 We start with the analysis of a feedback amplifier general amplifier the basic amplifier is unilateral what does that mean that if you give an input you will get an output okay it does not mean if you give an input at the output you will receive anything at the input so it is a unilateral device or circuit however please remember that when we evaluate for basic amplifier design even with feedback if I want to know what is the basic amplifier with feedback so the first thing I want open loop amplifier but in evaluation of gain for open loop amplifier please do not neglect the loading of components which you are going to create there by feedback so what essentially we saying that even if we are looking for open loop circuit the effect of feedback network and source and load resistances be taken care in your analysis for open loop so otherwise you will say you remove RF or whatever resistance or impedance you are putting and just do not solve for it so use that impedance well in the circuit for open loops let us see how we will do it you also assume in most cases that the feedback network is unilateral essentially we say there is no very there is there is no or very little feed forward in this case so when I have again and again saying I am actually first trying to find the open loop gain why because the closed loop gain with feedback is open loop gain divided by 1 plus a beta okay so I want to know what is AOL but in evaluation of AOL I do not want to neglect that circuit parts or components which would have come after the feedback so that those I want to retain some way so I have given I am writing down here for you or I have written down for you steps which you can follow whenever such analysis has to be performed so the first thing in any feedback amplifier is to identify the topology what does that mean whether the what kind of feedback is it is what is the sampling kind and how it mixes at the input whether it is series sample shunt sample series mixed or shunt mixed and if we know that then our analysis will become relatively simple if you know which kind of amplifier we are considering so first thing is given a network or amplifier circuit first find which kind of feedback topology this amplifier has then let us say for example if you have a series mixing and if they in the input circuit if in the input circuit there is a circuit component say W which is in series with the signal source then the feedback signal is XF equal to VF is a feedback signal okay so we will see how what does that mean however if you have a that means please remember if it is a series connection it must be voltage in series to the source okay whenever it is series mixing it has to be a voltage source in series to the signal source that is what we described as series mixing however if you have a shunt mixing the feedback must return the current okay because at that time the current will only allow you to shunt across the input terminals and the source will be current source so depending on the kind of input you see whether you have a feedback which leads to shunt mixing or series mixing first you should find if you know series it is the voltage is in series in the feedback if it is shunt then it must be the current which is shunted across those topologies which I have given you four figures please we revisit them again and check what I am saying is that okay to you this is just whatever we did in nutshell I am now saying so that this is the method you should follow in any amplifier analysis and later on designs having seen whether it is which kind of mixing we also will like to see which kind of sampling okay I repeat if the sampling is as a mixing a series the feedback must be voltage if the mixing is in shunt it must be a current which is in shunt to the input circuit is that okay typically shunt circuit will occur when the current has to be brought there what kind where it will current can be mixed with some other current at a node is that correct at a node voltage can be in series when it is in the mesh is that correct only then it can go into the series of the source okay so think of it whenever there is a node connection feedback it must be shunt kind whenever it is in loop kind of input inside that loop it must be a series feedback which must be voltage is that okay so obviously in a mesh you cannot have current additions there okay so this is trivial but must be understood and must be solved correctly because otherwise they will be a machine in actual solids okay so having said that this is how it will mix to get the sampling set the output 0 which is your output okay essentially you say short the load okay if now XF becomes 0 that is if output is V0 and you are shorting and now in no feedback will go because part of V0 was to be fed and you are shorted so feedback goes to 0 then you must be obviously voltage kind of sampling which is essentially shunt sampling across the output is that correct across the output means shunt figure is shown here this is my I have shorted the output and as soon as I short the output the feedback goes okay because if something by V0 any V0 is not there there is no feedback there okay so once I know it is this kind of circuit I shot and I say I do not see any feedback then I say I must be having a voltage sampling which we defined as shunt because it is shunt to the output therefore it is a shunt sample on the contrary if I make I00 which is I open circuit the resistor output load okay then if XF becomes 0 then it must be in series to the this because then you are open circuiting the loop and therefore no current can go and therefore we say your series sampling and that is what the current sampling will be is that correct so the conditions you should do first see at the input side whether your source is getting in in the loop of this then it is a series if not it is shunting then it is a current so say we shunt some mixing we know by making V0 or I00 if your feedback goes to 0 we know which kind of sampling we have done okay so having now known whether it is series series amplifier series shunt amplifier shunt series amplifier or a shunt shunt amplifier I know which topology now I am at okay so given a circuit first thing you have to find by doing this simple this which topology we are because you know in the circuit this kind of network will not be shown it will be a formal circuit with some components connected left and right okay so from there you must be able to figure out which topology we are working at okay also we have seen depending on the topology input resistance and output resistance change in some cases it increase in some cases it decreases so the topology will also tell you how the input output will respond to the input side addition anything coming or output side when it is driving so some idea of R I RO also should be immediately known because you know now that what kind of amplifier I am working at is that okay now these issues a priority you do it because as soon as I put a network or circuit you should be able to find what I am doing I have given example do not worry that this is the end of it now the next step having found the topology I want to find amplifier without feedback and I just said to start with what I am saying even if I am want to open loop circuit I do not say feedback network has been removed is that point clear feedback network has been I am not saying it I say I want feedback be broken but the effect of those components still be taken care so let us see what I am saying little later step A in the input circuit if I am looking for what is happening because of the feedback in the input circuit if you have a shunt sample make V 0 0 and if it is series sample make I 0 0 essentially the feedback you want to remove then the step B is first I figure out something while I give an example to find an input circuit make V 0 0 if it is shunt sample make I 0 0 if it is series sample now to get an output circuit what do I do make V input 0 okay if it is current mixed and if it is voltage mix remove the input current so either of the case you already find the topology so which know which ones have to be shorted or opened as for the conditions we are done okay. Now these two conditions once we do it may go originality me up a method is live at around keep people normally do analysis without knowing also it answers come correct nothing big about it but methods why they are shown this method because they are short so they will simplify your job that is the only reason we show all the methods otherwise what is the big method is put whole equivalent circuit and solve it will always come at the end of the day so to even do this can I small simplify a few things beforehand I do that okay that is the trick you want to use so what is that I am trying to say I want to find the closed loop gain with feedback by not directly calculating with all components present as normally should have been by Christia of law what I am going to use the expression for closed loop gain open loop gain divided by 1 plus a well beta that is the expression I had derived for feedback so I will say okay I will calculate a well I just calculated beta substitute okay and I am sure that calculation of a well will be much simpler than calculator to total ACL this is my belief if you are it is not your beliefs follow all of it no one no one is saying you have to solve ACL by first getting you actually can solve full network and once you write an equivalent circuit you can always find v0 by vs is that clear so there is that method stands anyway these techniques are only trying to minimize the effort so if I get my AOL where enough I know my beta then AOL upon 1 plus a beta is my closed loop gain feedback gain so I just want to do the two steps now so one of the step I should say once I know what is XF because I just know sampling as well as mixing so I know what XF I am talking then what X0 I am talking is that correct so the ratio of XF by X0 is your beta please remember XF XS is the return path coming from V0 side or I0 side it can be resistor it can be conductance or it can be voltage ratio or number or current ratio is that clear for possibility can exist I may return as a I we may return as a V we may return as I I may return as V so in any case there are four possibilities of the beta value is that clear because a beta should not have a beta should have what units in respect to what is a whether it is current gain voltage gain trans conductor what should be the a beta non non dimensional or it should not have unity that means a beta must be opposite that of a in the units is that correct therefore then only it become dimensionless this is essentially what we are saying okay so first find beta then get Al beta if you already calculate Al then you get Al beta that is T function evaluate closed loop which is also in some books called AF for the amplifier by what function Al upon 1 plus Al beta is the correct closed loop gain so evaluate that and then also evaluate as we did already earlier what is its RF and what is its ROF these are the three parameters of interest to us other than frequency response which will see that okay for normal amplifier first thing I want to know gain what does how much gain I got and what are the input output impedances I am going to get so is this method clear to you so what is first thing we will do first thing we must find the topology to get the topology we must find what is the kind of mixing and what is the kind of sampling from there we know what is the feedback going on okay correspondingly you actually find your beta using the network available of feedback and that is what to get an Al we will see by the example that will prove my point find Al you know the beta and therefore you know the closed loop by but by the same circuit you can always get your RF as well as our let us do one example which will clarify what I am saying okay in normal cases unless it otherwise assume feed feed forward is negligible unless it otherwise you can see the it is like superposition we always solve for feedback okay and if there is a feed forward which turn will appear in gain function a 0 will appear so that means there is a partial feed forward path is going on is that clear to you so if there are zeros this means there is some feed forward is going on is that otherwise poles will always give you feedback is that correct this is what the technique is to know what whether we are doing correctly okay here is an example which is very simple and very easy to understand let us say I have a source follower sorry the emitter follower which is essentially called common collector circuit please remember the other name of emitter follower is common collector circuit okay collector is grounded at the VCC grounded means to go to VCC there is a source Vs there is a source resistance RS there is a load which is RE please remember this RE itself is the load for source amplifier there is no additional load may have also but right now for in this we will just take RE and output is taken across this equivalently saying this is the VBE for the transistor please remember RE is common to the mesh of the voltage drop across RE is common in this mesh you see this mesh in this mesh the drop across RE is in series with vs is in series with vs so what mixing I am doing series mixing okay however if I shot v0 nothing goes inside the feedback so what sampling I am doing across I am sampling so what is this shunt sampling and series mixing so what amplifier I have series shunt amplifier is that clear if I shot v0 no feedback drop across RE becomes 0 so nothing changes in the input no feedback in the input so it is essentially voltage feedback which is shunt across the output okay so it is a shunt sample at the input side if you see this mesh this drop across RE is in series with the source so you have a series mixing and shunt sample so it is series shunt sample or it is essentially called voltage amplifier it is called voltage amplifier what is series we said then the feedback signal is in series with the source and that can only be voltages nothing current cannot be in series with something is it so only voltage can be in series so if you look at this input loop input circuit the drop across RE which is common which is the feedback V0 by this much is the current drop across this vf that is in series with the signal you can see this series in this is actually twice one because of I and one because of this but for the input side this column takes care of the drop across this so whatever voltage vf here is in series with the signal whenever there is a mesh the two voltage sources can be in series they may be plus or minus depends on the signs but they will be in series if you have a node like this there is a current here there is a current here and something like this what is the mixing done here I can add a node I brought let us say this is one I1 this is I2 and this is I3 so I3 is I1 plus I2 so it is no mixed that means current is getting mixed is that correct which is essentially shunt to the input circuit current is always shunt source is that correct so we say whenever there is a current feedback going on at the series at this it is a shunt feedback going on shunt mixing is going on if the voltage across the feedback network is in series with the source then we say it is a series mixing is that correct that is a voltage mixing please remember series cannot be currents it always will be share voltages so it is therefore voltage input voltage output so what amplifier I am looking for a voltage amplifier v0 by vs is my a is that correct that is the way I have figured it out so it is a series shunt amplifier which we already done earlier but let us do it again okay just to say again since RE is common between input and output this amplifier is a voltage amplifier now we want to find circuit without feedback okay I repeat I want to find AOL which is I say circuit without feedback but what is the condition I am still forcing you do not neglect the feedback components because if you neglect them then the feedback part will all this will be a normal amplifier there is no question of feedback there so if we say at the input what is the condition I said to get a input circuit short the output is that correct short the output so I said V0 is 0 so what what things get shorted in the input side the VF because if V0 is 0 RE does not exist it is a short circuit please look at the circuit again if V0 is shorted here this is grounded if V0 is grounded this is grounded okay so in the input side I have RE bypass now by short okay this is my input this is my input circuit now to get a output circuit what is the condition I told you short input so okay if I short input II is 0 if we make II zero there is dependent source and the output we have circuit only in the what happens here if I say this is going down the GM times that will also go away okay so what will remain at the output therefore only the RE factor GM times parallel RE but GM itself will be open circuit GM VI current source is open circuit so what is the resistance seen there at the output RE so that is the circuit I put this is my input circuit this is my output is that correct so this is which amplifier now I am calling this amplifier it is a open loop amplifier for the feedback circuit amplifier given to me take an in for to get an input circuit short V0 and then whatever you see in the inputs that is your input circuit to get an output circuit short inputs but as soon as you short input GM VI will open up because there is no current source then then the only resistance of course there is a RO but right now I say RO is infinite so the only resistance left is RE at the please remember you see circuit again again so if I see from here and this is this the only resistance I see the nothing else at the output is that correct so if that happens then the equivalent circuit of a transistor now is a common emitter amplifier with RE as a load drop across RE is the feedback voltage and then I write equivalent circuit of this this is VS RPI GM VI this is my emitter this is my base this is my selector GM VI parallel R0 if you want to make R0 infinite you can make that parallel RE and then I can get the gain of this ampere power again be no mean a push we have a gain over here we pie and now go GM V pie times RO parallel RE is the output voltage but V pie is how much R pie upon R pie plus S times signal is that okay potential divider a voltage this voltage divider this upon this this into VS is V pie so substitute V pie in the output so V0 by which is GM RPI RO EF RO is the parallel combination I make RPI plus RS so this is my open loop gain is that clear to you how did I get my open loop gain I got my input circuit I got my output circuit then I made a new amplifier now for me and I got the gain for this amplifier which I say it is open loop amplifier gain see normally it is a common emitter amplifier we have seen what is for a common emitter amplifier what is the load resistance we are seeing output resistance which is RE so it is a cross collector to me that is the equivalence that is what I keep saying it is not symmetric same as what we have it is common source amplifier common emitter amplifier sorry common collector amplifier that is emitter followers have an equivalence with the feedback of that RE is of this kind in open loop this is something you have to appreciate this is the output resistance RE I got what is output resistance will be across what it will be always across collector to emitter okay that is the output resistance of an amplifier substitute then solve this once I get this then how do I get the gain okay before the what is beta unity it is same voltage now why feedback so beta is one so the return law a loop gain T is a well beta which is this function then the feedback gain or a closed loop gain is a well upon 1 plus T substitute these values here and you get beta ROE upon RPI plus RS now I am now giving you a case this already we have solved source amplifier is that clear we have already solved normal common source as a source follower and emitter followers do not use feedback theory what do I do do not use any feedback I actually solve equivalent circuit for this is that as it is then evaluate this gain for that v0 by vs and verify whether using this a well upon 1 plus T kind of function is this expression is same as what I would have got if I would not assume any if you I just solve the network okay verify yourself and you will be surprised it is exactly what we got otherwise and why positive sign is coming everywhere because source followers or emitter followers as a same phase outputs as inputs by same logic we earlier said what is RIF for such shunt series shunt amplifier RIF is 1 plus T times RIF what is RIF this is 1 plus T what is RIF please look at our circuit equivalent circuit what is RIF is only R pi please look at the circuit what is RIF here R pi R pi times 1 plus T is the RIF that is what we have already said series shunt amplifier we have evaluated RIF RIF RIF already for in terms of RIF and RO so I substitute here and I get roughly if I solve it R5 plus beta ROE do you recollect this very well that we said if there is a source follower or emitter follower it is input impedance actually increases by beta times the feedback whatever RE there plus R5 this may be very small actually this may be much larger value so the input resistance of a series shunt amplifier is very high very high that is what essentially that is why it is called what what is the other name for common in this source followers or emitter followers buffers the buffers have larger input resistance and smaller output resistance so let us calculate output resistance you can do yourself that is not a big issue what did we calculate for this shunt sample RO RO by 1 by T we had done all that what is essentially RO for this small RO please remember RE is outside say load so the only resistance is RO for this RO upon 1 plus T if I substitute is RS plus R pi by beta beta being very high RS is typically few hundred ohms R pi is typically one or two kilo ohms so it is a at best 2 kilo ohm by 100 so how much it will be 2 kilo ohms by 120 ohms is that correct let us say it is this whole becomes 2k divided by 100 how much it is so the output resistance of a emitter follower is very very low typically of the order of for example I give you say 20 ohm 50 ohm kind and how much is the input resistance will be let us say RE is 1 kilo ohm so how much is R I will be arrive beta times are it is hundreds of K is that correct hundreds of K is that what we did in normal source or emitter follower you can verify once again I repeat yes RE is what RE is shunting loaded let us say 1k so in feedback is 100k at the input side beta times RE it will be reflected so input resistance will rise to hundreds of K okay whereas output resistance will be how much 10 to 20 or 50 ohms so buffer requirement that the unity gain with high input impedance and low output impedance is achievable by source follower or emitter followers and this problem can be solved using feedback is that correct whatever analysis we did without feedback knowing also we solved the network equivalent circuit like a network solve Kia okay was so be joe kareng a will say result yeah yeah that means our feedback you are asking the verify here is a verification okay you verify both value there will be some small change may occur because of some approximation we are making here there but if you do not make any approximation they will be identical in both cases okay is that okay this is a technique which essentially we use in feedbacks okay so what is the method I repeat what is the method I suggested first find topology then find what is the mixing going on sampling going on once we know we know what is there are and ROF can be because either by 1 plus T or multiplied by or divided by whatever that topology I get I also know for to get an open loop circuit first I say short input find the output short output find the input make a new amplifier using this input output circuit with a transistor as usual solve the gain for that that is your AOL if you know the topology you know the beta whether current by voltage current by current voltage by whatever you are getting so you know the beta you know beta you know AOL so you know AOL upon 1 plus AOL beta is your common closed loop is that clear with feedback I told you that output resistance is defined for the transistors and not for the loads RE is the load yeah but that is we will take always as seen by the I mean transistor RO is the resistance as seen by the transistor any external component you do not add to it is that correct that is the definition we say the final RIF or ROF will be shunted or by this and whatever the other side is that point here the actual someone asked you RIF so you calculate that okay then you say the net RIF dash whatever you call then you are looking from the source side and you are looking from the actual output side then whatever parallel or series combination they get you are right for them so in this case whatever ROF I got shunted by RE whatever I got here RIF in series to this is that clear so that method remain where to calculate first we always calculate at the input of the amplifier at the output and then actual outputs with loads and actual voltage or current sources but that is once you know this this is only additional is that clear but the definition wise we always do this is that clear this is nothing to say that why we do not want to use the other values because the source things I do not know what is RS value what is RIV so I say intrinsically it nahi of jobi component laga inga wo usko modify that is that correct that is why we do not want to use those values in our actual definitions is that clear but you are right the actual impedance phase will be somewhere at the output side so wo usko deko kiske path parallel okay if I have any equivalent circuit of that GM V V whatever V5 we are doing if the source is 0 then the GM V5 is 0 that means current source is in open circuit so the only impedance seen by me was are you there if that if there will be VB and GM VB aata to one upon GM maata aisa nahi ho usko aata liya maata is that okay okay so these techniques which I suggested maybe one more example on the mass will clarify some more doubts shunt shunt amplifier a bhe me pehile bol dia shunt shunt abhi aap ko to aap verify karlo here is a current node as soon as I say current feedback idar se aara hai RF ke saat me aisa of course your plus minus sign you correctly decide feed forward matlena so what we say as soon as I make V0 there is no current at the input is that correct as soon that means its feedback is removed by me which essentially mean this is a what sampling I am done a shunt sampling I did and when I say at this side at this node all three currents can meet so it can change at the node any current therefore it is shunt mixing so I have a shunt mixing and shunt sampling so this is shunt shunt amplifier fir se ek baar khut deko verify karlo the method abhi dek bata hi hai baisa ka baisa is me apply karo or verify karlo jo me ne kia hai is this shunt shunt amplifier so we first figure out what is the topology so I said it is shunt shunt by actually I knew it because I am actually seeing it yaan order yaan is ka 0 karna se jara hai to yeh shunt shunt hai is that okay V0 0 karo no feedback karan 0 kar dea maa okay so voltage sample oge hai that means shunt sample wha is yes if V0 is 0 no current from the output is going to the input side this is a 0 potential is that clear so we say it as soon as I get output 0 no feedback V0 0 kia that means I am sampling voltage no this sign I just made for the do not see IF will be in below down if you wish you can always use plus or minus sign that is I say we always write signs as they actually appear okay as they actually at a node this will only plus or minus it will be so signs will be correctly done whenever I just want to show you at a node if the three currents meet the sampling must be mixing must be how much should be shunt max mixing because currents are getting actually shunted to each other okay so this shunt shunt amplifier of a mask I can now show you how do I do it here is the circuit equivalent your GM VGS is your source this is get to source right now I assume source voltage is 0 and this is my RF is that correct from drain to gate is my feedback resistor RF is that circuit clear drain to get is the feedback resistor RF this is GM VGS R0 this is my RD this is my source now to get an open loop okay I said V0 0 input circuit do not know so what should I do short V0 as soon as I shot V0 this terminal goes to 0 whole of this terminal is going to 0 that means RF is that okay as soon as I make V0 0 this terminal is ground so is source was ground so that means the RF is between gate and source RF resistance appears when the V0 goes to 0 so the input circuit has a resistance shunting there as RF is that clear okay to get in output circuit what should I do I said short the input okay if that being equal to 0 even this goes to 0 so opens it so what is the output resistance see output things I see RO RD now this is shorted please remember this other terminal is shorted now so where it will now come from this to the ground so now I see RO RD RF in parallel at the output node is that correct at the input what is there RF shunting gate and source at the output I have three resistances in parallel shunting the output RO RD and RF is that correct this is for getting the AOL but remember I have not removed what does that mean without feedback so what would have done otherwise without feedback me kya karteya RF ko hattali or jai se RF ko hattaliya uska open loop oh yeah that is true but then these values would never have been seen by open loop so the loading effect of the values cannot be neglected in evaluation of open loop though feedback is still broken bias you can see now if I say equivalent circuit of this this is the input side RF this is the output side now there is no connection between input and output so this is open loop this is input this is output no connection from drain to gate so I have broken that so I made it open loop but what is the criteria I have chosen that the loading of RF I have not neglected loading of RF I have not neglected though broker I have certainly broken the feedback okay this is called open so this is it point clear it is different from what we call without feedback word because without feedback means you would have just taken RF out is that correct so we are not taking RF out we are saying for feedback break it into so that as if there is no output input connections equivalently saying this is the circuit okay since it is the shunt mixing means it should have a current source so voltage by current is the amplifier so L is V0 by is star star I am making for open loop okay star I am only trying to make it open loop so L is VO star upon is star which is VO star by V in into V in by is star this method you know how do not write directly V0 by is essentially what do you do V0 by V in into V in by is star a canceling right but this value I know by a normal amplifier how much is this V0 by V in minus GM times the load. Now output here we are star GM V in times RODF so VO star VO star by V in is GM RODF minus may minus sign how much is V in by is star RF there is nothing else so into RF okay so I got now correspondingly RI if you see is only RF correspondingly RO if you see it is only RODF what is the feedback factor here I should use which kind of amplifier I said it is shunt shunt input pe current Jara hair output say voltage sample okay I so IF star by V0 is 1 upon RF. Please take it verify IF times RF is V0 so feedback factor is 1 upon RF so we catch is a pata lagai we know our AOL we know our beta so what we can calculate closed loop or feedback gain okay that I did up put karka dekho to up ko jada samjega par main a up ko dikhaya methods closed loop game is VO please remember it is still voltage by current so which amplifier I am talking in a real sense not voltage of which is this amplifier trans resistance amplifier this is trans resistance amplifier okay so if I substitute all this I saw game khela so bold par humko kya chahir heta amplifier main what do you really need in normal amplifier it may be trans resistance it may be trans conductance it may be current at then khya dekhna chahir hum voltage gain at then humkhya dekhna chahir hum voltage gain so humko actual nikalne ko kaha tha V0 by VIN par humne to nikalha abhi V0 by IS okay so V0 by VIN can be written as V0 by IS into IS by VIN 2 part me kar dia V0 by IS to abhi me nikalne liya jaan se abhi mujhe kya nikalna a IS by VIN okay so if no do not write this you write now do not do anything now this V0 by IS is GM RODF RF ye jo ye hai upon one year this ye to RF RF cancel hogae now how much is IS by VIN abhi kya circuit me dekhna IS by VIN kitna hain one upon RF abhi input circuit me dekhna kitna IS by VIN one upon RF multiply kya so ye function aya this is your essentially the voltage gain close loop voltage gain of feedback amplifier what kind of feedback amplifier we started with shunt shunt okay this is a shunt shunt amplifier is ka kya faira hosakthaya ghatah hosakthaya is ka aray jaada hoga ke kum hoga RF jo hai feedback will kya please look at your circuit and tell me your tables in case of shunt shunt amplifier does aray increases aray should decrease current is it subtracting out of it so it is a negative feedback so aray to decrease hoga a but aray jo hai one plus T times bada gaya so it is opposite of what we did in the case of source follower or emitter follower their input impedance rose output impedance went down by making a trans resistance amplifier I can now make opposite of that aray and increase RO so this is that clear to you what is the feedback is trying to do feedback is trying to play whatever specs you are looking for by choice of proper feedback topology I can achieve aray RO and gains of my choice is that clear is that point clear why feedback because feedback allows me to tailor my input resistance output resistance and the gain and that is something which normal amplifier does not allow me is that if I take a source amplifier I cannot do much of that will always be one kind okay feedback allows me to play that is why feedback amplifiers and what is the most important thing in feedback we are getting it gain becomes constant very close to a convite becomes constantly negative feedback if there is a change of signal due to noise at the input and let us say it is plus then what will become to the output additional voltage will appear at the output so during feedback what it will do it will start that also will be higher now corresponding beta times v0 so the input will further rise now sorry it will oppose it will rise but will be subtract so in net input will go down so the output will go down this output went down feedback reduces so it will start again till it balances to the normal value so feedback stabilizes the gain and it also allows me to make different ROI different RO and different ACLs is that correct that is why feedback amplifiers are always utilized please remember instead of RF what is normally will be present in the case of all amplifiers this I did not put RF there but what what component will be always there in a MOS transistor which capacitor CGD so please remember CGD is a shunting actually between output to the input and it will give you a shunt mix is that correct so it will also try to stabilize you okay with that impedance of that that frequency the only problem why it is so different from this because it is a frequency dependent impedance R is constant but omega C different omega will have different this at certain frequency it may have something different phenomena at other frequency it may have other phenomena but that is what we want frequency response to be modified okay that is what CGD CGS and others will actually help us to achieve that is that point clear this is an issue which you should always understand that feedback is a generalized network and sometimes inbuiltly present sometimes you may actually put it okay when I say I put RF in reality what do I put in such circuit RF parallel CGD so it is an impedance which I am putting there is that clear so there is a some kind of a pole function starts appearing because of this RC network which I am going to put that is that clear so the if the pole changes then what changes bandwidth so you have to see that what kind of amplifiers will improve the bandwidth or decrease the bandwidth is that correct these are the techniques of controlling the bandwidth the gain and the ROI RO okay that is why I say feedback is very very important phenomena I am not going to do a great part of stability because why I thought I was thinking to teach a lot of things on that NICWIS criteria root locus management then you know I will go to the control side bit too much let us take that expression in closed loop AOL upon 1 plus T I have a I am looking for feed stability with feedback if T is positive what have what does that mean if T is positive means 1 plus T is higher means closed loop gain will be smaller than open loop is that a denominator will be larger so obviously you will get smaller gains okay what is the feedback essentially we say when this can occur only when negative feedback is present however if T is less than 0 then the denominator will actually enhance divide by smaller value it will actually enhance the ACL and if it enhances the ACL if it is negative then it will enhance and if that enhances what is the kind of thing will happen if the feedback signal is always in same sense as the input what will increase the net input if the net input increases what will increase the net output the feedback will bring back additional input now which is in series which is in plus to the input itself so further increase of input further increase of output what is it going to do so any given instant or time I do not know what is V0 because V0 is constantly increasing increasing is that correct V0 return to the series of that increases V0 further loop may be 0 but that is how cabling a field amplifier does not have any known gain is that correct because every instant of time V0 is not known to me okay so we say such amplifiers are unstable or they show instability would you like such things to happen for your amplifier why did we do feedback all this for this purpose can you gain constant we want that fixed is that correct with nothing changing this gain should not change everything changing but this game should be positive feedback yeah so I say sub button growth pattern should over so such will not be an amplifier is that correct it will not be a amplifier for a known gains so anytime positive feedback appears we say we have instability is that correct so guarantee kya karna apko amplifier design may what should we ever guarantee that it should always be negative feedback abhabek so-so output johai V0 is a function of frequency if the input is a function of frequency so is the output will be a function of frequency so there are two factors of any trans this return law return fact this t factor which is loop gain if you see a loop gain will it have will it have a real quantity or imaginary quantity or a complex quantity a is a complex so is a beta will be a complex quantity you will be a complex quantity is that correct so if it is a complex quantity how does how do we represent any complex number a plus jb is equal to magnitude of this value into e to the power j omega j j5 which is the phase part for that is that correct any complex function can be represent like this is that correct tan inverse the imaginary variable is the phase for that so you have not only amplitude but also you have a phase so now look at the situation which is very interesting this this is much easier to explain the closed loop gain is s upon s is instead of a well I am just remove a s upon 1 plus a s beta s now my general I am using little generalized what the what is generalization I did from the earlier one what is beta I am showing you that may be also a function of frequency right now normally what is the kind of betas we are used so far they are real values and there is no complex term with them okay but let us say it is also function of tk scoby general so we write at for a frequency acl at j omega is a j omega 1 plus a j omega b j omega the loop gain t is a j omega into b j omega is certainly a complex function okay how do I write complex function the magnitude of a omega a j omega this e to the power j phi which is a function of omega phi is the phase what is phase by definition of complex number tan inverse imaginary by real value so that is I and that is how we represent any complex value now look at the situation little carefully in that figure let us say feedback is coming okay so it has some magnitude what is being returned return power has some value which has magnitude and also has a phase if even if let us say the gain magnitude is higher than 5 10 20 but the phase is such that the return signal opposes the input signal so what it which kind of feedback will give me negative is that correct there is on the al itself yes itself there is a phase shift what is the phase shift between input or not for the AS how much degrees 180 degree amplifier shows phase out so there is a 180 degree is a normal input output on the return part because the complex function there is a phase going on if this phase is also 180 degree how much is the net phase it will give you 180 there and 180 here so how much is the phase now 360 degree or 0 you are right so what the now that say the amplitude is positive then what will it will do if the phase becomes 0 means in phase to the input which kind of feedback essentially I have gone into positive feedback the gain is not less than 1 gain is higher than 1 okay but the phase was such that is 180 degree from the feedback and 180 degree from the amplifier so the return signal to the input is in phase with input which is higher now because your AB times higher way you are chosen 10 let us say okay so now what is happening that your input has increased output will increase and input will so which system has become stable unstable unstable so it is not just the magnitude but also the phase is that correct so can you think from this a very simple calculations which we do if we say at the frequencies of operations which we are looking if the game does become where is the game will become 0 DB at the omega t term that is the unity gain point so if we see for the loop gain itself alone when it will become when it becomes 1 t j omega is 1 magnitude wise we said at that frequency if the phase of this function is how much less than 180 degree I repeat less than 180 degrees which feedback I am still talking negative feedback but if the gain is positive and feedback this has already crossed 180 degree phase then what will happen the feedback will become positive I repeat the gain is positive it has not cross 0 DB loop gain for example and its phase has crossed 180 okay or reached at 180 so now what will happen there is a positive return positive value which is in phase return to the input is that clear so which feedback I am now getting into positive feedback system will become unstable so the two term we define one we call phase margin and the other will call gain margin if the phase margin is positive we will see that then we say system will remain stable the phase margin becomes negative then we say system will become unstable so all feedback amplifier people try to see what is the phase margin they are getting is that correct if the phase margin is positive be assured that what does that essentially mean phase margin is negative means when the gain becomes less than 0 DB or one less than 1 your phase is still negative is that correct so it has not returning signal and the gain has already crossed one so it is partially is only returning now much lower is returning and you are always opposing that value is that correct so what does that mean that if the board is plot think of it something on the board S plot if your 0 DB point crossed by the magnitude at which point the phase is still not 180 degree or 0 essentially 180 plus 180 then what do we say the negative feedback exists if that crossed before after this then we say it is a positive feedback and we have a instability so is that point clear so in amplifiers it is not only the amplitude which is also there is a problem of phase and that is what essentially the stability is all about okay just even to give you a basic idea any generalized transfer function in a feedback can be written as square expand here so AF0 1 upon there will be large number of poles A1 S by 1 plus with feed this is all with feedback is transfer function code is there is a generalized form A1 plus A2 plus A3 S2 S3 S4 SN. What does this essentially means if there is a SKU term how many poles are there 3 poles if only first this term present is a single pole so depending on your transfer function of closed loop amplifier system first find how many poles are there then draw it is Bode diagram what do we draw then Bode diagram so what I do is the following here is some my definition I will come back to it again as I say we can dwell on this detailed theory of feedback it is a huge game interesting game rather much more interesting than many things I thought I like it that is what it is root locus technique is a very funny thing Nickwiz criteria how many times you circle the very nice thing to learn okay figure the kind of this say I have a sort of stability idea just single pole I have plotted for the transfer function sorry loop gain a single pole theory a single pole as I plot for the amplitude and this is this phase at this point what is the gain loop gain is how much 1 is that less than 0 positive than the pilot one you have a skin each of a minus over it okay is capable plus at this frequency if I plot my face correspondingly 45 degrees per decade and it intersects at point let us say some 160 degree minus how many how what is the phase there minus 160 then I say I put another value where the phase becomes 180 and I get the value of frequency at which that has happened so this value is that correct at this point this is the gain at this gain this is the phase at this frequency this is the phase at this phase this is the game is that clear so we say at this for the loop gain from this value where the T has become 1 or 0 dB use add 180 degree to it okay or subtract minus 180 means add 180 degree to it if that quantity is positive that is this number is called phase margin what is phase margin this value phase at this point ever the T is 1 minus of minus 180 means plus 180 so 180 minus this phase value if you do and if this value remains positive then what is the phase margin will be called positive phase margin we are just now said if it is less than 180 degree the output signal will never be in phase by feedback to the input so which feedback it will retain negative feedback because the signal is not returning to same phase 180 from the amplifier 180 from here so 360 degree so as long as this is less than 180 degree system will remain always stable is that correct so what is the criteria I am saying if the phase margin is positive the system is always stable when this should have occurred let us say at this value or this when the gain has become some you have reached 180 degree but the gain is still positive is that correct so which feedback it would have given negative positive feedback so if the phase margin becomes 0 or negative the system will become unstable as long as the phase and what is the definition of phase margin there should be the phase of T plus 180 why it is plus I wrote minus of minus 180 is plus 180 so 180 and this will be minus so if the net value is positive then we say feedback is always negative otherwise feedback is positive and system will become unstable or instability starts is that point clear is the definition clear to you I repeat if the return signal is in phase as is more than unity which means it will add to the signal and output will grow is that correct if it is not in it opposes the input it will always reduce the V0 and therefore it will never grow is that clear so for stability negative feedback is essential and to do this phase margin must be retained to less than or greater than 0 degree or rather prefer what is typical amplifier phase margin should be for normal phase margin which say up guaranteed Lee school negative feedback normally feed phase margin for normal amplifier should be kept between 45 to 60 I will not tell you now, but so to do the phase margin 80 90 or we are just stable on a chain to push to be over chalazhaya you may achieve very nice. So you do not want to reduce the gain too much at the same time you want to be stable so phase margin typical value 45 degree to 60 degree to 65 will not stabilize but what cost the gain actually will go down okay so a typical gain or stability for phase margin 45 to 60 degree where does it come from phase margin 10 inverse which you leave for T function in that T function the value of A and beta is that correct A value will be gain will be GM will be C will be R will be all will be there their value should be at 45 degree or a little bit higher phase margin then if they give it then we say system is amplifier is always stable is that correct otherwise even if you are thought it is stable initially at some frequency will find certainly unstable okay and that is why I say amplified design is very interesting if you have a feedback is that correct please remember what what is the phase margin I keep saying you 180 plus and this will be minus quantity is that correct because this is going down so minus then at 180 degree whatever is the gain from 0 is 0 and 180 per a gain is that clear 180 per k a gain a itna gain a gain follow on a at the here I am so 0 say here at up is called a gain margin plus a minus a minus a so if the gain margin plus a itka ka matlab hona wala phase margin negative hona wala ha ha uska matlab unstability to gain margin negative hona cheer phase margin positive hona chai ye tabhi system stable hoga is that clear is that clear this is something interesting which feedback amplifiers prove please do this before we quit on this last x slide dikharete shun shun output voltage a sample kiya gaya node paper return karan diya gaya to it is shun shun amplifier is that correct shun shun amplifier whenever I connect a capacitance between output and input we can separate them by which method input side output side Miller's theorem is called as the method may have come to the miller's compensation come to the miller's compensation abham x stability ka a idea dekho samjho jedi doh pole hain aur wo pass pass hain to build their face will reach 180 faster if the two poles are very close 90 10 itch a ana shuri ho gana 90db so the 180 anima to be for 10 times only ke palye bo 180 posh sakto 10 time hote hote is ka kya matlab hai gain would not have probably gone to 0 but your face might might reach to 180 so what system will become unstable so kya chate hain ki jedi doh pole ek dusre se door hain bo door hain so je dominant pole edi pehle a raha hain kaafi shift hoga bahut kum jago pe jara samye thoda bandwidth kum karne ke koshish ki kai hain to kya ho jayega phase will never reach 180 by then is that correct before the gain crosses 0 in that case what will happen then system will remain stable but at what cost bandwidth hode kum ki main hai to ke main hai shift kya usko thoda left main to uski bandwidth hode reduce karke me ne kya achyukar liya phase margin achyukar liya main so this ko bulte compensation so kya kar kte hain ki a jo initial pole hai samye ek circuit hai abhi a cf nahi hai samye feedback okay ek equivalent circuit a r r i r 1 a k resistance a c 1 a k a a a a a a is the current source this is my V0 or i0 be let us say or a feedback nahi likha hai normal amplifier a is ko nikal the MNM so what are the two poles we say without feedback no CF it is not a l kind it is just that there is no CF then R1 C1 will be one pole and R2 C2 will be other pole so omega p1 is 1 upon R1 C1 omega p2 is 1 upon R2 C2 these are the two poles available for you okay if I use this now new circuit I evaluated the transfer function V0 by that and I evaluated the two poles abhi a equivalent liqloge exact nahi hai a say this is the poles without feedback no CF these are the two poles with CF okay is function me dekho omega p1 dash me if I increase CF what will happen omega p1 kama badega ke kama kama kama kama kama kama kama kama kama kama kama kama kama kama kama kama kama kama kama kama kama kama separate kis method take a separate short connection be a CF so I now figure out by choice of CF value I can move the second pole to my right and one pole to my left so this is called split splitting. So the two spools will split, the same I split two poles split split, now in any condition you will split as much as you want, phase margin will never reach 180 degree before crossing of this value, is that correct? You can understand, if you shift it more, then crossing of 0 dB will be earlier before the phase becomes 180. So what does that mean? System will become stable. So by splitting the poles, I can make even an unstable system close to stable system. What is the method I suggested? It is called splitting of poles by adding a shunt feedback capacitor, all that I did, one of the poles I took left, other pole I shifted right, separation curve, you mean it is a fast phase decrease is that correct? So they may never reach 180 degree, minus 180 degree before the gale goes to 0 dB. If that happens, what is the phase margin I will get? Positive, which means system will become stable, is that clear? So any system which is unstable can also be stabilized using feedback, is that point clear to you? So that is the trick which we are saying, if the system is unstable, I have a way to actually stabilize it. What things I will reduce? I will reduce the gain, I may reduce some bandwidth otherwise to some extent, but I will make system stable for you, is that correct? This is what the feedback is all about. It should remain stable gain, so feedbacks allows you to achieve any stable, in nature the input signals which you receive from any of the like noise coming or any transducer you put to pick up temperatures, variations, all these are in nanovolts to microvolts, is that correct? Now I want to do some processing, so I must first amplify them, is that correct? Once I start amplifying, what is my problem? The signal is so small, I will increase its gain, so I will do the instability, so what I will do? What should be the first stage? It should be feedback, because it starts from lower gain, but the output which it brings will be stable. So now the output of the sensor is fixed, is that correct? Then I will give the normal gain stage, is that correct? So in all instrumentations, signal processing or any kind, the first stage is called low noise amplifier which is essentially a feedback amplifier with a low gains, is that correct? Why it is necessary? Because I want signal to be slightly larger than what I, even in antenna, it is a signal less than a millivolt, okay. So what should we do? We must amplify it, but as soon as I put a normal amplifier, what will happen? It will actually go to negative, it will go to positive, so we have to boost it, but it is not so much that it becomes unstable, so we have to stabilize it first, gain a small gain, boost it on a small bandwidth, then increase it a little bigger than a millivolt, then normal amplification is done, is that clear to you? This is the take, why we are so worried about particularly for all signal processing applications including communication in networks and everywhere, this will be the first stage of any input part, is that correct? So you need to understand why feedback is so much relevant, is that clear? This finishes our feedback part.