 So if you are all here we start so this is the book and I keep repeating I am one of the co-authors there now okay. We have been discussing yesterday about the bipolar transistors we shall continue with that I think something we started with a typical BJT. So the basic equations we wrote last time and very important for us that the emitter current is always some of base current and collector current and this is the same from the physics that whatever is injected from the emitter side partly recombines in the base and the rest goes to collector and because of that base current plus collector current must be equal to the emitter current okay. We also said that the collector current if you are in the active region of the transistor active means where the base emitter junction is forward biased at least greater than 0.65 volts and the base collector junction is reverse biased sufficiently enough then we say you are in a active mode of a transistor okay and in that mode we say IC equal to alpha times I or essentially IC equal to beta times ID this is the law only followed when the transistor in active mode if transistor is cut off mode when the both junctions are reverse biased then none of the current junctions are conducting or reverse currents are only flowing you may say transistor is in off state wondering if base emitter junction is not conducting and base collector junction is also reverse sorry base emitter junction is forward biased with base collector junction is also getting forward biased then both collector will emit as well as emitter will emit carriers in the base there will be huge base current convertly saying that the huge base current the transistor will enter saturation is that clear that is the theory which we learned earlier hopefully so so in our analog course we will neither work on cutoffs nor work on saturated states we will see saturation limit for us so we will see only work in normal active mode normal mode or active mode when base collector junction is reverse biased base emitter junction is forward biased so all of our analog theory assumes that if not we will tell you what has happened otherwise and then we say in case you are more interested in physics oh there is a leakage current coming from IC and everything so I see is the current so essentially what it says even if emitter junction is stopped that is VV on negative then the base collector current can still flow through base and collector junction and therefore that is the ICO okay that is exactly what that leakage current is about so more accuracy can be built in case but in circuits let us look at situation something like this unless it otherwise the typical current will be millions and typical reverse saturation current will be in sequence so adding something tens of amps millions to it few non-vans of two pick ones numerically does not matter okay that is how we are physics wise if you say you get out you know something some will shout at how can it happen and so we will never work then that is not our idea idea here is number and therefore to some extent we will bypass such a certain values in case but in case your IC is very small then our eye is very small when it just starts on yeah those that current may add actually so let us get a case unless it otherwise we will neglect small currents but you may write and then neglect saying oh I cannot add so in my circuit we normally do not believe too much these numbers are great you also said other day that the collector emitter junction our collector emitter voltage from one node collector to emitter difference is always equal to because at one node there cannot be two voltages so if you go through this loop or you go through this loop so Vbe plus Vbc must be equal to Vc at any cost now that is exactly we will see when the saturation starts something Vc must go down so that Vb and Vbc must go opposite that is why both junction gets forward biased therefore Vbe my Vbc will become opposite subtract out of Vbe or opposite this and Vc will fall otherwise it will always add otherwise Vbc plus Vbc this will always add to get Vc so Vc base 2 point some volt Vb is points and volts so Vc will be two points and volts that in normal active mode these two voltages Vbe and Vbc will always add to make your VC is that clear normal activity so this is something we said last time now we go ahead and we did something more also we also showed you some figure we are interested in small signals so we said okay this the model so far we talked are called large signal models okay the device is swinging in inputs too high and sometimes may not reach into it may enter saturation so we must take clear and we say our symbolization is capital I small b equal to small IB plus capital IB which essentially says the total base current is equal to AC current base current plus DC base current and similarly for all similarly you can also write for voltages for example I may write may be sorry I may write Vbe is equal to Vbe plus that is the total base emitter voltage is DC emitter the base emitter voltage plus AC emitter this so you can always say that the DC part plus the AC part is equal to the total and that is our symbolization nothing very great nothing just to say how do we take numbers or how do we express things we also said if I plot the output characteristic IC versus VC for a bipolar transistor for different base currents the slope of this characteristics is such each for each IB if we extrapolate them on the minus VC axis right now all of us are talking only of NPN transistors the polarities will change just opposite of that if we talked of PNP transistor so as normally PNPs will not be used as compared to anything why anyone okay you said it but if I say you are wrong or at least on face you are wrong why do I say the reason why I say the current in a semiconductor is there are two kinds of current transport we are discussed I hope so one is called the drift current the other is called the diffusion current the drift current is velocity proportion to velocity that is mu e so current is proportion to electric field and the mobility available but in the case of bipolar transistor the transport is diffusion limited you are injecting the majority carriers from emitter into a minor they become minor it in the base because that is opposite polarity electrons become minority in the base is that clear to you and they diffuse they do not drift there they actually diffuse since there is no drift part their mobility should not come into picture it is a diffusion term which should come but you are not wrong why I will say but in face you should not see it is the diffusion limited term which is gradient proportional how the gradient it creates j is proportional to dn by dx or dn delta if you are thinking that so essentially dn term by Einstein relation is related to kt by q into mu okay since D is proportional to mu you are not wrong but essentially that is not correct because physics says it is proportional to the current is diffusion limited and not represented so you should always say that it is a diffusion limited current the gradients are such that it always will dominate you are very large emitter source here and you are very few electrons the other side in the base p type npn is that correct since they create a huge gradient the current is that correct so you are right to some extent that dn is larger compared to dp and there also is the gradients normally because of the available doping of nnp in actual technology n channel or npn currents will be larger for the same area same bi-sync compared to pn your statement of it was not wrong why I said because fortunately d is proportional by Einstein relation to mu but otherwise the phenomena why it is not correct okay so to say okay so normally npn transistor will be preferred as far as we are concerned for because same area same everything I will get larger current from the same everything so fair enough it is not a profit that what we are looking for however I live it to you to think later maybe at the some way I may ask you query pnp transistors are never out many circuits still need a pnp why there must be something in pnp which makes it a first choice come over and 99 cases amplifying cases everywhere you use npn but certainly some circuits some blocks are they all put a pnp why do they say think of it if you cannot find in a book if you cannot get to your friends and find you come to me someday I will tell you why but otherwise npn should be normally used okay so we will not discuss too much about pnp not that is bad device the worst device because of advantages even fabrication I will tell npn are much easier to fabricate compared to pnps compared I do not mean very large difference in terms so these are characteristics of a npn and if you extrapolate all of them they end up in a single point and that voltage we call it early voltage and this is essentially telling that the base emitter junction or sorry base width is getting punched depletion layer from base collector junction touches the base emitter junction and short circuit can occur that is the ugly that is why current is infinite in fact okay but since the device will become infinite we will actually shut it off there is a limiter as we say therefore no current will be allowed okay this is what I think I did let us do now what is our actual work for the day we are interested in small signals I kept telling you why because the slope of v0 vn characteristic what did I say it falls sharply what is dv0 by dvn in your looking dv0 by dvn what is it no no no no think of it now that is a bullney v0 vn this is a device I am putting vn I am getting v0 v0 by vn essentially again if I see a normal transfer characteristics of a nMOS or cMOS or bipolar termisters inverters or amplifiers only in this region of vn you have large dv0 by dvn that is gain is only available in a small range of inputs this side gain may be 0 this side also gain may be 0 is that correct so we cannot use an amplifier in regions where there is no gain then why I call it amplifier and therefore most we must operate within this range of DC values and therefore signal should not exceed either side of let us say if I buy us here the signal which I put here should not cross these two points any day because otherwise you will get into gain 0 kind of stage or much lower gain and those points therefore the amplifier will not act like a good amplifier is that clear so small signal is not that I want I do not I cannot do better and therefore that is the limit which I will always try to follow however also in done this is fine we will like to see what parameters we shall be using in our circuit the first and the foremost parameter someone said wrongfully but now it is correct is the trans conductance words say current divided by voltage is the conductance what is in the output of a transistor collector current what is the input of a transistor base emitter voltage there where the signal is going to be applied so what do we say change in collector current for the change in base emitter voltage is called trans conductance okay is that clear of course VB is related to IB also how I see to the power QVB by NKT this is a diode so VB is related to IB directly in a diode and therefore we need not talk current we should talk about base emitter voltages as our inputs where signals will be actually applied with this is that okay so because of that we say change in collector current to the change in base emitter voltage is GM if I take delta IC of this I can write delta IC as DIC by DVB into del this is partial equations simple right change in IC to the change in VB will be DI by DV this is how you write partial terms okay or delta IC this is GM times delta VB so we say delta IC is what change in IC is what the AC current total current is DC plus AC if I subscribe DC part for what is change is the AC part to we say delta capital delta IC is nothing but AC components so we say small IC small IC is GM times small VB this is a very important relationship for us what is it trying to tell okay we may draw a little figure here I do not know in a my left hander and it becomes difficult for me to keep doing like this so if this is your base junction this is your emitter value this is your collector that I am surrounding this so voltage here AC voltage here is really okay so if I see the collector current here it is GM times is that okay so the collector current which I will see at the output side is essentially GM times the input signal at the base emitter side is that correct this is what amplifier is going to do now if this IC current flows through a resistor IC times that are RL will be the output voltage is that correct so if I apply a resistance here which is say load then the V0 is essentially minus IC RL okay why minus because our current is GM VB is opposite sign so it is minus ICRT but IC is proportional to IB through what term IC and IB are related by what term beta so I can write V0 is minus beta 0 IB times RL okay beta now I can say what is PBE then what is input value you say I also know sorry RL okay V0 ICRL and VB let us say put a small resistance here so IB times RI is equal to VBE let us say there is a resistance here RI so RI times IB is your VBE so if I substitute here I can get V0 by VBE is equal to minus beta 0 RL by is that okay just substitute IB from here and collect the terms is that correct and what is V0 by VBE gain AC gain AC is that correct AC so transistor has amplified your input voltage output voltage V0 and it can be evaluated if I know the beta of a transistor I know the load I have written if I know my input resistance is that clear is that clear so if I choose RL greater than RI and if my beta is large enough then I am certainly going to get sufficient gain from this amplifier is that correct so a small signal of the value of micro volt to millivolts can get into at least few words please should not be greater than power supply but at least few words and that is what amplification I can achieve of course it is a proportional to RL by RI the whole circuit theory which will now apply is to get to use to this how do I adjust this RL by RI to get different kinds of amplifier this is all that I will do so basic circuit will remain is this I have a base in emitter input signal and I will get the output current this is my basic because that is what I believe so tells me this is what I am going to use in my circuit analysis why do I want to do all this circuit equivalence of that because in real life if I am really solving equations and I write I is equal to I is e to the power 2 V by n KT and if I write this kind of non-linear equations or transcendent equations are difficult to solve analytically may be yes and every time even immediately long time so we say okay why do you want to do this anyway we are looking for small signals so we will put an equivalent of something there which represents the actual currents anyway is that clear so all that we are doing is putting an equivalent of what physics is telling in our so that circuit can be easily solved and which equations will use in circuits to Kershaw laws maybe two more feminins and Norton's equivalence and nothing more than that is needed to solve any of the circuit in this case of course I will give you some hints one is called the end without solving you can give the results there are methods called observation oh this must have this not only accurate but that may be sufficient to tell me okay it has a gain or it has something so much so how to choose that and how to get that values can be found but generally circuit is very simple what are how many moves you have one loop here and one loop here there is very simple to solve or two nodes whatever way though if you want a nodal equation solver or you want the current mesh equation solver you can solve either is that clear so four equations are all that we need to do analog circuit analysis to Kershaw laws and to one of the evidence equivalent theorem and Norton's equivalent nothing more and nothing less but there is one more theorem have you done any course in network so far good which is Telligan's theorem so some other day when it will come will come to you why why Telligan was so great okay okay just now I said IC the collector current is equal to IS some proportionate e to the power VB by VT this is from the theory of it understood so if I if I want to have a definition of GM I know DIC just now I wrote an equation of GM delta IC by delta VBE so I do this I differentiate this equation okay that is what I said so I differentiate and if I differentiate I differentiate this and I get IS by VT exponential VBE by VT this is again IC current so it is IC by VT by the way this VT will now onwards that is why I wrote ahead VT is thermal voltage and since few minutes after we are going for MOSFET there VT the thermal voltage is very important for a threshold world we will not confuse with this so we say okay onwards maybe use KT by Q okay so it is IC upon KT by Q so Q IC by KT so do you find something interesting on the left side GM is what parameter AC or DC AC delta we are said AC program on the right Q IC by KT IC is a DC current is that correct IC is the DC current so are you now thinking that the DC current where the transistor is going to be biased is going to decide the AC parameter trans conduct turns is that point clear this is the most important fact we must know the DC by that so I say biasing word I said the capital IC is going to decide the AC trans conductance of the time okay and that most important so if I say I am biasing the circuit for a 1 million DC current am I not directly give you GM if I say temperature at which we are if we do not specify any temperature 300 degree Kelvin is what we assume otherwise in some books may they use 25 degree centigrade some use 27 degree centigrade so assume that normally calculations can be performed to 300 degrees Kelvin typically 27 degree centigrade what is some using 25 degree centigrade then KT by Q will be 26 millivolts if you are using 300 27 degree slightly 26 point something okay so every we may use KT by Q is 26 millivolts which as a number is not okay even if you decide to use 25 fine but use same number everywhere okay KT by Q is 25 millivolts or 20 do not write 25.826.43 no use why I say you in circles these numbers do not matter very much okay at the end of the day okay so I already said it is roughly 26 millivolts is what KT by Q are you going to use and let us say IC is 1 milliamp which you are biasing then the GM is around 38 milliamps per volt please remember GM must not be given a must not be without units almost always be specified as amps by volts okay can you tell me gain should be specified the voltage gain should be specified by how V0 by Vn how should I specify this number AV volt by volt is that clear please write volt by volt is that clear why we say so because I am going to give you for gains later okay some may be volt by I V by I some I by V I by I so I want to be very clear to people that I must specify the units of gain V by V or whatever way I am doing I must specify the unit why we may say V by V is no because then same unit actually but we must write in analog circuit even if it is both sides same units is that clear this is some symbolization for correct thinking so this is the typical GM which I am going to get 38 milliamp per volt this is the trans conductance how will it increase or decrease only one expression written here now either the biasing current increases or the temperature increases I was sorry the temperature decrease okay so please take it that these are therefore very difficult to I see of course I will control but I see is limited by what just took out what is the way we started I see is equal to beta IV so if I keep increasing I be I see will start increasing because beta time but I said do not increase too much what I what is the reason I said it may saturation and then there is no amplification both get forward biased okay therefore I see will be some maximum is that correct so you cannot go beyond that you cannot reduce temperature to liquid nitrogen or liquid helium how can you operate you probably not see the device anytime okay you and your wires may not function at liquid I mean liquid helium because the conductivity of wire may not be remain at 0 maybe infinite also now it may become otherwise in some materials so one cannot operate circuits in a course in specific areas in satellite we do cooling as well as heating whenever we need but normally circuits will be open okay and therefore we should not we cannot play too much on the temper in the contrary we may have worries because temperature will keep rising and because temperature is rising your GM will start falling that means gain will start falling and that is my major worry okay so I must control my temperature as much as possible that here that is the worry which will be okay coming back to okay so this expression you are written QIC by KT there are certain limitation which I already said but I may repeat little more detail me I already said saturation measure manner chalo saturation where are we you know like this transfer characteristics we may not be here we may be here here also gain is less because slope is much smaller here the slope is larger now we are in a smaller this and we are moving other side now okay now here is the case if I add if I add a input AC signal along with the DC what is it it is super import or modulated I add an AC signal over a given DC value that in my hand I fix VB wherever I am then add a signal over it in the input side okay this is an NPN term so I believe if I change VBE the actual VB will be VBE plus V in because you have added input signal to the DC value of VBE then the collector current total will be IS exponential DC plus AC by KT right now my assumption is that N factor is one therefore in real life the diode ideality factor also come right now assume in one case and someone should say NKT of the NB of that we have my circuit may have children okay so if I say this is the total current and if I take the DC it is IC is equal to IS exponential VBE by VT no way in added so this is DC this is total so what is AC part in that so this total part is therefore IC times V in by VT just substitute here so you get total IC is equal to DC IC times exponential V in by VT is that okay this term substitute in this okay so you get IC which is this term IS exponential Q VBE by KT is IC the remainder term is exponential V in by VT exponential you can always e to the power a into e to the power b is a plus b is that correct the formula which I use the exponential okay so I get IC exponential V in by VT and here is that condition which I say other condition why a small signals are required this is exponential term V in by VT let us say V in is smaller than VT okay input signal is smaller than 26 millivolts is that correct V in by VT I expand this exponential function what is the exponential function is expanded 1 plus X on upon factorial 2 X square plus 1 over factorial 3 XQ and so on and so forth so if I expand this term I get 1 plus V in by VT half V in by VT square plus that remains 6 1 by 6 V in by VTQ plus 2 on and so forth higher terms is that clear to you is that clear to what do I say I just expanded this exponential function in the series form okay if you now say and we also know the small AC current is total AC I IC minus PC IC so you see from here if I subtract this IC minus IC 1 plus 1 will cancel one will go away because IC will subtract so if I do that I get IC is equal to IC by VT times V in plus half IC by VT square V in square plus 1 by 6 IC by VT Q V in Q and so on and so is that clear AC current how many terms I am getting first is the major term which is first order term which is second order term this is third order term and there will be any order terms if we now you can see if you are V in is closer to VT what when what does that mean or larger than VT the second order third order terms will start increasing or even dominating is that correct is that point clear so now you are trying to say that if that happens the gain should really increase because you are getting more and more terms out of it but really what will happen gain will finally go to 0 okay so what is the condition that this only term it comes to our requirement which is called a fundamental term V in should be very very small compared to VT then these two terms and all higher order terms can be if V in by VT is smaller much smaller than one then we can say the second order third order nth order terms are negligible is that clear if that happens IC is equal to IC by VT times V in then the GM is IC by V in therefore this Q IC by KT and if you want therefore this GM equivalent circuit to stand which we did earlier condition is what what is the condition on input signal it should be smaller or much smaller than 26 millivolts is that clear two ways I explained one is from the transfer category I say no you will get harmonics out even with without that I say normal thinking I can prove that I cannot exceed too many because remember V in will be sin omega t okay sin square omega t means omega 1 plus omega 2 omega 1 minus third order terms will start up here is that correct so you must understand in this there is only one omega t term going on which is called fundamental I have a signal at one frequency and I want output also at the same frequency if the power or energy is given to other harmonics I will not get enough power for my fundamental so my amplification will become lower and lower and is that clear to you so the second and third yes because the biasing is such done that we always remain in that okay that is exactly what I that is why I say biasing word is very good that is what why we are going because I want to go to circuit quicker but I want to make you clear that why I actually restrict myself every time so this is only few lectures I am taking for you modeling so that you know why I cannot do more or less than this is what is only possible for me is that clear so those limitations is only I am trying to come here if I go out of the ranges what we say will happen and physically what can happen is I may actually get into power and inner energy into other frequency terms which I do not want is that correct there is a total power is so much if I give 80% to other harmonics I am get 20% so I must restrict that that is the idea okay very good so is that small signal is clear why small signal why analog people do not want to talk too much about large is that okay that okay so this is only to prove my points that why I sometimes do something which I say okay yes no but because the output which you will put will have some RC time constants so it will only address to those one frequency one RC the time but that is frequency so at a given this it will only respond to a frequency okay what you are saying is not very absurd or wrong if I can tune those other harmonics that is what we say your power can be pumped back but then you require additional hardware to do that which is what in micro is we do that the higher harmony terms we actually convert back to fundamental but there is a huge circuitry to do that okay so we lose power in converting back okay that is the idea but that is doable you are right okay let us look into the other things of the BJT so far we looked into only one parameter which one GM which is our major parameter so we say okay pilot for that now with the other term cabola feminine of NL of KLA bandwidth is that bandwidth is something to relate with some output gain or gain of this amplifier remains constant till certain frequency okay you are looking for now frequency response whenever I gave just now I said to him frequency word comes time constants are associated is that correct 1 upon RC 2 by RC time frequency so whenever I say frequency I am looking for RT terms okay so now I must look on to more term GM of course is the trans-conductor now I must look for R as well as C is because I am now looking for bandwidth gain I know GM will probably help me out okay but I must also want bandwidths I want to know how well I control that how do I go in a small signal VN is applied as the circuit I showed you are there then we say delta VB is small again repeating is VN delta similarly the charge which electrons will inject emitter charge QE change in emitter charge is small QE similarly change in base charge is small QB but charge neutrality in transistor in a steady state what does it say the change in base charge should be same in emitter charge because there are what is injected cannot remain can increase their neutrality must hold so at them we will say small QB is equal to small because neutrality has to hold okay but right now I am giving separate name finalized okay QB screen okay but to make a point I have separated because in real physics if you are done it they will say the base cannot increase the concentration electrons in it because they must become mine because otherwise charge neutrality will be violated is that correct so that term is valid here also but just to make a point I am not changing so we define a capacitance which is related to base emitter junction and that is given by the change in base charge divided by input voltage Q is equal to CV no great thing till 7th standard physics Q is equal to CV in J I do not know because of this tick marking system otherwise we used to have many problems in this charge and capacitance Gauss's law you know point to point at least an older GE in our time there are huge problems in electro studies I do not know how much part now in your new energy what is the purpose in your GE to get 8000 people earlier we used to reject beyond 400 only so 6 7600 must go so for our rejection system good now we say the change in emitter or the emitter charge is nothing but the current times time or Q by T is current is that correct charge by time is current so emitter current which is received at the collector side through a transit time which is called base transit and remember electrons are injected at base emitter junction transit through the base are collected so there is a finite time which we say based on the time transit time please say it is not minority carrier now what is it called transit time time taken from here to here based on the time so whatever received is collector current so collector current based on the time must be the charge injected from the computer side so similarly we can also say delta QE is tau B time delta I why this delta I am adding I want to make AC part in that as soon as I add delta I get an AC value so delta QE is equal to tau B time delta I see please remember I said right now here delta QE will be equal to delta QB why I said so charge neutrality will always be held so we are interested to know this CB what are we trying to do we want to now show your equivalent circuit so any component which will change my bandwidth of the gain I must find so this is first thing after GM I want to see the capacitance so delta QE is tau B times delta is that okay is that okay you just say otherwise I will wait till you write delta QE is tau B times delta I see now this tau B and devices is what anyone remember device theory last semester related to what have you just think of it this is my base this is my base this is my base this is my base base width larger the base width larger the time smaller the base width smaller is that time is that correct is that correct so obviously tau B must be related to base width okay is that okay since I say delta QE is same as delta QB so delta QE is equal to delta QB is delta IC tau B or QB is IC times tau B and therefore the TVE which is called by the way this TVE is called diffusion capacitance what is it called diffusion kappa why it was called diffusion capacitance is related to diffusion phenomena of carriers in the base is that correct so it is called diffusion capacitance it is not a junction capacitance which we have to calculate so far it is only a carriers moving charge is changing any change in the charge means capacitive effect is there that is why charge changes is that Q is equal to CV so if charge changes there is a capacitance and since charge is a proportional to the voltages I apply therefore capacitance is varying come okay so CBE is also sometime called CPI dash is QIC by KT tau B and what is tau B now WB square by 2DN WB is the base width so smaller the base width smaller is tau B smaller is tau B smaller is CB CB is between base and so what will happen if CB is smaller what will happen for a lower frequency what is the impedance it will offer if CB is smaller for lower frequency omega is smaller CB is smaller impedance is very high if this impedance as seen from the input side is high what does that mean equivalently saying is it important or not important if input impedance across two terminals is very high is it is it important or not important not important like an open circuit it does not play games is that correct whatever voltage you are current applying it will pass because it is like a high Z sitting there however if omega is higher and CB is lower higher then what will happen then this shunting effect will start short circuiting will start if omega is larger and CB is also larger that is the base width is long enough okay then ZN will be very small and then whatever I will pass through this will be divided is that and in worst case if this is very very small everything will go through is that correct no divider there current will just go through shots therefore is that now clear why I am interested in CB because for my given operating signals and at frequencies I want to see whether this capacitance will have any influence or not have okay so I must know the value because if I get the value then I will say okay omega C will decide whether it is required or not required is that correct but I must know first what is T is that that is the point clear why I am doing this because I do not know if I otherwise if I increase my input signal frequency to 100 megahertz nothing will go to the output everything is here shorted out is that correct so input is not allowing signal to get in is that correct so I want to know where is that limitation am I reaching that okay that is why I want to know the value of CB other or what is called the diffusion capacity but that is not the only capacitance there will be another one is that point clear why I am doing this okay coming back few more things we should like we come to other capacitance but let us see the other two major worries about it I just now say for a bandwidth what are the important terms I said R and C one of the C I saw see other sees also but let us see are quickly first I am also interested at the looking at between they submitted what is the resistance of the same logic will go if the resistance is very small what will happen by same logic if this resistance is very very small any signal going from here will be short nothing will go out into the circuit is that correct so what do I expect this R to be as high as possible but I may not be able to control for variety of reasons very high value then at least I must know how much is this so how much is really made available to me at least that number I want to know okay I do not mind it is there but how much is there at least I should know because then only I know what is I am going to get here is that clear so I must evaluate the normal input this is not external what we can value we are calculating simply because the transistor sitting there for the additionally externally what we will do we will make more mission for us but at least internally what is happening we like so we say IC is equal to beta times IB our standard active region equation IB is 1 upon beta times IB again use delta IB so we write D by the IC IC of beta we define a AC beta as delta IC by delta IB or small IC by small this is called AC beta is that clear to you so far earlier what beta we define here this beta and this beta are not same that is called DC beta what is DC beta capital IC by capital IB is DC you apply DC signal DC voltage you see what is out so the collector current divided by base current is DC value this is DC beta if I now substitute in this equation I get IC by IB which is beta 0 delta IC but this however in this differential if beta DC beta is constant please look at the case what I am saying if DC beta is constant this beta can come out is that a differential it will not be useful then this will be one so what is it trying to say AC beta is equal to DC beta if beta is DC beta is so in your design or in your circuit you must ensure if you are using same values of beta that beta is constant why beta can change can you tell me you are done devices now beta can change because of the two things base width is correct but I am looking from external you are right base width is major because that is the beta fact directly it will decide alpha T temperature you are very good it also will be limited by the currents which you are passing levels of current beta falls as current increases as IC starts rising the beta will start falling initially as collector current rises beta will rise for a physical separate it will become constant for a great time and if you further increase IC it will start falling okay because of the emitter efficiency and transfer factor effects temperature effects beta is not constant so where we should therefore operate in those IC regions where beta roughly remains constant you can use DC beta as same as AC beta and therefore operation of that is the DC biasing again is very very important because I do not want to always separate DC and AC beta is that clear so I am giving you why we operate only this much because otherwise we are not sure what values we are actually going to get okay okay is that point here DC beta will be equal to AC beta as long as DC beta remains constant and that is the way we will actually make circuit to work so that AC beta value so manufacturers gives you beta of 200 I do not have to recalculate what beta I should use in my analysis because I will see I will operate by my conditions that beta remains constant okay the next thing which we like to know is the input resistance I mean from this we want to know actually input resistance what is input resistance will be input signal or AC input divided by base current there just now I showed you so it is being by IB but IB now can be written as IC by beta and now beta can be beta 0 or beta DC whatever you wish because we are made sure that beta is same for both is that clear so if I substitute IB by IC by beta like this but what is V in by IC by V in just have defined earlier first term first parameter GM IC by V in a GM so it is beta 0 by GM is that and GM is related to what I said which by thing in DC I am connected to collector current DC collector current I know the bias current I know GM I know GM and if I am ensuring you beta DC same as beta 0 the transistor will tell you what is beta so I know my beta I know where I am operating therefore I know my GM so I also know my input resistance our pie is that clear to you our pie is equal to beta by GM or to say this is very sangrous and relation beta is GM or pie beta is GM or pie this is a very good relation for all AC analysis for transistor is that correct conditions why we said DC AC constant otherwise you may have to work if I now substitute GM and RPI values as we did one can show from the way I had written here RPI is nothing but KT by Q IB so whatever your base current which is proportional to IC why IC by beta is IB so if you know your base current you also know your input resistance is that correct or if you know your bias current IC and you know beta which is saying IB is known you know your input resistance our pie is that clear so our pie is not a constant quantity it is very ill with what it is varying the biasing current so is that point got into all of you that bias curve no no no anything add you do it it will cannot be added across the junction inter many how do I get inside a junction transits under top hot mean also bar terminal may across that the bar they look at or come the other coming on anything you put a parallel to this will be really lesser than this is that clear so externally under the piece go hot mean a bar package Mila so I must know what is in that is the idea is that clear if I have a what you are saying in a way is that during your farm yes I can do something but once I have added that is the end that is the fixed value whatever doping I use whatever process I go through that will fix for you I cannot do anything on that beta I could be among this with this career with a middle junction the doping this career time on the time because they are minority career lifetime because they are something so yeah many other which externally it is going to spoil something but that is what the limit is coming this is internally itself creating a problem so first women like to say what is internal to us and then equivalent circuit when we make the transistor will be replaced by all this together and then externally we will put whatever we are actually getting in a circuit and then solve all of it is that point clear why I am doing it I want to represent this transistor as if it is in a circuit form okay otherwise I suck I say which may come out of that I cannot write IC is so much cosec as W by LB plus what I something that equations I cannot write for transistors okay in circuit so I want to put everything in circuit so this is also one value which I want to know equivalent very good the second parameter to us is R0 okay what is it output resistance I mean put the kind of let us get the output side what is the resistance I am saying that circuit which we did GM BBE a collector hey a here be R0 yes shunting why it will be shunting what is this what is this but can you convert into series kind which theorem Norton theorem says having in major GM times R0 work R0 is equivalent R be in equal section but right now we are only in the Norton's equivalent side okay so I want to know what is this so-called output resistance R0 so I said okay just now I did delta IC is delta VC into delta VCE okay delta IC can be written in a interesting format delta IC into delta VC no maths you do not know same term but we can always write like this but this term delta is VCE by delta IC essentially is early voltage up a bullet high schedule slope high early voltage so VA by IC schedule slope high go early voltage divided by IC is that point clear is that point clear so if I specify to you the early voltage 20 volt 50 volt then what I am saying I am biasing at this bias current of IC what I am giving you R0 value is that clear is that clear if I am specifying early voltage this is 50 volt transistor has a early voltage of 50 volt okay and if I say I am biasing at 1 million 50 by 1 million 50 kilo ohm so I had as soon as I know my bias current I am actually telling what is R0 okay so please remember every time which turn I am connecting everything to the biasing current is that point clear everything I am connecting to biasing current so what is important in analog circuit design or analysis where we are at IC which value of IP you are operating that decides everything is that okay is that okay IC is the main DC IC is the major parameter for us to get so that we know what is the final circuit equivalent is that clear okay so any time I early voltage is given to you which we will specify to you 20 volt 30 volt 40 volt 100 volt can be even 100 volts is it good or bad if it is 100 volt you go ahead number but I clean what is the reason I said you are right larger the early voltage good why R0 will be larger in a current source what should be the parallel resistance preferably or ideally infinite ideal current source to larger the R0 you are going to get closer the good current source you are going to get is that correct and that is why we will be very keen to get larger R0 if possible other possibility I may reduce IC but if I reduce IC what I am going to reduce GM where again I have that I am worried I cannot too low too high is that limitations clear to you I mean I am I have to worry everywhere if I want this I may do this if I want this I may do so somewhere what do I get that is why all these theories are again brought to your front is that R0 clear to you via by IC normally these values will be specified is that okay yes I see the collector currency your bias on this any point here actually it is via plus VC small let us say your point is taken okay you are biasing here sorry it is not a straight line property so actually this value plus this value divided by this IC is the slope is that correct but what I say how much is VC will be less than power supply value two volts how much will be a 10s and 50s or 100s of so in calculation via plus VC divided by that instead you can always use via by IC is that point clear what he said probably I should have said is that clear in reality slope is this this by this now okay this is little smaller compared to bigger value match match nothing more okay there is another term which transistor people keep talking is called okay it is not in KT kind it is a eta in very important factor it is decided as is defined as KT by Q 1 upon via where early voltage theory we can do someday I wish and if I substitute KT by Q please do what is the why I write all this fun you can directly write KT by Q AC the lack of AC over but this is one upon GM this is one upon R0 so GM R0 is a figure of merit eta GM R0 is one upon eta is a figure of merit for a transistor is that clear to you everyone GM is for a given the IC will decide GM and IC will also decide R0 is that correct therefore GM times R0 is a figure of merit is that correct it is one upon eta very important parameter in design not in analysis so much just to show you how so I actually search transistors which has smaller eta okay that means larger GM R0 terms is that correct so when I go into the so-called manuals of transistors and I am looking for higher game bandwidths then I should look for answers which has higher GM R0 essentially smaller eta values this is specified these are all figure of merits okay is that point here is that here this is something some day you design chip or circuit and you open a manual for me company you should know what you should look okay that is why I show you okay typically it will be order of 10 to power minus 4 minus 5 large larger smaller the value better is GM R0 so if you use given beta value typically R0 value which we have got here for early voltage of 100 and 1 milli amp current how much is R0 100 kilo ohms okay if it is 100 volt early voltage and 1 milli amp current 100 kilo ohm is all that you are getting across okay what is your preference will be at least mega ohm or plus okay so either you look for larger VA that means essentially look for good beta value smaller eta value 0.004 0.004 or 0.006 that is the idea behind the search the another resistance is worrying me you know after all you have a base collector junction is that correct in a transistor you have a base collector junction so if you see a between your base and collector there is a junction is that okay is that point clear to you what I am talking about this is my base which is my emitter and this is my collector collector collector between these two terminals base and collector there is a junction there is a diode sitting there which is the normal operation diode will be in what operation mode reverse bias a reverse bias diode what is the IV characteristic in reverse bias typically if you see I versus V very small very small so practically saturation current is the order of pico amps are lower so this slope is very very low okay very well if that is so if I take the delta VC by delta ID which is VC by IC by BC so I get R mu by same simple method R mu is beta times R0 R mu is beta times and R0 related to what early voltage by collector current okay so I know this really thing or beta is how much not less than 100 normally R0 is how much we calculated just now hundreds of kilo ohms okay in 200 how much it is tens of mega ohms are above so in between if this resistance R mu is greater than tens of mega ohms will it have any influence or will not have influence between two nodes if I short circuit that is R is 0 everything at the input will pass to the output if the resistance is very high you can say as if collector is separated from the base but it is not 0 it is not infinite resistance so there is a connection between output and input whether you like is that clear so R mu may be hundreds of mega ohms or tens of mega ohms but it exists finite value okay is that point here so we must know how finite is that finite value so that is why we calculate beta 0 times R0 as your R mu where is it exist between collector terminal and base terminal base collector junction reverse bias will give you a high resistance which is called R mu yes just now I say it is a diode reverse bias diode capacitance counter reverse bias diode main even at 0 bias junction is called forward bias reverse bias even at 0 bias junction is always there is a built-in voltage there sitting there is that correct there is a built-in voltage sitting there so the diode is even at 0 bias is equivalent of because there is a depletion a intrinsically present that value epsilon a by depletion layer width is the capacitance epsilon a by D is capacitance now the problem is if I apply larger VCB this depletion layer will increase or decrease increase that is what the by reverse biases the capacitance will decrease is that correct so we say this capacitance is function of reverse bias whatever VCB I apply okay so I say this junction capacitance is CJ0 what is CJ0 at 0 bias capacitance that is a depletion width at 0 bias at the built-in voltage and this V is the applied reverse bias and 5 0 is called built-in voltage for the junction which is KT by Q LN any and by another square so we may say for the transfer C mu is C mu 0 1- VCB by 5 0 is half is not very correct why it is not every time correct device theory say if it is a step junction this half it is linearly graded one-third and 4.3 or something exponential it will be further different and values but assume right now the way either of so I write n normally will be either linearly graded exponential is always assume linear or actually it is not error it is not a exponential the function which you get there is called complementary error function okay we are not looking to math right now and for that one-third is 0.3 value is or one-third value for n is good enough so can if I am given C mu 0 I know 5 0 I know the VCB I am applying then I can get is that here everyone this is like a diode capacitance nothing great so where is that diode capacitance will sit where this diode capacitance will sit it will be across R mu is that clear it will be across R mu so you have in between base and collector there is an RC parallel RC sitting there R mu and C mu does that give you some value R mu into C mu is what frequency term or some time constant so input the output may kind of time relationship have it forward or feedback either say there are such that I know so we want to know what is happening now earlier what we thought input and output are separate now these two have suddenly brought worries to us or you are it a connection so we must know how much is that this is very large impedance so well fantastic C mu is very small army is very large fantastic that is ideal but if it is not then how bad it is I must know similarly you can also see there is a base emitter junction is also there what emitter capacitance we calculated first CB which was it diffusion capacitance charge variation but apart from that there is a base emitter junction which is forward bias please remember base emitter junction is forward bias so if I write this standard relationship like CJ is equal to CJ is 0 1 this am I right because here VB is not negative now VB is positive so this kind of because depletion layer actually may be very very small or even negligible because we are forward biasing the base emitter so normally one does not evaluate like a reverse bias diode any capacitor I just want to show you why I did this is normal reverse bias capacitance calculations we see this will be negative this term will be positive so C will keep falling is that correct now we say we do not know exactly what is happening because depletion will collapse smaller and we do not know exactly how it is not linear proportions now not even one third not in half loop loss so we have now figured out over the experiments hundreds of them you can assume this CJE typically twice that of CJ is 0 which is 0 bias whatever capacitance you have of that junction twice you use it and that is good enough this is our what is it called when you do without any great physics on that empirical by lot of measurement lot of intuition we figure out generally twice the CJ0 is sufficient for accuracy is that correct so what will specify you CJ0 but when you write CJE you should multiply it by 2 that is the another value so what is the input capacitance now you have your two capacitances that they emit base emitter junction what is the first one the diffusion capacity what is the second one junction capacitor so the that total input capacitance is named as CBE plus CJE is that correct the total input capacitance is between base and emitter is C pi across this is our pie so have we taken many effects of actual transistor on the input side we got C pi we got R pi we got R mu we got C mu we also got GM other side we also got R0 so almost everyone is considered but few more few things about this if you see a bipolar transistor in real life it has four layers and not three layers okay we make transistor in one substrate this is one transistor there will be another transistor n transistor in the same substrate so the collector is here base is here emitter is here so there is a fourth layer which is called substrate so it is npn and there will be p epi layer or substrate layer so there is another junction sitting do you see that junction which is the junction collector substrate junction is also there is that correct normally I will short circuit substrate but still there will be reverse bias is that correct now that means additional capacitances even resistance but that normal is very high so at least CS must be calculated CJ collector to substrate capacitance which will follow like a diode say diode so we write CJS CJ CS CS CS 0 so whatever voltage between collector and substrate using that we must again calculate the capacitance in which is if this term is in 0 will it go to emitter then in common emitter circuit emitter is grounded is that correct but internal emitter is not grounded there is something else system so we say this capacitance must always be grounded and not taken to emitter is that here I just tell you what I am saying this capacitance from collector junction must be grounded independent of whatever you are because substrate is going to be grounded bias is that correct so CCS is capacitance between collector terminal and ground is called CCS oh guys have capacitance away of the final team resistance a guy or circuit see these are diffuse regions any semiconductor will have some resistance is that correct take a bar of a semiconductor or any material well by there is a resistance sitting there is that R is well by each region will also have some resistances of its that also added to it the contact resistance of metal with that layer so there is a resistance associated with emitter resistance associated with base and resistance associated with collector these essentially are called RBB dash RES and RC is that clear collector why it is because collector external pin to internal collector there will be a resistance external emitter to internal emitter there is a resistance and similarly for the base so if I use this final word for the day is this okay this is the final circuit you can see we start from the base the lower side is emitter this is external collector so this is the end of the all that we did is the equivalent circuit of a bipolar junction transistor so all the terms we are derived that layer every term which I wrote here I explained why they are coming and what will be their values okay that here only thing you should know what I just said there is a B dash C dash and E dash term this is called internal emitter base collector points these are the EC are external in between there is a resistances as I shown here RBS as our RES RBB dash and RC okay so that if you do that this is the equivalent otherwise actual equivalent will be have RC RBB dash as well as RES is that okay this equivalent circuit wherever transistor will appear in a actual circuit between these terminals I will just replace this okay and then solder case of law with external components connected here here here wherever is that correct some more loops some more notes call me okay is that okay.