 So, the topic we are going to discuss today is also about the last stage of an amplifier, all are last. Now, today's topic is on power amplifiers and as we all know, power amplifiers always would be the final stage in an amplifier. Now, if you take the example of the public system, which we have been talking about, starting from the microphone all the way to the loudspeaker, you would see that power amplifiers come just before the loudspeaker. It is the power amplifiers which actually drive the signal through the loudspeaker, which makes us to hear the audio well. Now, power amplifiers are very, very different from all that we discussed so far. We talked about common ampere amplifiers, we talked about common base amplifiers, we talked about common collector amplifiers. In those amplifiers, our consideration was mostly gain input resistance, output resistance and so on. And when we talked about feedback amplifiers, we saw how we could improve these parameters, especially input impedance and output impedance, depending on the type of the amplifier. We saw how we could get almost, let us say close to ideal condition by applying negative feedback. So, our consideration in the case of feedback amplifier was to how to make our amplifier, an ordinary amplifier, how to make it say close to ideal. When we talked about multi stage amplifiers, we said multi stage is the way you go about when you actually implement an application such as a publicator system or even in an op amp, we saw that you have at least two to three stages and the final stage is the output stage or the power amplifier stage. So, here the considerations which we are going to talk today are very, very different from all that we talked about so far. Now, let us get into the topic, I would quickly go through the kind of topics I plan to cover depending on the time. Now, when we talk about power amplifiers, they are conventionally classified into what are called class A, class B, class AB and class C. What we will do is, we would see the classification initially and then we will talk about class A power amplifiers, we would see their transfer characteristics, we will also observe their signal waveforms, we will also see about their power dissipation and power conversion efficiency we will see. Then, we will talk about class B power amplifiers, once again we will see the transfer characteristics, the power conversion efficiency and we will also talk about power dissipation. Now, once we talk about class B amplifiers, we need to talk about what is called the cross over distortion and we also need to wonder or rather worry about how to reduce the distortion and therefore, we have this intermediary between class A and class B called the class AB power amplifiers. We will see how it operates and we will talk about a simple biasing scheme for a class AB circuit and finally, we will just quickly talk about power BJTs and some of their basic characteristics. Now, one very important thing to remember in this particular topic is, the transistors which we use here are very different from the ones which we were considering so far, hence the word power BJTs. Now, so far the BJTs we were using, they were what are called a small signal, they are even sometimes called small signal amplifiers such as BC 147 or 547 or BC 109 and so on. Whereas, when we talk about power BJTs, the consideration is very different, they are primarily meant for high power application therefore, in terms of the size also they would be very very different. So, we will see quickly, we will talk about power BJTs. Now, let us get some idea about this topic of power amplifiers or the output stage in an amplifier. Now, the power amplifier or the output stage as I said right in the beginning of my lecture is the final stage of any practical amplifier, why is it so? Because it is in the final stage, you have to connect the output of the amplifier to the load. So, power amplifier, its main function is to drive the load. Now, again another very major difference from all that we talked so far and this particular amplifier is, so far we were talking about large signal levels, we did not concern ourselves with small signal. Now, in this particular amplifier, we are actually concerned about not the small signal, but large signals, why is it so? Because after two stages of amplification or three stages of amplification, let us say in a power, let us say a publicator system, the signal levels we are talking about are very large, take the example of a publicator system. The signal levels we are talking about could be of the order of say 20 or 30 volt peak to peak, could be quite high as compared to small signal. When we talk about the BJT amplifier, when you did in the laboratory, the levels you are talking about are say typically at the most let us say peak to peak 1 volt. So, here we are talking about large signal and that makes a very big departure from all that we are talking about. So, therefore whatever models we use so far, which were the small signal models, we cannot use them anymore. So, this something which we need to keep in mind very much. So, therefore we will not use any small signal model. And if you remember from the example we took in the, when we talked about multi stage amplifiers, I took a numerical example to illustrate a multi stage amplifier. And there I said that the multi stage amplifier, the final stage of the multi stage amplifier in that particular example had a unity gain. So, almost always power amplifiers are designed for unity power gain rather sorry unity voltage gain. And they have large current gain therefore they have large power gain. So, even though they have unity voltage gain because of the large current gain, they have a large power gain. And we know that power gain is nothing but voltage gain times current gain. Now, because we are talking about large signal currents at the output side, power amplifiers must have very low output resistance. So, this is definitely easy to understand. Whenever we have to drive lot of current, we need to ensure that the source resistance is very small. So, here we have a controlled voltage source. So, we need to make sure that the resistance are small. When we say small here, we would be talking about most of the time resistances say less than an ohm, much less than an ohm. Again higher the power application, much much lower the output resistance. Now, when we talked about small signal amplifier so far, we took something from granted. Why did we talk about small signals? We talked about small signals because we said that if you could keep your input signals in a common emitter or a common base or a common collector amplifier to be say about 10 millivolt or so. We said then we could assume that the distortion, the non-linear distortion is almost not there. So, therefore, we could assume the amplifier to be linear and in almost all the cases, we would find that the small signal approximation is fairly accurate. Now, here unfortunately, since we are our signal levels are much higher than 10 millivolt and they could be at the order of 10s of volts or at least a few volts. Generally, it would be 10s of volts if we talk about a kind of a power application. Now, here therefore, one you will have non-linearity. So, one very important parameter in the design of a output stage or a power amplifier is the amount of total harmonic distortion or what is called the THD. So, power amplifiers will always have some amount of THD as compared to normal small signal amplifiers. So, we need to kind of specify this. So, when you buy say a publicator system, they would mention that the total harmonic distortion is so many dB's and so on. Now, the THD or the total harmonic distortion is the RMS value of the harmonic components of the output signal excluding the fundamental. Now, again another extremely important parameter when we talk about an output stage is the efficiency. Now, this is something which we did not worry at all so far. We did not even use this but efficiency so far because when we talk about a small signal amplifier, the signal levels we are talking about are very small say milli volts and the typical power we are talking about again would be at the most let us say 10 to 20 milli watts very small. Therefore, even though our amplifiers were highly inefficient that did not bother us because even if you are talking about let us say a 10 percent efficiency in an amplifier which is delivering let us say 10 milli watt of power. You are talking about at the most 100 milli watt of power which we do not even bother about 100 milli watt is such a small number. But unfortunately, when you talk about a power amplifier since the power levels we are talking about are large. By the way, when we talk about power amplifiers we generally talk about applications which are which deliver power of say more than a watt let us say typically 10 watt or above. You would say 10 let us say 5 watt or so. So, we are talking about power power's order of say 10 watt or more. Therefore, efficiency is an extremely important parameter for an amplifier because now it is not just the amount of power we are wasting. But in some applications that may be an important consideration but in most of the applications it is the amount of power you need to dissipate that will be the main concern. So, therefore, if I have an efficiency of only 10 percent and I am if I talk about let us say a 10 watt then I need to somehow dissipate 90 watts of power. Now, that is definitely not an option. Therefore, we have to really be concerned about efficiency. Now, low efficiency would automatically mean much larger power dissipation and the reason why power dissipation is a problem for us is the following. Two reasons one is it is very difficult to dissipate the power and to keep the temperature and I am sure all of us are familiar with let us say if you visit a small let us say a mobile transmitting station or any electronic application where you have large amount of power. You will always see a huge amount of cooling being done through fans and so on. Sometimes even they would use coolants to do that. Now, so that is one concern to dissipate the power. Now, another very major concern is we are talking about semiconductor devices. Now, so far we never ever worried about the how much our device would get heated up or so because the powers we are talking about were a few milliwatts, but now we are talking about hyper high powers. Therefore, we need to be concerned whether our device would get heated up. Now, if our BJT gets let us say heated up beyond say 150 degrees, it will get damaged immediately. It is completely useless. In fact, it may not be a bad idea to may be just touch the body of one of this power transistors which you would find the bottom of or just the rear side of a publicator system or sometimes even in power supplies. It is a good idea to just touch it. You will always see it be warm and we are talking about 150 degrees which is very, very high. So, you need to ensure that the temperature of the BJT junction temperature does not increase and it is kept within as close as possible to the ambient temperature. Now, we are talking about say an application where you are using battery like especially a portable kind of application. Then the power efficiency is the concern there is the amount of reducing the drain in the power supply. Now, as we said the transistors used here are very special transistor and typical power dissipation capabilities of these transistors would be a few watts and sometimes may be hundreds of watts. For example, a very popular NPN transistor which you may be familiar is 2N3055 which has a dissipation power of 125 watts. So, we are talking about large power dissipation values. Now, we could design an output stage using both discrete and integrated circuits both are there in use. Now, these days you would find lot of power amplifier ICs available and which has much better features than the discrete ones, but what we are discussing here are basically concepts. So, it does not matter we are talking about discrete or integrated. Now, as I said right is the beginning, when we talk about power amplifiers we classify them into class A, class B, class C and so on. Now, this is done on the basis of the shape of the collector waveform in response to the input signal. Now, we would assume the input signal to be sinusoidal. Now, what we have here is a sketch of the typical collector current waveforms in 4 of these categories. Now, let us look at the first one. Now, the class A amplifier what we see here is that we have the signal here sinusoidal signal here and this is the collector current. Now, what you would see here is that even when the signal is negative even at the extreme negative excursion of the signal you see that there is still current, which means that this particular current IC which is the Q-SAN current or the operating current is greater than the peak value of the signal. So, this is a particular this is a very important feature of a class A amplifier. So, in a class A amplifier you would ensure that even for the largest swing of the signal your the amplifier would always have current this current the negative peak the current does not go below 0 you would ensure that. Now, that is class A when you come to class B what we see is that in a class B amplifier we would actually use two devices one device for one half cycle and the other device for the other half cycle. So, what we see here is the typical class B classification where the current would be in the previous case it was flowing throughout. So, if you talk about a conduction angle here it was 360 in this case the conduction angle is 180 degree. So, that is the classification of a class B and as I said because you are only taking care of one half cycle you need to have two devices working in tandem or in a complementary fashion. So, one device would take care of the positive half cycle the other device would take care of the negative half cycle. So, that is how a class B amplifier works. So, the conduction angle here is 180 degrees. Let us now talk about class C amplifiers. Now, class C amplifiers are amplifiers where the conduction angle is less than 180 degrees. Now, class C amplifiers are very special cases and we will not worry much about them. Now, class A amplifiers are used in very high power applications. So, generally these are very special kind of applications we will not worry much about them. What is important for us are class A, class B and class AB. Now, class AB is something which is in between class A and class B. We said class B the conduction angle is 180 degrees and in a class A it is essentially 360 degrees. Now, class AB is a case where the conduction angle is greater than 180 degrees, but less than 360 degrees. So, it is slightly more than 180 degrees and we will see why. So, let us look at these in some detail. So, what we saw in the signal which we just now saw was in a class A amplifier, the amplifier is biased in such a way that the DC operating current without the signal that was greater than the peak of the signal current I p, we saw that. Now, that is why we said in the case of a class A amplifier, the amplifier or the device in that amplifier conducts for the entire 360 degrees. Now, what are examples of class A amplifiers? Now, the amplifiers which we studied so far common emitter, common base and common collector, these amplifiers belong to the class A category. So, these are amplifiers where the device conducts for the entire 360 degrees, the entire the conduction angle is 360 degrees entire period. There is no interval during the signal, the device is not conducting. So, our common emitter, common base and common collector belong to the class A category. Now, what are class B? As we saw from the waveform there, the collector waveform of class B amplifiers, what we saw that these amplifiers were kind of biased at 0 DC current. So, therefore, they conducted only when the signal came and we said you would have two devices. So, normally there is no conduction and as soon as the signal comes one device conducts for the one half cycle. So, one device would take care of the positive half cycle, the other device would take care of the negative half cycle. Therefore, since they conduct only for half period of the sine wave, the conduction angle is 180 degrees. Now, as I said because they conduct only for 180 degrees, you need two such stages or let us say two such devices. Now, what is actually done is you would combine the currents from these two stages. So, that when it flows into the load you have a kind of continuous conduction. Now, class A B amplifiers as we saw in that the waveform there, these are biased at not 0. In class B, we would bias it at 0, which means there is no signal the amplifiers or the BJTs are off. But in this case, if we would bias the transistor at a very slight value of DC current, but this would be much smaller than the peak current of the sine wave. Now, if you compare this with class A, a class A amplifier we biased making sure that the biasing current is much greater than the peak of the sine wave. But here, we would bias it at a extremely small DC current, we will see why and how much. Therefore, the class A B category the transistor conducts for a period greater than 180 degrees, but much smaller than 360 degrees. Now, class A B also requires two class A B stages. Now, again just like the class B, you would kind of combine the currents from these two transistors and they are combined so that they would flow in a combined fashion into the load. Now, when we talk about class C amplifiers, now this was the waveform we saw in the last one, where we saw that the transistor conducts only for an interval which is less than half period. So, the conduction angle was less than 180 degree. Now, the output current waveform is actually a kind of a periodically pulsating waveform and so this kind of amplifiers are used for very high power application such as let us say a transmitting station, where the kind of powers you are talking about are in the orders of kilowatts or hundreds of watts. In those kind of situations, you would use a class C amplifiers and then what is done is the currents are passed through a parallel LC-LC circuit tuned to the frequency of the input sine wave and we will not this is a very special class and we will not study this because this is generally you would never ever come across a class A amplifier. Now, let us look at class A amplifiers in detail and then let us see why class A amplifiers are not preferred even though they conduct for the entire 360 degrees which is the ideal situation, we will see why they are not. So, we need to see in detail their operation. Now, you can think of a class A power amplifier as an emitter follower. In fact, that is the most popular choice because we know that emitter follower has low output resistance and we saw right in the beginning that one of the most important requirement of a power amplifier is that it should have low output resistance. Therefore, the obvious choice from the point of view of what we studied so far is to choose an emitter follower. Now, let us look at a typical class A amplifier using emitter follower and then let us see how it works. So, what we have here is basically a two transistor kind of combination. Now, what is done here is this stage here which we see in the bottom that is q 2 and this diode here and the resistor. Now, this are the q 2 is biased through this particular diode in such a way that there is a current I flowing all the time, a DC current I flowing all the time. Now, what we will do is the when we apply a signal here, we want to see how exactly the output looks like. Now, as we said in this particular case since we are talking about a power amplifier, we are actually interested not in this one signal operation but in the large signal operation. So, let us see how this particular circuit operates. So, to recap what we have here is a q 1 which is the one which gets the signal and it is biased through this two transistor combination and we have a emitter current flowing which is I e 1 and then what happens is a current I e 1 will be equal to I plus I L and I L is the current flowing through the load and we have the output voltage taken across the load. Now, what we need to see is for seeing the large signal operation, we need to find out the transfer function rather the transfer characteristics of this particular stage. Now, what we saw that it was biased with a constant current I supplied by the second transistor and we saw that the current flowing through the first device I e 1 is equal to I plus I L where I L was the current through the load. Now, we need to ensure that when we choose I e we need to ensure that the bias current I e must be greater than the negative peak of I L in order to ensure that q 1 is always in the active mode. So, this we saw when we saw the signal waveforms. So, when we design such a stage we need to ensure that the particular current is chosen such a way that the it exceeds the negative peak. So, that even when we have the negative peak still you have a certain value of DC current. Now, we can write a very simple equation for the transfer characteristics which as we saw the signal was supplied to the base of that transistor and we have a V B drop there. So, output was this was an emitter flow. So, output is taken from the emitter therefore, the output voltage is nothing but input voltage minus V B e 1 and this is an N P N transistor. So, this is the equation. Now, the important thing to remember here is this value of V B e 1 depends on I e 1 and it definitely also therefore, has bearing on the value of I L. Now, if we can neglect the small variation in V B e 1 due to I e 1 variation and we know that the being an exponential characteristics for a very small change in V B e 1 would get large current variation. So, if you assume that these variations in V B e 1 are small then from this equation we see that the V out versus V in characteristic is linear. Now, if you sketch it this is how we would get. Now, from that particular equation we wrote V out is equal to V i minus V B 1. So, we see that we see this particular characteristic. Now, what is important notice here is we assumed this to be linear which is not a bad assumption. Now, we need to be concerned about the upper limit and the lower limit and on the x axis we have V i and the y axis we have V out or V naught. Now, the upper transistor being in a common collector kind of a stage we are taking output from the emitter therefore, the maximum value the emitter voltage the maximum value of the emitter voltage is nothing but the V c the V cc the positive V cc minus V c sat that is the maximum voltage you can have. So, till that point you can operate. Now, coming to the absolute you can when you talk about the negative half you can think about 2 limits. Now, in case 1 the the absolute limit is the limit when that particular transistor would go into saturation. So, the bottom transistor let us see the circuit again. Now, so this is the first transistor Q 1 here now Q 1 the output voltage here can rise as high as V cc minus V c sat. So, that is the upper limit here. Now, coming to the lower limit the extreme is minus V cc plus V c sat. So, that is the extreme limit, but again depending on the current which you have chosen here you can have another limit. So, in case you are constrained by the current you have chosen there then the negative limit will be minus of I R L we must remember that we have chosen I such a way that the peak of the it is greater than the negative peak. So, if that is the constraint. So, the upper the lowest value would be minus of I R L, but the absolute limit would be minus V cc plus V c sat. Now, so we have these equations here which we talked about. Now, let us look at let us have a look at the output signal waveforms of this particular transistor stage we saw now. Now, what we can say is that if you can choose the bias current I properly then the output voltage V o can swing from approximately minus V cc to plus V cc and the equation value would be V out is equal to 0. Now, we can kind of sketch say 2 3 waveforms 1 waveform would be we would like to see the kind of V c 1 waveform when you apply a signal we want to see how the V c 1 signal varies. So, we know that since the V c 1 since we are talking about a common collector stage and the output is at the emitter. So, therefore V c 1 is nothing but V cc minus V out because V out is same as V e and V c is nothing but V cc. So, V c 1 is nothing but V cc minus V out. Now, we can also kind of sketch another waveform which would tell us the value of I. Now, we can also kind of sketch the instantaneous power dissipation which is defined as V c 1 times I c 1. So, if you look at these waveforms what we see here the first one is the V out waveform and we said that we would assume that it goes from the two extremes. So, this is the kind of maximum possibility on the positive side approximately it can go to plus V cc or the negative side it can say approximately go to minus V cc. So, that is the V out signal. Now, corresponding to that if you look at the V c 1 we wrote the equation there as V c 1 is equal to V cc minus V out. So, if you do that we see that this is if you substitute our V out there and we see that as far as V c 1 is concerned the it can go from all the way from if you go to the extremes we would see that it can go from 0 all the way to 2 V cc with a kind of a fission value being V cc. So, when V out is 0 we have V cc, but with signal the V c 1 changes all the way it can vary from 0 all the way to twice V cc. So, that is as far as the V c 1 waveform is concerned. Now, if you look at the I c 1 the current flowing through the top transistor if you think about that I c 1 current there now the equation value is I. So, when there is no signal it is I now with signal it can go up on the positive side all the way to twice I on the negative side it can go all the way to 0. So, that is the excursion of the collector current and we are just at the border of class A. Now, what we have here on the last waveform is the power dissipation the instantaneous power dissipation which is p d 1 which we see is have a very interesting waveform. Now, the equation value of current was I and the equation value of V c 1 was V cc. So, when there is no signal the power dissipation is V cc times I, but with signal we see that the power dissipation varies. So, what we see here is something very interesting which is very very very different and this is one of the reasons why we do not like to have a class A amplifier. So, from this particular waveform we see that this is a very important sketch. So, this particular one what is telling this is about the power dissipation of that transistor which is q 1. Now, what it says is that you have a maximum dissipation when there is no signal. So, if you have no signal then you are going to have the maximum dissipation. So, that is something very strange when we are not using it the the V j t is getting heated up the maximum with signal the power dissipation changes. So, this tells us gives us a clue about its efficiency. Now, let us work out some numbers write some expressions for the power conversion efficiency of a class A amplifier. Now, by definition power conversion efficiency is defined as the load power p l the power delivered to the load divided by the power supplied. Now, in our example we had two power supplies. So, that power let us call as the total power supplied by the power supplies as p s. So, p l by p s is what we would define as efficiency because this would directly tell us about the power conversion efficiency. Now, with a sinusoidal output voltage with a peak let us say V o max V o m the average load power p l would be p l is equal to V o m by a root 2. So, this would give us the RMS value. So, V o m divide by root to the whole square divide by R l which is nothing but half of V o m square by R l. So, this tells us the power supplied to the load. Now, the power drawn from the power supply is we can find out from the p d 1 which we said is V c 1 I c 1. Now, we know that the and that particular. So, the power conversion efficiency we can see as by substituting we would see that this would be one-fourth of V o m square divide by I R l V c c. Now, we know that the maximum which we can allow the output cannot rise more than V c c or it cannot it has to be within I R l. Therefore, the maximum efficiency we can get here is for the condition when the V o max is equal to V c c is equal to I R l and for that condition the maximum efficiency possible is 25 percent. So, this gives us an extremely important result as far as class a amplifier is concerned. So, for a class a amplifier the maximum theoretically possible efficiency is 25 percent. And we know that even this we said is an approximation the signal input signal cannot approach V c c we assumed it to be V c c. So, therefore, we said it is 25 percent. So, most of the time when you talk about a class a output stage you cannot operate at that kind of input level. So, typically the kind of efficiency you actually get in a normal operation is somewhere between say 10 to 20 percent because most of the time your output swing would be definitely the peak of the output thing would be less than V c c. So, we see one something which is extremely important to remember that is class a amplifier even though it gives us the least distortion because it conducts throughout is the least efficient. And we said an extremely important consideration it was not a consideration when we talked about small signal amplifiers because the powers where we are talking about there were in a few milliwatts. And the device getting heated up was not an issue at all because the collector currents typically we talked about where a few milliamps are the most. And we never ever had a problem of power dissipation, but here we are talking about several watts several tens of watts or in some cases let us say hundreds of watts we are talking about a publicator system we are talking about at least 100 watts or if you are talking about a major a publicator system we are talking about thousands of watts. So, efficiency is one of the most important consideration. So, therefore, we can conclude that for an output stage we should never ever use a class a amplifier unless otherwise our power requirement is extremely small. If our power requirement let us say is less than a watt then class a is the best choice, but if our power requirement is more than a watt or if you are let us say several watts then definitely we should not go for a class a stage. Now, let us look at the next class of circuit which is actually a class b amplifier. Now, in a class c class b amplifier we as we discussed right in the beginning since it conducts only for 180 degrees we have to use two stages. Now, what we have here is basically a complementary pair of transistors an n p n and a p n b. So, the top transistor we have an n p n transistor and the bottom transistor we have a p n p. So, it is used in a complementary fashion. Now, we can see from the signal here that when your input is positive the upper device the q n the p n p the n p n transistor will conduct when the input is negative the p n p transistor will conduct. So, we the way is connected we know that both of them cannot conduct in the same time simultaneously they cannot conduct. When you talk about a class b this is what we talk about ideally what we expect is that the top transistor would take care of the positive half cycle and the bottom transistor will take care of the negative half cycle. Now, let us look at the circuit operation in detail. Now, when the input is 0 so let us have a look at it. Now, when the input the voltage is 0 what we can say is that both of them are off. Now, as you keep increasing V i on the positive side we know that this particular V B you need at least 0.5 volts. So, till V i equals 0.5 q n cannot conduct once V i exceeds say about 0.5 this particular voltage may not be exactly 0.5, but somewhere around that we know that once it exceeds that say about 0.5 volts the q n would start conducting and the current now would start flowing into the load. Now, during the entire positive half cycle the q p device the bottom p n p device would be off. Now, coming into the negative half cycle when V i again when V i is equal to 0 we know that both of them are off because there is not enough forward bias when V i goes negative and the V e b or the V b e when it is less than minus 0.5 when V b e is less than minus 0.5 the p n p transistor would conduct till then it cannot conduct and beyond that point the p n p would conduct and you would have a current flowing into the load. Now, so this is what we discussed when V i is equal to 0 both are off when V i is positive and it crosses about 0.5 volt q n conducts. So, beyond 0.5 volt we can say the transistor the upper transistor the the the n p n transistor works like a emitter follower and we can say that V out is equal to V i minus V b n this n stands for that n p n V b value of the n p n transistor and during this p the q p the p n p transistor will be off as as long as V i is greater than 0. When V i is less than 0 and when it goes below minus 0.5 q p turns on and this now acts as a emitter follower the output voltage V out in this case we can write as V i plus V b e p mind you in a p n p transistor the emitter would be more positive. So, whereas in a n p n transistor the emitter would be less positive compared to the base. So, hence this changes now q n will be off for the entire duration when the input voltage is less than 0. Now, let us sketch what we talked about let us sketch it into a transfer characteristic. Now, this characteristic is extremely important this particular graph as a lot of significance in the design of a power amplifier. Now, what we have here is what we just said in words. So, on the positive what we have is V i on the x axis V out the output of the amplifier on the y axis and we said that when it is 0 both are off no current flows. Now, till about 0.5 volts the output is 0 once the input goes above plus 0.5 the current starts flowing the n p n transistor contacts and the current starts flowing and then you have an emitter follower and you have a slope of unity slope and then at the upper end we know that it cannot go beyond V c c minus V c sat because the it will go into saturation. So, that is the upper limit coming to the negative side we see that once the n p transistor can contact only when the input goes below minus 0.5 and once the input is below minus 0.5 you have an emitter follower again in action and the slope will be unity and again the you have a negative limit there would be minus V c c plus V c p sat this p stands for the p n p a saturation voltage of the p n p transistor. Now, having seen this so we somebody might wonder why if this and it is obvious seeing from the transfer characteristic that we are definitely going to get a distorted output, but then why are we interested in class B that will be very clear once we see the power conversion efficiency calculations of a class B amplifier. Now, a class B power amplifier once again we can write the same equations which we did for class A the average power we wrote there of the output sinusoid with a p amplitude V o m is P L equals half V o m square by R L. Now, the current drawn from the power supplies will be half sinusoids because we know that each of those transistors conduct only for half cycle and when the n p n transistor conducts the power is drawn from the positive supply when the n p n when the p n p transistor conducts the power is drawn from the negative power supply. So, we have current drawn about half sinusoids drawn from the power supplies and the peak amplitude there will be V o m which is the maximum value by R L that is the peak current drawn. Now, the average power drawn from the power supplies we can write as p s plus stands for the positive power supply equals p s minus which is the power drawn from the negative power supply and that will be 1 by pi V o by R L into V c c. Now, so the total power supplied we could that will be double of that. So, the total power supplied will be twice V o m V c c divided by pi R L. So, now we can write an expression for the power conversion efficiency. So, if you do the substitution we would get this expression we will see eta the power conversion efficiency as p l by p s as half V o m square by R L which is the power delivered to the load divided by the power supplied which is 2 by pi times V o m into V c c by R L. Now, this we would get it to be pi by 4 into V o m by V c c. Now, eta max happens when we have V o m equal to V c c. Now, that gives us 75 78.5 this is an extremely large number compare this with the class A amplifier. With the class A power amplifier we said the maximum possible was 25 percent. Now, there is a lot of difference between 25 percent and 78.5 percent extremely large difference. So, now we are very clear why we are interested in class B amplifier. We see that the interest in class B amplifier is primarily from the point of view of the efficiency. Now, what we have here is a plot of that equation which we just now wrote there with V o m rather V maximum on the x axis and the power dissipation on the y axis. Now, mind you the power dissipation would be the power supplied minus power delivered. So, whatever power you supply and the whatever if you subtract the power delivered to the load and the remaining power is dissipated in the device. So, we would see that in a class B amplifier the power dissipation would keep increasing as you keep increasing the input voltage. Now, it reaches a peak and the peak power dissipation is actually twice V c c square by pi square R L there and at that particular point the efficiency is only 50 percent, but even that is very high compared to a class A output stage. Now, this happens when the input signal is twice V c c by pi. So, that gives us the max the value of the input signal at which we get maximum power dissipation. Now, the point at which we get maximum efficiency is at that we saw that is the point at which where our maximum the V maximum is same as the V c c at that particular point we have an efficiency of 78.5 percent. Now, this gives us a very very good reason why we should go for class B. So, class B power output amplifiers or the output stages are very good from the point of your power conversion efficiency and 78 percent is not at all bad is extremely good. Now, unfortunately there is a problem this we saw from the transfer characteristics we saw that in the transfer characteristics we had a dead zone, dead zone meaning we had a region there that region was plus minus 5 when the V i is within plus minus 0.5 volts we saw that during that period we had a dead zone meaning we have no output. So, because of this we would have what is called crossover distortion. Now, crossover distortion is extremely disturbing it is a very I would suggest it is a very very good idea to design a very simple inter follower like the one which we have done maybe some little biasing changes can be there and you would see that if you apply a signal you could then apply you could just maybe speak into one such class B amplifiers and you can listen to the sound from a loud speaker and then you will understand what you mean by crossover distortion. Now, the crossover distortion would be extremely disturbing this is because of the reason that our ear is extremely sensitive it can pick up even the smallest distortion and again that is people dependent some people are much more sensitive than others, but crossover distortion is easily distinguishable. So, if you give a signal especially a voice signal maybe a music signal you put it through a class B amplifier and then you put it to a speaker it will be very evident what is crossover distortion the sound would be very displacing. So, we need to find so class B is very good from the point of view of efficiency, but it is very bad from the point of view of crossover distortion. So, we need to find a middle path we need to find a way of reducing the crossover distortion without sacrificing much on the efficiency. Now, this is where the next class of amplifier comes into picture and class AB amplifier is the amplifier which is actually used in practice. So, as we discussed so far class A amplifier we also discuss class B amplifiers both these amplifiers are actually done only for the sake of theoretical analysis. And we from our discussion so far we saw that both of them are bad from the point of view of an actual application and the problem with a class A amplifier was the class A amplifier was very good on the point of view of distortion it had it had no distortion because it conducted for throughout the period, but we saw that a class A amplifier unfortunately has only 25 percent efficiency while a class B amplifier we saw that was very efficient we could we could get a maximum efficiency of 78.5 percent but unfortunately because of the dead zone which we have in the transfer characteristic we have a what is called a crossover distortion which is displacing and which we cannot have. Now, in a class AB amplifier as the name itself suggest is kind of a let us say a mix of both class A and class B. In a class A we have the conduction throughout the period of the sine wave in a class B you had a conduction only half cycle. So, in a class AB you would have a conduction which is greater than 180 degrees, but that is less than 360 degrees. Now, let us have a kind of a look at say a kind of a conceptual diagram where we have what we have done is. So, you could see the signal being applied to the base here. Now, the difference between this particular circuit and the circuit of the class B amplifier was the case of a class B amplifier we did not have this small biasing here. Here we have introduced a small battery called VBB by 2 and we here also. So, both the transistors we have introduced a small battery here. Now, the purpose of this particular battery is to ensure that when there is no signal when V i is equal to 0 we would like the NPN transistor to be just at the threshold of conduction. Because if we have if we adjust that voltage on the higher side then the transistor would conduct then we will get into class A situation throughout. If you make it too small then what will happen is it will it will have distortion. So, this particular voltage need to be very very carefully chosen. So, let us tentatively take this value of this voltage to be 0.5 volts, but this is a voltage which we need to choose very carefully. Now, again it is not a bad idea if we have one of those old transistor radios with you a portable transistor radio. Most of this radio sets would have an adjustment for this cross out distortion. If you look at any kind of a portable application like a tape recorder or a radio all of them would use a class A B. And what is done is in kind of a cheap portable application this voltage adjustment of this voltage is very difficult. So, what is actually done is you would actually apply a signal you would listen because this is a you have a loudspeaker there. So, you would listen to the sound and then you would have a kind of a potential meter arrangement which would give you some voltage. So, what is done is you would slowly adjust the voltage in such a way that and what is generally done a symmetrical kind of arrangement is done. So, that the kind of a positive of that supply negative of that applies here or you can even think of two separate parts. So, what is done is you would apply voltage in such a way that you are just at the threshold that the distortion just disappears. In fact occasionally what people do to do this is to connect an ammeter in the VCC path. Now, if it is class B no current will be drawn from VCC when you apply no signal here. Now, as you keep a keep changing this VBB voltage here if as you go from say slightly conducting to more conduction huge amount of current will flow here. So, that is how this current this particular biasing is done, but we will not worry about it. So, let us assume that we know this particular value and we have applied that conductor voltage here. So, what now happens is when you apply a signal here the output now is going to be V i plus we would have this particular bias kind of adjusted here. So, what we would get is the just the output would then we would get rid of this particular the distortion there. So, the dead sound would disappear in this particular case of the PNB transistor we have the base being brought negative. So, we could see from here that through since the emitters of both the transistor connected together we need to ensure that this potential is less by VBB by 2. So, this is how we would implement a class AB amplifier. Now, once we do this we can see that we get a linear characteristics ideally and as I said rightly you need to choose this particular voltage very carefully and that is when we actually design a class AB amplifier you would see that this is one of the most challenging jobs or one of the most difficult part of because if you go from say no conduction to conduction you need to ensure that you do not drain the supply too much because if you have too much current flowing you are playing with the efficiency and the efficiency will drastically come down. Now, what we have here is a kind of a typical biasing of class AB amplifier which is typically used for kind of an IC kind of an application this is the way you would bias and you could also do this with kind of diodes. These days you would get in fact in fact what we get occasionally you would get some of these matched diodes or transistors in kind of arrays which could be used for this purpose, but this kind of biasing is easily done in an IC. So, what is done here is you would first decide what is the voltage you need here to ensure that it is just at the threshold and accordingly you would choose a current bias current. Now, we know that V that VB voltage V is related to the current bias current by the equation VT ln i by is. So, by adjusting this value of i by s to the decide value we could get whatever is the decide value of VB here. So, essentially what we are doing here now here is we are ensuring that this particular one is you have two VB between these two bases that would ensure that the if it is properly biased we can ensure that if we are adjust at the threshold of conduction and that would ensure that we have fairly large efficiency, but not as large as 78 percent, but the same time not as small as 25 percent. So, depending on the biasing here we would be able to get different kind of efficiency. So, far we studied we as of now we discussed class A amplifier we also talked about class B amplifiers we also talked about class AB and we saw why class AB amplifier was required here.