 We have discussed last time we show the circuit this is the equivalent circuit of a bipolar junction transistor is a common emitter equivalent circuit shown this is the base resistance called base spreading resistance RBB dash this is the CPY is the capacitance associated with value given last time which is between base and emitter please remember there are two capacitances here those CPY is only shown there are two capacitance between base and emitter which are the two one is because of the junction capacitance of the base emitter junction and the other is diffusion capacitance right now I am showing CPY as if it keeps care of both but otherwise we must find whichever is dominant the sum total is what is going to come in this parallel combinations then there is a resistance associated called QIB by KT which is our pie then there is a junction between base and collector which has a capacitance of reverse bias capacitance of C mu which has been shunted by a high huge resistance in the reverse bias of a diode which is our mu there is a resistance called spreading resistance to emitter because of the path it takes longer distance to travel to the collector from emitter to real emitter called RES then there is a current source this is the major feature of bipolar transfer if you have a VBE at the input the output current is GM times VBE which is larger current than the input current which enters of the base and since this current will be larger they will be gain output current by input current then there is a output resistance R0 which is essentially the slope of ICBC characteristic we last time discussed then there is a small capacity a small resistance associated with the collector region itself which is RC and there is a capacitance between substrate and the collector which is called CPS so this is the circuit last time we showed and we all derived it all the components it quickly will get into some of the features or some of the numbers so that you will get an idea what are the kind of numbers let us say I am working on biasing okay so the word bias is very important I keep saying earlier also if you are the characteristics of a transistor we are redraw it if I have a resist capacity sorry collector current versus VCE drawn at different VB or IB value this is IB 01234 and what did we say this is a DC current versus DC voltage so what we say that if I have fixed my VCE that is if I have a transistor this is all right now shown NPN I have a small resistance R here then the current flowing here is IC and this VCE is essentially VCC-ICRC RE call it RL right now so one can see from here depending on the value of RL and depending on the choice of IC I make I can draw this line itself on this graph and this line this is VCC this is ICC RL max we will discuss this little more detail this is called load line this is called load line I think I have been this is already known for a given bias current let us say IB2 this value VCE dash will use is called the and the current associated with this let us call it IC bias VCE bias so if I fixed my VCE bias I have for a given IB I get a fixed IC DC value of collector current this is called biasing okay we will do little more detail I just want to use those values so I am now said this is called the operating point this is called the operating point and we are all the time worried last time I said choice of my IC is essentially going to decide all my parameters to recollect our formula formula you see IC term is appearing QIC by KT is our GM so IC is therefore a major biasing from capital IC means DC value however what is the output we are looking small signal values but the biasing is DC is that correct biasing is DC which decides all small signal parameters for this circuit so having shown you this we did last time something like this let me quickly show you not really calculate anything a typical I am biasing across such an amplifier circuit be shown is IC of 1 million and I bias the reverse bias voltage to 3 volts VCS I use it 5 volt I mean these are arbitrary values do not get that these are the actual values we will have to evaluate for given data given to us right now take some value typical value for junction capacitance CJ E0 for the junction emitter capacitance C pi and what we were looking is 10 puff and what is this 0 stand for 0 bias with the bias change yes this value will also change okay and what is this pi 0 E this is the built-in voltage of base emitter junction okay this is 0.9 volts what is the value of that KT by Q LN any mindy by Ni square we are done this physics last year this is that any parameter which is you know because it is a step junction it is half it is exponential it is one third and so on so forth so right now I assume it half similarly I calculate the junction capacitance of the base collector which is around 10 centipedes similarly for base collector junction the sorry base collector junction the built-in voltage is 0.5 volt and C for the collector is 1 by 3 now you can see why I use half here generally base emitter junction can be made it is step junction whereas base collector junction is normally because of the process we do can be generally exponential or linearly but having given whatever we can choose any of the values specified if it is a linear everywhere we will put one third everywhere if it is other someone must specify what I should use for a given junction you are you fine similarly there is a between collector and substrate the capacitance at 0 bias is 20 centipedes the built-in voltage is 0.65 volt and corresponding E is one third so these are the values associated with the capacitance so there are other values which will be specified for BJT it is called beta 0 this is essentially same as AC beta when when the input signal is much smaller than 26 millivolt then we can say beta AC same as beta DC otherwise the two values will have to specify we are not working at close to much less than 26 millivolt so for a large signal analysis do not use beta 0 and beta DC same but for a small signal analysis this number is good enough that is 2 to 100 then we say typically based on the time is 10 picoseconds and early voltage can be 20 to 100 volts this is just a bit number 20 volt what does that 20 if it is less what is that it means which is the value which will become smaller anyone if early voltage is smaller what does that mean now output resistance will be smaller output resistance will be smaller and that is what we are not looking into we want output ideally how much infinite current source shunted by infinite resistance now it may shunt it really by some number so just to give value given an early voltage you are actually given something more than what we think it is giving you R0 value immediately from the slope okay and therefore BA by IC is the R0 of the transistor given at a given bias then the other resistance is given to us is RBB dash called base spreading resistance typically of 100 to 300 ohms the RES which is typically 5 ohm collector why collector resistance is higher than emitter device piano emitter is heavily dope N plus collector is likely dope in conductivity for N plus is much higher than collector region and therefore resistance wise is the opposite similarly we have a value of R mu which is the junction capacitance which is 10 beta 0 R0 beta is much higher 100 R0 is in kilo ohms to mega ohms therefore R mu will be order of mega ohms and above so it is almost open circuit across C mu what is I am saying I repeat most cases this resistance may be neglected why typically this value may be much higher than the short at the given frequency whatever offers as the impedance let us say it offers 10 ohms you are shunting 10 ohms by 1 mega ohms so how much is that can reduce 10 ohm maybe 9.998 so how do I care whether it is a mega ohm sitting there or not sitting there is that clear in most cases R mu may not be useful as a tool but if you draw a circuit if you are given a value do find what is it and use it in circuit because for circuit it does not matter if you have a parallel combination will make a parallel combination is that clear but otherwise in general R mu are not used because it is normally much higher than 1 upon g omega C mu in most frequencies of is that clear but when the omegas are much smaller and yes it may shunt the R mu as well and then you will have to find what is the equivalent value for this is that clear so this is something as a circuit we must appreciate while value which will go whenever we like to do this we can evaluate the other parameters for example I say Cj e is normally taken as twice that of Cj is 0 why this is called empirical calculations you just double the value of Cj is 0 given to you 10 puff 10 femto farad was given make it 20 femto is it okay 20 femto farad the C mu at a given bias 3 volt bias it is 10 upon 1 plus 3 upon built-in voltage 0.5 to the power one-third which may give you a value of 5.6 femto farad so we can calculate the C mu value at a given bias please remember these values have to be calculated for a given DC biases similarly you can calculate the collector capacitance in the substrate which is essentially 20 femto farad divided by 1 plus 5 volt the voltage given to you upon 0.65 which is built-in voltage for collector substrate junction one-third this gives you a value of 10.5 femto farads and if I calculate therefore the major small signal parameters for me then it is QIC by KT 10 to power minus 3 divided by 26 millivolts this is 38 milliamps per volt okay 38 milliamps per volt one can always say it is millisiemens as well but this is a common practice in analog circuit not to use the unit of scenes or whatever the reason is as I say we always have values which is current by current current by voltage voltage by current so we keep specifying the actual units of numerator and denominator V by V I by V I by I we write exactly as the units we see on the denominator and numerator is that clear that is the terminology if you use millisiemens word or millihomes nothing wrongs name house is perfectly justified but as it convention that what we use so I can also calculate the base emitter CVE which is very important GM times tau V GM is given to you tau V is given to you so it is 0.38 picofab please remember this value is so high point so if some capacitance is larger is it across the base emitter junction is it more important or it is not more smaller capacitance are important or larger capacitance are important please think of it 1 upon j omega C is the resistance of or impedance offered across if C is much higher then it will actually shunt the input voltage or is that correct so please remember these values may decided then how much real signal is entering the base before actually the amplification can be seen so these values are not trivial but it also depends on the omega term if omega is larger or omega is smaller these impedance may change so sometimes it may be dominant sometimes they may not be dominant that is exactly what we are trying to say that means the response of an amplifier or a circuit is also a function of frequency is that correct and that is most important for us what is the frequency this all that is doing is for to finally get a frequency response okay we can calculate therefore the net CPI as CBE plus CJE which is 0.38 puff just be calculated 20 pic front of a rod is 0.0 picofab so it is roughly 0.4 puff is the CPI value is that correct CPI is 0.4 by a similar expressions which we already told you it is R5 which is beta 0 by gm and that beta 0 is 100 gm is 38 milliampere volt it is around 26 kilo ohm which is not a very small value please remember R5 is 26 kilo ohms is it good or bad is do you believe the resistance across base emitter should be higher or lower if R5 across is very low what will it do it will short circuit every input signal okay so ideally input impedance should be infinite it should allow all the input voltage to go okay but how much is that therefore will reduce R5 upon R5 plus other resistances will decide how much is actual VB made available to you is that clear to you so that is most important what values you are operating please remember R5 has something to be beta as well as gm which is a function of collector current and collector current is our biasing current is that correct so bias is also going to decide my R5 bias is also going to decide my gm bias to some extent also decide beta 0 but normally distributed constant we can calculate our new which is typically 10 times beta 0 or 0 which is 20 mega ohms you can see this value can always neglect as far as shunting across the musical but if you keep it and solve nothing goes wrong numerically automatically that value will take care of it is that correct so ideally you need not neglect terms but as an engineering you must remember which terms should be used and which one should not be used why we want to because we are the smartest guys and we like to do calculations maybe by what we call back of the envelope what is this word I use even a small paper I should be able to tell you roughly how much is this okay to do this you must guess correctly which value I can neglect so smallest I can get I said okay this is the value because this is the first guess I must do when I actually implement the circuit on a board on a chip design when I do a actual silicon chip so this first evaluations can be done by just finding okay this is too large this is a so this a frequency this I can neglect oh so gain is so much this will fall at these values are your first guesses in all designs and all analysis therefore you must roughly know these are values because when you finally evaluate this should not be far away from these values this is your check okay how much is that okay 10 megahertz gain will fall okay now you got 100 megahertz in your actual cash something you made a mistake definitely is that yeah so first evaluation should be what we call back of the envelope well of being very small we can be able to do right this is engineering how much to do well is very crucial in this I am making this word design and design again the reason is at the end of the day you are not going to do analysis in your career we will have to design something for others okay if you are paid for it obviously will be paid for it and since you are an engineer you will be designing to do a good design you must do good analysis first because you should know what implement when I implement what influences what okay and therefore my design as direct connection to what the analysis I have learned through this course will quickly follow more analysis but why are we doing this analysis because at the end if I have to design I must know all of it beforehand okay that is the way we think we should do well one of the major parameters which all of you are last time I told all of you is the figure of merit of a BJT it is also called FT sometimes it is called Omega T what is Omega T 2 pi FT is Omega okay Omega T so if you some books say Omega T it is same as FT because 2 pi is a fixed number 6.3 this to it and that is good enough okay so normally either Omega T or FT is the value specified to you if it is frequency or its ingredients depends on what value people specify now what is the definition defined as it is the common emitter current gain when it falls to unity is that point clear FT means I am varying the frequency for an I am this kind of a circuit and I want to find at what value the beta which is collector current by the base current falls to what value unity what why why we want to find this value what does that why it is called figure of merit beyond this FT what will happen IC by IB will be less than 1 so no gain why are we doing an amplifier which has no gain okay so that is the maximum frequency of operation which you can use in a circuit but you should not use FT really you should typically use 1 by 10 of FT in your analysis because in your designs because FT is the point at which gain has fallen to 1 to that limit I want to know where is the gain going to 1 and beyond that I will not actually operate anytime and that is why it is called figure of merit okay how do I calculate this or how do I evaluate I already said it is going to be common emitter current gain when falls to unity so I say okay I short circuit the output what does that mean I make V0 0 but the current is not 0 please see collector current is still flowing in a circuit which I declared I0 my input current is II which is nothing but the base current both are AC currents both are AC current DC biasing is taken care okay then beta j omega is defined as I0 by II IC by IB and that is a function of frequencies input signal is varying with frequency current is function of I am actually increasing the frequency and let us see where at what frequency this term beta j omega becomes unity and that frequency will define as FT okay beyond unity current game if I have a resistance there there are two parts of the currents that means the actual transistor current is now shared between the resistance and the collector the collector external current would be then divided by the resistance V by R plus GM times that I am interested in FT of transistor not the circuit so I want to review that is that correct that means I must put only currents going at the output which is as a V0 short by of course we will come back to it if you write a small signal equivalent to get I by something you will have to make the other term equal to 0 okay network analysis A1 V1 plus something to make other terms you know only then you can get this ratio is that we will do that analysis again in real life this is just to give you the measurement so this is equivalent circuit is that clear this is my equivalent circuit this is my II R by actually I may write down neglect RBB dash also I may neglect R mu I may neglect the leave this I RES also I neglected actually you can forget about our face well if you wish by making output shorting I made V0 0 but the I 0 is flowing inside and how much is I 0 therefore at the at this node node 2 GMVB is that correct now something I made a machine in this my assumption is not much current is flowing across C mu okay but that an assumption which is not very bad as of now we will show you later it may not be as good an assumption okay so I 0 GM times VB this is the current only current flowing in this circuit okay because V0 is 0 so no current in R0 is that correct no current in R0 no current here so only this current source is same as the collector current if you see the input current II you can say VB times j omega C pi is one current here where one current is flowing here and one current is flowing here is that okay last people II current is divided into 2 arms one through C pi other to R pi again assumption is very little current is flowing in mu okay if that is to be taken care little complications will arise more accuracy can be built but as an engine that is good enough so if I write I was equal to VB j omega C pi plus VB j omega C mu okay this is R pi I made a mistake plus VB by R pi and if I collect I0 by II from these two node equations I can get I0 by II is GM R pi upon 1 plus R pi times C pi plus C mu into GM is that clear I got II I got I0 and then took the ratio of I0 by II and that what is the way I define that output current which is collector current II is the base current the ratio is beta this both currents are functions of frequency so is the beta is a function of frequency so I have a beta j omega is GM R pi are you if you are familiar with Laplace transforms I hope so you may start using S instead of j omega but I thought initially maybe I will show you later maybe will not use j omega term we start using S normally as everyone of us have been familiar just for a few days you may continue j omega then we will never use j omega term and maybe at the end we need we will put S is equal to j omega so yes the current going through this is the conductance multiplied by voltage GV this is GM this current okay I have taken here in this current also now in this case all that I said no current on this side but this current I have taken so there are three currents flowing here one through this please remember what is voltage here 0 V0 I assume 0 so I can find this current which is BB times j omega C mu this current because this voltage is going to 0 so I calculate this current I calculate this current I calculate this current is that okay so that is what I already said RC as far as since there is no other turn there is a RC I said drop right now that is what I said you know that is what I started neglect RBB died neglect RES neglect RC these are parasitics right now we are not worried about so this I0 by II is that last people is it clear to you how did I do I calculate currents here I calculate current here and took the ratio of this and that ratio we know is beta j omega is that okay so we move further and we say if I do this okay maybe we can keep it here so now to make this beta j omega equal to 1 what is the condition it will get to me let us put at okay maybe we will put a next slide at omega equal to omega t we say beta j omega is now we can say in normal cases is omega t is very high much higher frequencies in numerical numbers is this term is stronger than 1 if I take square of this plus 1 square or under root of this magnitude why this term will start please remember Rp Cp Cme into omega square plus 1 square under root of the when I do magnitude for this this one is much smaller compared to this number and if I do so then I write Rp Cp Cme omega t is then omega t is em Rp divided by if you wish to keep one I have no objection if you wish you can keep this one and then write one further it does not matter but then there is a one upon term comes right now I do not want to complicate I will just write Rp Cp plus uk what is gm Rp what is gm Rp beta 0 by Rp gm up I live okay you are right so omega t is what gm upon Cp and see what is gm kt by q sorry I am very sorry q I see by kt divided by so are you now getting a point that when I see becomes constant what is the from where I fix my I see I just showed you biasing if I fix my bias I fix my I see capital I see if I fix my I see I may fix my Cp mu and gm together all three of them are fixed by this omega t then becomes the figure of merit is that current what is the definition I said for it whenever beta falls to one beta j omega falls to one that is the frequency at which transistor will no more give you current gains and if there is no current gain there is no question of I times the R output if you put the voltage will be less than input voltage so even there will not be any voltage so if I am not getting an amplifier I am not getting an amplifier and any amplification then why do I do it okay of course this statement we may qualify later it is not really necessary that the amplifier should have a gain less than should not have a gain less than we may not call that you will say minus so many DVs it does not matter for me with the gain is less than one in some cases will show you why we say so it is very relevant for us as of now we say amplifier should have gain larger than one then we will call amplification is that correct so omega t is therefore what it is called figure of merit and this is technology constraint because please remember the values of Cp I see you are decided by the dope ring in base emitter junctions and base collector junction the lifetimes there I assume the base time I assume except the capital IC part which is external to me the rest parameters are internal to a transistor so they decide what GM by C I am going to get this normally in one word they say GM by C in so what GM by C in now you are understood what did I say so why it is called figure of merit because it decides the maximum frequency of operation calling amplifier circuit as an amplifier is that clear can you get me a unity gain amplifier unity gain is not this oh sorry when the beta becomes starts falling so what is this expression which I just show you this expression if I plot on a frequency scale what do what will you like to see beta times omega if I plot what will happen you start looking at these expressions if omega is much smaller is that correct if omega is much smaller this term will be smaller than one because Cp I see you the femtophilates and something Rp is close is that correct so at higher frequency this term will start dominating but for lower frequency one will start dominating so how much is the gain at very low frequencies GM R5 which is beta 0 so at low frequencies gain roughly is beta 0 and as you start increasing the frequency what will happen the denominator terms will become higher and higher and beta will start becoming lower and it will fall it will start falling in a log scale if you plot this will start falling at this point actually it will go by asymptote but this frequency when the beta falls by 3db or 1 upon root 2 of this beta beta 0 by root 2 3db down okay this value is called beta sorry omega beta what is this value called omega beta this frequency how do I calculate from here you can calculate find the 3db means 1 upon root 2 put this is equal to root 2 and whatever value you will get is called omega beta it is beta 0 by root 2 is that correct beta 0 by root 2 this omega beta what is the significance of omega beta and this value omega t how can they be related anyone okay you do this and find this omega beta times beta 0 is essentially omega t is that correct essentially omega t so what is the omega beta value you can immediately this is of course not exact like this so how do I calculate omega beta otherwise I calculate omega t which is my GM by 2 see to pass in and then just divide by beta 0 and I get my omega beta and what is this value I should use for anyone what is the beta why I am interested in omega beta because it is here up to this frequency your amplifier has a reasonable gains available is that correct if you go beyond omega of this beta will start falling still gain but it will start falling is that clear at omega t no further gains okay so now can you say that not even 10 times how much I should have a omega beta roughly will be beta will be 100 or 200 so omega beta will be 100 or 200 of omega t omega t maybe let us say 100 mega 1 gigahertz or something or 10 gigahertz 100 or 200 times less of that will be the operating frequency is that correct what is omega beta called the maximum operating frequency is omega beta for us is that correct please remember I can certainly go beyond omega beta as well till up to what omega t but I am assuming and I know when I am designing that my beta is falling but I am taking care by other parameters the lift up the gains okay by GM but I know I have some advantage of increasing the frequency but beyond a omega t of course I will not use it but preferably I will only use my transistor range range from 0 to this is called my operating frequency maximum operating frequency that is why this number is known must be known to us I will evaluate omega t divided by my beta 0 value and say okay this is the upper most frequency I will use okay is that clear to you therefore this is how the analog circuit bipolar circuits actually gets limited both on frequencies as well as gains because if you want to make gain larger or GM larger what should I increase GM I want larger and larger to get larger gains what should I increase IC what is the problem if I increase IC okay your one is worst case that IC may be so high that device saturate let us say it does not even know then what will it for increase something else yeah to some extent yes but there is a major worry start if the collector current or the current in the circuit start rising no device V times I what is it power so the I showed you yesterday first slide power is my major worry so power dissipation will start enhancing and once power dissipation increases what increases temperature increases all my parameters of device are a function of T okay so they keep changing beta changes are by everything will change with temperature and now as they change and you will find very interesting some of the parameters have positive coefficients so they may further boost IC may further boost T further boost IC so what will happen it may actually burn or what we call thermal runaway device may actually burn okay is that clear so even if what she said is correct first aid device may enter saturation but let us say it is at the age it does not enter even then your circuit may actually fail at then is that clear this is the reason why we say there are limitations of everything which we work out is that clear otherwise on a normal mode many things can be tried what do we do like I use open any computer or any other system there is a huge fan on the backside of the system okay so it keeps cooling so any desktop system I can keep a good coolant cooling system and I will never allow temperature to rise but on a chip which is our major worry when I actually make a chip there is no fan in because this is a package inside there is no fan inside okay so this chip will burn in respect to what to do is that clear to you and therefore in designs we must worry about the limitation and limitations come from the theory of the transistor is that correct so why all that so far we are doing to show you because we wanted to convince you that why we are getting limited otherwise you know why not work everywhere whatever value I substitute numerically something will come okay but it may not be useful as far as circuit circuit so this as a engineers we must know where we are bound not spadaena lower bound upper bound we must work within the bounds okay let us do something more okay the major device of course as I say why I keep teaching bipolar because every book will start with bipolar so I do not want to take you away immediately from but the first amplifier which we are going to design will not be bipolar we will first do most design and then say okay equivalent bipolar catapact okay so now with the next technology of interest or next device of interest which is based on MOSFET here is a n-channel MOSFET maybe if there are four possible MOSFET we may use one is NMOS announcement mode please see a symbol this is a cross section of n-channel announcement mode transistor how many terminal MOSFETs have four please remember MOSFET is a four terminal device actually so is the bipolar I show you substrate is the fourth there also in circuits actual terminals are four but the normally substrates are grounded with the other grounds and therefore you see three by bipolar transistor but in MOS you will always have four terminals of course you can connect base this substrate as well as source common then it will also become three terminal device please I have a figures first is n-channel announcement mode transistor and MOS this second is n-channel depletion mode MOSFET and complementary to them is P-channel announcement mode and P-channel depletion modes what a symbol this has just shown you to use whatever symbols I am going to use in my course I just thought I should show you my circuit symbols in the case of enhancement mode n-channel the base arrow is inside this arrow is inside this is the symbol for NMOS announcement mode is that okay n-channel announcement mode the substrate terminal arrow gets inside okay that is my symbol by contrast this is a complimentary P-channel transistors the arrow is opposite coming out towards substrate B is called bulk bulk or substrate B is called bulk other name is also so the arrow in P-channel is out arrow in n-channel is in there are three terminals otherwise gate drain and source for each of them and forth is the bulk now what is depletion transistor you are have they discussed okay if the channel exists pre-exist before the gate voltage is applied then there is already a current flowing between source and drain independent of gate voltage essentially what we are saying is the following or maybe I have a figure if you are drawn this is standard you can see in any book including the book which I happen to now co-author for that if you do not buy your choice any of the book you buy is fine if you use library books fantastic absolutely no problems so if I plot okay n-channel NMOS this is the third one is a normal NMOS announcement mode I am drawing what is called as what characteristic this IDS VGS IDS is at what point very good someone has said transfer drain source current is the output current VGS at the input therefore it is called input to output transfer okay so it is transfer characteristics you can see at 0 bias VGS no current as I start increasing VGS channel will start appearing and at certain voltage we call turn on voltage or threshold voltage current will start rising sufficiently sufficient electrons will be made available in N-channel there P-channel this voltage is called threshold voltage where current starts substantially higher N-channel negative VT has some advantage this is called depletion transistor what is it trying to show you in depletion even at 0 VGS there is a current flowing and to shut it off I will have to apply negative VT negative VGS equal to a VT value which will make this electrons which were sitting there must deplete they must go away and that is called negative threshold voltage minus VT and the upper two are just the complementary of the only see the sign for P-channel are minus IDS minus VDS minus everything I could have shown on the fourth quadrant but that is shown essentially on the fourth quadrant okay these are two are fourth quadrant these two are the first quadrants is that okay these first two are on the fourth quadrant second two are on the first quadrant curves what is the VT value we said we say in a transistor whenever inversion channel comes we say that voltage of VGS we define as turn on voltage or a threshold voltage turn on only circuit people call as the device we always called threshold voltage okay so the threshold voltage by theory which will not use now but just to show you for both N-channel P-channel common formula as in specified 5ms what is 5ms what function different between metal gate as well as the semiconductor to fire what is fire for me energy KT LN KT by Q LN any by Ni or in D by Ni therefore plus and minus both signs in D by Ni will be minus or any by Ni will be minus if the P-channel device I N D by Ni will be minus because potential above is negative and lower is positive opposite happens in both okay please remember E by Q is V but a sign Q as a minus sign is that correct you as a minus sign and therefore potential energy rise plus means potential negative energy going down means potential positive band diagrams throughout they appear okay this Q ox is the fixed charges in the oxide normally 99.99 they would be always positive unless we do some radiation or something we force it to become lower or minus otherwise Q ox term is always positive for this always is negative what is the ox value essentially capacitance of oxide is epsilon ox divided by T of this is oxide capacitance per unit area get area and plus minus QB QB is Q NA XD depletion layer charge Q NA XD or Q ND XD is that correct so that is plus minus is that correct Q NA XD will be minus Q ND XD will be plus but this sign is minus outside so minus Q NA XD will become positive because of the outer minus sign and plus Q ND XD will become minus so what is it trying to show you VT can be known to us from the device side I have no control once given me a transistor my VTs are given to me I am this bother what is 5ms what are fixed charges why they are operating why band diagram goes like this or goes like this held to them so we will now onward we not use this expression but just to give an idea that from where they were appearing now typical output characteristics of a bipolar mass transistor is of this ideas versus VDS at different VDS values are plotted here whenever VDS is less than VT there is no inversion channel but there is a small current what is it because of VDS is less than VT so no inversion channel firstly this statement itself is not correct why do I say because the definition of inversion was given when the band band bending is equal to 2 times the 5 but between 5F and 2 5 the inversion was existing so one reason why but assuming it even meant to fire there is still current going on from where if you see the device quickly and that is very in the circuits also now these are two diodes even if get is not controlling any charge here these two diodes are reverse bias diodes and reverse bias diode will constitute reverse bias currents this is the leakage current junction leakage current which is independent of what oxide does or does not is that clear to you these are diode reverse bias currents so leakage currents are always present independent of now what is the first slice I show you that is becoming now major worry since we are scaling scaling reducing everything the currents in these are increasing this saturation currents are increasing enormously because the doping I am using see these currents are increasing and on currents I cannot increase because size will increase and I am reducing the size so what is happening I told you one in bad thing about our good thing for you that the recent mobile people say keep it on because the off current is much larger than the off current on current so on rakhoga the battery come drain of Karthi stand by me during I just talk about okay okay so this region which in a digital we use very often what is this region VGS less than VT or 0 roughly off state of the transistor okay we say 0 current but it is not 0 some finite small then we say if I start increasing VGS further beyond VT inversion channel will exist and current for given VGS will start each has one character now these essentially means if I increase VGS I am going to increase ideas but so is if you see at this region at least in this region those slopes are not very much but there is a finite slope that if I increase VDS current still marginally but if you see this region for every VGS if I increase VDS current increases linearly roughly linearly so what is this region called linear region of a mass transistor what is this region call in transistor because characteristics roughly looks to be saturated this is called saturated region these names are opposite in the case of bipolar in the case of bipolar this region we call as saturated because they are both junctions became forward bias okay the maximum collector current was made available so there this region we call saturated in the mass we call this region is that clear flight definition why this definition came the first difference you should realize between bipolar transistor and a mass transfer what is the input of a mass transistor we say all the time VGS that is voltage driven what is the input in the case of bipolar current input base current so it is a current driven circuit I 0 by I I I so the first worries are in the case of bipolar obviously you will find the input impedance will be lower is that correct because there is a current flowing so V by I since I will be larger so resistance at the input will be always smaller QIB by KT which is HIV as we call or KT by QIB whereas what do we really want larger input resistance can you tell me why I am saying from the circuit point of view I have one circuit here circuit 1 circuit 1 and I am connecting this to circuit 2 now it has some input impedance and it has some output impedance is these two value are something to play a game if this value is infinite let us say R in then this device will not be loaded or this will not share currents from here otherwise what will happen these two trans resistors will parallel and this value will start influencing the output of the first stage itself if this resistance is finite in 0 or small then these two will become smaller and V0 will be then function of second circuit which no designer will like because I do not know what where I am going to connect so how do I decide what the first block what I am going to connect next so ideally my R in should be infinite I also want my R to be as small as possible as it is a series resistance because I do not want large currents to flow there okay. Now if that is so happened the decision is how to control R O and R in MOSFET has the biggest band what is this R in you see a mass transistor what is between this between gate and transistor bulb oxide large resistance large resistance is that a mega ohms hundreds of mega ohms which means its input impedance is extremely high so MOSFET circuits are better because they can be directly connected or the bipolar may cracker na padega is key beach may do no key beach may a block down na padega is called the buffer I will have to match resistance on this side and also this is called the key if you have one huge W Jojo box a world of cow fight wallet Karthai if there is a huge wrestler and a smaller wrestler they cannot fight a beach may refree Karate is for month but they both are saved so buffer is a very important circuit in all bipolar circuit it is not that important I am not saying that not important that important in the case of most not that is not required not we will never use buffer we will apply any time but in general what is the advantage of bipolar over MOS and what is the disadvantage of that bipolar have larger GM why Q IC by KG ICs are always larger than ideas for given voltage collector currents will be larger compared to the drain currents is that correct what does that mean for a same voltage operations GM will be larger for bipolar and GM will be smaller for MOS transverse so what will be the voltage gain from same same currents and same voltages bipolar will give higher gains than MOSFETs what is the disadvantage is giving it is consuming larger power it is input impedance is low is that correct whereas in the case of MOSFET is input impedance is very large and closer to infinity and currents being smaller what is it going to consume power much lower power is that correct so you must know when to use bipolar and then so larger GM ka ekor kya advantage hoga omega badega ki kum hoga beta higher hai to fall b long hoga to omega t b higher hoga so higher bandwidth can also be attained by bipolar compared to MOS I do not say the MOS does not is not coming closer to bipolar but intrinsically one sees bipolar have a larger power larger bandwidth and larger gains whereas MOS transistors have larger lower bandwidth lower gains and lower power but then we will continue to use everything lower these days because power is our major try to everywhere meet up to mobile laptops hote hote handheld system they will start draining power in next seconds that here so we are looking for low power so that is why I say MOS transistors are preferred blocks compared to this because this is not only reason we were looking for digital which is much better in the K come in case of MOS than in bipolar and therefore prefer MOS feds as a universal device is that universal device but if I want specific circuits which has a higher bandwidth higher gain then I will look for bipolar I will look for bipolar and therefore bipolar circuit though only 6% of the world semiconductor IC market has only 6% bipolar 94% and I am told now soon it may be 98% will be MOS and 2% bipolar so maybe after a few years I may not be teaching but we will not teach bipolar at all okay okay so having told you that this is our MOS characteristics we must operate where in this region which is our saturation region what is the saturation region we are saying what will happen in linear mode we will say in a linear mode VDS has direct relationship with ideas so it is a resistive circuit I would now prefer that this current may remain roughly constant for given VG VDS or varying VDS only should change with VGS what does that mean external voltages should not influence too much of the output current only the input should change okay and output should be seen so I will prefer to work only if I extrapolate these which unfortunately this length is not good enough for me if I extrapolate these as I did in bipolar where they will meet at a point which is not really early voltage in strictest sense what do you mean by strictest sense because this early effect is not seen in MOSFET really is that correct but we say as if they are same so we say VA which is early voltage for the case of MOSFET also by same logic what will be the R0 for MOS transistor VA by IDS okay will be the R0 so given the biasing IDS given the early voltage I know my output resistance is that correct VA by IDS please remember at this point for example if I buy us VA plus this much I must add but I do not add why I said you because VDD will be how much 3 volt 1.5 volt 1.8 volts how much will be this 100 volts 50 volts so 50 plus 1.5 divided by so much by so much 50 by this and 51 by this will not give you much a difference and therefore we say we normally do not write this plus this divided by this we just write VA by IDS in reality this must be added okay this must be added but numerically 100 may 1 volts add Kia no Kia divided by same number will not matter okay you have done this theory I will just give the expression for you and then when the transistor in linear mode what do in my linear mode just now I show you this mode what is the mean what do in my linear mode in transistor when the channel exists between source and drain throughout okay okay some symbols may be quickly seen there sorry I think we just repeat between source and drain we have a channel length L the third dimension there is no duster here but okay may be this you can see this is your source this is your drain this is your channel length but this is three dimensional device this is your width okay so this width is shown on the third dimensions my definitions is I always have this axis x y this is how I define so along the z axis I have the width along the y axis I have the length and I have the best along x this is how we define in our device theory so I have a fixed width of the device fixed channel length of the device then this oxide thickness T ox is also fixed by the process people so capacitance of this is also fixed epsilon ox by T ox what is K ox dielectric constant of oxide is how much silicon guy well 3.9 okay or if you are numerically 4-3.9 okay what is the epsilon 0 value 8.8 very good 8.854 10 to the power minus 14 parameters please remember analysis of course in this course will not require in device if I am teaching I insist that you use CJ system and not MK systems because there is huge problems in microns conversion to meters to down so here of course we are. So channel length channel width oxide capacitance these are the specific given by transistor people I do not care what the value is this specific once given to me I will use this so I have derived this expression by a simple theory Mu C ox W by L Vgs- Vt what is Vgs okay let me show again if I apply gate voltage with reference to source which is grounded with reference to be which is grounded and I apply Vds at the drain this is Vds across why Vgs is across x axis is that field effect clear to you field effect is clear to you Vgs is along x direction is creating a electric field along this direction current is along this direction the current transport on a lateral plane is governed by field across all orthogonal to it and therefore it was called field effect will be the e y ex field which is controlling the ideas along the lateral line that is why it was named field effect is that correct. So since this is going to control I see Mu is the mobility of the carriers so should I use n channel device or a P channel device n channel device because Mu n is much larger than how much is larger how much is this Mu n channel or P channel can you tell me that a ratio but how much is Mu n in the MOS transistors and how much is the best of Mu n you can get in a MOS transistor is 600 centimeter square per volt second how much Mu n is the best of the value you can get 600 centimeter square volt second and Mu P as he said is not even best of it is 200 centimeter square volt second. So what does that mean why this is not 1350 or 1300 and this is not 500 what I know the electron mobility is essentially in 1300 or 1350 sometimes even 1500 possible the whole mobility in silicon is just 500 why this number is so small it is called surface mobility there is a oxide surface sitting on the top a lot of recombination going on there so these mobilities are much smaller so these numbers should not be used at 1300 and 500 as in the case of bipolar because there is a bulk transport here where it is surface transport okay please look at these numbers carefully. So can you think this value PGS-VT what is it essentially tells if PGS exceeds VT then only inversion starts is that correct so this value in circuits we define this value VGS-VT is called over voltage what is it called over V okay this is very important some books I do not know any other book may be called V excess is that correct why it is called excess or over over VT when you go VGS only then current is available to you and therefore it is called over voltage or excess now in the linear mode please remember the condition which we applied essentially e VGS-VT is greater than that correct why this condition is valid because at the drain end VGS please look at the drain end voltage this is VGS so what is the difference at the drain end of the difference this voltage VGS-VT if I want inversion to appear at the edge what should be this greater than VT which means VGS-VT should be greater than VDS so for inversion channel to go till drain VGS-VT must exceed VDS so that is the point where then we say it is a linear because if VDS is smaller this term can be neglected so I get ideas proportional to VDS this is constant V is constant ideas is proportional to VDS therefore it is called linear mode of operation since VDS is smaller than VGS- but as you come closer this linear relationship is not linear it starts bending partly because square term starts coming into however if the condition is such that VGS-VT is less than VDS there will not be any channel at the drain end and larger the VDS first the channel may not exist here when VGS-VT is equal to VDS VGS-VT is equal to VDS no channel okay if VGS-VT is still smaller than VDS even here it will be 0 less than VT here so channel will become saturated or pinch of it and the pinch of point will start shifting towards the source as VDS starts increasing is that correct that means the effective channel length is not L but it is something L-the depletion layer which is a function of this doping and this bias how much is VDS will decide the depletion larger the depletion larger will be depletion layer and smaller will be L effective what is the importance of this word I am saying if you see this expression if L becomes L effective and smaller then what does that mean ideas will increase or decrease increase because L is decreasing L effective in decreasing means I increasing that is exactly what you saw in the characteristics slope if VDS starts increasing the depletion layer will start enhancing L- will become smaller and there will be a increase of current with VDS well is that clear to you is that clear to you that is why the slope is appearing for you therefore the slope is appearing for you so first we said in the saturation normally we say it should be independent of VDS so normal current what do we write this should have been our normal come sorry if I would have been if I ideal saturation would I exist I say ideas will be half new York's W by L VGS-VT square okay such good asset but now just now I said that if VDS increases L effective actually changes okay and therefore that effect can be taken care by additional term which is one plus lambda VDS which is lambda is a saturation factor lambda is saturation factor and it is defined by in actual this lambda dash by L what does this also means larger the channel length lambda will be higher or smaller this is the parameter this is technology parameter this is fixed for a given transistor so larger the channel length smaller is lambda smaller is lambda here is good or bad you look at it if lambda is smaller this will be independent of VDS is that correct what does mean R0 is how much if what is R0 delta ideas by delta VDS if they do not change with VDS R0 is infinite ideal ideal is that correct so I would prefer channel lengths to be higher and higher and higher such that lambda is smaller such that lambda VDS come become smaller but this means channel length larger if I do what will happen to actual ideas value will decrease ways will see GM also decrease so one advantage I got please remember what I am saying GM decreases if I increase channel length however if I define R0 which is nothing but related to lambda so is that correct so what is R0 is higher when lambda is smaller which means channel length is higher larger