 does not actually depend on whether there is a s in the numerator or denominator, I get my standard for my circuit looks identical, then it goes here and goes here and absolutely not worried whether there was a s in the numerator or not, my method is all uniform. So, what is the uniform advantage, I only know this, how to do it that is all. I do not know any other form, what are the other forms, the forms are required if I have to do this in random. So, I go to method 1, what I have I can be smart and put this here it does not matter. So, one of them has to have s. So, now, I have to design two different types of circuits and put them in random. So, now, I have to have a circuit which gives me this. So, the solution is very easy, I have a circuit going like that of course, do not take my work for it I am going to do. So, this is my z in. So, this we call it r 1 c 1 and this is simply r f. So, what is the z of this z in r plus 1 over s c 1. So, in my output that transfer function is minus z f by z in. So, minus z f is a simple register r f and now I got this you want me to write I will write it, but s c 1 r 1 plus 1 upon s c 1. So, it goes up minus r f c 1 s upon s c 1 r 1 plus 1 I got that. So, this is what I get. So, this is the second circuit I have to remember. So, once I get this second circuit I am happy. So, if I know both circuits I can always do this I can always and then I am not limited by any number of any number of terms. I have lots of varieties if you give me s plus 1 and s square I am still ok. I can have one of them as s upon s plus 1 into s upon s plus 2 into 6 upon s plus 3, but you give me a polynomial s square plus s and all that I should be happy doing it by partial fractions. Partial fractions is a magic as if it is magic it will remove partial fraction does not care. So, partial fraction does not care. So, what is the vote today? What is the vote? Partial fraction if you do well you are the happiest person, because then you have to remember only one type of circuit. One type of circuit is then as a routine policy choose this arbitrarily and then you get better too. So, if the mug up curke is a chalayan, but now we have to mug up the method. Now, we have to understand why method 1 and 2 are different and which one is easy for you it depends if you can know both the circuits you can tackle s upon s plus 1 that is also easy that is another circuit, but I personally feel that knowing one type of type of circuit and one procedure is much better. So, I think today's tutorial therefore, and we have lots of questions and certain time that a tutorial session when I take it I spend first half an hour in giving the background. Do not assume that they have understood in the class repeat it like I have not gone into the details of it, but I repeated it then take the simplest form. The problem is difficult take one simplest form and do that then show that this simplest form can go some distance then show a anomaly or some satellite problem where that cannot be used then you have to do that also and then finally, evaluate which method of course, we should know all methods as a student I can ask them to do this by only using tandem circuit. You know I can give an examination where I do not give a choice solve this by using three op-amps in tandem or I can ask them to do it by partial fraction followed by a summing circuit, but as a student I should know both the methods. So, this is the break up that you have to give now is the question which I will take a few questions now is this called design or is this called analysis is called design because I am finding all values of components. If I do not give this at all and draw a circuit let me draw it more carefully. So, that descent v 1 of t 10 kilo ohm 100 kilo ohm 10 micro farad I remember that. So, I put it then I put another one 100 kilo ohm 1 micro farad and 10 kilo ohm does not make sense 100 kilo ohm then I find the function v of t if v 1 of t is a step function or v 1 of t is sinusoidal this is called the analysis problem. I have given all values and you have to determine what is at the end of it the other one I have given only the formulae or the transfer function and I have asked you to derive no reference was given for anything you have to find all values of components, but as I told you it is only two conditions of given in after all what is what was it realizing say some 6 upon s 2 that means, when s was very small it was 3 and the product of this was equivalent to 0.5 s that is one that means, the product of the register in capacitor was 0.5 that means, only two conditions are there, but I have got three values to be determined. So, I have begin with one arbitrary. So, very clearly you have to write what is that arbitrary value and then everything becomes a design. So, if you similarly make an amplifier with gain of 10 and there are 6 components in that amplifier there will be 5 arbitrary values of components and that is why in the laboratory that amplifier does not work. So, you give only one specification and there are 5 values of components. So, it should not be like that you have to say that this is the 12 volt supply Poisson point should be right in the middle you should specify Poisson point should be at 6 volt and the current should be exactly 5 milli ampere. So, two conditions you have to measure for Poisson point and then you have to say the gain should be so much that is the third condition. The third one you have to say the total power in that amplifier should be so much that means, you have to bring down the unknown values to 1 and only one unknown can be taken as arbitrary because you just say make a amplifier of gain 10 and everybody will do anything and there is nothing left in that, but good practice actually believes that Poisson point should be in the middle etcetera etcetera, but to a student we cannot hope because he cannot do this. He cannot find 5 arbitrary values for one specification even I find it difficult to you know imagine some 5 values which are arbitrary and then. So, I have to have a process. So, madam has to give me a sheet after this class will meet give me a analysis procedure and the instruction for full design you said the instruction for full design therefore, is at the most only one arbitrary parameter and one arbitrary parameter is ok, but even here I can remove that arbitrary arbitrariness by saying that the range of registers cannot be less than 1 kilo ohm here. I can put some condition that you do not use any register 1 ohm 10 ohm like that. So, the register here cannot be less than 1 kilo ohm register anywhere cannot be more than 1 mega ohm like that I can put condition. So, even there are arbitrariness become within limits and therefore, I think we now know if this appears easy to you is not necessarily easy for student for the student designing equally difficult compared to this. This also is difficult from this he will be spending all the time in getting this y of f then inverting it and after that he will be converting it to polar coordinates, Cartesian coordinates and it will drive him crazy. The students are very fond of getting into a corner where they do not know what to do. So, I keep telling as a thumb rule to all students multiplication and division only I need polar coordinates that is magnitude and addition subtractions algebraic I need Cartesian coordinates. So, this is like a plus j b, but I know they can get totally confused. So, this problem many a students will not able to find that final function though it is very easy, but they will be able to do the design because the design is very easy. Because from this value to find this value is easier, but to go on actually doing it as if from fundamentals then it become tough. So, somewhere you have to be more familiar with one type of circuit. If I am familiar how to design this circuit I am comfortable with partial fractions. So, partial fractions have solved my problem forever any filter with this kind of characteristics I have solved that problem because I get only one type of circuit every time. So, I think I stop this tutorial right here if I just show you that second problem of the tutorial because I had asked students also to do it will just think over it. So, what you say? So, I am of course for partial fraction, but if you do not want to do it by partial fraction what are the choices you can do 8 of s and all this plus 6 upon all this and split it, but it goes a very wide distance away. So, in this case I cannot even advise that you know do it in any other way simply partial fraction because s plus 2 is the problem because that plus 2 has come. So, in partial fraction there will be none of these a upon s plus 1 a upon s plus 3 a upon I mean b upon s plus 3 c upon s plus 5. So, that is why I left it to students to partly confuse them because for the problem one I have given two methods problem 2 I have expect them to try both methods and they should go crazy with the second method. So, there is a problem there s plus 2. So, let us have a little discussion if you are not too tired little discussion on what is that connection you have to make between theory and reality which is called laboratory. So, my suggestion is now this way suppose there are 9 laboratories to be done in the next big course. How many days? 10 days? 10 afternoon maybe 9 of those afternoon are laboratories maybe 2 simple laboratory problems. So, maximum of 18 I do not know what is the final number on that, but otherwise even if you take 9 lab problems none of them should read as what it reads today in my opinion. It should not read common emitter amplifier it should not read like that it should say audio amplifier speaker resistance is 32 ohm and the power is 220 milliwatts. I have to create a few more specification and of course audio amplifier immediately implies up to 16 kilo hertz cut off I want it between 100 hertz to 16 kilo hertz. So, please you try to understand I have to create as many specification which are relevant to operational audio amplifier not for confusing the student for making him zoom on to the reality. So, he has an amplifier this circuit this is my speaker. So, I show it like R load and I have got this R C R E C E and I have either this kind of biasing and then I have got this capacity will be coupled here and I have got a source here. Then I can say audio amplifier this is a microphone microphone has got total range of 100 millivolt of signal and internal impedance is 150 kilo ohm so why am I creating so many details because our student has to find this, this, this, this and this assuming that the beta does not play any role it should not play any role in any amplifier beta should not play any role as long as beta is more than 150 it should not have anything to do with it. I am just saying any microphone will have a large resistance if it is a capacity of type isoelectric type thing is resistance is very high, but signal is very high if you have got a magnetic coil type then signals will be in micro volt and the resistance will be small I have just specified one. So, it sets a tune as to what this resistance will be the 220 milliwatt sets a tone what should be the current flowing to this we anyway know that this is the frequency range so probably this will be known from that this will be known from that etcetera. So, this decides the lower frequency it has to pass 100 hertz at least and this has to give me some gain at 16 kilo hertz or more depends. So, what I am saying is not that I am trying to make that problem complicated actually I am giving a proper hint for him to have phi unknowns right he has got phi unknowns I must give phi conditions. So, I feel that we should create that many conditions at the most one arbitrary thing one arbitrary thing will get. So, what it means is when the maximum signal is here I must get 220 milliwatt that is what it means this is the maximum signal. So, gain is not even specified otherwise if you do not give this value you say the gain should be so much. So, give me any other laboratory session that you did I want to word it with some solid specification from reality say multivibrator you will be doing using op-amps tomorrow right. So, suppose you want to make this multivibrator for making a digital clock digital clock. So, after some frequency I create. So, this is my original clock and after some 2 raise to n division I should get 1 second right then I must use a divide by 60 to get 1 minute and I use another divide by 60 to get 1 hour then I use divide by 24 to get 1 day. So, we are not making a multivibrator just like that I am making to this specification that is the criticality in the process the student will also know what is all this he is not going to make all this, but he has a specification to do that. So, that means this 2 raise to n will decide what frequency he will choose 4096. So, any frequency near about multiples of this he will choose otherwise the portfolio will make a 1 hertz oscillator and it will not work properly. So, you can now specify that he has to make either 4 so called rough number 4 k hertz the other one could be k hertz nearby the exact number is some near as 2 raise to p because crystals are now available with that kind of frequency 32 k hertz some 32 some other 3 digits. So, that now we can have this division to bring exactly equal to 1. So, let him make that oscillator and get that frequency very close to 4096 that is his objective instead of putting any register or any capacitor and getting any frequency you should not even tell him that he should make this frequency you tell him that this is the job I need a vibrator at the beginning of it. So, like this please invent please invent a word statement which is connecting it to reality and provide him with enough information about his design. So, that he can design it and all the other design parameters will be corresponding to your op-amp. The op-amp you say that the register cannot be less than 1 kilo ohm nor it can be more than 1 mega ohm. Secondly, the capacitors will also have to be not going too much away. Let us say the range of capacitor should be 0.01 micro farad to 10 micro farad I do not know 1 micro farad to give me range. Let him choose a frequency which is in multiple something either higher or lower. So, I think it gives him a little challenge he thinks that he has made something original experiment remains the same. So, this is a purpose and a purpose mention any other experiment what you did first day lighting LEDs. Now, clamper and clipper any applications we know yeah, but any real application no that is a function you are describing a function where is it required which real application can be used I know possibly I do not know about that anybody else any real application no you want to use a clipper here no this no this no this applications are finished. I am just talking about this third experiment that we had like that or you had another one like clipping 5 volt 5 volt both sides is there a real application we are making the circuit is ok. Is there a real application there is a real application if you have got a board in which lots of ICs are there right at the beginning. So, there is a board power supply and all that right this is the power V c c or V d d minus V e they should be actually having a clipper or clamper attached to it which has this characteristics of suppose you want to limit it to 5 5 no 6 volt. So, when it is 5 volt plus minus it would not do anything, but you cannot by mistake apply 110 volts or by mistake apply 12 volts where will clip it. So, clipper and all this is a wave shaping I have to understand the wave shaping is not clipping and clamping, but wave shaping is creating a thing like this or creating a strobe like monostable. Monostable use should be used for creating a strobe line at the following I create a strobe. So, a monostable use for creating a strobe of a given width. So, when you give a monostable project you must say that this strobe are used for activating sequential circuits and we cannot just depend on a differentiator with use a very narrow thing and all that. I must give a 100 nanosecond wide strobe a nice square pulse of 100 nanosecond while this could be 1 millisecond. So, when it goes down I must create a strobe here. So, when that switch for counting people going in the lift and coming out and all that it cannot depend only on the thing which is going down at that point it should create a strobe which the next circuit will not miss. So, the strobes of some very small amounts are very good as an example for monostable experiment. A monostable multivibrator experiment should have a preface like this that this is going to be used for strobing and operating a toggle flip flop. So, this should go to a toggle flip flop and students have to demonstrate that after such a strobe is created and given to a toggle flip flop it flips. So, such exercise has to be given which is a little beyond that making a monostable otherwise the people will make a monostable of any arbitrary value. Multivibrator I have already told you that you should mention that it is likely to be used in a wall clock. So, they have to make it worthy of 2 raise to n and then nearest sample frequency is 4096. So, they can take it be the one or a smaller one. So, if a monostable we can give that. The pulse shaping circuit the transient for example, if there is a experiment on DC transient. So, you have a pulse going like that and I want a transient to either do it like this quickly go and saturate or do it like that. That means it is not even saturating before that and then it falls down like that. So, we say that I need a curve which has a small time constant both wise going up and coming down. Then you say a variation that this should be one tenth of the pulse width. So, in real practice it should never go anywhere near it otherwise you end up in getting almost a triangular wave. The next exercise can be that this should be of one different value and this is of different value. So, this slope can be different. So, this time constant is different and that time constant. Because this is called wave shaping. So, we have this need for a pulse is coming and I have to find out whether this particular pulse a real pulse will be somewhat like that in a real application the pulse is like that. So, now I have to find what is the width at half power or half value. So, now you say given a pulse like this which is a distorted version of this. So, rise time is different fall time is different and you have known a very generic pulse as the student to make something to find the width at this point. So, he should study the pulse shaping circuit in this way. So, he has to create this pulse by this time constant tau 1 and tau 1. So, this is tau 1 and that is. So, it should begin like that. For example, all these astronomy people make this experiment about neutron measuring neutron shower and all that and they get pulses like this. So, from this pulses you have to really you will get an idea what is this width of pulse and this is typically in nanoseconds. So, you have to say that these are very short pulses and of course, nanosecond if you make then student cannot do it. You should say it is a small 100 nanosecond width pulse. So, they have to find this width. So, in a sense you are asking them to create a similar that is the connection like that you invent and I think every center should have freedom to invent that part of the story. We will also try if you keep as in when we prepare such a list we will also try to for example, the audio amplifier I have already created full. The filter of op-amp I have already created a full story right. We are now defining my filter and I am now designing according to that. So, similarly we should create a connection to reality for each of those experiments and then become very easy for student to determine all parameters. Otherwise, there is so much flexibility that he would not be able to determine anything at all. Practical should be on that only, but I personally feel. Here we were not teaching anything the lectures were just sample yes. So, if the practicals are 9 into 280 n that means there should be 18 lectures also right. That is what I understand, but I think the practicals should be less than the lectures because you cannot just grasp everything in one lecture. A one and half hour lecture you cannot conduct a one and half hour practical is impossible. So, I think 18 lectures and 9 practicals is more like it. In the practicals you should have those satellite problems like I do. So, when I give you a particular thing you say ok determine what you can do to move the frequency this way that way etcetera. So, I agree with him perfectly two lectures of one and half one and half hour each should lead to a reasonably good practical. So, only thing is I am requesting organizers I will also be party to that to furnish a real connection or connection with reality. Not only the connection it also makes specifications for that practical. So, that arbitrariness of that practical goes away. So, how do you reduce the arbitrariness normally by making ready made kits. See what is the college doing by ready made kits it is removing arbitrariness otherwise student would not be able to do anything. That is the reason why we are doing ready made kits is not it because we have no arbitrary design possible students will not be able to do it. So, we only say we ready either input lagga either output measure curve. So, instead of that now there are professors who are going to attend next time we must specify as many parameters as possible. So, that the arbitrariness goes and then we do not have a ready made kit I mean ready soldered circuit for it you have to make a circuit. So, I perfectly agree madam please note suggestion came and I agree with it that if there are two one and half hour lectures only one practical should be aimed with that. And that practical should have a few variations connecting it to some reality. So, that the students are able to make connection with it not 18 practicals you have got 9 slots right 9 afternoon. Even if you have 3 3 hours you make enough variation in that practical to make it worthy because we found one and half hour we cannot actually do so many things. Thank you very much.