 So there are three parameters for a small signal as in the case of bipolar will be interested in one is of course gm the other is output resistance and the third I made mistake I should not say capacitance the model where we are really looking for there is the bandwidth okay and bandwidth is related to capacitance. So we will be interested to know in the small signal model of a MOSFET how much is this capacitance and how much are the resistances around so that we can put a good equivalent circuit and from that we will be able to get the gain gm therefore gm and r0 that is the gain part we can get and also from gm and capacitance we will be able to get the bandwidths. So once we get the equivalent circuit correctly we will be able to get all the physical parameters known then circuit parameters can always be evaluated and if circuit parameters are evaluated the actual system performance gain and bandwidth they also can be always found out. So that is a general technique which will follow so there is nothing much to say on that so the first major small signal parameter which makes MOSFET interesting of course all device has a major interest in the word trans conductance which is essentially in the case of MOSFET is change in drain current with change in gate bias okay. Now in this case unless said otherwise source is always grounded okay source is always grounded so Vgs is essentially Vg but if not we will say what is Vs and then you must find Vgs accordingly is that point clear if s is 0 grounded then Vs is 0 but in case there is a Vs then you will have to find Vg-Vs as Vgs is that clear so right now I am assuming source is grounded so difference is Vgs so change in drain current to change in gate source voltage will give you the trans conductance this is the output and this is the input of a MOS transistor therefore this is transfer trans conductance normally as I say we will never operate the transistor in which mode I said of course cutoff will never because then the device is off anyway but in even a linear because there the gains are very low so we will not operate but just for the heck of it I can calculate gm linear as well as gm saturation all that I have to do is write the current equation and differentiate with delta by delta Vgs of that and evaluate whatever is the gm for linear so if I do this evaluation and I neglect Vds square because we say Vgs-Vt is much larger than Vds that is why it is in linear zone using this condition I can evaluate gm linear is Mu C of W bar into Vds okay but that as I say it is like a resistance do you get a point it is like a resistance linear means ideas Vds characteristics proportional say resistance so this is essentially a validation of a resistance however we are not very and is also short formed as beta okay my symbols and book symbols are different please note down somewhere I have been habituated that many are 30 years K what is constant we use in all books KN or KP I write beta N and beta P is that correct KN dash is BN dash KP dash is BP dash beta N we define as beta and dash into W size W by L that is to just smaller the expressions because if writing every time you see of Mu C of W by L we just write beta beta has a what units you can think can you suggest from here what will be the unit of beta if you cannot get you find from here this has a unit of old square current has a unit of amps so amps per world square is the unit of beta or K whatever is the book why I am saying K because I just today after many days I saw the book which I constantly say read said our Smith book and they have used K as the constant okay why they have used is maybe I just want to know how to operate the spice spice time for what S of course is simulation P must be programmed simulating program for special emphasis on integrated circuits this is a Berkeley program which solve circuit simple network nothing great nothing simple or nothing great just solve nodal equations I GV and nothing more all that will happen it will have a matter eyes because I will be I1 I2 I3 we will be V1 V2 V3 and therefore G will be and G will also have the similar matrix value so you will have a some kind of a matrix solver so all that spies does it but spies require models for the transistors so it requires constant W by L C ox T ox VT everything it has to be specified there is a default parameter for a given technology let us say 5 micron process they will get these values it is called default so initially when we are not giving our data we can assume whatever spies parameters are there are there and just solve the circuit for given input output circuit parameters is that correct so spies as an advantage it can solve digital it can solve analog AC it can solve mixed signal it can do all kinds of analysis very easy okay and it is related if pastries come from Berkeley and it is a industry standard of course buys as many version model versions like the one which we are using for say 20 nanometer now has a it is called B sim models okay that is the Berkeley simulating models which is level 3 and the model we are using is 58 or 16 or something recently I don't know maybe 58 by the last so these models keep changing as the device physics are changing because of shrinking otherwise basic idea in spies remain same it is all circuit or it is our network okay so I think you should know this because some problems we may give you which need not be analytically solve a little complicated circuit but then you can substitute there and by stroke of luck everything will come correct now that is good thing about simulations it always gives you results irrespective whether you are good student or a basketball now I don't mean bad in any sense but I mean those who are not wanting to do even if they substitute some number some result will come the only problem is spicy and which any simulation program is how do you know the result you got is correct because you get something and got something anyone can do it even a kid of 3 years can clean something and may something does not mean he is correct spice is correct because it will receive something and it will give you better whether device in saturation it doesn't know anything it only receives values it is a mathematical tool there is where your intervention is required that you should know what you are feeling and that is where that much part you should know better is that clear otherwise spice does almost everything okay all industries have all designs of analog digital mix signal circuits RF circuits are using spies spies are different model RF model this model various models by the way versions which we use called specter or very different company each is a very costly business typically one computer license spice version may cost you a million dollars of course this is called industry standard but the academic standards are much lower and we may get it in 5000 that is why accuracy is what we get and what they okay so don't worry if you don't know I think if you sit on a PC lab some day and some basic introduction someone give you will be much more I think I use much less spice now compared to what I use 20 15 years ago 20 years so then what you can use and it doesn't require it can be even downloaded on your own piece laptop if you have and can it doesn't require use memory the spice version which I am talking which is the old version for a 5 micron process that is very cheap 3G version and you can always try circuits on that the results cannot be as accurate as could have been in the cadence tools but it is good enough for our course is that okay so please learn spice because I have nothing to do with my course spice is some kind of a general tool required for digital analog any circuit you do want even communication at the end even in communication you will get some circuit okay solving a circuit is easiest on spice okay there is another program which does very great job is Metlab I don't know whether you already started working somewhere because signal processing people cannot survive probably without the Metlab or vice versa okay okay Metlab would not have been of course Metlab also has a circuit simulator okay but it is not as good as spice so better okay this is all general because as second year right you should now start thinking ahead and I am trying to push you to little ahead of what you should be as you are okay the interest for us is in the when the analog circuit we said mass transistors are always maintained in saturation what does the condition in DC wave we say when devices in saturation what is the condition of VGS videos that VGS-VT should be smaller than PDS at any point okay every time we just should exceed VGS-VT okay if that is so one can say the current equation then can be written as beta by 2 VGS-VT square 1 plus lambda VGS this is current when the device is in saturation if I take delta of delta VGS of this now under this case slightly interesting case we should look for our assumption is V try VT is constant okay VT does not change with VGS does not change with VDS this is slightly secondary we shall assume is okay does not matter okay in real life we VT is not a constant quantity so when I differentiate that VGS also VT also has to be differentiated then it become more complicated expressions and hand solving becomes sometimes difficult and spice does this automatically you do not have the best thing about spices it does not allow you to think and that is good for us okay so if I initially for most circuit unless stated otherwise we will assume lambda to be 0 only what cases will assume lambda to be 0 when I write currents but when I write R0 I will not make lambda 0 what does that mean will be R0 is how much infinite is that correct lambda 0 slope is 0 which means resistance is infinite but that is never infinite and therefore calculation of R0 will definitely you get a value of lambda otherwise in normal current equation if you neglect lambda nothing much worse will happen in actual analysis okay so initially to guess get to a correct simple value I neglect lambda so 1 plus lambda VDS is 1 and if I differentiate this with VGS then it becomes GM not beta dash sorry maybe or if you if it is a beta dash I will just go for the sake of correctness I will multiply it by W by L but that dash unnecessarily there but does not if I substitute the current equation assuming lambda 0 back to this expression you can write beta by 2 okay beta VGS minus VT I can write beta by 2 VGS minus VT square into 2 upon VGS minus VT then the first part is ideas is that okay this part is ideas okay also in both this S part is normally miss not used I they only use ID this I write ideas because from the device side current cannot be drain current unless it reaches source okay so in our case we always believe that it should be written ideas if you write ID it is okay there they are saying drain current this drain current has to go to source any source is grounded but said and done my symbols are more from the device point of view because we have been working on devices for 30 years so on design so on circuits so our symbolization is more on the device side so I can write 2 ideas upon VGS minus VT but what is VGS minus VT we said it is called over voltage Vov so it is 2 ideas by Vov so GM is 2 ideas by Vov if I instead of doing this I replace VGS minus VT from this in terms of GM and beta I repeat I replace this VGS minus VT from this expression that is 2 GM upon beta under root of that as VGS minus VT and substitute back I can read IDM as 2 beta NG ideas is that clear what I wrote this is ideas is that correct so 2 ideas upon beta and under root of that is VGS minus VT substitute here that value and you will get GM is equal to this expression many times to beta in ideas so if I am given a bias current I am given the sizes given the technology that is beta in dash use your so I can immediately evaluate what is the GM of this is that clear this is assumption is that someone is giving me Vov someone is giving me Vov but if I am given ideas only still I can evaluate is that clear so that is the method of evaluation either cases can be used okay either cases they are same by the way expressions are the second parameter of interest to us is R0 which is the output resistance and I said you are the date is 1 upon lambda ideas it is also written as VA upon ideas VA is only voltage also can be we also explain other way that lambda has some technology parameter called lambda dash and that is why what I said is that day that lambda is lambda dash which is technology parameter which is fixed to us for given technology and L is the channel length why I wrote this why I wrote this expression specific can you think R0 will lambda dash for a given technology is fixed okay ideas is my bias problem I am going to decide 1 milliamp half a milliamp whatever way I want 2 milliamp or 1.5 milliamp so if I want to increase R0 what should I increase channel length for the circuit person this is foolish because I have I am getting a transistor already given on board I cannot change length but why I showed you this because tomorrow if you become a analog designer that is chip designers that time what parameter you will start controlling for R0 the lengths I will start increasing lengths but if I increase length what I will lose there from here GM is that point clear to you the other day that is why I brought this expression if I increase channel length I will include R0 which is obvious okay is that clear however if I increase channel length W will go down and therefore GM will go down is that correct so now you have to understand in design why it is called design because if I control R0 I lose track on GM if I start controlling GM I start tracking losing back on R01 that is what people say I want gain of this much now the designer has to I want so much GM and so much R0 how like it that is where the whole design issues are issued in this course R2 will fix game is known but I am just trying to give you that why what is the design word coming from okay analysis is shown from there we start thinking what spec I have to meet when I am behind okay is that okay yes who said oh you mean current gain yes that is because mass transistor is not a current driven device so obviously we are IGs are treated 0 you can say infinite ideas by IG no in the sense but trans conductance is with the response to voltage input voltage not from current we are across even an insulator which is a capacitor voltage can be used so I am saying change in input signal this is voltage I will still see the output current varying and therefore that is what I am interested in what is the change in output current with reference to change in input voltage is that correct current gain is yes it does not exist in the case of mass transistor IG as you said there is no DC gate current at least unless we say leakage is exist in the case of by the way that IG is not here now that is our worry but today of course yes IG is here that means insulator is perfect insulator no DC current can flow from gate to be any of the substrate source or that is why the insulator was kept okay. However in real life as I say that issue is now worryness but not for this very good thinking is very good so if I compare the two before we go to circuits I wrote an expression GM is equal to two ideas by VOV is that clear GM is equal to two ideas by VOV if I use this expression I get GM my ideas is 2 by view is that okay simple typically VGS minus VT should not be very large why should not be very large because device has to remain in saturation and condition there is video should be larger than VGS minus VT so VGS minus VT if it is too large then device may not remain in saturation but if it is too small the current made available to you because current is proportional to VGS minus VT square so if I reduce too much VGS minus VT I do not get current at all okay so I must balance I must have VOV which is relatively higher but much smaller than possible VDS values which I am going to be is that okay VDS has to be larger than VGS minus VT or VOV as we called if we reduce VOV too much then the current made available is very small okay. However since I want to push large current for deliver I cannot reduce VOV too small but I do not want VOV to be very large because then my condition of saturation may not be valid and therefore I keep somewhere around 200 300 millivolts some kind of values which most technologies use it can be at best 500 600 millivolts at best okay is that point clear to everyone that how why we this value typically 200 millivolts can be 500 also just to give some criteria if I put this 200 millivolts value I get GM by ideas roughly equal to 10 okay GM by ideas is equal to 10 now if I use the similar value please take it if I increase VOV then GM by ideas will be less than 10 is that correct GM by ideas will be even less than 10 if I look a BJT what is the value there we calculated for GM by IC QI by Q by KT what is GM QIC by KT so GM by IC Q by KT typical value at 300 degree Kelvin is how much we calculated 38 okay so we see this number is 38 and how much is GM by ideas is going to be less than 10 even less than 10 5 4 it can be of that kind so do you always feel that GM by IC will always be larger at least 3 4 times larger than a 5 term 8 times larger than GM by ideas what does that have influence at the end of the day therefore as far as the this part is concerned providing GM by IC ratio GM by ratio by pullers are always superior to mass transistors is that here by pullers are always superior to mass transistors so is that point clear when I did day one I said bipolar circuits are far superior compared to mass circuits but then why are we working on mass because world has four stars they say digital circuits are going to be only on the mass because mass performance on digital is far superior to BJT much smaller circuit much low power circuit so if I had to do digital and very very small technologies which has a very small voltages then I will work only for MOSFETs but I do not have only analog blocks to be sold I have to be part of this digital block so I say okay I will work on MOS okay so that day one I said why analog people are facing problem because they have been given bad tools and say produce the best designs okay now can I do it over to everything is against stacked against me and say no do better that is exactly what we do for you lot of courses we give you lot of home assignment lot of this and expect you to get a grade in everyone that is what the life is all about okay so please realize that this is nothing but with my course it is true for life so we are just following that okay okay let us look for limitations as we did for bipolar what is the bipolar limitation I say how much signal should be less than KT by Q sufficiently smaller than KT by Q let us see what happens in the case of MOSFET this is a typical amplifier shown here but we will not look for amplification we are just trying to say there is a power supply there is a ground range source there is a Rd and we say there is a capital Vgs is the DC bias okay over which AC signal of small Vgs is overriding what is it called in mass superposition so a DC signal is superimposed by an AC signal and we expect the output voltage also will have then two parts DC part and if I want to get rid of DC what should I do put a capacitor then only AC will pass that is what amplifiers will do later when we only look for small signal AC outputs so if this is V0 this and I know ideas what is this ideas means this is the total current DC plus AC which is equal to beta n by 2 and assuming right now which devices and channel devices will be used till said otherwise beta n by 2 Vgs minus BT plus Vgs you are superimposing square 1 plus lambda Vgs as usual lambda is small the second order term is neglected and therefore so what is the small current AC current then will be ideas be how much the net current minus the DC current ID capital DS minus capital IDS then that is the AC current is that okay what is AC current total current minus the DC current so I just so I now use expression for this expression for this this is the expression for total current this is the expression for DC current is that okay this is the total current this is the DC so I just subtracted nothing very serious I did and I expanded the terms to see which terms cancels if I do this if you write down is that point clear I just want to know how much is the AC current and or small signal current I am to be 2 beta n by 2 Vgs minus BT into small Vgs into 1 plus Vgs upon 2 capital Vgs minus this is just a fraction nothing very great about which terms will cancel Vgs capital Vgs minus BT where term will cancel because that DC and this DC this is the term remainder which can be rewritten in this form is that okay last expression is okay just collecting the terms okay is that expression root down TK so just after in case you are not written just again I had written those you are not ready to can write so small ideas is GM times Vgs into 1 then I replaced my GM formula in the first part of the expression and therefore I get ideas is GM Vgs 1 plus Vgs upon 2 Vgs minus now if I want to say this term I do not want which one 1 plus plus term I do not then what is the condition I am saying I want to Vgs minus BT should be much larger than Vgs numerator should be smaller than denominator by order okay and if this condition I of course then I get ideas is equal to GM times Vgs that is what small signal equivalent model I want if I have a small signal input voltage Vgs the output AC current should be GM times that Vgs as straight as that is that clear that is what the network theory is saying I is equal to G times V so I want that expression to appear this can appear only when it can appear when 2 Vgs minus Vt is larger than AC signal which is Vgs if you put some typical value say Vgs will be order of say 2 volt Vgs minus Vt will be order of say 2 volt then Vgs should be at least much smaller than 2 volt and this is slightly better than bipolar degree there it is only 26 millivolts so mass has little advantage that the AC signal can be slightly larger than by is that point clear to you why I brought this expression to you that compare to bipolar mass transistor small signals can be little larger okay but what is the problem there GM is smaller as we see earlier so all that we say if Vgs can be larger but GM is smaller so GM Vgs is not increasing even as compared to bipolar is that clear to you so all said and advantages it there are bonnaband oh nothing is that small Vgs typically less than 20 millivolts see order order means this will be V o V so 200 millivolts order so 10 times corollus so roughly 10 means one order okay so one order less one expansion cold zero currently so typically 20 but in there we do not even use 20 millivolts 5 millivolts 3 millivolts at best 10 millivolts in bipolar here we can exceed little but I tell you what is the problem this GM is much lower so GM Vgs will not be larger than bipolar either okay so that is where the issues are that why bipolar and why mass yes I agree with you but what did I do is I have substituted linear part voltage part there I have never said the current is linear but I really want GM to be linear okay so I said okay this is a nonlinear term definitely say nonlinear term I am subtracting also another nonlinear term out of it so this term is nonlinear to make a linear case I said this can this term should be smaller what you are saying is true this expression is nonlinear so to make it linear I say the condition I can have is 2 Vgs minus Vt should be order higher than the small Vgs and then I say it is linearized because all the time I said this circuits are called linear circuits so I want to linearize it faster okay so I say what condition I can linearize so I say okay if I use this I am linearized is that okay okay so equivalent circuit of a mass transistor at the end of the day using so called what we did you have a gate you have a drain and you have a common source okay there is no current or resistance right now between gate and source because gates to source resistance is how much it is an insulator sitting there how much say hundreds of mega ohms so practically open circuit but what can happen there what can occur instead of resistance the capacitance we are not looked into right now capacity we only looked into the simple equivalent part coming from I and GM the output current just now I wrote GM Vgs so it should be GM Vgs okay and if I include my R0 term then the equivalent circuit of a mass transistor is Vgs here GM Vgs shunted by R0 and how much will be R0 much higher tens of mega ohm or 1 to tens of mega ohm so this will be relatively good current source is that clear it will be good current but just take a case which is interesting case yeah maybe our circuit is here if I let's get bigger if you use this circuit where this Rd will appear where this Rd will appear in this small signal Rd is between this has to be understood all of you know well but the I have re instead restate what is the actual for AC this point is ground this point is ground for AC so Rd is between drain and ground so if I is that clear drain and ground so where this will appear here externally Rd is that okay so Rd will be shunting R0 R0 is if the order of how much tens of mega ohm at least one but even depends on what lambda which will be given to us say whatever lambda this is if that is so what is the actual resistance I am going to get here Rd only because Rd will be in few kilo ohms tens of kilo ohms 20 of kilo ohms but this will be in tens of mega ohms so essentially what will be V0 if I calculate V0 here after I have another slide but just for the heck of it how much will be V0-gm Vgs R0 parallel Rd and if Rd is much smaller compared to other it is GM Rd so is that correct at the end of the day in a circuit the lobe decides the output voltage is that clear but in an integrated circuit there are no Rds we put okay I will show you some in the end of the course what ICs do okay we will replace Rd by resist transistor itself and if that happens this will be much larger and if that happens this will be typically order of R0 itself so for integrated circuit gains are GM times are 0 but for normal our open circuits with transfer given to us the gains will be decided by Rd which is provided externally bias is that correct GM times Rd is what gain will be actually is that clear this part has to be understood because R0 is very high so GM R0 is okay that part let me do again before we go here the expression if I use the same once V in is equal to Vgs so V0 is GM Vgs R0 so GM R0 V in so the V0 by V in is AV-gm R0 is that correct this is called intrinsic gain of an transistor this is called intrinsic gain of a transistor is that correct this is not extrinsic why it is not called extrinsic because Rd is not connected this is intrinsic is that okay why it is called a intrinsic because there is no external component right now sitting on it is internal to what is this game okay so this is also to some extent figure of merit for us what is the maximum gain this transistor can provide okay typically say let us say this is 10 mega ohms GM will be order of some milliamp per volt square per volt so you can say this will be order of 1000 at best at times is that correct it will be highest value will be 1000 so when I shunt it with Rd whether it will be more than 1000 or less always be less than 1000 is that correct so the typical gains you can get is 10 to 100 to 400 or no more than not even 1000 is that clear 1000 is what we say is the upper limit okay so analog amplifier cannot actually intrinsically go beyond say few hundreds of an amplification but actual the implementation we must smaller as Rds will decide I will show why Rd and so decide something okay if the GM is two ideas by the way R0 is this I can say GM R0 is 2 upon lambda Vgs-ET or two ideas something like this so given a over voltage for a circuit I can also find the intrinsic gain is that correct given the lambda and Vov for the circuit or transistor sorry then I will be able to find what is the intrinsic gain of this transistor so when I why I am giving you this because when I am making a circuit on the board how to choose a transistor from the box they give you so okay I say I wanted so much gain so let us see what is the intrinsic gain I can get these value will be specified in the manual data sheets so you find okay so this is 500 fine and then that much is good enough this has to be done when I actually go on the boat before and I should know how much is that okay so certain things as a when we do experiment we ought to know a priori these are the way a priori values are evaluated now coming to the last part of the transistor which is related to bandwidth is the capacitance this is a typical N channel MOS transistor shown here this is your source this is your drain this is your bulb this is your gate separated by oxide of thickness T ox and the oxide capacitance is always expressed as oxide capacitance per unit why did we do this because this device people have habit of using charge density is that clear Q capital Q they will say charge density so Q is equal to CV so if I use charge density now if I do not see as per unit area then that equation is not balanced so I say either be per centimeter would there be per centimeter Q CV sub jaggery that is why they did it as a man yeah but I want to talk about so T ox is epsilon ox by T ox for a different technologies T ox may vary what is the smallest T ox right now in the new Intel 22 nanometer Intel processor have come how much is T ox they are using I already said technology is known by the number I keep telling 22 nanometers okay 22 nanometers so something less than that will be much less than that will be your these days we actually want less than some Armstrong say one or two Armstrong's of oxide okay now we cannot create two Armstrong's of occur why can you tell me why because the band bond to bond atom to atom bond distance itself will be learned less than 1.6 Armstrong's okay so far even one more layer of atoms you cannot have that kind of thickness of oxide okay because you need two atoms minimum silicon and oxygen the separation is a company in cup Diabe head so I suppose Kermit so what how can we do we are still working on less than a nanometer kind of oxide thicknesses how do we do that epsilon we are increasing proportionately epsilon so that T also can be increased capacitance held okay that is what is called high K dielectrics new technologies use no silicon dioxide but dielectrics like half name oxide half name oxenoid rights gallium oxide lanthanum European oxide for example I have been working in last summer on very stack of lanthanum and gallium oxides in Japan when I was two months there so we are looking for very high K typically I am looking for K of 60 or 70 and we may use it in memory done and trans okay so the kind of research going on in the material side for the circuits is high K now okay so the capacitance is associated you can see from here if there is no inversion channel what is the capacitance between gate and bulk CGB is that correct if there is no channel what is the capacitance CGB which is nothing but how much see ox no inversion channel let us say there is a inversion channel throughout then bulk is not connected now so what is the capacitance now associated between channel channel as heavy number of electrons they are connected to high NNN so again a capacitance is see ox is that correct instead of bulk now the black back plate is provided by the channel earlier the back plate was here there was a resistance here but much smaller and there was a capacitor now that R is also removed only a capacity now the problem with most unnecessary PS I have told you this is a distributed capacity this is not uniform everywhere so what do we do actually there are n such capacitances so what we say for simplicity half see ox is provided at the source end and half capacitance is provided at the drain end so I say CGS and CGD will be half see often half see ox is that correct is that point clear CGS half see ox CGD half see ox and if CGD then there is I will give full see ox to see yes that is the way modeling is done okay so here is something CGS is half see ox into gate area how much is gate area W into L CGD is also half see ox into AG which is again W by L but let us take it same is CGS or CDD which is see ox times W into L is that correct simple in case there is no channel what is the capacitance same see ox into W into L because there is between the bulk the gate area and the oxide nothing else so CGV is also see ox into W but when the device really goes into saturation sorry this is not correct this half is only for non saturation in real life it is two thirds see ox at the source end why it is so because if channel pinches earlier there is no drain end the path is that correct so I say all of this see ox is now pushed to force side and CGD I said does not exist as it goes CGD may come because of the depletion layer at the drain side so CGD is not 0 but that CGD which was coming from oxide is now sure push to source side is that point here I repeat since in a MOS transistor when the channel pinches here okay the drain is now sorry drain is now not connected to the oxide because there is a semiconductor depletion layer here so the capacitance here is due to depletion layer and not due to the oxide is that correct not due to the oxide so CGD is now essentially because of the semiconductor capacitance on the lateral side and not so much from the upper side where if you look at the source side oxide is still sitting here so all of see ox is pushed to the source side okay so in saturation you may use seen as see ox in W by L in any mode of transfer any mode that may not be accurate but that is good enough for our calculation as far as numbers are concerned in physics yes we have to find what exact value is that okay then there are two more capacitances we see what is this n plus p what is n plus p in physics diode this n plus p is also diode reverse bias why it is reverse bias I say if the bulk is rounded what is the voltage I will apply on drain plus value VDS so this is heavily reverse bias large depletion layer will come here in fact okay and therefore there will be a smaller capacitance on this side okay however even at 0 bias the diode is reverse bias there will be a smaller depletion layer but there will be there and there will be cgs also and a source gate now can you think I can actually putting source to ground and still this reverse bias can be increased by what if I put minus value or rather for a p-voltage at the bulk source to bulk voltage will increase minus so is source to great to drain to bulk also will increase further is that correct so if there is a VSV available per se then the capacitance will change is that okay is that okay the depletion layer will enhance with applied bulk bias okay and if that happens the capacitance will increase or decrease decrease or increase if I increase VSV negative more what will decrease decrease because X will increase epsilon by T or D so D increases means capacitance falls if the capacitance is smaller it is more worrying or it is larger is more smaller is worrying me more why 1 upon j omega C will come into picture then okay at frequencies of my lower so I am worried how much this seems okay therefore I calculate diode capacitance is assuming step junction what is this 5 SP and 5 DV I wrote there which are these terms built-in voltage for source drain junctions and source to bulk and drain to bulk junction generally they will be same but not every time there is a device which is called lightly drain dope what is the structure called LDB mass drain is likely dope like SI core N rather in that case the doping are different and 5 is also different so if general formula we write 5 SB and 5 sorry yeah 5 SB and 5 DB but normally 5 SB for equal to 5 DB in our case okay so I can calculate all capacity I have in our course we may not calculate but we just want to show you that we can evaluate for a given technology given bias the capacity yes it depends on whether the device are capacitors series or capacitors parallel is that clear if it is in series something else will happen because it will path shorting or opening in passion if it is open good because it opens okay but if it shorts then I am worried is that clear in series if it shorts shorts good that means that component is not relevant in shunting parallel if it shunts everything goes down so capacitance where decides the choice is that clear so I do not upriar you want to tell you which will be where depends on wherever it occurs I will see whether the impedance offered for me puts me into difficulty either way okay so typical equivalent circuit of a MOS transistor for capacitance shows a CGD here a CGS here then between bulk and the source and bulk and the drain okay these are the minimum 4 capacitance can occur in the circuits is that okay however I repeat these values will be specified maybe in the first tutorial I may solve one or two values to show what they get but otherwise circuit people have not asked to the value okay why I showed you this because you should know connection you have done a course on devices from there I am picking those values finally for this therefore we have the FT what is FT value we said other day unity gain frequency which is GM upon 2 CN capacitance at the input or 2 pie CN is FT and the input capacitance is can you tell me why I am adding all of it sorry are you getting both together now this and this at this end CN please remember unity gain means this is directly connected to the ground V0 is 0 is that point here how do I call FT voltage output voltage is shorted okay so for this case this is down in this is also in parallel to CGS is that this capacitance and this capacitance both are parallel and why the CGB I added for the sake in case there is no inversion channel device in off state whatever is the capacitance is CGB whatever happens whichever is dominant I will put so I said okay in general I should write CGS plus CGB plus CGB in general CGB plus CGB will be 0 for saturated device unless stated otherwise then it equal to CGS which is C ox into W boy is that clear so in devices we do evaluate everything and verify circuit will give you this value and just get that okay if I specify your CGD you do use that if I not specify do not do okay if I say this is point so center for and you actually connect is that clear is that point here so any capacitance is specified do not ask me physics you say okay that as far as circuit is concerned we are only looking which connect to where okay but how to get them is physics which you have learned I thought you should know connections because I promised you that first two three hours lectures I will explain you from devices how do we come to why I show we do not show so much in digital because they are 0 1 I told you just now CGS is to get to source capacitance which is oxide capacitance half C ox CGD is half C ox if the channel exists throughout but in analog circuit drain will not be getting connected okay rain is saturated there so no CGD will occur so all the oxide capacitance is given to CGS okay CGB is the value if there is no channel get to bulk capacitance exists that is the oxide capacity if no channel VGS is very small less than no channel exists between gate to bulk there is whole capacitance of the oxide to W into N into C ox now all three may not be exist simultaneously is that point here but in general all three can be as if added whichever dominates in zone of operation use that in our case I already said CGD and CGD can be neglected as far as CN is concerned and you write see just CGS sorry it is CGS which is C ox into W is that okay this is to show you in general what specific in saturation the other two can be and CGS is given all of it all of it is that okay now you should have asked that sir L correct okay source the channel link so it may have but that assumption that is I said two-third than oh oh two-third because I said trapezoidal rule lia or trapezoidal any exponential okay so you know maths very complicated if I increase little bit more what is I am doing actually I am protecting myself some other parasitic would have anyway added their per se if I use little higher value my bandwidth may go down is that clear so I am always on the safer side because I am using 10th of that out hundreds of that in my use so if I initially say 100 megahertz and use one megahertz it is okay it would have been really 120 megahertz so what I am actually reducing the operating frequency even lower so that I am guaranteedly remained in this correct operating values is that correct so by it will be enhancing that see I am not actually losing in circuit I am just saving my what is it called engineering approximately for a margin that you can after given if there is a cutoff situation gate voltage is less than BT the mass transistor still has a capacitance between gate and the battery that CG is that correct that is yours oh so what you are saying adding I I do not mean really that all of them should be added simultaneously for a given mode of operation of the transistor one of them or two of them will be working let us say it is in linear mode CGV will be 0 each will be half hour yeah because yeah yeah your point says the channel exist here it is cleaning the bulb channel has a large number of electrons one side is source connected the plate is already made available to see ox there is a resistance here which you may say object to the semiconductor resistance is in series there but that we are anyway saying is much smaller okay because the area is very large of the vapor so epsilon well by a why that resistance is smaller room may not be very small okay but a is very large area so the resistance offered by the substrate is smaller in a very very high frequency maybe we will have to worry that but as of now if it is in saturation I said the channel moved away so I say okay all capacitance because when I say I am summing 3 I do not mean actual calculate and for a given mode of operation I will use whichever the value I should get if off I will use CGV if linear I will use CGS plus CGV but both I will describe half-half so it is against you and if it is saturation I will only use CGS and I still use here is that clear so I am only saying in general they are they are together whichever dominates will take okay is that okay okay so finally before we do this this is the equivalent circuit of a mass transistor a term I will be this is called high frequency mass model okay this is high why it is called high frequency all capacitances have been added okay in small frequency what will you do will remove all capacitances as the 1 upon j omega c is either open circuit or a short circuit if it series parallel with your weight we will remove all of them there is a gate here there is a drain here something I have not drawn here also maybe you can think of it there also there will be another resistance here which is RGG dash there will be another resistance here which is RDD there will be another resistance here source to source dash RSS dash I will just explain you maybe we may use this we may not use this as GMB term this is not small that is why I have given you that term so what is CDV and CSB these are the diode capacitances is that correct CSB and CDB are diode capacitor drain to bulk source to bulk CGS abhi apko Bola CGD abhi apko Bola R0 is no this is gate there may be a gate resistance itself RGG dash there will be a drain resistance also available there will be a source resistance also what are these because of source and drain N plus regions and contact they will have some resistance like base collector abhi have shown in bipolar there will be a resistance RGG dash which is not very relevant why because no DC current really flows through this okay but for AC there is a drop there someone asked to worry about that generally it is small because of metal use there GMVGS is the current source proportional to your VGS input is VGS gate to source current source at the output is GM times VGS this is our argument now the term which I have not yet explained is GMV not VGS I am sorry I am very sorry it should be VBS I am sorry made a mistake that is why I think you might have got worried VSB or VSB okay I am sorry okay what is this GMV VSB this is another current source what is there okay this is plus value so what whether it will add to the net current only to subscribe both are in no same sense they will add so GMVGS plus GMV VSB total current if not how a capital VSB actually biased kicker abhi aapko uska quickly example they say why we are saying so just now few minutes ago I said we are show VT is constant what did I say VT is constant but in real life VT is also decided by how much is the bulk voltage just now few minutes ago I said if I apply minus VSB to the bulk what happens to save source drain and get to a source bulk and drain bulk the depletion layer enhances is that correct if you know your theory well most on theory any depletion chart below the channel where does it contributes to in VT minus QB by C ox to add an additional QB the VT will enhance the expression given is VT is equal to VT 0 that is 0 VSB value plus gamma times gamma is a constant under root 2 5 some value I will explain 2 5 for me level permanent voltage plus VSB minus 2 5 up to the power half so essentially saying with VSB it is VT without VSB it is VT 0 so additional VT will appear if the gate tube bias is that point clear if there is a depletion layer in the channel region now because the source drain then the additional charge in the depletion layer enhances the VT value because there the value was QB by C ox initial depletion was because of what because of the gate voltage I am applying now there is additional bias I am giving from bottom plate it will also put large depletion charge at the channel side that additional charge will enhance VT by same logic if I have put VSB positive what would I happen VT would have gone down this is fantastic this in fourth year or some year later if you are engineers in this area VLSI any time or in communication chip designs then you will realize that VT control is now external so external are a under the fixers have transistor for future same a bias laga K I can vary the VT of my choice okay this is very great control this is VSB control okay but that is not my job if I write this VT like this ideas will be like this if I take delta ideas by delta VSB which I am defining as GMB why it is called the bulk transconductor change in current with change in bulk voltage is called GMB bulk transconductor that is can be if I differentiate this I get gamma upon 2 ? plus V times GM and this whole factor ? upon 2 ? plus under root of this is given a name ? is given a name ? typical ? value is 0.6 so how much is an equivalent circuit let us say GMB VGS is some value and GMB is how much 0.6 GM value him after actually 1.6 GM million up any VSB laga otherwise still one GM will not have the 1.6 GM value up from this is that clear to you that is the trick in actually controlling the game of thread bias can actually change the game so is that GM in our cases sometimes we may say GMB 0 you need not use but just because that actual circuit equivalent was shown GMB value may be specified and maybe you draw it okay is that okay okay I have a mass transistor right now I am not showing you any great DC things here no biasing that what will start next time I am actually biasing this circuit by something what is called constant current source okay what is the impedance of constant current source infinite that is why it is called constant current source output resistance of a constant current source is infinite is that clear so I am biasing with the DC bias current I IDS capital IDS DC current is pushed through this I am putting a V in I am finding B0 and then I want to find B0 by V in the gain if you have done network theory and present are and being so great one can say change in this at this 2 port network if I solve here change in current through this transistor if delta IDS it can be written as GM times V in plus G0 times V0 this is network to a port equivalent network G0 GM shunting GM VGS R0 R0 is 1 upon R0 is GC so I say GM V in and the kind of figure the kayak GM V in plus G0 V0 is delta IDS change in current through the transistor if I apply V in now current source biasing since we did we define GM now that is the definition of small signal values GM is delta IDS by V in and what condition when V0 is when this term 0 then delta IDS by V in is GM by same logic G0 is equal to delta IDS by V0 and V in is maths nothing great a tongue was you know correct to do some in my East turn go to the M in simple maths however please look at the situation IDS is a fixed current DC fixed current okay so delta idea there is no change because that is what I say fixed DC current if delta IDS is 0 and I substitute here then GM V in plus G0 V0 is 0 so V0 by V in is GM by G0 minus or minus GM R0. So depends on how do you want to solve a circuit the result would be same from any way is that correct what is V as V0 or V in means the voltage gain AV voltage gain so voltage gain of a transistor is when bias with constant current source is my that is why called intrinsic GM times R0 next time we will start the actual MOSFET amplifiers first we will start with biasing then we will show you some amplifiers and then we will do by bipolar why we want to postpone bipolar because I said 60 70 percent MOSFET so let us do MOSFET thank you for the day.