 Today, we will talk about common emitter amplifier. Before we talk about common emitter amplifier, we would see basically some details about an amplifier. Now, amplifier, when we talk about an amplifier, generally we mean a voltage amplifier, but actually there are 4 types of amplifiers. Now, you can think of amplifier as a controlled source. So, you can, you have, you can, you have 4 types of amplifiers. So, amplifiers are controlled sources either voltage, controlled voltage sources or controlled current sources. Now, a voltage amplifier is a voltage controlled voltage source. Whereas, when you talk about a current amplifier, it is a current controlled current source meaning in a current amplifier the input as well as the output are both currents. When we come to the third type of amplifier, the trans conductance amplifier, it is a voltage controlled current source meaning the input is a voltage source whereas the output is a current. Now, the last type of amplifier is called a trans resistance amplifier which is also called a current controlled voltage source meaning the input is a current and that current controls the voltage source the output is a voltage. Now, most of the time we are talking about a voltage amplifier. Let us see the equivalent circuit of an voltage amplifier. Now, essentially voltage amplifier can be shown by the figure which is shown here. At the input side, you have a resistance R i which essentially models the input resistance of the amplifier and the voltage which is to be amplified V i develops across that particular resistance. Now, the output side you have a controlled voltage source whose amplitude is a V o times V i and a V o meaning the open circuit voltage. Now, being a voltage source, it is represented as a Thevenin equivalent by its Thevenin equivalent model. So, you have the open circuit voltage and in series with a resistance R naught which is the output resistance of the amplifier. Now, since voltage amplifier is the most commonly used amplifier, let us look at what are some of the requirements. Now, we would connect an input to the voltage amplifier and what we want is the entire voltage should develop across R i which means that this R i the input resistance here must be as high as possible. Ideally, it should be infinite. Now, the voltage gain could be as we require. Now, coming to the output resistance, that resistance should be as small as possible. Since it is a voltage source, the resistance should be as small as possible because any load when you connect a load across the output, any current which flows into the load would develop a voltage drop across R naught. So, ideally the output resistance should be 0 and again bandwidth as required. So, when we talk about a voltage amplifier, ideally we would like to have infinite input resistance and 0 output resistance. Let us look at one more amplifier, the current amplifier. Now, the equivalent circuit of the current amplifier is shown here where again you have an input resistance R i. We would like the entire current from the input to flow through R i and the output being a current source. It is represented by the Norton equivalent and we have an A i s i i whereas, A i s is a short circuit current and R naught which is the output resistance of the current source. Now, coming to the ideal characteristics of a current amplifier, since we would like the entire current input current to flow through R i, ideally the input resistance should be low, ideally it should be 0. Coming to the output side, since we would like the entire current to flow through the load R naught ideally the output resistance R naught ideally should be infinite. There is a very common misconception that for every amplifier the input resistance should be infinite. This particular equivalent circuit of the current amplifier shows that that is not so. We need to look at the particular amplifier in question to decide what its input and output resistance should be. If the input is a voltage source, it is a voltage controlled then we need to have infinite input resistance. If it is a current controlled then you should have R i 0. Most of the time when we talk about an amplifier we actually mean a voltage amplifier. This is because most of the time we require a voltage amplifier and the reason is most of the sensors give a voltage output and we more often come across voltage signals than current signals. However, there are applications where you might come across currents as well. Let us take an example to illustrate the requirements of an amplifier and to set the context for today's lecture. Let us think about a public address system. Right now I am speaking into a microphone which may be a condenser microphone in this case or it may be in some cases a dynamic type microphone. So, the signal at the output of the microphone need to be amplified and you would have a preamplifier in the public address system and followed by a post amplifier and finally, you would have an output stage or a power amplifier and the signal then flows into a loud speaker. So, this is a good example to consider the amplifiers and the typical requirements of amplifier. Now, when you look at an ideal voltage amplifier, we studied last week that an op-amp almost you can think of an op-amp as an almost an ideal voltage amplifier. This is because of the reason that when you use negative feedback in an op-amp circuit and especially if you think about the non-inverting amplifier circuit, you would see that the input impedance is very high which is requirement for a voltage amplifier and again because of the negative feedback, you would see that the output resistance is extremely small again what is required of a voltage amplifier. However, when we think about an op-amp very often we think of op-amps as ideal blocks, but there are a few disadvantages which op-amps have general purpose op-amps have. Let us look at 741. Now, 741 and other general purpose op-amps cannot be used for applications beyond about 10 kilohertz. This is because of the slew rate limitation which happens because of the compensation internal compensation provided in an op-amp. So, therefore, most of the time you cannot use a 741 for applications beyond 10 kilohertz. Then somebody might ask then what is the use of an op-amp. Interestingly, most of the sensor outputs the frequencies do not exceed about 1 kilohertz. There are very few sensors which would give you signals beyond 1 kilohertz. So, therefore, when 741 or other op-amps were made the manufacturers had that in mind. So, they know that for the 95 percent of the applications you could use a simple op-amp and have an ideal case. There are op-amps which can be used for high frequency applications also. However, they are very costly. Now, let us come to the case of discrete amplifiers. Now, common emitter amplifier is an example of a discrete amplifier. Now, when you think about a discrete amplifier as compared to an IC amplifier like 741, a discrete amplifier can be tailor made as per our need, especially as we said the frequency response of an op-amp is very small. We could actually make a discrete amplifier to meet our requirement and most of the time discrete amplifiers would not be very complicated and they are easy to build and also analyze. However, since there are many components and they need to be assembled either soldered or made into a PCB or into a breadboard, the reliability of discrete amplifiers is very low. Another very important thing to kept in mind is discrete amplifiers need to be biased and designed very carefully. Also, in a discrete amplifier, the gain and other amplifier parameters are device dependent. If you compare this with an op-amp amplifier, you would see in an op-amp the gain is independent of the device parameters. Whereas, in a discrete amplifier, most of the time you would see that even when negative feedback are applied, only in an approximation, we can take the gain to be independent. When we talk about BJT based discrete amplifier voltage amplifiers, we have three amplifiers. One is the common emitter amplifier which is the most commonly used. We will see with later why. Then you have the common base amplifier and you also have the common collector amplifier. Now, in my last lecture, last week, I had mentioned the meaning of the word common. When you say common emitter amplifier, what we mean is the input signal is applied between the base and the emitter and the output signal is taken between collector and emitter. Hence, emitter is a common terminal and most of the time it is at ground potential and hence the word common emitter. In a common base amplifier, the base terminal would be most of the time almost at ground potential and the input will be applied between emitter and base and the output will be taken between collector and base terminals. In a common collector amplifier, collector would be the common terminal and collector would be at AC ground potential. Input would be applied between base and collector and the output would be taken between emitter and collector. Now, let us look at common emitter amplifier in some detail. Now, the first thing we need to consider when we talk about a common emitter amplifier is to have an idea about the output characteristics and to decide how you go about. Now, as I said in my just right now, one of the most important things about a discrete amplifier is that you need to bias the device in this case a BJT in the proper operating point. Now, what we have here is the ICE VCE characteristics which is also called the output characteristics. On x axis we have VCE and on the y axis we have the collector current ICE. Now, the output of a common emitter amplifier would be VCE voltage. Now, as we know from this characteristics we see that the extreme left side we know is the saturation region and when we talk about an amplifier, we are talking about a linear application. Hence, we should not the transistor should never get into the saturation region. So, we should choose an operating point somewhere in the middle. Also, we should ensure that the transistor never goes into the cutoff which is the towards the x axis. So, you would choose somewhere in the middle. Another very important consideration when you talk about a discrete amplifier is what is called the signal swing. Now, what we essentially do assuming this particular point here as the Q point or the quiescent point or the operating point. Now, this particular point you have a certain base current and corresponding to that you have a collector current and you have a VCE voltage. Now, when we apply an input to the base voltage which we apply gets superimposed to the DC voltage and the base current increases and decreases in accordance with the input signal as the base current increases and decreases correspondingly the collector current decreases and increases. Now, corresponding to that the voltage VCE voltage would change and later we see we would have a resistance R C collector resistance and we need to ensure that we need to choose this resistance value at the operating point such that even for the maximum signal swing we are far away from the saturation region and the cutoff region. If not the output signal will be distorted. So, one of the first things we do in a discrete amplifier is to do a proper biasing. So, we need to choose an appropriate operating point thereby we are actually choosing a I C value and a VCE value on this particular I C V C characteristics. Now, as I said we need to ensure that we keep away from both saturation and cutoff regions. Now, when we talk about biasing circuits there are a few other considerations as well. Now, we need to ensure we need to make sure that the small VB variations which occur because of temperature variations should not upset our operating point. So, we need to make sure that the circuit can take care of small VB variations. Another important consideration is in a discrete amplifier since we are using discrete components the beta value of BJT of the same type would vary very much sometimes as much as 50 percent. If you pick a BC 147 transistor and measure its beta and you go to the market and buy it 10 such transistors and if you measure the beta you would be very surprised to see that there is large variation of beta sometimes as much as 50 percent. Hence, we need to make sure that the circuit is able to tolerate large variations in the value of beta. What we have here are two bad biasing circuits. Let us see why they are bad. This first circuit what it does is it essentially establishes a DC VB voltage using a potential divider and it assumes that once you do that the operating point would be stable. Now, the emitter is grounded here. Now, what happens is by in case of any temperature variation, ambient temperature variation or junction temperature variations, we know that the VB has a negative temperature coefficient of 2 millivolt per degree centigrade rise. So, if for some reason the temperature rises then what happens is we have a fixed value of VB at the potential divider, but the VB value because of the increase in temperature the VB required for the same current which we had is now less or equivalently since the VB value as because of the negative temperature coefficient the current now increases. Now, once the current increases we would have another increase in temperature junction temperature which would again make the VB to again decrease. And then we have what is a process called thermal runaway which essentially would make the circuit essentially that is a name given for unstable biasing condition. So, we see that this circuit is not suitable say bad biasing circuit. Now, the second circuit here what we have here here the what is done is a resistance RB is connected between VCC and directly to the base here. Now, what is aimed here is to have a fixed value of IB by choosing an appropriate value of RB. Now, as we said there is large variation of beta between different discrete transistors. So, if you do this what will happen is what we designed may not be what we get the collector current which we decide we will not get hence these two circuits are not suitable. Now, what is commonly used is the biasing circuit which is also used in RC coupled amplifier where we have a single power supply a voltage divider at the base just like the previous case. And the difference here is now we added a series emitter resistance here. Now, the emitter resistance here as a very important role we said in the previous case these emitter resistance was 0. Therefore, what happened was whenever there was a temperature variation when the VB changed and when the current changed that resulted in something like a positive feedback. In this case what happens is if the same thing happens that is why that is I mean what we mean if the temperature increases and if the VB value decreases and the current increases what is going to happen is since we have a resistance here the emitter potential now will rise. Now, with this rise in emitter potential the VB would now reduce what we assume is that the increase in current does not change the VB the base voltage which can be satisfied by choosing R 1 and R 2 appropriately. So, what happens is whenever there is a temperature variation and the VB value decreases that effect is countered by the emitter resistance here and a kind of a negative feedback is comes into picture and that opposes this because of this the biasing point would be quite stable and also we need to make sure that for large beta variations also this particular circuit works. Now, this can be taken care of by choosing R 1 and R 2 quite small. Now, what we do is we need to ensure one thing is to ensure that VB small VB variation are not upset we need to make sure that the voltage here the VBV voltage which is the voltage at the potential divider should be much higher than what is the required DC VB value and we need to make sure that the RE value the resistance at the emitter should be greater than R B by beta plus 1 we will see how we ensure this. So, as a thumb rule what we generally do is to ensure stable biasing and also to ensure that the operating point stays somewhere in the middle of the characteristics what we do is we choose the VBB which is the voltage the base potential VCE and ICRC the drop ICRC we take all these three to be roughly one third of the supply voltage. And to ensure that beta variations do not have upset we approximately we could take the current through R 1 and R 2 the current flowing through R 1 and R 2 to be approximately 10 percent of the current IE the emitter current. Now, the reason for doing this you can think of this in another way now the base current is much much smaller than the emitter current. Now, what we need to make sure is that the current flowing through R 1 plus R 2 should be much greater than the current flowing into the base if we can do that then beta variations will not upset. So, this is the circuit which is commonly used now for tomorrow your lab for tomorrow afternoon slab you have the common emitter amplifier and the same rules you would be applying. So, what we discussed today can be implemented now before we talk about the so we now saw the biasing and we saw how to choose biasing. Now, before we talk about BJT amplifier see common emitter amplifier model one very important thing we need to keep it in mind is what is called the small signal approximation you might remember last week in my lecture I we talked about the abert small model and there we use the term large signal model and we said using abert small model we could get DC currents or large values of currents for any value of base emitter and base collector voltages. Now, in an amplifier one of the most important thing we need to keep it in mind is that it is a small signal application meaning a BJT as we see from the characteristics as we know from the BJT characteristics is a non-linear device we need to operate we need to ensure that our application amplifier application is a linear application. So, we need to make sure that the variation in the VB value is much smaller compared to the VB the DC VB. So, generally what we do in any circuit we if you look at the instantaneous VB value it would have two components one would be the DC VB value which we obtain by choosing an appropriate biasing circuit and an AC VB which is our signal. Now, in the small signal approximation what we mean is the signal which we apply VB should be much smaller than VT which is the thermal voltage 25 approximately 25 millivolts. So, typically we are talking about the small VB to be the order of about 10 millivolt. If we do not have signals as small as 10 millivolt what would happen is there will be distortion most of the time we may not be able to appreciate distortion when we see it on an oscilloscope, but if we use a signal analyzer then we would see that there is distortion for that matter any amplifier has distortion that is not a single amplifier which does not have all that we can do is to reduce the distortion. So, if we keep the VB value as small as possible say less than 10 millivolt then we can get reasonably good amplification without much distortion. Now, before we look at the common amplifier let us look at an appropriate model. Now, the most commonly used model and fairly accurate model for analyzing a BJT amplifier is what is called the hybrid pi model. Here let us look at the conceptual circuit and the model what we have here is a common amplifier and this is what is called a conceptual diagram. This particular diagram has no biasing is only the AC signals are shown. So, that is why you find a short circuit here. Now, for as far as AC is concerned a battery is a short circuit you can think of since the battery voltage does not change we can for as far as AC is concerned it is a short circuit and we have small VB as the input here and that causes a small IB current flowing into the base and that would cause a collector current. Now, in the hybrid pi model the input circuit based to emitter you we have a resistance R pi which is essentially small VB by IB the small IB would give you R pi. Now, the other parameter here is GM and GM is IC by VT, IC is our DC current biasing current and VT is thermal voltage. So, once we are able to finalize our biasing circuit once we determine our IC we can get GM. Now, GM and R pi are related through beta. So, once we know what is GM we can find R pi also. So, once we have that we can get the hybrid pi model. Now, this particular model what is shown here neglects early effect. Now, if you remember when we talked about early effect last week we said early effect is basically the it basically talking it is about variation in the collector current as a function of the VCE the collector to emitter voltage. Now, in a hybrid pi model early effect can be modeled by putting a resistance across the current source and that resistance R naught is defined as early voltage divide by IC. So, we see that once we complete our biasing and once we are able to determine the value of IC we can determine all these small signal parameters that is GM R pi and R naught. So, we are once we do this we are at a position to analyze the amplifier circuit. Now, before we analyze our common amplifier we need to look at the amplifier parameters bit more carefully. We talked about input resistance we talked about voltage gain we talked about output resistance let us define them properly. What we have here is a block schematic of an amplifier and what we are shown here is the input signal represented by the Thevenin equivalent an open circuit voltage V C and a resistance Thevenin resistance R C and in a current I I flows into the amplifier and at the input of the amplifier a voltage V I develops and from the output a current I naught flows into the load R L and across R L we develop the output voltage V naught. Now, the definitions the parameter definitions for an amplifier are R as follows input resistance with no load is defined as V I by I I that is for R L equal to infinity. Now, input resistance R in is defined as V I by I I with R L in place we will come to this in a minute. Now, we might remember when we model the voltage amplifier we had an open circuit voltage called A V O. Now, that open circuit voltage gain which is the voltage voltage gain is defined as V out by V I with R L infinity or without R L here and voltage normal voltage gain is V out defined as V out by V I with R L in place. Now, coming to output resistance it is a bit more tricky what is generally done is we would apply in a very simple in a simple circuit is very easy to determine the output resistance, but in complicated circuits what we would do is we would connect a voltage source called V X and find and connect that is output side and find the current flowing I X if that is the case output resistance R naught will be V X by I X at V I is equal to 0 which means the input to the amplifier at side should be shorted. Similarly, you have another definition of output resistance R out which is defined as V X by X at naught V I is equal to 0, but V SIG is equal to 0. Now, in the previous case the assumption is that your R SIG is 0 equivalent to saying R SIG is 0, but in a general case the series resistance of the source may not be 0. So, you would make R V SIG 0 which means you would have the effect of R SIG. Now, let us it may be confusing why it is quite confusing to see why we have two sets of input resistances and two sets of output resistances. Now, to understand that we need to talk about what are called unilateral amplifiers. Now, when you talk about an amplifier certain types of amplifiers are called unilateral amplifiers. Now, in these amplifiers the input resistance does not depend on the load resistance that is there is no output to input internal feedback. So, in a unilateral amplifier R in would be the same as R i and R out would be the same as R naught many amplifiers are non unilateral. Now, let us look at common emitter amplifier. Now, as we said one of the first things we need to do is to choose the values the biasing circuit carefully that is we would choose R 1 and R 2 carefully we would choose R e and R c we would we would these resistances would be chosen such that we have I c R c approximately one third V c c and we have a V b voltage of V b b voltage of one third V c c and a V c of one third V c c. Now, what we are drawn here is the common emitter amplifier. Now, we have the signal source here V c and an R c here. So, in general it is always better to keep the the revenue equal resistance of the voltage signal source. Now, this is connected to the common emitter amplifier through a capacitor. Now, why do we need this capacitor? Now, what will happen if I do not connect this capacitor? Now, we see that we have chosen R 1 and R 2. So, as to establish a certain DC bias here. Now, if we do not connect this capacitor what is going to happen is we are going to have this resistance and this voltage source also coming into picture. This will completely upset our biasing and the transistor will not work. Now, most of the time this capacitor which we have here would be the order of tens of p f or few p f sorry a few micro a few micro farad. So, typically let us say 10 micro farad. Now, again how do we choose the polarity? Now, 10 micro farad corresponds to a electrolytic capacitor which has polarity. Now, how do we decide the polarity of this capacitor? Now, in such cases what is important is we need to look at one of these sides of the capacitor where we are sure about a certain voltage. In this case we see that this capacitor the base side has a certain positive voltage whereas, this side we are talking about an AC. So, it is almost 0 here. So, the capacitor would have a positive polarity towards the base side and negative polarity towards the signal source side. Similarly, we have a capacitor here at the output side and that is connected to the load here R L here. Again why do we need a capacitor here? Now, if you remember when we talked about biasing we said we would choose the biasing point based on R 1, R 2, R c and R e which means that if I do not have this capacitor the moment I connect R L once again this value of R L will disrupt my biasing. So, for the same reason I need to have this coupling capacitor C 2 here. Once again how do I decide the polarity of C 2? Now, here again the same principle we need to look at the side we are sure about the polarity. Now, we know that the collector side of the capacitor has a higher positive voltage whereas the load side is connected to ground. So, we would choose a positive polarity on the collector side and a negative polarity of the lethargy capacitor on the load side. Once again typically the value of C 2 would be about 10 microfarad typically. Now, we can have two types of common amplifier depending on whether we have a capacitor connected between emitter to ground or not. Now, in the first case the most common case we would have a capacitor C e connected between emitter and ground. Now, in today's lecture we will not look at the details of the low frequency response. Now, what we see is that the when we do the analysis we would see that the value of C e would be much much higher compared to C 1 and C 2. Typically, C e would be the order of about 100 microfarad or around 50 to 100 microfarad. Here again the polarity is quite straight forward towards the emitter you would have positive polarity for the ultrasonic capacitor and the ground negative polarity. Now, before we start analysis one very very important thing to keep it in mind is that we are talking about mid band frequency analysis. Again what do we mean by mid band? We can draw the frequency response of a common emitter amplifier the one which I showed just now something like this. Now, we see that the amplifier characteristics we see is like a band pass filter. It has two cut off frequencies and let us call the first one the lower cut off frequency and the upper one as the upper cut off frequency. Now, we have a region in the middle which is called the mid band. Now, the frequencies below f l the lower cut off frequency you have a high pass response whereas, frequencies above f h the upper cut off frequency we have a low pass response. Now, what is the reason for the high pass response? Now, we can see that this coupling capacitors and the C e. So, these three capacitors contribute towards the low frequency response of the amplifier. So, we depending on the kind of value of the low frequency cut off we require we can choose appropriate values for C 1, C 2 and C e. Similarly, when we talk about the upper cut off frequency. Now, that is a region which is due to the device capacitances this we will see a little later. Now, when we talk about mid band, mid band frequency is the region where the frequency response is flat or the gain is constant. So, we assume that in this particular region the coupling capacitors as well as C e are short circuits their impedance are negligible. So, they are short circuits and the device capacitances are open circuits. So, when you talk about an AC analysis we are talking about the mid band analysis. Now, again let us look at the equivalent circuit and try to get some expressions for the amplifier parameters. Now, R in we defined as V i by I i. Now, in this particular circuit here we see that the I i is the current flowing V i is the voltage across R b. Therefore, the input resistance R in is nothing but R b parallel to R i b. Now, R i b as we see here is nothing but R pi which we would have determined and we know that R b is generally quite high compared to R pi. R pi would be typically of the order of 1 kilo ohms or so typically or sometimes even less depending on the value of the collector current and the beta. Now, so therefore, we see that the input resistance R in is approximately R pi which means the input resistance of a common amplifier is approximately 1 kilo ohms of kind of that order. Now, when we talk about V i that is the voltage at the input of the amplifier. Now, our signal source is V sig. Now, if you write an expression for V i in terms of the signal source V sig we can write V i as V sig times R in by R in plus R sig. Now, we know that R in is equal to R b parallel R pi. So, substituting will get this as V sig into R b parallel R pi divided by R b parallel R pi plus R sig. Now, we said that R b parallel R pi is approximately equal to R pi therefore, we can write V i as approximately V sig times R pi by R pi plus R sig. Now, we see here that when we use a common amplifier if we have R sig significant in comparison to R pi then we are going to get a much smaller fraction of the input voltage developed here. So, in this case we see that V pi is same as V i here. Now, coming to the output side we can see that the voltage V out here is nothing but the current here times R naught I have not shown here R c. So, should have been an R c also here. So, R naught parallel R c parallel R l. So, I am with a minus sign because the current is flowing towards the away from the output towards the ground. So, the output voltage is minus of g m V pi into R naught parallel R c parallel R l. Now, the voltage gain A v with load then would be V out by V pi or V out by V i which is nothing but minus of g m R naught parallel R c parallel R l. Now, if you assume R l is equal to infinity you would get the open circuit voltage gain which would be minus of g m times R naught parallel R c. Most of the time R naught which is the output resistance which we put which models the early effect most of the time would be quite high. This is in a special for discrete amplifiers. This is because of the reason that R v A the early voltage for most of the transistors could be the order of about 200 volts. So, if you are talking about 1 milli amp and 200 volt then R naught is much much much higher. So, most of the time you would find that the output voltage open circuit output voltage is nothing but minus of g m times R c. Now, coming to the output resistance v is it would be nothing but R naught parallel R c or we can say as we said R out would be approximately it will be R c since R naught small R naught will be very high. Now, another very important parameter is what is called the overall voltage gain which measures from end to end that is from V naught to V sick. Now, that we can get as V i by V sick times into V naught by V i which would be nothing but V i by V sick times A v. Now, if we assume that the resistance of the signal source R sick it is much smaller than R pi then we see that the overall voltage gain is approximately equal to the voltage gain. Now, this is an extremely important parameter to be important point to be kept in mind and we see here a major disadvantage of the common ampere amplifier. Now, most of the time when we do an experiment in the lab the signal source would have a resistance R sick for the order of 50 ohms most of the time. Now, the R pi I said it will be the order of somewhere around 1 k to 2 k. So, therefore, we would see that whatever calculations we do we will be able to see that we can get we get the same value. But if we use a common ampere amplifier directly for let us say for a sensor application we would see that we have get much smaller voltage gain and the reason is the large value of R sick. This is something which is very important to be kept in mind. Now, I would tomorrow the lab you have a BJT amplifier circuit and there is a detailed design procedure is given there. So, I request all of you to go through the sample there and you could all the equations are also given in your lab handout you could work it out and in the lab you can check carefully. And as I said when you wire the circuit a few things you need to keep it in mind keep in mind carefully. One thing is to connect the transistor correctly the collector base and emitter terminals should be connect correctly connected and we know since we talked about the reverse active mode and the normal active mode if you interchange emitter and collector we know what will happen you would you will get much smaller beta and therefore, the it is as good as the transistor having no gain. So, next time you do not get a proper gain is quite likely that you have interchanged the collector and the emitter terminals. So, keep that also in mind and before you come to the lab do some hand calculations using the equations given in your handout and also in this and then you could compare that with the values you get. Now, the previous example of the common emitter amplifier we use the hybrid pi model to analyze it. There is another model called the T model this particular model is useful in some situations we will see which situations where this is convenient. Now, the hybrid pi model is useful whenever your emitter is at ground potential like in the common emitter amplifier with a C E connected there we know that the emitter is at ground potential in such a case the hybrid pi model is very simple, but in case if you have a situation where your emitter has a resistance to ground then the hybrid pi model would be quite complex. In such a situation this model T model would give you very very simple solutions. Now, what this T model has is it has essentially a voltage control current source model something similar to what we used in the large signal model in the last week's lecture. So, you have an I B here you have a V B voltage developed across a small R E and you have a control current source which is g m V B this value was same as the value we had in the hybrid pi model. You also have a this was a voltage control current source model whereas, here it is a current control. Now, in this case the only difference is the control source has alpha times I E. So, the controlling parameter is I E here and you have a small R E and in this model you need only g m and small R E and g m we know is I C by V T and small R E is defined as V T by I E the emitter current. So, once again this would be nothing but alpha by g m. So, once we know the biasing the operating value and the biasing conditions we can determine these values also. Now, let us analyze now the common emitter amplifier with an unbypass series emitter resistance you have this in tomorrows lab also and once again we could analyze this. So, the only difference between this particular circuit and the circuit which we saw just before this is that here the emitter is unbypass which means there is no capacitor from emitter to ground. Otherwise you have the coupling capacitors C 1 and C 2 which we said are must otherwise the biasing will get upset. Now, what we have done here is we have used the T model here and we can see here and in this case it gives you an extremely simple equivalent circuit and in fact this will be much much simpler. You could use hybrid pi model also, but you would find that the expressions would be much more complicated. Now, in this case we have connected the V C here you have R C here you have R B here and then between these three points here you have connected the transistor you have between emitter and ground you have R E which is the resistance there and you have small R E which is a small signal parameter and you have a R C there coming from between collector to ground and R L. Now, once again we can determine what is R in here which is nothing but V i by i i again R in is R B parallel R i B. Now, compared to the previous case when we had a capacitor between emitter and ground here you would see that R B R i B or the resistance looking into the base is quite different. In this case R i B is V i by i B and i B we know is i E by beta plus 1 and i E we see since we have V i here the same V i is appearing at this particular terminal. So, therefore, i E can be easily calculated as V i by small R E plus capital R E therefore, i B would be V i by beta plus 1 times V R E plus capital R E therefore, R i B would be beta plus 1 times small R E plus capital R E and R in therefore would be R B parallel R i B which will be R B parallel beta plus 1 small R E plus capital R E. Now, most of the time we would choose R B such that it is much greater than R i B. So, we see that if we can do that if we can choose R B to be very high then we would see that just by increasing R E we would see that the input resistance of the common emitter amplifier without a emitter bypass capacitor will be very high. If you remember the previous case our main minus point was that the input resistance was very small. So, in this case we would see that there will be a substantial increase in the input resistance. However, there is one thing we need to keep it in mind there is a limit to be up to which you can increase R B. We know that if you increase R B too much then we would have the problem of the piecin circuit becoming unstable due to beta variations. So, we see a typical design situation here in any engineering design we have trade-offs. So, we see a simple common emitter amplifier circuit design also giving you this kind of interesting features. So, the input resistance of a common emitter amplifier without a emitter bypass capacitor would be very high. Let us look at the voltage gain. The voltage gain in this case would be V 0 will be minus of I c into R c parallel R L. Now, in our analysis here we have removed small R minus R naught which was modeling the early effect for simplicity and we said last time also that R naught is for a fully for a discrete amplifier R naught small R naught we said is very high. So, we could so if you do that then we see that V out is equal to minus of R c R c parallel R e and if you substitute for R I c I c would be nothing but alpha times I e and we know that I e is equal to V i by R e plus capital R e. Therefore, A v the voltage gain with load we can write as V out by V i equal to minus of alpha R c parallel R L divided by small R e plus capital R e. This would be approximately if you assume alpha to be 1 then this will be approximately minus of R c parallel R L by R e plus R e. Now, most of the time small R e would be a very small number typically say about 25 ohms or 50 ohms in comparison to capital R e. So, we would see that the voltage gain of a common amplifier without an emitter bypass capacitor we see that would be R c parallel R e divided by approximately R c parallel R L divided by R e which would be quite small. Again you could try the lab handout given to you and you could work out these numbers. So, we see that in this particular case what we have is actually a negative feedback and when we talk about negative feedback in one of the later lectures we will see whenever we apply a negative feedback the price we pay is the voltage gain. In fact, we trade off voltage gain for other useful parameters. So, in this case by getting a much lower voltage gain we got in return a much higher input resistance and also we would see that you will also get much higher frequency response. In this case the output resistance R out will be R c. Now, another important thing to keep it in keep in mind both for the this particular amplifier we consider the considered now and also the amplifier we considered the common emitter amplifier with a emitter bypass capacitor. We said in both the cases they are unilateral amplifiers and as we said when we say unilateral amplifier what we mean is that these are amplifiers where we assume that anything we do at the input does not upset the output meaning we change the input signal source and that R sick value will not change the output resistance. Similarly, whatever we do at the output should not upset the input which means if you change the R L load resistance then that should not change the input. So, in a unilateral amplifier R in will be same as R I. Now, in this particular model we assumed we did not have the device capacitor therefore, our approximation of unilateral amplifier was correct. Now, let us compare these two amplifiers the common emitter amplifier with an emitter bypass capacitor and the common emitter amplifier without an emitter capacitor. Now, in one case we saw that the amplifier with an emitter resistance which is generally called the degeneration resistance we saw that the input resistance increases, but we saw also that the voltage gain will get reduced, but the advantage of the voltage gain expression we saw there was that the voltage gain expression was much less dependent on beta value and also because of the negative feedback the other parameters of the amplifier also improves.