 My name is Joseph John. The topic I am going to cover is bipolar ejection transistor. So, this is would be a very basic topic. There will be two lectures on transistors. The first one is an introductory lecture. The second one which will be held next week will go into the details of common emitter amplifier. Now, bipolar ejection transistor was invented in 1948. And as you may be aware, a Nobel Prize was awarded for that. And since then, this particular invention led to the era of solid state circuits and also integrated circuits. Till early 80s, BJT, as it is called, was the device of choice in the design of both discrete and integrated circuits. Today, MOSFET is the most widely commonly used. But still in some applications, BJT is still the device of choice. Now, coming to the basic structure of a BJT, BJT is a three terminal device which needs automatically that it needs at least two characteristics to characterize it. And it has three semiconductor regions, emitter base and collector regions. The transistor consists of has two junctions. The emitter base junction and the collector base junction will see more of it soon. Now, in the last lecture by Professor Shama, he talked about the charge carriers, both electrons and holes. Now, in a BJT, both electrons and holes are involved. And hence, the name bipolar junction transistor. In an NPN transistor, it has an N-type emitter, a P-type base and an N-type collector. Whereas, a PNB transistor has a P-type emitter, an N-type base and a P-type collector. Now, what you have here is the basic structure. So, the first one is a PNB transistor. You can see a P-type emitter, an N-type base and a P-type collector. And this is the symbol of a PNB transistor. This arrow here indicates the actual direction of current. So, this is the emitter current flows into the device and the both the base and the collector current leaves the device. An NPN transistor has an N-type emitter, a P-type base and an N-type collector. The symbol for NPN transistor is shown here. Here again, the arrow indicates the actual direction of current. In a NPN transistor, the emitter current flows out of the device, whereas both base current and collector current flows into the device. Now, if you look a bit more detail into the collector, emitter and the base regions, the collector has the largest area in a BJT. This is to take care of the power dissipation requirement due to large current and large the collector base junction voltage. And emitter has slightly less than the collector and this is because the emitter base junction has lower junction voltage. Base is made very thin to minimize recombination. Now, in terms of doping, we heard Professor Shamas in the last lecture about doping. Now, the emitter junction, emitter region is heavily doped, while the base region is lightly doped. Collector has a doping somewhere in between the emitter and the base. Now, coming to the modes of operation of a BJT, there are four modes of operation. We can see them the way as shown here. There are two junctions. So, there are four possibilities. Now, if you look at one of the possibilities, if you reverse bias both the junctions, that is the emitter base junction and the collector base junction, you can think of the device being cut off. Now, active mode is the most commonly used mode and that is the most desirable for amplifiers and other applications. Now, in this particular case, for an active mode of operation, you need to keep the emitter base junction forward biased, while the collector base junction should be reverse biased. Now, in switching applications and so on, you occasionally have the saturation mode also. In this particular case, both the emitter base and the collector base junctions get forward biased. There is another mode of operation, which is very seldom used. Yet, there are applications especially in logic circuits such as TTL gates and TTL logic uses this particular mode of operation. This is what is called the reverse active. The previous active mode is actually called forward active mode. This is called reverse active. Now, if you look here, essentially, in this particular case, the emitter base junction is reverse biased, while the collector base junction is forward biased. This is just the, you can think of the reverse active mode as an interchange of emitter and collector junctions in terms of the forward active mode. What I will do is, we will spend almost 45 to 1 hour on the basics of a BJT and then we will take some numerical examples to illustrate the problem, the basic operation. Now, coming to the operation of an NPN transistor in the active mode, now you would see that most of the circuits, which you would come across, make you some NPN transistor. Very seldom would come across a PNP transistor. However, there are applications where PNP also. Now, what we have here is, what we have shown here is a basic kind of a block schematic of an NPN transistor. Now, here this, the left side is the emitter region. The middle you have the base region and then you have the collector region on the right side. The emitter base junction is forward biased, which means you would see that the base, this being an NPN transistor. So, the base would have more positive voltage compared to the emitter. The collector base junction is reverse biased, which means the collector would be applied a more positive voltage as compared to the base. As you would see from the biasing shown here in terms of two batteries, you would see that the voltage, which you apply to the base emitter junction is much smaller compared to the voltage you apply to the reverse bias, which you apply to the collector base junction. Now, coming into the currents in a BJT, the emitter current as we saw from the previous diagram, the emitter is heavily doped and this is an N type region and when you forward bias the emitter base junction, what happens is you have carriers electrons injected from the emitter into the base. Simultaneously, you also have holes injected from the base into the emitter and both these constitute the emitter current, but as we know the doping of the emitter is much higher than the doping of the base. Hence, you could say that the emitter current is mostly consisting of the electron current due to the electrons. Now, once they are the electrons, the injector electrons reach the base region, they diffuse towards the collector base junction. Now, base is made extremely thin, because you would like to minimize loss of carriers there. Now, since the electrons are minority carriers in the base region, some of them recombine and so the base current is due to has two components. One component is due to the injected holes from base to emitter, the other component is due to the holes need to be supplied due to the recombination. Now, the diffusing electrons, once they reach the reverse bias junction, the collector base junction, they are swept away and the depletion region, they are swept away into the collector and that constitutes the current. Since the current, emitter current is basically due to electrons being injected from the emitter to the base, the actual direction of current would be the opposite of the electron flow. So, in actual case, when it is in transistor, you would have the emitter current flowing out of the emitter, base current flowing into the base and the collector current flowing into the collector terminal. So, we have seen briefly these three currents, the emitter current, the collector current and the base current and their constituents and how they actually flow. There is another important current, which is a very basic device parameter for a BJT, which is called the saturation current. Now, this saturation current in our equations, which we would see later, would be indicated as I subscript s. This current is also called a scale current. This is for the reason that the current, this particular current is proportional, directly proportional to the area of the emitter base junction. So, larger the area, larger would be the value of I s. In the same time, I s is inversely proportional to the base width. Typical range of I s is between 10 power minus 12 to about 10 to 10 power minus 18 amps. Now, having seen the currents, let us look at the kind of relationships between these three currents. Now, the forward bias voltage between the base and the emitter causes first the injection of carriers into the base and subsequently a collector current. Now, this current, which is flowing and the collector current can be expressed as I c equal to I s times e to the power V b by V t, where V b is the forward bias voltage and V t is the thermal voltage, which is typically about 26 millivolt at room temperature. Now, for an NPN transistor, as we saw earlier, the emitter current leaves the device, whereas the collector current and the base current both enters the device. Therefore, applying Kirchoff's current law, we can write I e, which is the emitter current, is equal to collector current plus base current. Now, this is one of the fundamental current equations and is always valid irrespective of which mode of operation the BJT is operating. Now, we can write another expression, which as I b, the base current is equal to I c by beta or I c is equal to beta times I b, where beta is called the common emitter current gain. We will see later why this name. Now, since I c is much greater than I b, beta is much greater than unity. Now, again using the previous equations, we can write another equation for I e in terms of I c, that is emitter current. We can write an expression for emitter current in terms of the collector current as beta plus 1 by beta times I c. Now, combining this, we can write I c as alpha times I e, where alpha is beta by beta plus 1. Now, alpha is called the common base current gain. Since I e is less than I c, alpha will always be less than 1. Now, we could have a relation between the relationship between beta and alpha, which is written as beta will be equal to alpha by 1 minus alpha. Since beta would be typically of the order of typically from about 50 to about 200 or so, most of the time you would see that alpha will be almost equal to unity. Now, alpha and beta as they are normally written are the current gains in the forward active mode. Occasionally, they are also denoted as alpha subscript f and beta subscript f to indicate that they belong to the forward active mode. So, as I said, the beta can be anywhere between 50 to 400 and if beta is 100, then alpha would be 0.99, 0.9901. Now, we could combine the previous equation, which we wrote two equations, equations 1 and 5 and we can write an expression for I e as I s by alpha times e to the power p b by v t. Now, the previous equation we had was I c equal to I s times e to the power v b by v t and we know that I e is equal to I c by alpha hence this relation. Now, we could just summarize what we did so far. Now, what we said is in a forward bias voltage V b applied between the emitter and base causes an exponentially rising collector current I c to flow in the collector terminal. The collector terminal I the collector current I c is independent of the value of the collector voltage as long as the collector base junction is reverse biased. Now, therefore, we can say that in the active mode, the collector terminal behaves as a controlled current source where V b controls the current. We also said the collector current is a fraction of the emitter current and we said again beta f is much greater than unity, whereas alpha f is approximately equal to unity. Now, to make calculations and current calculations and to understand it better, we could come up with a model for the forward active mode n p n transistor. What we have here shown here in figure 3 is a large signal model. Later when we talk about amplifiers, we will talk about small signal model. So, here we are talking about these models can be used for say kind of d c values or large signal. So, what you have here is the n p n transistor and the in figure 3 a here is shown. You can see the collector terminal here, the base terminal here, the emitter terminal here. The base to emitter junction is shown as a diode and you have the V b voltage applied as a forward bias and you have a current source here, which is a controlled current source having a current I s into the e to the power V b by V t. This is the current we wrote earlier. So, this particular kind of a model is a voltage controlled current source. We could write, we could modify this into a current controlled current source as the way is shown here. You could see that here the control parameter would be I e, which is the emitter current and the control current source would be alpha f times I e. What is important to notice here is that the control current source we have is a non-linear current source, because we have an exponential relationship. Now, we can think of b j t as a two port network coming back to the diagram. We could see that we could think of the b j t as a two port network having an input port. In this case, you could think of the b e as the between base to emitter as the input port and collector to emitter as the output port. So, this you can think of a b j t as a two port device. Now, since we have, now that we have studied forward active mode in some detail, we could look at the actual structure of a b j t. Now, what we have in figure 4 is the typical cross section of an NPN transistor we see here the outer portion here is the collector. You could see emitter being surrounded by base and which is surrounded by collector. As I as we saw earlier the collector region collector is the largest region and you see that the way it is constructed almost all the electrons which are injected into the base gets collected because of this kind of a structure. One very important thing to notice here is that the even though both emitter and collector are both end type semiconductor material, the actual area is very different. Let us look at now the reverse active mode. In a reverse active mode as we discussed earlier you can think of reverse active mode which is very seldom used as a case where a special case of the forward active mode where the base and the sorry the collector and the emitter terminals getting interchanged. Now, as we saw just now since b j t is not symmetrical the current gains which would get in a reverse active mode you would see would be very different from the current gains you have alpha f and beta f. Now, since b j t is optimized for forward active mode operation alpha r and beta r which are the current gains in the reverse active mode would be much lower compared to alpha f and beta f. However, alpha r and beta r are related by the same equations which we wrote earlier for alpha f and beta f. So, typically alpha r would be in the range of 0.01 to 0.5 and the corresponding range of beta r would be 0.01 to 1. If you compare this with the values of alpha f we said alpha f is approximately unity and beta f we said is typically 100 or so. We could see that alpha r and beta r are much much smaller than alpha f and beta f. Now, we could attempt a large signal model for the n p n transistor in the reverse active mode. Now, to do this we could there is a very simple relationship which connects the scale currents. Now, in the large signal model the diode which we used for the forward active mode we used a diode called d e. Now, in the reverse active mode we would use since the collector base junction is forward biased and the base symmetry junction is reverse biased we would use a diode d c to represent the forward biased diode. Now, the scale current for the that particular diode i s e would be i s by alpha r and we know that alpha r is much less than unity. Therefore, we would see that the i s e the scale current for this particular diode would be much higher than the diode which we use in the other model for the forward active mode. Now, these scale currents are related by a simple relationship alpha f times i s e is equal to alpha r times i s c equals i s. Now, one important thing to notice here is that because of the large i s e which is a scale current the same current for the same current in the collector base junction you would need only much lower voltage drop forward biased drop compared to the emitter base junction. Now, this particular phenomena has lot of implication when you talk about the saturation mode of a transistor. So, in the large signal model of the n p n transistor is shown here. Now, since now that we have seen the forward active mode and reverse active mode in some detail we could now talk about we could come up with a model which models the n p n transistor in all its possible modes. Now, a bus mode model or the em model is one such model where the n p n transistor can be model to predict the operation in all its possible modes. This particular model is nothing but a combination of the last two large signal models we used you could we will see that the only difference is the currents have been rewritten slightly. Now, so what we have this is the base terminal you have the collector terminal and the emitter terminal and you can see the n p n transistor emitter current is leaving base current is entering and the collector current is also entering the device. And applying KCL we can write three expressions we will not go into great detail. Now, the advantage of the a bus mode model is that we could predict the currents. So, we could write IE from the IE as IDE minus alpha r times IDC IC as minus of IDC plus alpha f IDE and IB as 1 minus alpha f IDE plus 1 minus alpha r IDC. Now, if we substitute values for IDC and IDE as IDE is equal to ISE times e to the power VB by VT minus 1 and IDE this should be IDC. We would see that the current is going that these expressions we would get detail expressions for all the three currents. Now, these equations look very complicated, but if you look at it carefully we would see let us look at these two terms look at the collector current let us look at the first two terms. Now, the first term as an exponential term e to the power VB by VT and the second term you have an exponential term e to the power VB C by VT. So, you could think of the above small equation showing you the terminal currents as a sum of two currents. For example, the collector current is basically the sum of the forward biased emitter based junction and the forward biased collector based junction. Now, in a normal forward active mode we know that the base collector junction is reverse biased which means e VB C would be negative. So, we would see that this entire second term would disappear. So, we would see the collector current being governed just by the emitter to base junction forward biased. So, these two these equations can be used to find the values of the current for all possible cases. Now, these equations give a very good understanding of the active and the saturation modes of an in p n transistor. Now, the active mode of a BJT is fairly well understood. However, the saturation mode is one of the most complicated and most misunderstood and above small model gives you a very good understanding and it shows you when a device is saturated and when it is active. Now, from the as I said in the in the above small equation, if you consider the forward biased case that corresponds to the base emitter junction being forward biased which means VB will be positive and the base collector base junction being reverse biased which means the base to collector voltage would be negative. This is because of the reason that we saw earlier that the collector potential would be always much more positive than base with the result that VBC would be negative with the result the entire term would the entire exponential term will disappear and that way the current in an active mode is governed only by the first term and very similar thing you would find the emitter current also. Now, one of the best ways of understanding the saturation mode is to plot the above small equation for the for IC. If you plot IC as a function of VCB for a given what we have here is a plot of the expression for IC for a for a for a for a particular value of VB for VB is equal to 0.7 what we are doing here is we are changing VCB all the way from minus 0.75 to plus let us say 2.5 volts. Now, as generally when we say forward biased we said that in the forward active mode the collector base junction should be reverse biased. Now, what do you mean by reverse biased? Now, what we see from here is that the current the collector current does not change at all even till up to the about about point about minus 0.4 volt. This is because of the reason that even though collector to base voltage is reduced till the collector to or the base to collector voltage is becomes forward active more than what 0.5 volt that particular junction is not properly forward biased with the result that till about 0.4 volt of forward biased to the base to collector junction the second term in the previous equation which we saw has no effect. Therefore, we can safely say that as long as we ensure that the collector voltage. So, we will we will we will we will we will we can ensure that the we are able to keep the collector voltage down to even even up to about minus 0.4 with compared to the base we would still be in the active region. Now, from the some of we will see later some expressions to illustrate this. Now, above small model you can use to explain the other model other other modes of operation also. The reverse active mode we said is a case where the collector base junction is forward biased and the emitter base junction is reverse biased. Now, in the in the same previous equations if we put the appropriate values that is forward biasing the collector base junction and reverse biasing we can get currents in the reverse active mode. Now, in the cutoff mode again in the above small model if you substitute one case if you reverse bias both emitter base junction and the collector base junction we would see that the collector current would be negligible or this will be the case even if you make V be less than 0.5 also you would see the collector current would be would be negligible. So, we is we so therefore, we find that the above small equations give you a very fairly accurate large signal model as far as the transistor operations concern and using above small equations you could compute the all the currents in all kinds of voltages. Today itself I will be uploading a home assignment for your own use where I have asked you I am asking you to calculate some of this. So, that you can actually see transistor in all kinds of possible modes having seen the NPN transistor in detail. Let us have a quick look at the PNP transistor. Now, in a PNP transistor we have the emitter region as P made of P material you have a N material for the base and another P material for the collector. Now, in a PNP transistor the emitter since you have to forward bias the emitter base junction the emitter would be kept at a higher potential compared to the base. Now, since we have to reverse bias the collector base junction the collector would be kept at a much more negative voltage compared to the base. Now, here the current flow in a PNP transistor can be thought of as injection of holes from the emitter into the base as opposed to the injection of electrons in the case of the NPN transistor. Now, the since emitter is heavily doped and base is slightly doped we would see that the injected holes from emitter to base would be much much higher than the injected electrons from the base to emitter. Since the direction of holes would be the same as the direction of current in a PNP transistor the actual direction of emitter current would be into the device and the direction of the base current and the collector current would be out of the device. Now, we could apply the above small equations for the PNP transistor also just by replacing VB in those equations by V EB and VBC by VCB. Now, we have since we have seen BJT in kind of fairly greater detail. Let us look at the BJT configurations. Now, these BJT configurations are quite important when we talk about amplifiers and in my next lecture on BJT common amplifier we look at this in some detail. Now, the why do we have different BJT configurations? As we saw earlier we said that a BJT can be thought of as a two port network the device can be thought of as a two port network with since there are three terminals you can have one terminal as the common terminal for both the input and the output ports. So, you have three possibilities let us look at the common emitter configuration. So, what we have listed in this particular table is basically shown the common terminal the input port and the output port. Now, in a common emitter configuration emitter terminal will be the common terminal. So, the input would be between base and emitter and the output port would be between collector and emitter. Now, the word hence the word common emitter. In a common base configuration base would be the terminal which is common to both the input and the output ports and the common collector configuration the collector terminal would be the common terminal between the input and the output port. Now, we earlier saw the current gains alpha and beta. Now, that we have understanding of the BJT configurations alpha is called the common base current gain as we saw earlier. Now, alpha also we wrote earlier as I c by I e. Now, we saw in the common base configuration the input port is between emitter and base and the input current is the emitter current and the output is between the collector and base and the output current is the collector current. Therefore, alpha can be thought of as the kind of a transfer parameter. So, output current by input current hence the name common base current gain. Similarly, we saw earlier we saw beta and beta was called the common emitter current gain and again here we know that in a common emitter configuration the input current would be the base current and the output current would be the collector current. Therefore, the transfer parameter here is I c by I b and hence the name common emitter current gain. Now, later when we talk about amplifiers we will see that when BJT is used as amplifiers in these three configurations they would have very different performance parameters. We will see that in detail later. Now, at the moment since in now that we have understood to some extent the operation of a BJT and the modes of operation as well as the modes basic configurations. Let us look at the current voltage characteristics to get some more insight. Now, two current two voltage characteristics are in common use and generally they are called the input and the output characteristics to describe the operation of a BJT in the chosen configuration. The most commonly used configuration is the common emitter configuration. So, we shall see the current voltage characteristics in the common emitter configuration. There are two characteristics. First one is the input characteristic where we would plot the base current which is the input current as a function of the input voltage V BE and in the output characteristic we would plot I c the collector current as a function of the output voltage V CE. Let us first look at the input characteristic which is the base current versus V BE. Now, from our previous equations we saw that we can write I B as I s divided by beta f times e to the power V BE by V t. We might remember you might remember that we are written earlier I c as I s times e to the power V BE by V t. Therefore, the expression divided by beta f would give you I B. A typical plot of I B versus V BE shown here and we could see here an exponential relationship. What is interesting to see here is that we earlier when we talked about active mode, we said that till about 0.5 volt hardly any current flows. We can see here that when V BE is 0.5 the current is extremely small. You could see that any appreciable current flows only when the forward bias voltage V BE exceeds 0.6. Now, the most commonly used forward bias voltage is 0.7 which you can see here variable that at 0.7 volts you have appreciable base current. So, for most of the DC calculations we would use 0.7 as the as a first order approximation for the V BE voltage. Another very important thing to remember as we know as we can see the input characteristic is nothing but a diode characteristic and just like a normal diode the BJT is also highly sensitive to temperature variations. We would see that the V BE will decrease by 2 millivolt per degree centigrade rise in temperature if the junction is operating at a constant current which means that as temperature increases for lesser and lesser V BE voltage you would get the same current. This particular feature is used these days very extensively for making sensors, very cheap sensors. So, we can use a very good we can use a simple diode as a very good sensor temperature sensor if you could pass a constant current through a diode and just monitor the voltage across it. We would see that for a very 1 degree rise in temperature the voltage across the diode would decrease by 2 millivolt. So, this principle is used in diode senses and we would see that input characteristics also would have a very similar behavior. Let us now come to the output characteristic where the collector current is plotted as a function of the V CE which is the output voltage. Now, here what we have plotted here is the collector current as the value of the collector current for various values of base currents. Now, if the base current is 0 which corresponds to the x axis the corresponding collector current will be 0, but as we keep increasing base current let us say I B 1 we would get a particular value of I C and so on. So, we could choose any particular any value of I B for our operation. Let us assume that we would use a point we would use the BJT to operate at a certain point say Q. Now, we could find the operating point or the corresponding I C and V C at that point as V CE Q and I C Q. One very important thing to notice from this particular graph is that we see that once the V CE exceeds a certain voltage we see that the current is almost constant, but we see a small slope here we will talk about it later. Otherwise we would see that as a first order approximation we would see that the current is almost constant once you exceed a certain voltage. At the same time we see that below a certain value of V CE we see that the current drops. Now, this particular dividing line is the dividing line between the saturation region and the active region. Now, so in the saturation region as V CE keeps decreasing you would see that the current would also keep decreasing. This can be easily seen from the above small equations. Now, the typically this particular value of V CE at the kind of dividing line between active region and saturation region is typically in DC circuits we would use that to be about 0.2 volts and it is called the V CE SAT or the V CE saturation voltage. Now, let us talk about the current gain the common emitter current gain. Now, beta DC is defined as the current which we had the collector current divided by the base current at the particular equation point Q which we saw earlier. Now, this particular current gain is also called the large signal gain large signal beta or the DC beta and it is often written as beta DC. We can also define another parameter which is the incremental or AC beta. We can write this as the as delta IC by delta IB for a particular value of V CE. Coming back to the diagram we can see that at this particular let us say at this particular value of V CE if we go from say IB equal to IB 3 to IB is equal to IB 4 we get delta IB here. Now, if you measure the corresponding change in the collector current we get delta IC. So, we can find beta AC as delta IC by delta IB at a particular value of V CE. Now, we would see that the values of beta DC and beta AC differ by typically about 10 percent. So, most of the time the distinction is not made between beta DC and beta AC value of simple beta is written. Occasionally in some models you will also find beta being written as HFE this comes from the hybrid parameter model and HFE is called the short secured common emitter current gain. Having seen the characteristics now let us talk about another important behavior which we can see of BJT which you can see from this particular characteristics. We said that above V CE sat which is the dividing line between the saturation region and the active region. We said that the IC V CE characteristic has a certain positive slope. So, this is now if you extrapolate this you would see that this line would meet the negative axis the x axis at a certain point. Now, at that particular point if you denote that as say a particular voltage let us say VA that is called the early voltage. So, what we are trying to see from the transistor is that as you even though we said earlier that the collector current is independent of the V CE, but what we are seeing here is that actually the collector current keeps increasing as we keep increasing V CE. Now, this particular voltage which you get by extrapolating the characteristic to the x axis and you generally write it by a voltage called VA which is a particular which which depends on fabrication of the transistor and it is a particular parameter for a particular BJT and typically this will be in the range of 50 to 200 volts. Now, VA is called the early voltage and this particular effect is early effect. Now, if you look at early effect we could maybe take a minute to explain why current increased when we increased V CE we know that V CE which is the voltage between the collector and the emitter is V BE which is the voltage between the base and the emitter plus the voltage between the collector and the base V CP. So, if we increase V CE for a given V BE because V BE will be typically let us say 0.7. So, if we keep increasing V CE we see we would see that that amounts to increasing V C BE which is the reverse bias voltage. Now, when we increase the reverse bias the depletion region width reduces. Now, this would effectively reduce the width of the base earlier we saw that the scale current I S we said it is inversely proportional to the base width. So, since here the base width is reducing the I S value would increase this would give you a proportionate increase in I C. So, this effect is called early effect and most of the calculations we would generally neglect early effect. However, in models we would use it. Now, having seen the basic operation of BJT in some detail let us look at some examples. One of the best circuits which I found from my own teaching career in explaining especially the different modes of a transistor in terms from a circuit is the BJT inverter circuit. So, we will use the BJT inverter circuit to illustrate the meaning of cut off active and saturation modes in an actual circuit and also the interplay between them. So, here what we would assume that the V BE with a forward bias voltage would be 0.7 we would assume a beta of about 50 and a V CE sat voltage of 0.2. So, essentially what we have is a this is a BJT inverter circuit where you would apply a input voltage to the base to a resistor and you have a collector resistance here. So, we would apply input between the base and the emitter you would see output from between collector and ground and ground and the emitter is here grounded here. This is an extremely useful and a simple circuit to explain all these three modes. Now, initially let us consider the first case let us assume that. So, effectively we will vary V 1 or the V in voltage here all the way from 0 all the way to V CC. As it as we go from 0 to V CC let us see what happens to the transistor and also let us see what happens to the output voltage. Now, initially let us assume that your V in is less than V BE. So, since V BE is 0.7 you would see that as long as you keep the input less than 0.7 the base diameter junction is not getting forward biased. Therefore, no base current will flow since there is no base current there will be no collector current. Since there is no collector current we would see that the output voltage would be the same as the supply voltage. So, this is the first case which is very easy to understand. So, this illustrates the one of the modes which we talked about earlier which is the cut off mode which means effectively the base is not getting the base diameter junction is not getting forward biased and even though you have a proper reverse bias for the collector to base junction the transistor is off. So, this shows the V J T in the cut off mode. Now, let us increase the voltage applied to the between base and emitter. Now, as we increase it beyond V BE we would see that a correct current base current would start flowing. Now, let us increase it till a particular voltage we will name as V I H we will look at this particular voltage later and how to get it, but one very important thing to remember is that as we keep increasing V in beyond V BE the V J T would turn on and now we can write an expression for the base current as V in minus V BE by R 1. Let us look at the circuit again. So, if you apply Kirchhoff's voltage law in the base to emitter loop we would see that V in is equal to I B times R 1 plus V BE from where we can write I B as V in minus V BE by R 1. Now, once we get I B we can get I C as beta times I B. Now, in the output loop again if you apply Kirchhoff's voltage law we would see that V CC is equal to I C times R 2 plus V CE here V CE is same as V V out or V O. So, in the output loop V CC is equal to I C R 2 plus V CE or V out which is same as V CE would be nothing but V CC minus I C R 2. Hence, as V in increases V out will keep decreasing. Now, the issue is how low can V out or V CE become can it become 0 can it become negative. Now, this is a point at which generally students would have lot of questions and lot of confusion. Now, this is where we need to spend some time in explaining what is the limit on that particular voltage. Now, we saw earlier from the I C V C characteristics in the common emitter configuration and as we would have noticed the VJT inverter circuit we just now drew which we considered is actually a common emitter configuration. Emitter is grounded input is between base and emitter output is between collector and emitter. Now, since we know it very well from the characteristic that since it is a common emitter configuration V CE is definitely greater than 0. We saw that in the characteristic. So, that is answers one question that V CE cannot be negative. Now, we need to see whether what is that voltage. Now, what we saw also that even though it is greater than 0 we saw that there is a region up to which the both the junctions get forward biased and we said that is the region we called as the saturation region where both voltages get forward biased. Now, let us understand this from the transistor. So, this voltage is V CE between the collector and the emitter terminals. We see that we wrote this earlier also. So, we can see applying KVL that V CE is equal to V BE plus V CB. Therefore, we know that to start with V CB since it was a reverse bias V CB was positive to start with V BE was anyway positive. We know that to start with since V CB was reverse bias voltage it is much greater than V BE. But, as IC increases the potential V CE or V CE will keep decreasing and V CB will keep decreasing. Now, the lowest value of V CE possible for an NPN transistor is V C SAT which we saw in the characteristic which is typically in the range of 50 to 200 millivolt and we said for most DC calculations we would assume it to be 0.2 volt or 200 millivolt. So, one this is one one very important observation or thing to notice here is that V CE cannot be negative in an NPN transistor. So, now that we know the smallest value possible for V CE. Now we can calculate the maximum possible value of collector current that we can find as this is the same KVL we wrote. So, we said that in the output loop IC is equal to V CC minus V C by R 2 since the lowest value of V C is V C SAT the maximum value of IC is IC max is V CC minus V C SAT by R 2. So, that gives us the maximum possible value since it is from KVL this is the this is the value which cannot change. Now the value at which V out first becomes V C SAT the corresponding I value V I value is what we will call as V IH. Now how do we calculate V IH? So, we will call V IH the input voltage at which output first becomes V C SAT how do we calculate that. Now we can calculate that by calculating the maximum base current rather the base current corresponding to this IC max that we can find as IC max by beta if we call that IB 2. Now we know that IB is equal to V in minus V BE by R 1 and here we can substitute IB as IB 2 and get V IH as V BE plus IB 2 times R 2. Now what we have here is a plot of the BJT inverter. So, we saw earlier that up to about 0.7 volts the BJT was in cut off therefore, the output was fully V CC and we said that once the input voltage. So, here we have x axis V in y axis V out. Which is same as V CE. So, this is the BJT inverter transfer characteristics. Now we said that once V in increased above V BE we said the output dropped and this drops linearly. This is because of reason that V out is equal to V CC minus IC R is a linear relationship and we said the minimum it can reach is V CC set and that particular input value voltage value will call as V IH. So, we see that this particular second region is the active now the BJT is operating in the active region. So, now we already seen two modes of operation cut off and active. So, we can say that as long as V in is between V BE and V IH the BJT is in the active mode and for this range I see various linearly with IB. Now let us consider the third case that is V in is greater than V IH that particular V IH value where we had the it first reached V CC set. Now we know that once you V in is beyond V IH IB will keep increasing because IB is equal to V in minus V BE by R 1 because that is the KVL. So, IB will keep increasing but IC cannot increase because we wrote IC as the maximum value of IC. So, we see that IC gets clamped at IC is equal to IC max and also V naught cannot decrease we said that is the minimum voltage can reach. So, it will get clamped to V CC set. So, this is called the saturation region. So, as we wrote earlier V CE would be equal to V BE plus V CB or V CB is equal to V CE minus V BE. Now V BE is 0.7 V CC set is 0.2 therefore, we can find V CB to be minus 0.5 or V BC is plus 0.5. So, we see here that both the base emitter and the collector base junction or the emitter base and the collector base junction are forward biased. So, this is indeed the saturation region which we talked about. So, we see two interesting features of the saturation mode. One thing is in saturation mode the IC value would be less than IB times beta DC value. Now, the second thing is both the emitter base and the collector base junctions get forward biased. So, this particular circuit is an extremely useful circuit especially for teaching students the modes of a transistor for the first time after talking about the basic relationship to explain and that most of the time clarifies the doubts maybe we may have to go over it a few times. And I have included a BJT inverter problem in the home assignment. So, you will also have another chance to work it out for yourself and understand. So, I hope you would take time to do the home assignment problem. Now, let us spend a little bit of time on the last circuit I have which again extremely important circuit the common emitter biasing circuit. This particular circuit clarifies again lot of doubts about biasing and about especially about active mode and saturation mode. What I plan to do is next 15 minutes roughly 10 minutes I will spend some time on this circuit and we will keep about 10 minutes for any quick questions you might have. So, let us spend another 10 minutes on this particular circuit. Now, here what we have this is the most commonly used biasing circuit for a common emitter amplifier which we will discuss in the next lecture. Now, given a circuit like this how do we calculate all the currents and all node voltages most of the time as we saw in the I C V C characteristics all that we need to calculate is the I C value and the V C value. Now, this particular circuit can be simplified using Thevenin's theorem again this is one of the most one of the common confusion which students have given a circuit like this how to simplify it. Now, Thevenin's theorem is one of the most elegant theorem. So, again I very commonly use this as an example of how Thevenin's theorem makes this circuit very simple. If somebody tries to solve this particular I mean try to find the current the base current through node equations you would need at least two equations whereas, here a single one equation you can solve it. Now, what we have here we applied Thevenin's theorem between the base and the emitter terminal or the base and the ground not emitter between base and the ground. So, what Thevenin's theorem says is open this particular port look towards the side find the open circuit voltage that will be the Thevenin's voltage. So, the open circuit voltage here V B B is nothing but V C C times R 2 by R 1 plus R 2. Now, the Thevenin's resistance will be the parallel combination of R 1 and R 2. So, the circuit now reduces to a very very simple circuit where calculation of currents becomes very very simple. So, this is the first step in solving this particular circuit. So, once few we do this by writing getting V B B and R B. Once we do that now we need to in all transistor circuits before we solve it this kind of biasing circuits you need to make an assumption. Since, there are many unknowns here the best way to solve it is to by making an assumption that the BJT is in the active mode. Why is it so? If the moment I assume that the BJT is in the active mode I can use the relationship between collector current and base current as I C is equal to beta times I B. So, if I find I B I can find all the currents and that is the common way of the easiest way of solving it. So, we will first assume the BJT be active the moment I do that I can apply K V L in the base diameter loop I can write then V B B as I B times R B plus V B plus I B into beta plus 1 times I R E I B into beta plus 1 is nothing but the I E flowing here. Now, once I do this I can rearrange and find I B as V B B minus V B by R B plus beta plus 1 times R E once I find the value of I B I can find I C to be beta times I B and I E to be beta plus 1 times I B. So, at by at the end of this step I would I would have known all the currents assuming the BJT is active. Now, these are extremely important thing you need to verify whether assumption is right to do that we need to write an equation again K V L for the output loop. Now, for the output loop the K V L equation is nothing but V C C is equal to I C R C plus V C plus V E. Now, assuming active we can write we can write V C as V C C minus I C R C V E as I E R E then I can write V C as V C minus V E. Now, if V C if I get at this step V C to be greater than V C side which is 0.2 then my assumption was right then the BJT is active if that condition is not satisfied then you would see that the BJT is in saturation. Now, if in saturation then two equations are required one for the input loop and one for the output loop and we can then use the equation I E is equal to I C plus I B. So, we have three unknowns and three equations and it can be solved. Again I have given one problem one nomenical problem in the assignment. So, I hope you do it where you would be able to understand how the interplay of this. Now, before we end I want to talk about the interplay of the role of R C and R E. Now, as I said previously if you look at the circuit here we would see that R C has a very important role to play in the mode of operation of the BJT R C cannot be anything, but the same time one of the most commonly encountered misconceptions from the student side is that if R C is extremely small let us say if R C is 0 if I ask a question whether the transistor will operate most of the time students will say the transistor will not operate, but we saw if you remember the models we used earlier we saw that the collector current is modeled was modeled as a controlled current source and it was entirely controlled by V BE. So, as long as this particular voltage here V C is greater than the voltage is required to ensure that this is reverse biased it will work that is the important thing to remember. So, therefore, the same time if you keep increasing R C we would see that the value of V C will keep drop dropping and that is one point V CE would become equal to V C sat or less than V C sat. So, therefore, R C has a very big role to play. So, in a amplifier circuit you cannot choose R C arbitrarily. Now, again I have included one problem in the assignment where I asked you to choose the maximum value of R C possible in a given circuit. Now, similarly R E has a role, but this is a bit tricky here the role of R E is a bit more tricky because in the previous case R C because this is a controlled current source and since the collector current was not dependent on anything else other than the voltage and the collector there was no problem, but the moment you touch R E the whole scenario changes. Now, interesting thing to notice here is for the R C case we had a situation where R C had an upper limit you cannot increase it beyond a certain value. You can keep it as we could keep it 0 not for an amplifier, but for a DC operation you could keep it 0, but R C cannot be increased above a certain value, but the case of R E is the other way. If you keep increasing R E nothing will happen the transistor will be still in active region, but since R E has a role in determining the I B value the currents will all reduce. If you increase R E what will happen is that if you keep increasing R E the base current will decrease the collector current will decrease the the emitter current will decrease, but the transistor will continue to be in the active region. So, increasing R E is no problem, but if it decrease R E you see that I B will increase which will increase I C which will increase I E. So, we will reach a scenario where the increased if you keep increasing if you keep decreasing R E the current will keep increasing and at a stage the transistor can enter saturation. Again I have I have not included a problem because it is tricky, but it is important to remember that for R E you have a lower limit. So, for a given circuit your R E has a lower limit whereas, R C has an upper limit this is extremely important when you design an amplifier circuit. So, just to I have reached the end of my lecture just before I stop let me just talk about a very good reference book which we very commonly use as a text book here. Now, all this material most of the material which I covered today was mostly taken from this reference book Cedra and Smith Michaelronics circuit strip edition. It is an Indian edition available very easily and it extremely useful text book as compared to the commonly used text book in most engineering colleges Millman and Halkias. Unfortunately that is a very old book and it was correct may be technology wise 30 years ago, but today most of the materials mentioned in Millman and Halkias is not accurate. So, I think that is not a good book to follow, but this is an extremely good book to follow. So, let us wind up just have a quick summary of all that we did so far. We talked about the BJT modes of operation. We saw the four modes and we said active region is the most commonly used mode and we said for the active mode of operation you need to keep the base emitter or the emitter base junction forward bias, the collector base junction reverse bias and we said for all amplifiers circuits and so on that is the mode and we will see more of that in the next lecture. And we also talked about saturation region which is one of the most confusing mode of operation where both the junction gets reverse bias and we see we saw how that particular mode of operation can be explained easily using a very simple, but elegant circuit BJT inverter and I find that are extremely good circuit to explain the concept of saturation to students. We also saw that cutoff that if the base emitter junction does not get sufficient forward bias, the circuit the BJT goes into cutoff mode and we also said there is a mode called reverse active mode which is almost say never used except in logic circuits and that is a situation where you could think of active mode where the collector and the emitter terminals are interchanged. And then we saw the IC-VC characteristics we also saw the relationships between the currents and in the IC-VC characteristics we saw that the currents are on a first order approximation the collector current as long as it is above V C sat it is constant, but then we saw that once you increase V C the current slowly increases which we said is what is called the early effect and we talked about an early voltage and we also saw the input characteristics in the common emitter mode where we said that the input current varies exponentially and finally, we saw the base emitter we saw the common emitter biasing circuit and where we explained again how we actually work out the currents and voltages. Now, in the assignment which I have which we will upload soon I have included above small equations and I have given a number of scenarios if you work it out I can guarantee you you would understand all the modes of operation thoroughly including reverse active mode and all that you need is a calculator and please assume you know I mean you can use approximations, but you would find that extremely useful and I have included again one problem on VJT inverter and two or three problems on on VJT DC circuits.