 So here we go, we were talking about the current and voltage references, we were looking for some kind of current mirrors and we looked into Wilson current mirror and then we said okay it has a good output resistance, it has a feedback so it stabilizes faster and better. All that we did last time was the Wilson current mirror. So let us start with the part ahead. Another current source which is very popular and one of the reason why we said Wilson as there is a how much voltage across that we will get that is the resistance across the source is relevant in many applications. So we want to see now, there is another reference available in the book, please take it, this references both current mirrors and current sources, current voltage references are I am actually teaching it from Lee Boyce and Baker's book okay. So some data if I am missing here you can go and look at that book, exact title is not this but roughly this, Lee Boyce and is that okay. Okay, so as I said this is a good chapter there, the value is given essentially for very old technology 5 microns but that does not matter actually the principle behind we can utilize it to any technology no later. So I will start with the another reference which is the threshold reference as it is called VT reference current source, the advantage of this is it is a good stable source, if I0 increases, we have done earlier in Wilson, if this current increases the drop across this increases, so VGS of this increases, so this current increases, this drop increases because of the saturation current point, this reduces the VGS for this and it feedbacks itself to a constant value as we did earlier okay. So this advantage of this is that it is a quite stable source and typically one has to choose these R2 values suitably and so that a faster recovery is possible, is that okay. Of course as I said this is only to show you what is the way, Wilson has done same thing but slightly modified from this is the Wilson mirror which we have said, there is no R2 I think okay, here we have given a R2 drop which is VGS for the next transistor and that changes the current in the other arm, feedbacks to the from here to here and keeps still that adjust to itself okay. So thus it has a stability because of negative feedbacks as we said, is that okay, this as I said please do not write all that I have written it because I thought maybe I should not miss what I have to say, but other things you can read yourself, maybe I repeat the theory is this, any change here is reflected change here, change here, reflect back here and there is a loop going on there okay. This is the technique behind stabilizing the sources, is that okay, this you can write which is the final version of output currents. The output current is given by threshold voltage plus under root of 2 IN upon VT, what is this value essentially, VGS by R is essentially the current, is that correct, VGS by R is the current okay, so that is written in the same form with nothing very serious okay, I0 R2 is VGS and VGS is written in this form, so I0 is only a function of VT, VT is normally fixed for a technology 0.8 volt, 0.7 volt, 0.6 volt, whichever value you fix, however temperature dependence is not very good and not very bad either, but let us see how much we have done earlier and we will not do DCF for this because the modified version of this which is the source I have shown you is now shown, have you written down this expression, we are not going to use this because it has a VT direct function, temperature dependence both from R from beta dash and from thresholds okay. So we will like to see can we improve the DCF for this source, though it is what is the advantage of this source was stable, it is a negative feedback, it is stable. So modified version of the same which has been created instead of the resistance, we can replace it by some diode or rather a current, a transistor itself which is in active mode that is in saturation mode, just let us say anything which you think I am not, please look the book and if they are still various, I just want to finish this current because next time I want to start with open ends. So I am little fast today, please note down, a better version of VT reference current source is called regulated cost code CS, current source. You can see this part is same, M2, M4, M1, this is same, all that I have replaced is now R by a transistor which is biased by me to my choice okay, which is this. But what will happen to M4, M3 combination, this is like a cost code okay, this is like, so what is the advantage of this circuit, output resistance is boosted up. So one of the major advantage or major requirement of a good, last time someone was asking what is good current source. The question asked was that whether it is temperature dependent, how small is temperature dependence, how small is the or how large is the allowed and how much is depending on VDD variations. A good current source should have lower VDD variation, this lower temperature variation and larger R0s, those are called good current sources. The current sources given to you in exam both are bad because they are strongly dependent on the temperature as well as VDD okay, so they were not good current sources. If someone has written good and forgot not, then he is getting 0 on that okay, those you are not good, so both may say, so please take it, these are the trials but that is the choices are made in real life okay. If you have seen this, as I already calculated R0 for a cost code and it is the AC output impedance is around gm square R0 cube assuming all terms are same W, volume, same lambdas. And if you look at the current now, it is VT divided by R2 because the maximum voltage across this will be VT and this R2 essentially is coming from, sorry the R2 has been okay, it is essentially trying to say whatever resistance offered here is divided by VTY, this is the one which will give you the current which is equal to I0. Now this analysis which we have done earlier, all that it shows that it is stable because it is a feedback, now it is only a function of threshold voltage which is given to you, so only one temperature dependence and this is opposite polarity because please remember one interesting feature you should all remember, resistances normally if you have learnt earlier I hope so some of you have, it has a positive temperature coefficient that is resistance increases with temperature but all semiconductor resistances have negative temperature coefficients, is that correct? Mu is the proportion T to the power minus 3 by 2, is that clear? And therefore the semiconductor resistances have minus TCFs typically 2000, 3000 PPM per degree centigrade okay, like N plus transistor source, if I use it it is around 3000, if you use a poly resistor, polydope resistor it can be 2000 okay, so is that point clear? So the resistor in semiconductors are my negative temperature coefficient and that is sometimes advantages, sometimes disadvantages because both minus may add, the other quantity is plus, it may actually subtract okay, in that case semiconductor resistors are preferred over external resistance, you can always put in a board separate resistor, after all this chip is there you can always put a resistor at the board okay but that is never done, is that correct? That is never done because that will give you positive temperature coefficient, it is a carbon resistor, carbon shows positive temperature coefficients okay, so the same source slightly modified gives you better VoV, VoV is VGS minus VT which is less than this, so typically you can say I0 is threshold by resistance which you can calculate and you can see R0 is very high, R0 is, R out is very high, so this is closer to what you are looking for good current source okay, is that okay, read more about it, now let us start with, this was the part which I should have finished last time, so I just now start with the real one which I am now looking for there I spend time, the other requirement other than the current source is the voltage reference, what is the, why it is called reference again because this voltage, otherwise you take a power supply directly, that also is the voltage reference okay, but what is the problem with those power supply voltages because they will change with all kinds of things okay, by the load, by the VD, whatever the inside transformers, all currents everything will shift to, though we may stabilize it, though normally most power supplies are stabilized power supply, but there is still a ripple on, you cannot reduce to 0, so a good reference DC source because we are requiring now a DC output which is strongly, which is very strong in the sense that it does not change very much with temperatures and it also is independent of VD okay. Of course the easiest reference how can you create by using resistors, easiest the first one voltage divider, take two resistors, take a tap out of it and that can still do the job which you are looking, so this is a question for those who want to work with analog in future, these days all mixed signal circuits have analog power supply as well as digital power supply, unit is created there, this is management, power management unit, all chips have, they require 1 volt, 1.5 volt, 2 volt, 5 volts kind of supplies they need and they use what they call as DC to DC converters okay, questions to all of you, why DC to DC, I mean if DC is available just put a divider and take any amount of taps on it okay, but why do we create DC to DC converters on chip, we will come back to it later okay, he has a point but that has a cost on it okay, it is not free okay, is it visible, yes, I take care that I remain inside but you know it is only my thinking I am doing it, the easiest reference as I say is can be created by two resistance network or what we call divider which is R2 upon R1 plus R2, if I take D reference by VDD then it becomes R2 upon R1 plus R2 and if we take the sensitivity of V reference with VDD, this is VDD by V reference, V reference which is unity okay, so the sensitivity of reference voltage with VDD is 1 which essentially means every change there is transferred to the reference, which is obvious, you can see if I change this output is proportionately changing, so there is nothing I can do about because you are just using the divider part there, if I do this DV reference by V reference that is changing by this percentage, so this is same as we say, so if you calculate the temperature coefficient of V reference, I differentiate this with temperatures equations, then I get 1 upon V reference DV reference by DT is equal to R1 by R2 V reference by VDD and this function, this is CFR2 minus TCR1 okay, if you are making the same material resistance, the difference will be smaller because this 1 upon R term is going to still come, DR by DT may be same but 1 upon R values are different, so these are not equals, is that point clear, otherwise sometimes you may feel why I am putting it because 1 upon RDR by DR by DT will be same for the same material but 1 upon R are different, so these 2 values may have difference, so one of the criteria is R2 should be closer to R1 but what does that mean, 50 percent shifts nothing more, I cannot do 0.2 VDD or point I have to do only half a VDD kind, which is not every time you may require, so it is a good to have simple divider if you are only using VDD by 2 okay, but it is a very strong function of change in VDD, temperature wise it may not be that strong function if you keep closer but it still has a problem of VDD, sensitivity is very strong with that okay. So let us look at it, if this is not very good, what should I do, I replace at least one of the resistor by a transistor okay, is that okay, everyone this is 3L, all that I am going, I was trying to say that this look to be simple, the problem it creates is only be close to 50 percent VDD shifts only are possible but even then it is proportional to VDD as a variation, whereas temperature wise you may probably minimize it okay, so the next stage we replace the R2 by a MOS transistor in saturation and we know in saturation transistor has larger resistor but it is value can be modified by VJS itself okay, so one can adjust and W by L's okay, so here is we are made the reference voltage is across the diode, of course this is a diode connection, so VJS is V reference, the current in the transistor is through current in the resistor, so VDD minus V reference by R, but we know ideas is beta by 2 VoV square for the transistor assuming lambda to be very small, so VDD minus V reference is something like this, solving we get V reference as VT plus 2 beta R VDD minus V reference, still this V reference is there, so let us assume VDD is very large compared to V reference, then I can leave this V reference here and I can directly write V reference is VT plus 2 by root beta R VDD by 2, what do you say this will be a good you can directly say it is a function of VDD is that correct, it is a function of temperature okay, it is also a function of temperature through beta dash okay, so as far as this dependency is concerned does not seem to be a great this divider I mean great voltage reference for the sake of my I have not solved it as I said I have taken it this from the boy this of course I solved but the next two formulas I just copied I hope so I am I have done some rough calculation I thought they are done correct I hope so is that okay, is that everyone wrote the function V reference is VT plus 2 root beta R VDD to the power half is the reference so how do I just V reference value therefore by adjusting the value of W by L by adjusting the value of R and of course the supply which is given to you okay that will decide your reference for please remember VDD is not in your hand why technology will say 1.2 volt 1.5 volt 2.1 volt whatever they say that is the voltage you have so we are no game on VDD but we can always look for beta which are sides or which is we are actually can you know what this R could also be instead of this another transistor but which one you will prefer there a P channel device is much easier preferred and then the ratio of W by L will give you this voltage output at this is that clear just replace a P channel device and gate connected to drain as usual and then that means the same gate goes to these so it looks like more like a CMOS okay but the input is connected to the output because they are two diodes is that clear that clear so this essentially gives me this formula and as I repeat I had taken it from the book so I am not saying they are wrong but the owners of right or wrong with is Mr. Baker okay not with me so it says that SV reference though I have done it but you know in hurry I did not know exactly whether I roughly what same but I just copied it then nothing very just differentiate there is one upon this there is nothing great we are doing VDD upon V reference D reference this and this comes to be VT times 2 beta R by VDD plus 2 and if you look at the temperature coefficient this gives me a long expression VT time TCF VT minus half but 2 by W by L VDD upon R beta dash T into 1 upon R DR by VT minus 1.5 by T is that correct this 1.5 by T is coming from where d beta dash by beta dash that last time we did in a class also I forgot so I remember while going to main building that I am not given that data to you okay please remember one catch here which I said in the class also T is here in Kelvin's all other things are expressed in part per million per degree centigrade but when you divide 1.5 by TT is in Kelvin so how if I divided by 300 how much it will be roughly 5000 ppm per degree centigrade is that clear 5000 I think so yeah 1 upon 1.5 5000 ppm per degree centigrade so this remember that this number looks to be small but that is giving a huge value for you okay so do not think that it is neglected okay 1.5 by T is equal to 5000 ppm per degree centigrade which is huge number is that clear and actually that is the one which observes most of it okay that is the great fun of this part okay so this also reference how you can see though I have not done I mean next time I will show you a problem or maybe I will post it on the few problems on this this still has a 3000 ppm to 1000 to 3000 or 4000 ppm per degree centigrade TCFs which is not fantastic less than 1000 or 1000 is acceptable or anything more than 1000 is not very good TCF if you can get around 1000 or lower what is the ideal one I want 0 okay I want 0 now is try to see this word I say 0 can I really get 0 how can I get 0 if 2 terms 1 is plus and 1 is minus and I adjust the values of either or 1 at least so that the 2 terms have same value in opposite sign then TCF can go to 0 and that is exactly what the last part of this today is this will be what we call band gap reference okay and we will show is TCF could be close to 0 if you can move 0 also but then W bias will be so odd you cannot put it on the chip and therefore you may probably not be getting exactly 0 but close to 0 okay so let us see so this is a voltage reference no great problems with this making it is easiest of it because anyway CMOS there is a sitting there just connect the gate to the output and you have a divider and adjust W bias to get the ratio you want so it is the easiest divider they see and digital circuit this is very often used where do you think we use this this divider is extremely useful in digital circuits it is also called voltage translator the reason is let us say I cannot statement but you are using a by CMOS chips also with I mean by CMOS bipolar and CMOS there are new technologies rather old one which is re-circuiting now therefore called name by CMOS started in 1987 88 was given up in 90s useless 2005 again old let us look at it so it has come back so by CMOS this issue may come that bipolar requires for example noise margin or a shift point is around 1.2 volt from 0 to 2.4 for a supply of this it may require 0.6 1.2 supply so you may have to actually get half of that equal to half of the other is that clear CMOS half should be equal to half of the bipolar swing okay which may not be same whatever we do okay so unique translators so there in all digital by CMOS circuits a translator is essential and this the simplest answer to the uses a CMOS divider okay so please take it why they are using it because they are not really looking so much temperature sensitivity because they feel 1 and 0 has enough margin for me as long as 4 corner design I am in thank you very much kind of thing analog goes haywire so we are worried there okay is that okay so please remember these circuits which I show sometimes you may not feel that they are relevant but they are relevant somewhere else and therefore I thought I should show you okay now I show you another voltage reference okay here is a better reference which is called bootstrap what is a bootstrap what is the word bootstrap came from so in voltage levels are actually pulled up okay that is why it is called bootstrap we have you pilot circuit bull job okay one can see it is not very different from threshold reference which we are done all that is there see m3 and m4 are identical okay and they are connected in diode form here so what does that mean m3 mirrors m4 currents okay m3 mirrors and if these are sizes are same current in m3 same as current in m4 so I have written current I1 and I2 in fact I1 and I2 will be equal provided m3 and m4 are same W by else same thresholds and connected in this fashion is the and therefore it will mirror this current into this okay. So in real sense I will put I1 equal to I2 but right now I show in two separate currents now this there is another term this is like a feedback circuit which we did just now is that correct at VT reference this is same circuit so this current goes through R these are all gates so no current can go either side so this all I2 will go through R okay. So it will create a voltage drop here which is the voltage drop here connected and so now you can see the current here is because of VGS1 and this is coming from here so they will again do a feedback and adjust I1 equal to I2 at the end is that point clear so how much is the current I2 VGS1 by R is equal to I both I1 and I2 is that correct this is what we want to we did earlier just that is repeated only difference here is this is coming from P channel sources down is that okay the problem starts okay what is the problem now if you see still you forget this and these are outputs one is current source other is current since this is N channel this is P channel just connect it here okay I connected from here you can also extend this here because they are the same terminals now sometimes I showed direct line sometime this I just thought now let us see is that okay this currents are this currents and they are transferred to M5 and M6 and right now their W bias are same as in this is same as this and this is same as this and therefore same current is flowing in N channel as well as in P channel please remember I can make that difference if I need what do I do I increase the size and I have the other currents possible but normally I may suggest you as an example if I want to I0 current I never duplicate double this transistor what do I do I take another N and put it double think of it why this itself is not double but you have another gate and you put another transistor there thinking with two W bias okay wise preference is given to a separations okay this is thinking now let us say is that okay figure so I will start looking here I already said let us say I1 and I2 are mirrored so equal I1 flows through VDD to VSS and M5 and M1 I2 flows through M4 to M2 which is what I am saying this going here this going here so VGS1 is I2R which is same as I1R same as IR you can say that IQR let us define a current I1 equal to I2 as Iq sent why I was started using Q word now because this is DC current and going to bias next circuit for your choice is that correct so it is called quiescent currents so I1 is equal to I2 into IQ and if I write this expression for VGS1 which is VTN to I1 upon this and if I1 I2 this I1 can be replaced by IQ so I1R drop is VTN plus 2I I1 or I2 whichever it is upon beta N dash W by L1 okay so I now have an equation which can be derived simply by VGS equivalence equal to IR drop is that VGS1 is same as IR of the drop across the resistance I repeat those were not the drop across this is the voltage here so there is nothing seriously with done so far okay so I got this expression that IR drop is equal to VTN plus 2I upon beta NW dash L and once I get this expression then I am going to write figure it out please remember I is here I is here so what is it means when I calculate such things it may lead to a what is called which kind of equation leads to quadratic or essentially called Transdental okay so what is the problem in Transdental there is a non-linearity and since there is a non-linearity quadratic always we can solve because it is a first order non-linearity so it is much easier to solve but if it is second order third order you can only do numerically and there is no other technique very very simple Newton-Raphson mini techniques are available to solve such Transdental equation okay is that drawn everyone so I 1 I 2 is equal to IQ IQ just substitute I 1 equal to I 2 equal to IQ so it is IQ R is VTN plus 2 IQ upon beta dash W L 1 I expand this square it and this I get this kind of so called first order non-linear equation or a quadratic term and if I a quadratic equation I can always solve this equation by simple quadratic nature. So the first solution is minus B under root plus minus under draw B square minus 4 AC by 2 a same solution okay a solution IR 1 of VTN by R 1 upon beta 1 R square plus 1 upon R under root of 2 VTN beta 1 R plus 1 upon beta 1 square R square but the other solution also existed for this what is that solution IQ equal to 0 also has I 1 equal to I 2 okay but that solution we call it as trivial but this tree word is good for mathematics but in real life circuit may actually enter trivial point and there is no way once those voltages in feedback you have put it and if both are 0 nothing can be done circuit will remain switched off even if power supply is on everything is on so you may land in this situation at the start sometimes not necessarily but may start is that clear in case it is there so how to start the current source then or how to create reference then okay so I must actually now come out of that 0 situation is that clear so essentially I 1 equal to I 2 equation what I wrote you write down this and I will come back to figure again so it will be very clear to you okay is that expression drawn so we come back basically what was the time this VGS 1 we were getting equal to IR is that correct so if I only draw this line I versus V and I draw this line straight line I 2 which is V is equal to IR so a straight line V is equal to IR is a straight line and if I see a current through this VGS because of VGS 1 it has a square law okay okay so this current is because of the transistor which is giving me VGS 1 and when they are equal what do in the equal these two intersect when they are equal they to intersect so this is the point where the VGS 1 and this are matching and therefore Q is the bias point which you are getting okay corresponding to this VQ and this IQ but I just now said I 1 equal to I 2 can be attained at this point one is this one is this if that happens then the circuit will never start because it does not have any voltage to change the voltage because why it does not change there is a feedback if there is no feedback open loop it will it is trying to adjust to whatever value you have got it it wants to detail those values that is the problem with feedback that is stable so it makes this point as much stable at this point so if you are closer here you will sit here is that correct this feedback word is good for stability fair enough the situation is here you are now landing in a stable point here okay and no way unless you physically change the value this can move from here to here and the circuit which does this is called the startup is that correct is the word clear startup startup means if you are per se here then it should change the voltage so that I 1 I to start playing when no current is flowing obviously this transistor does not get VGS this time there is nothing the voltages are such that everything is 0 so this potential is also 0 is that clear no current open arm is 0 paris now if this is at 0 when the startup starts the way start of circuit is this is our bias this also can be replaced by what I can always replace this like this okay it is a diode essentially I am making a diode drop we really minus diode drop so there is some potential which is larger than I am a smaller than VDD but I am adjusting that so that this 1 diode drop gets me VGS here this potential is 0 now is that okay when everything is 0 this potential at 0 this potential is that positive value so what is it creating a VGS for N 7 which is larger than threshold okay VGS for 7 to be VGS for 7 is larger than VT so what it will start doing M7 starts conducting as soon as M7 starts conducting the oven starts flowing down because this current has no path here no path here so it starts conducting through M1 is that correct as soon as M1 starts conducting what will happen to VGS it will appear amount VGS by R will appear in I2 other side once this sets up some this now there is a feedback and this voltage will start rising as the video starts increasing is that clear as this voltage starts increasing this potential is less 1 VT above not 1 VT above node 1 voltage is that correct that means M7 will switch off is that correct once M7 switches off now I1 I2 where feedback paths are taking care and whenever they will become equal you will reach table point of this so is that correct yes let us say initially this was at 0 and both currents are 0 this is ground or ground so this is 0 so there is a VGS sufficiently high because only 1 diode drop was taken out of it so VGS was larger than VT for M7 is that correct so M7 conducts means it pushes the current in M1 whenever current goes into transistor what it shows VGS otherwise I cannot have current inversely saying apply VGS so that the current up force the current so it will create VGS if VGS increases because I7 is going through this drop increases VGS by R currents flows but this current is essentially taken from this arm current cannot be hanging is that correct so I2 starts flowing now I2 whenever I2 this drop and this this feedback will keep pushing videos of this transistor so that these two currents are equal the way these values are adjusted that the point where you reach here VGS minus VT showed a VGS should be slightly lower than VT so that M7 switches off and switches of wear at this point is that clear now we say once M7 switches off it does not participate why because once the circuit is on this remains off okay. Per se because of some reasons of fluctuation comes again it start changing currents then it will start pushing the current from here and again bring it to Iq is that correct so you achieve a stable bias point by putting a startup and one startup occurs it does not participate in the remainder current source behavior is that correct so this is the feature of a why it is called bootstrap anything I am pulling this voltage up bootstrap less co-cage there is whenever I need a be I am supplying a VDD but I need to VDD search what do I do I must hold somewhere on a earlier VDD on a capacitor and the lower transistor should switch off then it becomes to VDD so bootstrap can actually pushes the voltages like a doubler kind of thing to more than VDD and where do you think you need double more than VDD you need for a short time transients which will dip some other time so this point is stable now and therefore you have a good stable IQ VQ situation and one can say now that this circuit only participates to the Ion I2 becomes equal and reaches this value and once that happens M7 switches off and therefore the startup circuit does not participate afterwards is that clear so this is only as long as the circuits are you are not here otherwise it is just switches off so you are not bothered about you know it continue to hold there what do it will not it will automatically switch it off itself but per se because of any environmental situation it goes it will start to pull up again okay. So it is some kind of a feedback second feedback kept there to make output reference as much constant as possible is that correct and that is something what this bootstrap circuit is famous for okay there is another reference which is very interesting and I thought it is for similar forms but very interesting this is called beta multiplier V reference what is beta multiplier means so something to do with increase of betas and there is some word is shown here the kind of circuit I have shown here also requires start up they are not shown it is identical similar circuit so it will also require start up if this node does not become as it should okay so right now I am not showing a startup the startup does have exist on the left now this is very simple one P channel mirror and one N channel mirror connected okay with a Wilson like resistor sitting here okay so why are we so keen about this we are interested to find this circuit is used what is called as self biasing circuit okay that is used in biasing I 0 is created from this circuit okay what is the requirement of a good circuit reference it should not change with temperature in specific we should not change the VDD but it should not change with temperature very much any good word means the variation should be small whatever variations you are looking thermal is the strongest of them so that people more worried on thermal part because why thermal part is very some because chip starts getting heated okay so the thermal variations are immediately seen okay in analog even it is worse why eyes are higher than digital okay so I square R is even stronger so more temperature likely to rise in analog parts and in digital so there is why we say look into constantly temperature very worries okay all that we did here if you are drawn the figure this is my output current this is my current in this arm and if they are M3 and M4 are identical I 0 will also flow as in M1 arm please remember M3 and M4 are identical in every respect VT and W by else okay both are P channel device current I 0 however M1 and M2 they are not 100% identical the only difference is that VT of course is same but the size of this is some k times size of M1 that is the why I never say W by L what should I say really because lengths are normally never changed unless you need specifically otherwise only widths are changed so widths of M2 is some numbers k greater than 1 no no you can always say 0.8 because it is not wrong but my assumption k is greater than 1 okay now we can see from here this voltage VGS 1 is VGS 2 plus drop across resistor the way diodes are connected or way M1 M2 are connected so I say VGS 1 is equal to VGS 2 plus this drop is that correct so VGS 1 is VGS 2 plus I 0 are this but we know VGS 1 I can write as VTN plus 2 I 0 by beta 1 VGS 2 I can write VTN plus 2 I 0 by k times beta 1 because now size is double k times earlier 1 so I do not have to write beta 2 I write k beta 1 and then I 0 are collect the terms of I 0 by quadratic equations and roughly maybe I should say to great extent this may come but roughly 2 upon R square beta 1 1 minus 1 upon root k is that okay I 0 is 2 upon R square beta 1 into 1 minus 1 upon root k to the power square okay this VTN cancels this line and exactly okay so okay so what should I calculate now for this current this source the TCF I like to see temperature dependence of this current source okay. The VGS 1 is essentially referred this is taken out and that should remain constant with temperature is that correct VGS 1 is the reference voltage is that clear VGS 1 is the reference voltage okay so let us start so which register I should use madam if I want larger R which material I should use and plus is the smallest register I can clear it because doping higher means conductivities higher resistance is smaller if I want larger R then what should I use poly silicon I do not know whether you have reached poly silicon and mass silicon gate technology in your technology course but do look at there that gate is automatically will diffuse same as source and drain and n channel device it will become n plus in P channel it will become P plus of course you can engineer it that also can be made and plus if needed okay okay so this expression now I come back and show you on this let us say I am using poly silicon layer dope to n plus if I want higher register so what should I do two ways I can create higher resistance in poly or any region kya okay please remember resistance is created 8 minute a circuit this is how resistors are made. So this is poly and plus or anything. I can separately do poly. So what will happen then? What is the extra thing I had to another mass because only for those polys I will have to open and rest I have to close in a lithography. So additional mass, few million dollars, 8 resistors are likely. So generally even if it is you want exact resistance of value you can always create. Poly has a sheet resistance of 10 to power 8 ohm per square which is very huge okay. So I can create mega ohms of resistor in fact okay. But if I do that I have an issue that I need another mass to create different resistors. Different kinds of resistors in different masks means this is high enough length to width ratio I want to keep small so that the area is small okay. So that is how sheet resistance is RS is decided by the doping in the poly okay. So RS known to us for that dope poly then you can adjust length width get your exact resistance values. You never play with RS you only play with length and width okay. So this part which polysiricant layer TCFR is one upon this typically it is minus 2000 this is for N plus poly in the CMOS okay that gives minus 2000 PPM per degree centigrade RS TCF okay. For the beta F multiple beta multiplier circuit just shown for that I 0 which I wrote I can get TCF of I 0 is 2 times the TCF of this plus 1.5 by T okay. So it gives you 2 into TCF of R 2 upon R dr by dt plus 1.5 by T. So now this is 2000 so it is minus 4000 this is 1.5 T is around 5000 okay. So oh sorry this will be plus I am sorry 5000 minus 4000. So you have 1000 PPM per degree centigrade as TCF for I 0 300 degree Kelvin. Now very interesting thing I am going to show you why big time multiplier became very popular also. How much is TCF around 1000 that means reasonably within your limit okay not preferably I want how much 0 but it is not 0 but not very very bad okay. So V reference is taken from VGS 1 which is 2 upon root beta R 1 by K plus VTN I differentiate this with temperature V reference value okay. So I get T VTN by dt 2 beta R is called differentiate that expression anyway I have written to some extent 1 upon V reference times. Now one can see from here if I want this term to be 0 what do you see from here it is called the V reference 1 upon V reference by dt is TCF is that correct but if I want TCF to be small as 0 I want V reference differential with temperature should be 0. Now your two terms the threshold voltage goes how much what is the way I said how many millivolt per degree centigrade 2.3 millivolt per degree centigrade minus okay is the threshold variation with temperature. So you know this you see the values put here and you know another term which is R and K two parameters in your hand or of course is decided deciding your VGS 1 also that is reference value but for this two together you are now you can fix this value and fix this value to its minimum preferably 0 is that correct if you do that we say TCF of V reference will be small or 0. So is that point clear why we chose this one because we figured it out that these terms I can correspondingly adjust such that V reference can be referenced by dt could be smaller is that point clear this is the feature of beta multiplier circuit in which TCF could be minimized even better control of this is what the next circuit in which is the most popular circuit in the case what is that reference voltage circuit which is most popular for NL of people any name band gap reference why this word band gap has come so busy band gap what you have keep my silicon band gap 1.2 normal 1.1 say 1.2 the other measurements since the reference voltage you get is typically around 1.2 we call it band gap reference it is not directly function to some extent it can be brought from ni square term as well e to the power minus e g by kt was make saturation current I got V so easy term the R a but basically the idea was that the value you get is very close to the band gap of silicon and therefore we say it is band gap reference what should be the advantage of band gap reference it should be as seen from this formulas it should have lower temperature coefficient preferably 0 no variation is VDD and 0 variation with temperature if that happens you say you have created a good voltage reference why do you need good voltage reference Raj is a circuit may good voltage reference what kind of biasing so far we are showing you only by current biasing but if the of a transistor voltage a bias cannot I am carrying it you need a constant voltage which is generated VDD is not in your both this so I want a good reference which is constant okay so we reference voltage is an essential part of any nl option it is separately created and used okay is that correct and that is called band gap reference so let us look at it what is p tat p stand for proportional yes p to proportional to a stand for absolute p stand for temperature p tat okay proportional to absolute temperature okay that is what are value we reference is directly proportional to VDD okay so it is called p tat this is going to be the part of my band gap reference so I thought first let me show you the p tat itself okay this itself can be used as a bias current of biasing okay you can see here I can use this itself as a current biasing circuit okay your point of view is very taken I said this is a part of the circuit which I am going to use in the band gap reference okay this does not have good TCF anyway is that okay but it is not very very bad either as you are thinking calculate that proportion is much better than otherwise okay okay now look at it this is how many what are these four looking for you to P channel current sources and to N channel current things to P channel to N channel is that correct then this M2 below M2 is again K times as we did earlier M2 is K times M1 as far as widths go there is a resistor R here Abhitha reference the Kajara VT reference same as circuit Yantak this is R can be check something else we put two diodes we put why do I show you this kind of diodes because in technology there is always a parasitic transistor sitting NPN PNP where I write if you see a CMOS process there are always transistors sitting there the problem there is they should not turn on so we take care that they never have beta more than one less than one it should but there is a transistor sitting there so if I connect base collector then I get a diode which is base emitter junction taking there one such hour base I can leak collector base emitter direct I can have base collector base emitter open collect or shot it there are three possibilities which I can do base collector junction a collector should I have base emitter junction come later base collector come later come later when I want to hire voltage breakdown systems I use base collector junction base doping in a collector when I want a smaller this I use base emitter junction so I need a smaller values so I use base emitter junction as the diode here anyway as I said this is your choice but I am just trying to show you this is how one does okay so these are two diodes D1 and D2 so now you can say again VGS1 is this drop plus this drop A plus A is that here please remember VGS1 is the same terminal VGS1 plus this sorry I must tell you this potential is VGS which is same as VDS this voltage plus this whatever is the drop here must be equal to this voltage plus this drop plus this voltage but these diodes are taken identical so to fall practical where previous this must be equal to this plus this is that clear so I wrote it but I obviously was not clear so I repeat this potential is this or this equal to this potential plus this because drop here and drop here is same okay so reference but subtraction may they are equal okay so what is the diode current now here is that band gap where now we are so obvious here is the diode current is I saturation Q to the power VV by NKT if I say VBE for this is nothing but VDS for the other one okay which is same as just now I said so I calculate VDS1 and VDS2 from this diode currents okay please remember why I make it K here because M2 has a size of VGS2 has a K times beta 1 as the value of beta 2 so now I calculate drop here I calculate drop here in terms of saturation currents what is N ideality factor how much is the ideality factor normally I should choose for silicon diodes 1 why 1 because you are in diffusion current limited situation you are neither in high current side or not in generation side so in between e to the power VB by KT on the N is 1 there if you are in a very high injection state it becomes 1 upon 2 KT if you are in a very low current state which is generation state and again QE by 2 KT okay otherwise most cases N is 1 for silicon okay so if I substitute 2 in 1 then I get NKT L and ISAT equal to NKT by Q L and I by K ISAT plus IR NKT for Mathematics Kia so I get I is equal to NKT by QR L and K KT by you go many books write VT like bias writes for N channel P channel he puts VT and then VTP to separate from this VT okay but many a time I do not do that so I I wrote full name V thermal KT by Q okay so I get now the current in the p-tab circuit output current is V thermal by R LNK okay V thermal is KT by Q okay so R is proportional to temperature directly proportional to temperature so this current source is called proportional to absolute temperatures. What is the advantage of this is a current source is not important what is that is advantages using this where do you think you can use this sensor thermal sensor you have to monitor the current so this is not useful as a current source but it is useful as a same temperature sensor is that correct that is why the word came proportional to absolute temperatures okay is that clear is that so do not ask me it is a TCF actually it is clear TCF we are not using this as a good this okay so now this circuit is a part of my band of reference is that should be is that point clear why I shown you this because this is going to be a part of the next circuit and the advantage here I keep saying is I is proportional to T any scale you create if it is proportional as much easier to draw and figure it out extrapolation is the easiest thing to happen so therefore these are used as thermal sensors okay okay now here is the band of reference which is most important this is some KT by Q source okay VTHM you multiply again factor so it becomes K times VTM as to an adder so VBE plus K VTCM adkiyaan do no ko the output jo hai wo VBE plus K be thermal hai okay is that clear this is the principle of band gap reference now the way it will happen the two quantities have opposite TCF in polarity I repeat this and this have opposite in polarity as their TCF values this is a function of K is that correct so I can always adjust this one value this may not be adjusted but this value so that it is exactly becomes equal to the other forest coefficient is that clear to you if that happens what will happen TCF of this reference will be 0 so ideal reference can be created is that clear is the principle clear not that this is the how I actually am doing it the principle is shown here whatever VBE is added with K times the thermal voltage both have different polarity of TCF this values TCF can be changed by K and since I can change the TCF by K value by K I can adjust the values such that the difference of TCF is 0 that is the trick in making a band gap reference. Is that that is clear why I showed Peter I am going to use that Peter here right now okay for the thermal I will create from there okay is that okay all of you two parts have different polarities of TCF values can be adjusted through K and the difference can be made as close to 0 as is possible is it okay all of you okay now here is that circuit. In the output circuit I put another resistance which is L times this resistance R this M2 as a K times the width of M1 but this resistance is L is some number more than one of this and then another equivalent I would say now D1 D2 D3 which is kept here is that correct this is Ptatt and I added this much additionally okay if I do this for a Ptatt we just calculated I is equal to be thermal L and K by R that is the current in Ptatt okay just now we derived okay where is the V reference voltage I am now taking what is the V reference I am using madam you can write now show Ptatt only and put R this so we do not have to redraw all of it okay is that okay that Ptatt a block now I will just get another okay so to Ptatt circuit I additional diode D3 and LR resistor series put there and output is taken across so what is the output in V reference here drop across D3 plus drop across LR is the reference voltage please do not draw this again you write 8 transistor to show okay or 2 diodes 10 plus these 2 10 is it okay all of you so V reference is nothing but the diode drop V D3 plus I times LR the drop across the resistor V D3 as we just said last time Nikola work NKT by I by KSAT H P L thermal we I current this car Nikola thought into LR so yeah that R cancels I into R is R cancels okay so I get V reference is L times V thermal into ln K plus V thermal ln I by KSAT K I said that diode temperature change voltage VV minus 2 millivolt to 2.3 millivolt per degree centigrade change okay this is a plus it is proportional a plus a minus V D3 change with temperature is minus the right term is all positive so is thermal is proportional temperature if I just ln K okay so is that whatever is V D3 coefficient coefficient for ln K values becomes exactly same with the opposite sign because this is minus this is plus so TCF can be made 0 is that correct so what are the choices for us choice of ln K if I use this reference value shown here I for a given normal CMOS technology I normally use L of 12 K of 8 saturation is current of the order of 10 to power minus 12 pico amps typical I used in micro amps few micro amps 10 micro amp 20 micro amps okay I is typically of the order of 10 to 20 micro amps okay saturation current is typically from 10s of nano amps to I sorry 0.1 nano amp to 100s of nano amps or not 100 point pico amps 10s of pico amps to 100s of pico amps okay or 0.1 nano amps K is typically around 4 to 8 L is typically between 12 to 16 okay and if I try to adjust please remember if I adjust these values the TCF may not become 0 okay too much because same values will decide my reference so please check it that reference voltage how much accuracy you want it may be 1.2 or 1.25 anyway you need to a fixed value so you better try for TCF to be smaller as the first criteria of making this because of last 12 to 16 or 4 to 8 this value will not change other than the second or third decimal okay so it is not very good very bad for anyway typical reference value which you get for these is of the order of 1.2 volt which is the band gap of silicon therefore this is called band gap reference what is the TCF value as small as you think you can okay may be 0 in best case okay thank you very much