# (Refer Slide Time: 1:22)

Size: px
Start display at page:

Transcription

1 Analog Electronic Circuits Professor S. C. Dutta Roy Department of Electrical Engineering Indian Institute of Technology Delhi Lecture no 19 Module no 01 Problem Session 5 on Frequency Response of Small Signal Amplifiers And we have a problem session 5 and Frequency response of small signal amplifier, I shall work out only one problem today just one problem but it is a loaded problem, the problem has a problem okay we will see what this problem is take down with me. (Refer Slide Time: 1:22) There is a V cc V cc what does it mean what kind of transistor? NPN alright smart, a resistance of 2.4 K, we have a transistor as guess it is a PNP, there is a small resistance here 0.1 K as you shall see creates the problem and this is unbypassed this is unbypassed. The output is taken from here through a capacitor which goes to infinity so the output is V 0 and the biasing is done in the usual manner but this resistance R 1 parallel R 2 is much larger than R i, where R i is the input impedance looking into the transistor, which means that R B can be ignored okay, these values are also not given but this is given 0.6K and the voltage source is her V s, the data that are given are that this current is 2.5 milliampere the collector current is 2.5 milliampere DC of course 2.5 milliampere and Beta is given as 150, V sub A is given as infinity which means that r

2 0 is infinity effect of r 0 can be ignored, even with this simplification you will see what the problem is. FT is given as 100 megahertz, you remember what FT is, FT is the transition frequency that is the frequency at which the common emitter short-circuit current application factor reduces to unity okay and C Mu has been measured independently as 0.5 puf this is all the data that is given. What is required is A vs 0 that is the mid band gain to be found out and the high frequency 3 db cut-off point f H, these are only 2 quantities which are to be found out, the simplification looks simple but even then there is a problem as we shall see. V A is the early voltage, you recall r 0 = V A divided by R sub C, is V A is given as infinity that means r 0 goes to infinity okay. (Refer Slide Time: 4:55) Now in in drawing the equivalent circuit we require the value of R Pi, we require the value of g m and therefore the 1st thing we do to solve the problem is to find out g m, g m is 2.5 milliampere that is I sub C divided by 26 millivolts let us take it as 25 to keep life simple okay 25 millivolts and therefore this is 0.1 mho okay. Therefore RFID which is Beta by g m is 150 divided by 0.1 mho which = 1.5 K and C Mu of course has been given as 0.5 puf, we also require the value of C Pi that is one of the ideas I have in mind when picking up this problem, how to calculate C Pi? Now if FT is C 1 you know Omega T which = 2 Pi multiplied by FT, which is 10 to the power 8 hertz this = g m divided by C Pi + C Mu, now g m is known 0.1 mho and C Mu is known 0.5 puf

3 and therefore this relationship gives you the value of C Pi alright the value of C Pi, and C Pi in my calculation comes out as 159 puf it is fairly large value. And we are pretty sure that it is C Pi which will dominate the high frequency 3 db cut-off, no we cannot be sure why not because C Mu will cause Miller effect and C Mu 1 + g m R L prime may be much larger than C Pi so large C Pi does not necessarily mean that C Pi will dominate, C Pi at the most will contribute okay, now let us draw the equivalent circuit. (Refer Slide Time: 7:12) By looking at the original circuit, the equivalent circuit becomes Vs, 0.6 K then R B is negligible effect of R B can be ignored and therefore we shall have R Pi that it is a PNP transistor does not change the equivalent circuit, PNP transistor only means that the biasing has to be done properly okay. The voltage here is V Pi then we have the C Pi this is R s, R Pi is 1.5 K, C Pi is 159 puf then we have the g m V Pi which = 0.1 V Pi alright and r 0 is ignored, is there a load resistance, no everything is same as far as incremental equivalent circuit is concerned it depends on the polarity of V s okay, with this polarity this is the direction, the direction you see directions are not changed this is also one of the points that I wanted to mention. This is only the DC biasing, as far as DC is concerned this equivalent circuit is valid for both PNP as well as NPN okay there is no load but there is a load of 2.4 K this is R sub C and this voltage is V 0 and the complication is this 0.1 K, in addition there is this inevitable C Mu which

4 = 0.5 puf and this resistance is R sub E. Now C 0 is not given so we assume it to be 0 okay, the complication is this we cannot apply miller simplification here that is the problem, we cannot apply Miller simplification miller simplification if R E was = 0 or it was bypassed then it was perfectly alright this would have been the input voltage this is the output voltage so you can find the gain and C Mu 1 + g m R L. Here the gain shall be controlled by R E, not only that what capacitance is reflected shall also be controlled by R E and it is not only capacitance, there would be a resistance of also across it both of which shall be frequency dependent and therefore in this situation we cannot apply miller simplification so what are the alternatives then? What are the alternatives then? One of the alternatives is that you take this load V 1 and this load V 2 and this is V 0, this is V S so you have to write 2 node equations or 3 node equations okay. The 0 is this voltage, we have to write 3 node equations and solve 3 by 3 matrix. Student: Sir, Can you once again please repeat why can we not apply miller simplification? Miller simplification was if you recall C Mu 1 - A v okay this was the miller voltage, what is A v? A v is this output divided by this input. Now the input here is from here to ground not across r Pi, the output is not across g m V Pi it is this and therefore the Miller simplification which was derived on the assumption that R E was bypassed is not true we cannot make that simplification you must recognise this fact. If this was shorted perfectly alright, we could have done that but not otherwise, unfortunately this is the point that I wanted to make. Fortunately there is an alternative technique that is available whenever Miller cannot be used that technique is more general, it can be used always although a fairly rough approximation although a fairly rough approximation. And this simplification I will give the logic later alright 1 st let me say the principle. The principle is as I said in electronic circuits and also in other fields logic can be supplied if the method works some logic can be worked out, logic may not be necessary to workout, if the method works it works that is it okay suppose there is not more than 10 percent deviation we do not care then we do not care. Now the method that is available let me tell you that this is a very simple circuit 1 transistor, a couple of resistors and 2 capacitors have to be taken.

5 Even here we do not want to write the node equation okay because in design on paper and pencil, node equation writing and inversion of matrix is complicated, you can use one of the subroutines one of the algorithms that is available a package like SPICE this is the most commonly used algorithm for this purpose for network analysis but even there conditions the numerical calculations may be ill conditioned and you may not get the result that you want, it has to be applied with precaution and it may not be available, for a simple circuit like this we do not want use SPICE. Now as you go ahead you will receive when 2 transistors are involved if it is a cascade or cascode or some other combination as we shall see later the problem becomes tougher then you have to write 6 to 7 node equations. If it is an integrated circuit card containing some 1000 transistors okay then of course it is an ocean there is nothing that you can do except to go to the computer and believe in that box blindly alright. The problem is very tough in integrated circuit design where indeed there is very large number of transistors, even an Opamp contains as many as 19 to 20 transistors connected in a very complicated manner, you know for biasing you require current mirrors, every transistor will have to have a current mirror unless there is a current repeater then there will be level shifting, there will be power amplification, there will be voltage amplification, there will be buffer, all kinds of things okay. And if you draw the equivalent circuit and try to analyse it by Miller or by some other means, you will go absolutely crazy and therefore but f H and f L that is the gain if I plot it, it would be something like this, there would be a mid-band at which the gain will be nearly constant, we want to know what this frequency is and what this frequency is f H that determines the character of the amplifier, that determines whether the amplifier is suitable or not. For example, if it is an audio amplifier then you want to know if f L is of the order of 16 hertz or no, f H is of the order of 16 kilohertz or no okay this is the range that you want to amplify and you must know what is f L and what is f H is. The problem is the reverse way, you are asked to design an amplifier for the specified f L and f H.

6 (Refer Slide Time: 16:15) Now given an amplifier particularly in multiple transistor circuits as in indicated circuits, this method that I am going to talk about is the only method and many textbooks do not even mention this okay, Burns and Bonds do not mention this so please do follow me carefully. The method is called the method of time constant and we shall use this to solve this circuit. Method of time constant; it can be used to determine f L as well as f H, both f L and f H can be determined by the method of time constant and the method is this. If your problem is to determine f H then identify the capacitors in the circuit identifier capacitors, in this particular case the capacitors are C Pi and C Mu okay. Now assume C Mu to the open and find out the Thevenin s resistance that is seen by C Pi, assume C Mu assume all other capacitors to be open if there are more than 2 assume all capacitors except one to be open and find out across C Pi what is the Thevenin resistance okay, let this resistance be called R Pi, R Pi is not R B parallel small R Pi, here R Pi is the Thevenin resistance seen by C Pi and to distinguish between that R Pi and this R Pi and also to indicate that all other capacitors are open, we use a superscript this is not a power, it is not R Pi to the power to 0, it is R Pi super O okay O for open circuit, not this capacitor but other capacitors. Similarly, you find out you open C Pi and find out what is R Mu o that is the Thevenin resistance or the resistance seen by C Mu. I am mentioning Thevenin because independent sources are eliminated, in this calculation independent sources are eliminated okay.

7 Then after you find these 2 resistors, this will not be very tough this will not be very tough because if it contain some controlled sources and resistors that is all, nothing else no other capacitors and therefore it is a purely resistive circuit and resistive circuit solution is not bad problem at all. So what you do is you find out these 2 time constant Tau Pi o which = V can simply say Tau Pi C Pi R Pi o and Tau Mu time constant which is the product of C Mu and R Mu o, add them to find out Tau which = Tau Pi + Tau Mu and call this Tau H, Pardon me... Student: We put a code Tau Pi. No, I do not have to it is understood, it is understood that time constant is calculated under open circuit condition for all other capacitors. Once you calculate the time constants for the various capacitors there may be more than 2 for example in the ordinary common emitter circuit in shortcircuited emitter resistors there are 3 capacitors; C Pi, C Mu and C 0, fortunately C 0 is not given here we will bring that complication later okay you must follow this carefully because this is the only method available for IC design okay. After calculate the time constants add them up at them up and call the total time constant as Tau H this capital H subscript stands for high frequency okay. (Refer Slide Time: 20:21) Professor student conversation starts

8 Professor: And then Omega H, the high frequency 3 db point in radiance per 2nd is approximately = 1 over Tau H, it could be... Student: Inverted 2 Pi... Professor: Not 2 Pi, 2 Pi will come if we find out f H, f H would be 1 over 2 Pi Tau H okay. Student: Sir, Can you give justification for it? Professor: I will come to the logic later I will come to the logic later, 1st I want to make the calculation then I will supply the logic now please listen to me. Professor student conversation ends If instead of 2 capacitors if it is a complicated circuit with C 1, C 2, C n, n number of capacitors okay maybe 3 transistor circuit we have 9 capacitors then okay. Then what we do is we find out Tau H which = C i, R i o, where i goes from 1 to n alright and then f H = approximately an approximation 2 Pi Tau H okay. Now quickly a look at the logic since the question has been raised a look at the logic. (Refer Slide Time: 22:15) Now if we are calculating high frequency response, each capacitor contributes to a pole each capacitor contributes to a pole and therefore due to n capacitors the high frequency response

9 would be of the form some constant divided by 1 + j Omega by Omega 1 times 1 + j Omega by Omega 2 and so on alright, which can be written as constant divided by this is the logic, logic is also rough the approximation is rough the logic is also not very strict logic okay, so I can write this as 1 + j Omega 1 over Omega over Omega 2 and so on + higher order terms higher order in Omega that is we will have Omega square j Omega cube and so on and so forth alright. And if we ignore if we ignore all these higher-order terms which we usually can do for frequency around Omega H then obviously this can be written approximately as constant divided by 1 + j Omega by Omega H. And obviously Omega H obviously 1 over Omega H is approximately = 1 by Omega by Omega 2 and so on. 1 by Omega H by definition is Tau H and therefore Tau H = Tau 1 + Tau 2 and so on that is the logic. The logic is that you retain only the 1 st order terms in the denominator and neglect the rest. And you remember that when Tau 1 was calculated, the other capacitors were left open and therefore these are all open circuit time constants so I can use the subscript 0 okay these are all open circuit time constants that is all other capacitors are left open. We shall apply it to the circuit that we have already calculated by Miller and also an exact expression and we shall see what kind of an approximation it affords but before that let us complete this example. (Refer Slide Time: 24:53)

10 The equivalent circuit if I draw it once again was 0.6 K yes... Oh I will come to that I will come to that... let me finish this then I will come to assume okay. We have 1.5 K, V Pi, then 159 puf, 0.1 K then 0.1 V Pi that is g m V Pi and 2.4 K, this is V0. Now in order to calculate... Student: C Mu is where? Oh, how could I forget that, I will put it in red because this is the source of all problems, C Mu is 0.5 puf. Now if I want to calculate R Pi o, what I want to do is the resistance seen by 159 puf and therefore what I will do is and we will leave 0.5 picofarad open so let us see what the circuit becomes, also it is the Thevenin s equivalent so therefore V s shall be shorted. (Refer Slide Time: 26:27) So the equivalent circuit determine R Pi o becomes this R Pi o is across C Pi we have a 1.5 K and this is V Pi then we have from here a 0.6 K to ground agreed because V s is shorted Thevenin resistance and we have from here by 0.1 K, then we have from here 0.1 V Pi and we have 2.4 Kalright. Since 2.4 K in in series with a current source it has no effects and therefore I can replace a whole thing whole thing by a current source 0.1 V Pi okay, I can ignore the whole thing the 2.4 K drops out of consideration alright. So what we have to do now is to connect voltage source, I want to calculate this resistance, this resistance cannot be calculated by combination of resistances because there is a controlled source there is a dependent source so what I want to do is I connect a V here and I find the current I and R Pi o shall be V by I okay let

11 me draw this circuit it has become a little messy, let me draw this circuit on a clean slate, this is not a slate, this is a plate (Refer Slide Time: 28:05) 1.5K, this current is I and then we have 0.6 K, 0.1 K, to emphasise that these are connected I am not drawing the ground, I am connecting them together and then we have a current source 0.1, what is V Pi? V Pi is also V so why keep another variable just put V alright so I have to calculate I now these are ways of one has to improvise without writing any loop equation node equation or simultaneous solution one can do it by inspection, what is this current? I V by 1.5 K alright and pardon me... Is that okay then what is this current? I V by 1.5 K V, this current comes here breaks up into 2 parts, one is 0.1 V and the other is this alright. So if I write a loop equation around this, let me use a different colour I want a lighter colour okay around this if I write the loop equation my equation becomes V = drop in 0.6 K, 0.6 K multiplied by I V by 1.5 K alright + the drop in 1 K which would be K multiplied by I V by 1.5 K V alright, is this point clear? This loop equation this equation contains only V and I and therefore we can find out the ratio of V by I and my calculation shows that V by I = K it is only 61 ohms that is what C Pi see alright okay. Then we have to calculate R Mu 0, well that is not all that one has to do is to be careful in drawing the equivalent circuit.

12 (Refer Slide Time: 31:45) If I draw C Mu 0 well R Mu 0, R Mu 0 is across C Mu and C Pi is open and therefore what we have is a 1.5 K V Pi remains, we have a 0.1 K and I will not draw the ground I will show them connected a little later then we have a current generator 0.1 V Pi, now 2.4 K can no longer be ignored, 2.4 K because what you have to do is to connect a voltage source here + - and calculate the current I, is my circuit complete? No, there is a 0.6 K and these come together. What I will do now is to write what we have to find out is V by I and the intermediate variable is V Pi so let us 1st identify the currents. What is this current? Current I comes here and the current that goes here is V Pi divided by 1.5 K, V 5 is no longer = V okay so this current must be I V Pi divided by 1.5 K alright then what is this current? Student: I V Wonderful, how did you calculate this because this current must be I and this current is 0.1 V Pi so this current must be I V Pi outright therefore, we can write a loop equation like this a big loop the outside loop okay, it will be this drop + this drop would be = V. And the other equation that we can write is this loop okay, what about this loop? Take any 2 independent loops, you cannot write this loop because there is a current generator here you must be careful about this okay, we do not know what the drop across this is so I cannot write KVL here okay so the only other loop that is available to me is this for which I know this current okay I know this voltage

13 this voltage across 0.6 K this would be the voltage across this which is V Pi + the voltage across this now therefore I have to find the current, what is this current? Okay by 1.5 K times V Pi so we know this current no... You must be careful about the scale, what is the unit of this 0.1? mho, and therefore when you write 1.5 do not write 1 by 1.5 it that will be absolutely wrong, it is 1 by 1500 mhos okay that is why I am retaining the dimension, ultimately when you solve you do that. So you write 2 loop equations from which you eliminate V Pi this algebra I leave to you, my calculation gives R Mu 0, if there is any equation now ask me you may not get another problem of this type I mean I may not solve another problem of this type. Student: (())(35:31) (Refer Slide Time: 35:58) Oh because the 1st loop contains V Pi, V and I do not want V Pi, I want only the ratio V by I so I need a 2nd loop to eliminate V Pi alright and my value comes R Mu o as 15.5K therefore the total Tau, Tau H which = Tau Pi o + Tau Mu o that = 0.061K multiplied by 159 puf, what would be the unit of this? 10 to the 9 which is nanoseconds so this would be in time it is nano second K multiplied by 0.5 so many nanoseconds ns and therefore f H which = 1 over 2 Pi Tau = 9.11 megahertz it is a good amplifier it goes right up to 9.11 megahertz. And as far as the other part of the problem was to find out A vs o the mid band gain well, that should be simple mid

14 band gain you ignore all the capacitors, draw the equivalent circuit let me do it, I will tell you what the value is. (Refer Slide Time: 37:12) My equivalent circuit for A vs o is V s, 0.6 K, 1.5 K, this is V Pi, 0.1 K, we have already done it I suppose we must have done it is this unbypassed resistor unbypassed okay approximately we want the exact gain oh that is a good clue, what should what is the gain that you expect? divided 0.2 which is 20 okay now see what happens here, this is 2.4 K and this is V 0 can you solve it by inspection? Yes there is nothing much you see this is Beta + 1 by R Pi this is over 1.5 K V Pi this current and then you can write the loop equation, find out V Pi and the output voltage V 0 is V Pi multiplied by 2.4 K so you can find out, this is almost by inspection the value comes as 20.9 the approximate value was 24 it is not too bad it is not too bad, so this calculation I leave it to you.

15 (Refer Slide Time: 39:11) Now the other part of the calculation well let me illustrate this principle so that it sticks to your mind by considering the common emitter amplifier with bypassed R E, let us see what happens there if we apply the same principle. With bypassed R E the ordinary C E amplifier at high frequencies you have V s, R s, then you have R Pi which is the parallel combination of R B and r Pi, this is V Pi and then you have C Pi, C Mu, no Miller I am trying to calculate by the method of open circuit time constant now I shall put an adjective open circuit because in the low frequency case it will be the short-circuit time constant. Now let us see C Mu you have g m V Pi, now there is no problem in incorporating r 0 and therefore we say R L prime which is the parallel combination of small r 0, R sub C and R sub L and then of course you have the output capacitance C0, this is V0 okay. Now to calculate, a couple of things we can calculate directly you can see directly what these are for example, what is R o o that is what is the resistance seen by C o? Simply R L prime agreed because there is a current generator and this voltage is 0 A vs is 0 okay however, the other 2 are not obvious. To calculate R Pi no... We also know what C Pi sees, what does C Pi sees? Student: R pi parallel R s. Professor: That is right R Pi parallel R s that is right it is only C Mu that gives us the problem let us see what this problem is.

16 (Refer Slide Time: 41:15) From C Mu you calculate you find out V and find the current I, this is the terminal of C Mu, V Pi is open so you have R Pi what is this resistance? R Pi parallel R s, and on the other side this is V Pi on the other side you have g m V Pi in parallel with R L prime so that is not too bad, you can see that V Pi is simply I times what is this resistance? R Pi o so V Pi is I times R Pi o and this is g m V Pi, this is R L prime so it is not difficult to find out what the current is you have to write one equation that is all okay, let me leave this calculation to you, you can show that R Mu o = R Pi o + R L prime 1 + g m R Pi o, I hope I am right R Pi + R L prime or I can write it the other way round, I can also write this as R L prime + R Pi o 1 + g m R L prime, this is simple circuit analysis so I will skip this. After you find out the 3 resistances then your Tau H pardon me... Well, let us go directly to Omega H. Omega H becomes R Pi parallel R s times if you add them up see I wanted to write in this form why? Because I have this g m R L prime here so I will multiply this by C Mu okay and you can see that C Mu 1 + g m R L prime that C M the Miller capacitance come okay that is why I wanted to write this in this form alright. Student: Sir what is R L prime? Professor: R L prime is the parallel combination of small r 0, R C and R L. Student: In the question we do not have any R L.

17 Professor: We are not doing any equation we have gone to the ordinary common emitter amplifier with bypassed R E, I wanted to show that the method of time constant open circuit time constant works here also okay. (Refer Slide Time: 44:11) So if you add them up and take the reciprocal this is the result that you get; C T + C 0 + C Mu R L prime. If you recall the exact analysis that we had done for the same circuit, our expression was from exact analysis node analysis our expression was g m R L prime let me recall R Pi divided by R Pi + R s times 1 j Omega divided by g m over C Mu divided by, you recall this we had put th= Omega 3 and we said Omega C is very large therefore we shall ignore this term so this calculates this qualifies is the A vs 0 and in the denominator we had 1 + j Omega multiplied by R Pi parallel R s C T + exactly this expression C 0 + C Mu R L prime then Omega square and Omega square term R L prime et cetera et cetera. And we have said that usually this term can be ignored and therefore Omega H is the reciprocal of this quantity. Do not you see that the method of open circuit time constant gives exactly the same result, is not Miller, what does Miller give? What does Miller approximation give? Miller gives only this part, Miller gives R pi parallel R s multiplied by C T alright so the 3 approaches are quite similar and it brings in confidence by the method of open circuit time constant perhaps is a bit better than Miller approximation. However, if Miller approximation can be applied we do not go to method of time constant because that is a bit time consuming method of open circuit time constant is a

18 bit time consuming have to calculate R Pi 0, R Mu 0, R L0 okay then add them up and then take the reciprocal, if Miller is available nothing else is required okay and you see the results are not far from the exact values. (Refer Slide Time: 47:33) Now about the low frequency response okay, in the low frequency response let me 1 st give the logic alright. In the low frequency response, the response will be of the form constant divided by 1 - j Omega 1 by Omega so at DC = the value = 0, then we have 1 j Omega 2 by Omega and in addition we had a factor of... Due to C E we had 1 + j Omega by Omega 3 and 1 + j Omega by Omega 4. First let us look at this term let us look at this term due to C E, now you know which one is greater Omega 3 or Omega 4? Omega 3 is much greater than Omega 4 well above 50 times so I can write this 1 + j Omega by Omega divided by 1 + j these are some tricks of the traits usually not mentioned in books okay, there is only a C Mu who will tell you do remember. I can write this as let us multiply both numerator and denominator by Omega 3 by j Omega let us do that, if I do that than in the denominator what do I get? I multiply by Omega 3 by j Omega so I get 1 j Omega 3 by Omega alright and if I multiply the numerator by Omega 3 by j Omega then I get Omega 3 by j Omega + what do I get? Omega 3 by Omega 4 agreed is the point clear? Student: No.

19 Professor: No... What is the problem? I multiplied this, I multiplied this both numerator and denominator okay. Now notice the trick, notice that around Omega 3 around Omega 3 this term magnitude is approximately unity whereas this is approximately 50 and therefore I can write this as approximately a constant, it is this frequency which are of concern a constant divided by 1 j Omega 3 by mega. Why is the largest frequency of concern? Because we are calculate thing the low frequency response, the largest frequency determines the low frequency response. So even if C E gives a kind of a low pass combination with high pass and as I had mentioned the characteristics is like this, we can approximate it by a high pass characteristics like this goes to 0, this is what we have done here agreed. (Refer Slide Time: 50:28) So my low frequency transfer functions would be of this form 1 j Omega 2 by mega, 1 j Omega 3 by Omega approximately and I can write this as constant divided by 1 j by Omega mega 1 + Omega 2 + Omega 3 + higher order terms, which diminish as Omega increases alright and if we want to calculate f L which will be dominated by this term obviously if we ignore this I can write this as constant divided by 1 j Omega L by Omega, and Omega L therefore is simply the sum of the 3 poles.

20 (Refer Slide Time: 51:33) That is Omega L = submission Omega i, i = 1 to 3 in terms of time constant 1 over Tau L = submission i = 1 to 3 1 over Tau i. In the previous case in the high frequency case the time constant were added, now the reciprocals of the time constants are added okay the reciprocals of time constant and f L is simply = 1 over twice Pi Tau alright. Now under what conditions will these time constants be calculated, obviously short-circuit and therefore these time constants are written with a superscript of infinity, short-circuit means the capacitors are infinite or capacitors are shorted, in the previous case capacitors were open, this is also the only method that is available for a very complicated circuit engineering method engineer s approximation. These resistances as I said can be calculated almost by inspection and therefore this gives a quick calculation and this method is known as the method of short-circuit time constant. We shall apply both these methods when we come to complicated circuit that is Cascade, Cascode and dialling tone connection and CB-CC, CB-CE all-time the connections when you consider wide banding techniques and that is the point to stop today.

### (Refer Slide Time: 1:41)

Analog Electronic Circuits Professor S. C. Dutta Roy Department of Electrical Engineering Indian Institute of Technology Delhi Lecture no 13 Module no 01 Midband Analysis of CB and CC Amplifiers We are

### (Refer Slide Time: 1:49)

Analog Electronic Circuits Professor S. C. Dutta Roy Department of Electrical Engineering Indian Institute of Technology Delhi Lecture no 14 Module no 01 Midband analysis of FET Amplifiers (Refer Slide

### Basic Electronics Prof. Dr. Chitralekha Mahanta Department of Electronics and Communication Engineering Indian Institute of Technology, Guwahati

Basic Electronics Prof. Dr. Chitralekha Mahanta Department of Electronics and Communication Engineering Indian Institute of Technology, Guwahati Module: 2 Bipolar Junction Transistors Lecture-4 Biasing

### (Refer Time Slide: 1:35)

Analog Electronic Circuits Prof. S. C. Dutta Roy Department of Electrical Engineering. Indian Institute of Technology Delhi Lecture No 04 Problem Session 1 On DC Analysis of BJT Circuits This is the fourth

### Circuit Theory Prof. S.C. Dutta Roy Department of Electrical Engineering Indian Institute of Technology, Delhi

Circuit Theory Prof. S.C. Dutta Roy Department of Electrical Engineering Indian Institute of Technology, Delhi Lecture - 43 RC and RL Driving Point Synthesis People will also have to be told I will tell,

### Circuit Theory Prof. S.C. Dutta Roy Department of Electrical Engineering Indian Institute of Technology, Delhi

Circuit Theory Prof. S.C. Dutta Roy Department of Electrical Engineering Indian Institute of Technology, Delhi Lecture - 1 Review of Signals and Systems Welcome to this course E E 202 circuit theory 4

### Analog Integrated Circuit Design Prof. Nagendra Krishnapura Department of Electrical Engineering Indian Institute of Technology, Madras

Analog Integrated Circuit Design Prof. Nagendra Krishnapura Department of Electrical Engineering Indian Institute of Technology, Madras Lecture No - 42 Fully Differential Single Stage Opamp Hello and welcome

### Communication Engineering Prof. Surendra Prasad Department of Electrical Engineering Indian Institute of Technology, Delhi

Communication Engineering Prof. Surendra Prasad Department of Electrical Engineering Indian Institute of Technology, Delhi Lecture - 41 Pulse Code Modulation (PCM) So, if you remember we have been talking

### Energy Resources and Technology Prof. S. Banerjee Department of Electrical Engineering Indian Institute of Technology - Kharagpur

Energy Resources and Technology Prof. S. Banerjee Department of Electrical Engineering Indian Institute of Technology - Kharagpur Lecture - 39 Magnetohydrodynamic Power Generation (Contd.) Let us start

### Electronics for Analog Signal Processing - II Prof. K. Radhakrishna Rao Department of Electrical Engineering Indian Institute of Technology Madras

Electronics for Analog Signal Processing - II Prof. K. Radhakrishna Rao Department of Electrical Engineering Indian Institute of Technology Madras Lecture - 14 Oscillators Let us consider sinusoidal oscillators.

### Operational amplifiers (Op amps)

Operational amplifiers (Op amps) Recall the basic two-port model for an amplifier. It has three components: input resistance, Ri, output resistance, Ro, and the voltage gain, A. v R o R i v d Av d v Also

### Introductory Quantum Chemistry Prof. K. L. Sebastian Department of Inorganic and Physical Chemistry Indian Institute of Science, Bangalore

Introductory Quantum Chemistry Prof. K. L. Sebastian Department of Inorganic and Physical Chemistry Indian Institute of Science, Bangalore Lecture - 4 Postulates Part 1 (Refer Slide Time: 00:59) So, I

### Ordinary Differential Equations Prof. A. K. Nandakumaran Department of Mathematics Indian Institute of Science Bangalore

Ordinary Differential Equations Prof. A. K. Nandakumaran Department of Mathematics Indian Institute of Science Bangalore Module - 3 Lecture - 10 First Order Linear Equations (Refer Slide Time: 00:33) Welcome

### BASIC ELECTRONICS PROF. T.S. NATARAJAN DEPT OF PHYSICS IIT MADRAS LECTURE-3 ELECTRONIC DEVICES -II RESISTOR SERIES & PARALLEL

BASIC ELECTRONICS PROF. T.S. NATARAJAN DEPT OF PHYSICS IIT MADRAS LECTURE-3 ELECTRONIC DEVICES -II RESISTOR SERIES & PARALLEL Hello everybody we are doing a course on basic electronics by the method of

### Hydraulics Prof Dr Arup Kumar Sarma Department of Civil Engineering Indian Institute of Technology, Guwahati

Hydraulics Prof Dr Arup Kumar Sarma Department of Civil Engineering Indian Institute of Technology, Guwahati Module No # 08 Pipe Flow Lecture No # 04 Pipe Network Analysis Friends, today we will be starting

### (Refer Slide Time: 00:01:30 min)

Control Engineering Prof. M. Gopal Department of Electrical Engineering Indian Institute of Technology, Delhi Lecture - 3 Introduction to Control Problem (Contd.) Well friends, I have been giving you various

### Networks and Systems Prof. V. G. K. Murti Department of Electrical Engineering Indian Institute of Technology, Madras

Networks and Systems Prof. V. G. K. Murti Department of Electrical Engineering Indian Institute of Technology, Madras Lecture - 34 Network Theorems (1) Superposition Theorem Substitution Theorem The next

### (Refer Slide Time: 02:11 to 04:19)

Digital Signal Processing Prof. S. C. Dutta Roy Department of Electrical Engineering Indian Institute of Technology, Delhi Lecture - 24 Analog Chebyshev LPF Design This is the 24 th lecture on DSP and

### Circuits for Analog System Design Prof. Gunashekaran M K Center for Electronics Design and Technology Indian Institute of Science, Bangalore

Circuits for Analog System Design Prof. Gunashekaran M K Center for Electronics Design and Technology Indian Institute of Science, Bangalore Lecture No. # 08 Temperature Indicator Design Using Op-amp Today,

### Antennas Prof. Girish Kumar Department of Electrical Engineering Indian Institute of Technology, Bombay. Module 02 Lecture 08 Dipole Antennas-I

Antennas Prof. Girish Kumar Department of Electrical Engineering Indian Institute of Technology, Bombay Module 02 Lecture 08 Dipole Antennas-I Hello, and welcome to today s lecture. Now in the last lecture

### Modern Algebra Prof. Manindra Agrawal Department of Computer Science and Engineering Indian Institute of Technology, Kanpur

Modern Algebra Prof. Manindra Agrawal Department of Computer Science and Engineering Indian Institute of Technology, Kanpur Lecture 02 Groups: Subgroups and homomorphism (Refer Slide Time: 00:13) We looked

### Networks and Systems Prof. V. G. K. Murti Department of Electrical Engineering Indian Institution of Technology, Madras

Networks and Systems Prof. V. G. K. Murti Department of Electrical Engineering Indian Institution of Technology, Madras Lecture - 32 Network Function (3) 2-port networks: Symmetry Equivalent networks Examples

### (Refer Slide Time: 1:42)

Control Engineering Prof. Madan Gopal Department of Electrical Engineering Indian Institute of Technology, Delhi Lecture - 21 Basic Principles of Feedback Control (Contd..) Friends, let me get started

### Electronics Prof. D C Dube Department of Physics Indian Institute of Technology Delhi

Electronics Prof. D C Dube Department of Physics Indian Institute of Technology Delhi Module No. 07 Differential and Operational Amplifiers Lecture No. 39 Summing, Scaling and Averaging Amplifiers (Refer

### Dynamics of Ocean Structures Prof. Dr Srinivasan Chandrasekaran Department of Ocean Engineering Indian Institute of Technology, Madras

Dynamics of Ocean Structures Prof. Dr Srinivasan Chandrasekaran Department of Ocean Engineering Indian Institute of Technology, Madras Module - 1 Lecture - 7 Duhamel's Integrals (Refer Slide Time: 00:14)

### (Refer Slide Time: 2:11)

Control Engineering Prof. Madan Gopal Department of Electrical Engineering Indian institute of Technology, Delhi Lecture - 40 Feedback System Performance based on the Frequency Response (Contd.) The summary

### (Refer Slide Time: 03:41)

Solid State Devices Dr. S. Karmalkar Department of Electronics and Communication Engineering Indian Institute of Technology, Madras Lecture - 25 PN Junction (Contd ) This is the 25th lecture of this course

### Chapter 2. - DC Biasing - BJTs

Chapter 2. - DC Biasing - BJTs Objectives To Understand : Concept of Operating point and stability Analyzing Various biasing circuits and their comparison with respect to stability BJT A Review Invented

### Section 5.4 BJT Circuits at DC

12/3/2004 section 5_4 JT Circuits at DC 1/1 Section 5.4 JT Circuits at DC Reading Assignment: pp. 421-436 To analyze a JT circuit, we follow the same boring procedure as always: ASSUME, ENFORCE, ANALYZE

### Basic Quantum Mechanics Prof. Ajoy Ghatak Department of Physics Indian Institute of Technology, Delhi

Basic Quantum Mechanics Prof. Ajoy Ghatak Department of Physics Indian Institute of Technology, Delhi Module No. # 07 Bra-Ket Algebra and Linear Harmonic Oscillator II Lecture No. # 02 Dirac s Bra and

### Series, Parallel, and other Resistance

EELE 2310 Analysis Lecture 3 Equivalent s Series, Parallel, Delta-to-Wye, Voltage Divider and Current Divider Rules Dr Hala El-Khozondar Series, Parallel, and other Resistance Equivalent s ١ Overview Series,

### Design and Optimization of Energy Systems Prof. C. Balaji Department of Mechanical Engineering Indian Institute of Technology, Madras

Design and Optimization of Energy Systems Prof. C. Balaji Department of Mechanical Engineering Indian Institute of Technology, Madras Lecture - 31 Fibonacci search method So, I am continuing with our treatment

### Analog Circuits Prof. Jayanta Mukherjee Department of Electrical Engineering Indian Institute of Technology - Bombay

Analog Circuits Prof. Jayanta Mukherjee Department of Electrical Engineering Indian Institute of Technology - Bombay Week 05 Module - 05 Tutorial No.4 Welcome everyone my name is Basudev Majumder, I am

### Hydrostatics and Stability Dr. Hari V Warrior Department of Ocean Engineering and Naval Architecture Indian Institute of Technology, Kharagpur

Hydrostatics and Stability Dr. Hari V Warrior Department of Ocean Engineering and Naval Architecture Indian Institute of Technology, Kharagpur Module No. # 01 Lecture No. # 09 Free Surface Effect In the

### D is the voltage difference = (V + - V - ).

1 Operational amplifier is one of the most common electronic building blocks used by engineers. It has two input terminals: V + and V -, and one output terminal Y. It provides a gain A, which is usually

### In this lecture, we will consider how to analyse an electrical circuit by applying KVL and KCL. As a result, we can predict the voltages and currents

In this lecture, we will consider how to analyse an electrical circuit by applying KVL and KCL. As a result, we can predict the voltages and currents around an electrical circuit. This is a short lecture,

### Low Power VLSI Circuits and Systems Prof. Ajit Pal Department of Computer Science and Engineering Indian Institute of Technology, Kharagpur

Low Power VLSI Circuits and Systems Prof. Ajit Pal Department of Computer Science and Engineering Indian Institute of Technology, Kharagpur Lecture No. # 08 MOS Inverters - III Hello, and welcome to today

### Power System Operations and Control Prof. S.N. Singh Department of Electrical Engineering Indian Institute of Technology, Kanpur. Module 3 Lecture 8

Power System Operations and Control Prof. S.N. Singh Department of Electrical Engineering Indian Institute of Technology, Kanpur Module 3 Lecture 8 Welcome to lecture number 8 of module 3. In the previous

### MITOCW ocw f99-lec05_300k

MITOCW ocw-18.06-f99-lec05_300k This is lecture five in linear algebra. And, it will complete this chapter of the book. So the last section of this chapter is two point seven that talks about permutations,

### Biasing BJTs CHAPTER OBJECTIVES 4.1 INTRODUCTION

4 DC Biasing BJTs CHAPTER OBJECTIVES Be able to determine the dc levels for the variety of important BJT configurations. Understand how to measure the important voltage levels of a BJT transistor configuration

### Advanced Structural Analysis Prof. Devdas Menon Department of Civil Engineering Indian Institute of Technology, Madras

Advanced Structural Analysis Prof. Devdas Menon Department of Civil Engineering Indian Institute of Technology, Madras Module - 4.3 Lecture - 24 Matrix Analysis of Structures with Axial Elements (Refer

### Dynamics of Ocean Structures Prof. Dr. Srinivasan Chandrasekaran Department of Ocean Engineering Indian Institute of Technology, Madras

Dynamics of Ocean Structures Prof. Dr. Srinivasan Chandrasekaran Department of Ocean Engineering Indian Institute of Technology, Madras Lecture 25 Continuous System In the last class, in this, we will

### Real Analysis Prof. S.H. Kulkarni Department of Mathematics Indian Institute of Technology, Madras. Lecture - 13 Conditional Convergence

Real Analysis Prof. S.H. Kulkarni Department of Mathematics Indian Institute of Technology, Madras Lecture - 13 Conditional Convergence Now, there are a few things that are remaining in the discussion

### Lecture 7: Transistors and Amplifiers

Lecture 7: Transistors and Amplifiers Hybrid Transistor Model for small AC : The previous model for a transistor used one parameter (β, the current gain) to describe the transistor. doesn't explain many

### Electronic Circuits 1. Transistor Devices. Contents BJT and FET Characteristics Operations. Prof. C.K. Tse: Transistor devices

Electronic Circuits 1 Transistor Devices Contents BJT and FET Characteristics Operations 1 What is a transistor? Three-terminal device whose voltage-current relationship is controlled by a third voltage

### (Refer Slide Time: )

Digital Signal Processing Prof. S. C. Dutta Roy Department of Electrical Engineering Indian Institute of Technology, Delhi FIR Lattice Synthesis Lecture - 32 This is the 32nd lecture and our topic for

### Chapter 2 - DC Biasing - BJTs

Objectives Chapter 2 - DC Biasing - BJTs To Understand: Concept of Operating point and stability Analyzing Various biasing circuits and their comparison with respect to stability BJT A Review Invented

### Instructor (Brad Osgood)

TheFourierTransformAndItsApplications-Lecture26 Instructor (Brad Osgood): Relax, but no, no, no, the TV is on. It's time to hit the road. Time to rock and roll. We're going to now turn to our last topic

### Quantum Field Theory Prof. Dr. Prasanta Kumar Tripathy Department of Physics Indian Institute of Technology, Madras

Quantum Field Theory Prof. Dr. Prasanta Kumar Tripathy Department of Physics Indian Institute of Technology, Madras Module - 1 Free Field Quantization Scalar Fields Lecture - 4 Quantization of Real Scalar

### Special Theory Of Relativity Prof. Shiva Prasad Department of Physics Indian Institute of Technology, Bombay

Special Theory Of Relativity Prof. Shiva Prasad Department of Physics Indian Institute of Technology, Bombay Lecture - 6 Length Contraction and Time Dilation (Refer Slide Time: 00:29) In our last lecture,

### Chemical Applications of Symmetry and Group Theory Prof. Manabendra Chandra Department of Chemistry Indian Institute of Technology, Kanpur.

Chemical Applications of Symmetry and Group Theory Prof. Manabendra Chandra Department of Chemistry Indian Institute of Technology, Kanpur Lecture 08 Hello and welcome to the day 3 of the second week of

### Physics I: Oscillations and Waves Prof. S. Bharadwaj Department of Physics and Meteorology. Indian Institute of Technology, Kharagpur

Physics I: Oscillations and Waves Prof. S. Bharadwaj Department of Physics and Meteorology Indian Institute of Technology, Kharagpur Lecture No 03 Damped Oscillator II We were discussing, the damped oscillator

### (Refer Slide Time: 1:13)

Linear Algebra By Professor K. C. Sivakumar Department of Mathematics Indian Institute of Technology, Madras Lecture 6 Elementary Matrices, Homogeneous Equaions and Non-homogeneous Equations See the next

### Semiconductor Optoelectronics Prof. M. R. Shenoy Department of physics Indian Institute of Technology, Delhi

Semiconductor Optoelectronics Prof. M. R. Shenoy Department of physics Indian Institute of Technology, Delhi Lecture - 18 Optical Joint Density of States So, today we will discuss the concept of optical

### Computational Techniques Prof. Dr. Niket Kaisare Department of Chemical Engineering Indian Institute of Technology, Madras

Computational Techniques Prof. Dr. Niket Kaisare Department of Chemical Engineering Indian Institute of Technology, Madras Module No. # 07 Lecture No. # 05 Ordinary Differential Equations (Refer Slide

### Lecture 24 Multistage Amplifiers (I) MULTISTAGE AMPLIFIER

Lecture 24 Multistage Amplifiers (I) MULTISTAGE AMPLIFIER Outline. Introduction 2. CMOS multi-stage voltage amplifier 3. BiCMOS multistage voltage amplifier 4. BiCMOS current buffer 5. Coupling amplifier

### Dynamics of Ocean Structures Prof. Dr. Srinivasan Chandrasekaran Department of Ocean Engineering Indian Institute of Technology, Madras

Dynamics of Ocean Structures Prof. Dr. Srinivasan Chandrasekaran Department of Ocean Engineering Indian Institute of Technology, Madras Module - 1 Lecture - 20 Orthogonality of modes (Refer Slide Time:

### Chapter 5. BJT AC Analysis

Chapter 5. Outline: The r e transistor model CB, CE & CC AC analysis through r e model common-emitter fixed-bias voltage-divider bias emitter-bias & emitter-follower common-base configuration Transistor

### Algebra Year 10. Language

Algebra Year 10 Introduction In Algebra we do Maths with numbers, but some of those numbers are not known. They are represented with letters, and called unknowns, variables or, most formally, literals.

### MITOCW MITRES18_005S10_DiffEqnsMotion_300k_512kb-mp4

MITOCW MITRES18_005S10_DiffEqnsMotion_300k_512kb-mp4 PROFESSOR: OK, this lecture, this day, is differential equations day. I just feel even though these are not on the BC exams, that we've got everything

### ESE319 Introduction to Microelectronics. BJT Biasing Cont.

BJT Biasing Cont. Biasing for DC Operating Point Stability BJT Bias Using Emitter Negative Feedback Single Supply BJT Bias Scheme Constant Current BJT Bias Scheme Rule of Thumb BJT Bias Design 1 Simple

### ESE319 Introduction to Microelectronics Bode Plot Review High Frequency BJT Model

Bode Plot Review High Frequency BJT Model 1 Logarithmic Frequency Response Plots (Bode Plots) Generic form of frequency response rational polynomial, where we substitute jω for s: H s=k sm a m 1 s m 1

### Chemical Applications of Symmetry and Group Theory Prof. Manabendra Chandra Department of Chemistry Indian Institute of Technology, Kanpur

Chemical Applications of Symmetry and Group Theory Prof. Manabendra Chandra Department of Chemistry Indian Institute of Technology, Kanpur Lecture - 09 Hello, welcome to the day 4 of our second week of

### Notes for course EE1.1 Circuit Analysis TOPIC 10 2-PORT CIRCUITS

Objectives: Introduction Notes for course EE1.1 Circuit Analysis 4-5 Re-examination of 1-port sub-circuits Admittance parameters for -port circuits TOPIC 1 -PORT CIRCUITS Gain and port impedance from -port

### Bipolar Junction Transistor (BJT) - Introduction

Bipolar Junction Transistor (BJT) - Introduction It was found in 1948 at the Bell Telephone Laboratories. It is a three terminal device and has three semiconductor regions. It can be used in signal amplification

### Chapter 1 Review of Equations and Inequalities

Chapter 1 Review of Equations and Inequalities Part I Review of Basic Equations Recall that an equation is an expression with an equal sign in the middle. Also recall that, if a question asks you to solve

### CHAPTER.4: Transistor at low frequencies

CHAPTER.4: Transistor at low frequencies Introduction Amplification in the AC domain BJT transistor modeling The re Transistor Model The Hybrid equivalent Model Introduction There are three models commonly

### Foundation Engineering Dr. Priti Maheshwari Department Of Civil Engineering Indian Institute Of Technology, Roorkee

Foundation Engineering Dr. Priti Maheshwari Department Of Civil Engineering Indian Institute Of Technology, Roorkee Module - 02 Lecture - 15 Machine Foundations - 3 Hello viewers, In the last class we

### (Refer Slide Time: 01:30)

Networks and Systems Prof V.G K.Murti Department of Electrical Engineering Indian Institute of Technology, Madras Lecture - 11 Fourier Series (5) Continuing our discussion of Fourier series today, we will

### Analog Circuits Prof. Jayanta Mukherjee Department of Electrical Engineering Indian Institute of Technology -Bombay

Analog Circuits Prof. Jayanta Mukherjee Department of Electrical Engineering Indian Institute of Technology -Bombay Week -01 Module -05 Inverting amplifier and Non-inverting amplifier Welcome to another

### CE/CS Amplifier Response at High Frequencies

.. CE/CS Amplifier Response at High Frequencies INEL 4202 - Manuel Toledo August 20, 2012 INEL 4202 - Manuel Toledo CE/CS High Frequency Analysis 1/ 24 Outline.1 High Frequency Models.2 Simplified Method.3

### Communication Engineering Prof. Surendra Prasad Department of Electrical Engineering Indian Institute of Technology, Delhi

Communication Engineering Prof. Surendra Prasad Department of Electrical Engineering Indian Institute of Technology, Delhi Lecture - 3 Brief Review of Signals and Systems My subject for today s discussion

### Multistage Amplifier Frequency Response

Multistage Amplifier Frequency Response * Summary of frequency response of single-stages: CE/CS: suffers from Miller effect CC/CD: wideband -- see Section 0.5 CB/CG: wideband -- see Section 0.6 (wideband

### Plantwide Control of Chemical Processes Prof. Nitin Kaistha Department of Chemical Engineering Indian Institute of Technology, Kanpur

Plantwide Control of Chemical Processes Prof. Nitin Kaistha Department of Chemical Engineering Indian Institute of Technology, Kanpur Lecture - 41 Cumene Process Plantwide Control (Refer Slide Time: 00:18)

### VI. Transistor amplifiers: Biasing and Small Signal Model

VI. Transistor amplifiers: iasing and Small Signal Model 6.1 Introduction Transistor amplifiers utilizing JT or FET are similar in design and analysis. Accordingly we will discuss JT amplifiers thoroughly.

### Semiconductor Optoelectronics Prof. M. R. Shenoy Department of Physics Indian Institute of Technology, Delhi

Semiconductor Optoelectronics Prof. M. R. Shenoy Department of Physics Indian Institute of Technology, Delhi Lecture - 20 Amplification by Stimulated Emission (Refer Slide Time: 00:37) So, we start today

### Lecture - 30 Stationary Processes

Probability and Random Variables Prof. M. Chakraborty Department of Electronics and Electrical Communication Engineering Indian Institute of Technology, Kharagpur Lecture - 30 Stationary Processes So,

### Basics Quantum Mechanics Prof. Ajoy Ghatak Department of physics Indian Institute of Technology, Delhi

Basics Quantum Mechanics Prof. Ajoy Ghatak Department of physics Indian Institute of Technology, Delhi Module No. # 03 Linear Harmonic Oscillator-1 Lecture No. # 04 Linear Harmonic Oscillator (Contd.)

### Quadratic Equations Part I

Quadratic Equations Part I Before proceeding with this section we should note that the topic of solving quadratic equations will be covered in two sections. This is done for the benefit of those viewing

### Electromagnetic Theory Prof. D. K. Ghosh Department of Physics Indian Institute of Technology, Bombay

Electromagnetic Theory Prof. D. K. Ghosh Department of Physics Indian Institute of Technology, Bombay Module - 4 Time Varying Field Lecture - 30 Maxwell s Equations In the last lecture we had introduced

### Power System Engineering Prof. Debapriya Das Department of Electrical Engineering Indian Institute of Technology, Kharagpur

Power System Engineering Prof. Debapriya Das Department of Electrical Engineering Indian Institute of Technology, Kharagpur Lecture 41 Application of capacitors in distribution system (Contd.) (Refer Slide

### MITOCW ocw f99-lec09_300k

MITOCW ocw-18.06-f99-lec09_300k OK, this is linear algebra lecture nine. And this is a key lecture, this is where we get these ideas of linear independence, when a bunch of vectors are independent -- or

### Homework Assignment 08

Homework Assignment 08 Question 1 (Short Takes) Two points each unless otherwise indicated. 1. Give one phrase/sentence that describes the primary advantage of an active load. Answer: Large effective resistance

### EE105 Fall 2015 Microelectronic Devices and Circuits Frequency Response. Prof. Ming C. Wu 511 Sutardja Dai Hall (SDH)

EE05 Fall 205 Microelectronic Devices and Circuits Frequency Response Prof. Ming C. Wu wu@eecs.berkeley.edu 5 Sutardja Dai Hall (SDH) Amplifier Frequency Response: Lower and Upper Cutoff Frequency Midband

### Homework Assignment 09

Homework Assignment 09 Question 1 (Short Takes) Two points each unless otherwise indicated. 1. What is the 3-dB bandwidth of the amplifier shown below if r π = 2.5K, r o = 100K, g m = 40 ms, and C L =

### EIT Review. Electrical Circuits DC Circuits. Lecturer: Russ Tatro. Presented by Tau Beta Pi The Engineering Honor Society 10/3/2006 1

EIT Review Electrical Circuits DC Circuits Lecturer: Russ Tatro Presented by Tau Beta Pi The Engineering Honor Society 10/3/2006 1 Session Outline Basic Concepts Basic Laws Methods of Analysis Circuit

### Tutorial #4: Bias Point Analysis in Multisim

SCHOOL OF ENGINEERING AND APPLIED SCIENCE DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING ECE 2115: ENGINEERING ELECTRONICS LABORATORY Tutorial #4: Bias Point Analysis in Multisim INTRODUCTION When BJTs

### Computational Techniques Prof. Dr. Niket Kaisare Department of Chemical Engineering Indian Institute of Technology, Madras

Computational Techniques Prof. Dr. Niket Kaisare Department of Chemical Engineering Indian Institute of Technology, Madras Module No. # 07 Lecture No. # 04 Ordinary Differential Equations (Initial Value

### Dynamics of Ocean Structures Prof. Dr. Srinivasan Chandrasekaran Department of Ocean Engineering Indian Institute of Technology, Madras

Dynamics of Ocean Structures Prof. Dr. Srinivasan Chandrasekaran Department of Ocean Engineering Indian Institute of Technology, Madras Module - 1 Lecture - 10 Methods of Writing Equation of Motion (Refer

### Whereas the diode was a 1-junction device, the transistor contains two junctions. This leads to two possibilities:

Part Recall: two types of charge carriers in semiconductors: electrons & holes two types of doped semiconductors: n-type (favor e-), p-type (favor holes) for conduction Whereas the diode was a -junction

### Electric Circuits Part 2: Kirchhoff s Rules

Electric Circuits Part 2: Kirchhoff s Rules Last modified: 31/07/2018 Contents Links Complex Circuits Applying Kirchhoff s Rules Example Circuit Labelling the currents Kirchhoff s First Rule Meaning Kirchhoff

### Plasma Physics Prof. V. K. Tripathi Department of Physics Indian Institute of Technology, Delhi

Plasma Physics Prof. V. K. Tripathi Department of Physics Indian Institute of Technology, Delhi Module No. # 01 Lecture No. # 22 Adiabatic Invariance of Magnetic Moment and Mirror Confinement Today, we

### Basic Quantum Mechanics Prof. Ajoy Ghatak Department of Physics Indian Institute of Technology, Delhi

Basic Quantum Mechanics Prof. Ajoy Ghatak Department of Physics Indian Institute of Technology, Delhi Module No. # 05 The Angular Momentum I Lecture No. # 02 The Angular Momentum Problem (Contd.) In the

### Roberto s Notes on Linear Algebra Chapter 4: Matrix Algebra Section 7. Inverse matrices

Roberto s Notes on Linear Algebra Chapter 4: Matrix Algebra Section 7 Inverse matrices What you need to know already: How to add and multiply matrices. What elementary matrices are. What you can learn

### Introduction to Fluid Machines and Compressible Flow Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Introduction to Fluid Machines and Compressible Flow Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 8 Specific Speed, Governing and Limitation

### Transistor amplifiers: Biasing and Small Signal Model

Transistor amplifiers: iasing and Small Signal Model Transistor amplifiers utilizing JT or FT are similar in design and analysis. Accordingly we will discuss JT amplifiers thoroughly. Then, similar FT

### Digital Signal Processing Prof. T.K. Basu Department of Electrical Engineering Indian Institute of Technology, Kharagpur

Digital Signal Processing Prof. T.K. Basu Department of Electrical Engineering Indian Institute of Technology, Kharagpur Lecture - 33 Multirate Signal Processing Good afternoon friends, last time we discussed

### ECE 220 Laboratory 4 Volt Meter, Comparators, and Timer

ECE 220 Laboratory 4 Volt Meter, Comparators, and Timer Michael W. Marcellin Please follow all rules, procedures and report requirements as described at the beginning of the document entitled ECE 220 Laboratory