 Today we are going to continue with amplifiers feedback amplifier design in the last class lecture 16 ahh 15 we had started with how to design negative feedback amplifiers ideal amplifiers and today we will be continuing with the methodology of feedback amplifier design. We have already classified ideal amplifiers as voltage amplifiers, current amplifiers, transconductance amplifiers and trans resistance amplifiers. These are the ideal amplifiers which have a unique way of representation voltage amplifier being represented by G actually should be G current amplifier by H fact there is a mistake here. So voltage amplifier by G current amplifier by H okay trans conductance amplifier by in fact here also trans resistance amplifier by Z and trans conductance amplifier by Y. So we have these ways of representing ideal amplifiers and what is the feedback for obtaining voltage amplifier voltage amplifiers can be obtained by H feedback which is the inverse of G feedback. So where the H parameters are and the inverse of H is resulting in G right. So voltage amplifier is represented by G matrix in order to reach the G matrix we have to start with H feedback that means H parameter of the amplifier as with H parameter of the feedback networks so that it becomes a series arrangement at the input and shunt arrangement at the output series arrangement input increases the input impedance shunt arrangement at the output decreases the output impedance. So it reaches an idealization of voltage controlled voltage source. So you can see here current amplifier on the other hand is ideally represented by H parameter. So we start with G feedback in order to reach idealization the G feedback okay inverted results in the H matrix the G feedback topology is where G parameters are it is shunt at the input admittances at series at the output impedances at so it becomes current controlled current source. So it is an ideal current amplifier realization G parameters at and inverted G results in ideal H. So trans conductance amplifier the ideal matrix is represented by Y matrix so that means this Y is the inversion of Z matrix Z parameters at both at the input and at the output so it is series at the input and series at the output. So the amplifier becomes a voltage controlled current source and it is ideally represented by a Y parameter which is the inverse of the Z parameter. The trans resistance amplifier on the other hand is ideally represented by Z is the inverse of Y Y parameters at if they are in shunt at the input and shunt at the output so the Y parameters at and inverted Y is the Z parameter of the trans resistance idealization. So these are the procedures these are the topologies of feedback arrangement okay this is the mathematical technique of adding the parameters simply and inverting to get what we want adding the parameters simply and getting the inversion what we want. So this is the way it is going to start right if you want the current amplifier okay which is the H parameter you start with G if you want the voltage amplifier which is the G parameter okay you start with H. So if you want the trans conductance amplifier you start with Z okay if you want trans resistance amplifier you start with Y. So let us we have demonstrated this procedure very clearly earlier in the 15th lecture by designing the Y feedback that is realization of Z matrix okay. So the trans impedance amplifier was designed systematically and give an example of such a trans impedance amplifier design we are now going to design a general amplifier topology okay. So that was also illustrated by taking immittance matrix and today the examples are chosen on the other 3 amplifiers voltage amplifier trans impedance amplifier and current amplifiers these 3 examples are going to be illustrated in today's examples. So let us start with the voltage amplifier design so ideal voltage control voltage source okay so the procedure is going to be that we have to start with the ideal amplifier matrix which is the G matrix 000 it should be and GF which is independent of the amplifier parameters it should be dependent only on the feedback network parameter. So this is what we want to achieve which means we go to the H parameters for the amplifier non ideal amplifier H parameter of the non ideal amplifiers will be adding with the H parameter of the suitable feedback network okay in order to sort of get the ideal G we have to invert the composite H matrix. So let us consider this amplifier now HIE is going to be nothing but RIA HIE is the H parameter of this amplifier that means it is shorted at the output and HIE is nothing but the impedance seen at the input when the output is shorted since there is no feedback whatever we do at the output has no role okay at the input so it is nothing but straight away RIA. HIE on the other hand is open circuit the input and open circuit admittance at the output so it is nothing but HOA is 1 over ROA next HFA is the short circuit current gain the current at the input if it is II so II is the current at the input this generates a voltage at the input which is RIA into II that into A is the voltage okay at the output which gets transferred that divided by ROA is the short circuit current and since it is going to flow case even this is positive negative this will be positive and this is negative okay it is II RIA divided by ROA is the output current short circuit current with a negative sign because it is going to flow out current flowing gain is considered as positive so what is the short circuit current gain HFA is nothing but A times RIA by ROA so HFA is minus A times RIA divided by ROA so the other parameters are this for the amplifier that is going to be used here the feedback arrangement to obtain near ideal voltage control voltage so the this is the arrangement it is shunt at the output so that output impedance comes down it becomes a voltage control device because input impedance is increasing right they are they are in series so current is common okay voltages add okay input voltage to the amplifier as to the feedback voltage to the network right of the passive feedback network and here it is in shunt that means output current of the amplifier and output current of the feedback they get added and output current is update. So the feedback network in this particular case is nothing but a attenuator network okay so this is R1 this is R2 this is the feedback network that is going to be used here to modify the property of this amplifier so that it becomes an ideal near ideal voltage controlled voltage source shunt at the output series at the input. So this is the parameters add that means the g parameter of the amplifier now okay as with sorry h parameter of the amplifier as with the h parameter of the feedback network in order to give you the composite network this is the feedback network R2 and R1 output voltages went back to the input VFB by VO is R1 by R1 plus R2. So again h parameter of this is R1 parallel R2 when you short this okay so the h parameter of this is R1 parallel R2 okay and the h f feed forward here from this to this is going to be current short circuit current is going to be R1 by R1 plus R2 with a negative sign and then the open circuit the input and the admittance 1 over R1 plus R2 that is the admittance of this open circuit admittance and the feedback when you open circuit voltage at the input for an output voltage is R1 by R1 plus R2 positive. So I can see that the h R feedback is same as h f feedback okay feed forward only opposite in sign that is the case with h and g parameters in general of passing networks okay. So we have now written this composite the g parameters composite h parameters of the whole network and converted into g parameters inverse here this is the g matrix. So this g matrix comes by transforming the composite h matrix okay and it is inverse so you have the feedback parameters getting added with the amplifier network h parameter and the h parameter is inverted to give you the g matrix as shown here. So this is the inverted g matrix of the network so you can see that this is nothing but 1 over PR of the feedback network which is 1 plus R2 over R1 R1 by R1 plus R2 inverse of that is 1 plus R2 over R and the rest of the parameters you can see clearly here that the loop gain of the whole system okay makes this rest of the parameters all go towards 0 because A is very large okay RIA may be also pretty large R1 is very small this is what I call as okay 0th that is 0 of third order because this is going towards 0 this is going towards infinity this is going towards infinity the third order 0 that means this is definitely going fast towards 0 this is 1 over A okay first order 0 second order 0 so this is a second order 0 this is again a second order 0 this is finite. So it is very clear that we have achieved a voltage controlled voltage source of gain 1 plus R2 over R1 hearing the ideal element values for the other parameters of the matrix G matrix this is the model right this will be a very high impedance okay or very low conductance okay this is also very high impedance or in fact very low resistance not this the output impedance which is becoming very low output conductance is okay going to be very high. So this is going towards voltage control voltage source so we have reached this voltage control voltage source that we desire with very high input impedance seen here which is equal to the original impedance into loop gain which is A of this stage loop gain is roughly this you can just note that approximately it can be evaluated very quickly okay this is the impedance that comes in between. So if the gain is A and this attenuation is R1 by R1 plus R2 the loop gain is roughly equal to R1 by R1 plus R2 into A okay if you ignore the effect of loading due to this on R1 okay. So what happens is loop gain in this case is roughly equal to A into R1 by R1 plus R2 so the input impedance of the amplifier gets enhanced roughly to this value original value into the loop gain this is the new impedance that means impedance goes very high and output impedance should be reduced it is going to be reduced by the same factor of the loop gain so it goes towards 0 this goes towards infinity that is how it is becoming voltage control voltage source and the gain becomes only dependent upon the inverse transfer parameter here which is 1 over inverse transfer parameter 1 over R1 by R1 plus R2 or 1 plus R2 by R1. So an example we want to design using 741 for example okay PAMP with nearly 10 to power 6 10 to power 5 to 10 to power 6 decibels that is 100 to 120 decibels of gain DC gain input resistance of 1 mega ohm output resistance of 100 ohm let us say RS is source resistance 10K and RL is also 10K let us consider the design of a non-inverting amplifier of gain 100. Now 1 plus R2 over R1 is equal to 100 because 1 over feed deck parameter R1 by R1 plus R2 is this so R2 by R1 okay you get it as 99 so R2 is equal to 99 R1 so we can actually say that R1 plus R2 is equal to 100 R1 so substituting these values we will note that the GI that you have as the first parameter of the G matrix inverted matrix going towards 0 10 to power minus 10 you can see and you can also have a means of finding out what should be the value of R1 plus R2 in order to make this negligible okay this is the output impedance in order to make this insensitivity output impedance you have to select R1 plus R2 accordingly that means if you select R1 plus R2 much greater than 100 you have in desensitized it with respect to the output impedance similarly as far as input impedance is concerned you can actually desensitize with respect to input impedance okay if RS okay plus R1 parallel R2 is chosen to be much lower than input impedance okay which can be approximated to 0 G naught is also coming out to be approximate to 0 right so this is output impedance GR is going to be the reverse transmission after feedback this is also very nearly 0 minus 10 to power minus 10 R1 A by A into RI this is the third order 0 I am talking about so these are the sort of conditions that must be fulfilled in order to make these things insensitivity to input impedance of the amplifier and output impedance of the amplifier R1 plus R2 should be much greater than 100 ohms and RAA should be much greater than R1 parallel R2 all resistors are so this is the way resistors are selected so actually speaking I think final diagram there is this was started as 10 key it does not make much of an influence right so this is the final circuit which gives us voltage control voltage source with gain equal to 100 the next to design is the voltage control current source trans conductance amplifier trans conductance amplifiers are pretty common in high frequency filter design to these days analog multiplexes sample and hold circuit modulators and mixers in fact op amp was relatively first offered as a trans conductance type of op amp okay for these communication applications like modulators and mixers these are the 1TIT 3080 OPA 860 these types let us see how we will go about designing an ideal voltage control current source as you can see there control voltage VI results in an output current of GM times VI coming in coming into the code so the matrix that we are interested in reaching when we go to the idealization is nothing but the Y matrix I I I I I not in terms of Y matrix when the independent variables are VI and Vietnam so Y matrix will be 0 0 0 and GM which is independent of the amplifier active device parameters dependent solely on the passive device so feedback around non-ideal amplifier to convert it into a voltage control current source okay so this is for a current control voltage control current source so voltage control again means that input impedance should go high current source means output impedance should go high so the arrangement is series at the input and series at the output and what is the parameter that adds we have to start with we want an ideal Y parameter so we have to start with Z parameters and the Z parameters which are called open circuit parameters add simply VI A adds to VI P VI A adds to BOP and the final load voltage occurs here and final input voltage occurs here so the current is common both at the input and the output this should be strictly I I so input current is common both at the input and output current is common for both the ports so this is the topology for a voltage control current source realization Z parameters are the ones to be taken and added so let us consider the Z parameters for the non-ideal active device so Z I A equals R I A because the reverse transmitted meter is 0 input and output are isolated so this is simply Z I A and this one is simply Z O I A is equal to R O A now what is the Z F A for this so Z F A is defined as when you have an input current of I I okay I I into R I A is the input voltage that times A is the open circuit voltage at the output so let us see the polarity this is plus and that is minus so it is positive so we have the Z parameter of this in this manner R I A R O A and this Z F A is nothing but okay this is Z F A so let us see the composite actually feedback network is going to be again nothing but any impedance between the output and input okay so this is the feedback network so it is just a network Z F so what is the Z parameter of this it will be Z F I mean I I pumped into this result in a voltage which is I I into Z F okay so Z F at the output open circuit parameters of this feedback network okay minus Z F and minus Z F here because when I pump a current through this the voltage is going to be minus Z F into I I okay at the output similarly if I pump a current from the output it will be minus Z F into I O right because this total arrangement is going to be coming like this so you can see that the grounding is done for this if we use single ended I mean differential input single ended output or PAMP is used this is already grounded and this ground comes here so these voltages will be getting added with this as positive and when I am pumping I I okay this develops I I into RF and that will be in opposition to this voltage so if this is A B I A which is A into R I A into I I this is going to be minus that so that is how okay that minus sign is attributed to both feedback and feed forward parameters of the feedback network so the composite Z parameter is going to be this A times R I A with this as minus okay this as plus okay and then this as plus RF is one way of looking at it for that particular direction for which we have marked right we can consider it as plus and this as minus and this as minus so this is one way of looking at the whole thing right it depends upon the direction unit we have marked the current so if you have marked I naught as this then actually this particular thing is going to be plus here minus here minus that as we had indicated earlier right so this will be ahh minus here okay and plus here when it is inverted plus here okay so the determinant okay of the matrix is changing the parameters this way that this becomes equal to okay minus 1 over RF this is RF RF gets sort of A R I A A R I A minus 1 over RF is the parameter this it is reaching this is going to be 0 0 0 that is the final by matrix of this whole thing so this is the network this voltage VS is going to carry make this RF carry a current of VS by RF VS appears here this is VS so this is VS by RF okay and that current is going to flow in the opposite direction to what is marked as I L so that transfer parameter is minus 1 over RF design a voltage control current source with trans conductance of 1 milli siemens for a source with RS equal to 10 kilo ohm and with a load of 1 kilo ohm using 741 op amp 741 is a general purpose voltage op amp with DC voltage gain of 10 to power 500 decibels input resistance R I A 1 mega ohm and output resistance of RO to 100 ohm RF is equal to 1 kilo ohm this is what is chosen in order to make the conductance 1 milli siemens so we have it here now according to us this is going to be plus and this is going to be minus for that particular direction marked okay that is the only if you change the direction there up in the block to the opposite direction as positive then this will retain the previous side and here it is minus and this is plus this is plus okay and therefore this becomes now okay minus plus this becomes minus so this minus plus this is plus so you can see that ultimately for the values that we have given there the determinant of the matrix is 10 to power 14 into RA into RF roughly okay and it is that that magnifies this matrix parameters so A comes everywhere in the denominator here it gets cancelled and therefore it is minus 1 over RF so you can see that by matrix goes to a 0 0 0 and minus 1 milli siemens design a voltage control current source with trans conductance of 1 milli siemens for a source resistance of RS equal to 10 kilo ohm and load resistance of 1 kilo ohm using TL 0 8 1 op amp TL 0 8 1 is a general purpose bifat voltage op amp with the DC voltage gain of 10 to power 5 100 decibels input resistance of 10 to power 6 mega ohms and output resistance of 100 ohms you will see that the by matrix of such a network now becomes 10 to power minus 14 close to 0 10 minus 10 to power minus 17 again very close to 0 and 10 to power minus 14 that is the order compared to 10 to power minus 3 so this become 0 compared to this 1 milli siemens totally independent of the device parameters finally we come to the current control current source current amplifier with the supply voltages getting reduced to even less than 1 volt and the present day amplifiers have to become current amplifiers in order to deliver a required amount of power the only swing that can be achieved is current swing so the future of current amplifier is very bright compared to voltage amplifiers where voltage things are in demand and supply voltages have to be very large for that is not strictly compatible with the current day technology of supply voltage reduction in order to keep up with the advances or in digital design operational current amplifiers are for some reason not very popular commercially okay but they have to become popular in future so what is the ideal current amplifier it is current control short circuit at the input and a current source please note that output is shorted same thing we should have done we should have done with voltage controlled current source that the output should be kept shorted in order to deliver 0 power and keeping it open is a mistake here we I and I naught are the dependent variable I I and V naught are the independent variable and these matrix as 0 0 0 and HF independent of the active device and dependent solely on the passive network that is used for feedback ideally represented by H parameters the arrangement of feedback is since it is current control shunt at the input since it is a current source series at the output so currents add here voltages add at the input impedance can be brought down by current control by shunt arrangement at the input and output impedance can be increased by series arrangement at the output so we have the composite matrix now actually the network is going to be the amplifier network here which has to be put RIA and we are going to start with the we have to ultimately obtain an ideal H matrix we have to start with G matrix for the amplifier as with G matrix of the feedback network and this has to be the whole thing has to be inverted to get the H matrix ideal H matrix with 0 0 0 and HF independent of the amplifier parameters so this is going to be ROA this is going to be A times VI so the feedback network is going to be such that we can introduce the feedback network so you can introduce the feedback network here right such that the current here portion of the current here is fed back as voltage at this point right so the current is sensed here and fed back as current into the feedback okay so current sensing is done by putting a resistance across it and feeding it back as current okay at the output okay so this is the composite arrangement and let us see what happens to the G matrix that we get here we start with G matrix add 1 over RIA is the G parameter at the input of the amplifier 1 over R1 plus R2 is that due to the feedback network okay at the input okay plus 1 over RS due to the source and the feedback is R1 by R1 plus R2 okay and as far as current is concerned and this one is A plus R1 by R1 plus R2 right actually there is a negative sign associated with this okay this is the current fed back okay so this is negative feedback because loop gain is determined mainly by this into this divided by this into this okay so the H matrix is going to be this divided by determinant of the matrix minus this divided by again determinant so here since A is coming both a denominator and denominator this particular thing is finite and all these three parameters go to 0 this 1 plus R2 over R1 it becomes okay so this is actually the current gain minus so this is the current amplifier that is designed here can see that this is the G parameter getting added to the G parameter of this our current is sensed at the output and front head back to the input is minus R1 by R1 plus R2 okay so that is incorporated as a composite okay the G matrix so this is the feedback arrangement this is the load so this is where V naught is taken this is I naught okay this is V naught across the load so we have this current gain I naught by I I becoming equal to 1 plus R2 over R1 with the negative sign totally independent of the active device parameters okay so this is the final current control current source okay source resistance load resistance R1 and R2 this current I I goes through this develops a potential I I into R2 that gets dropped across R1 this potential is nearly 0 so that I I into R2 by R1 flows through this this way these two add on the output current so in conclusion we have seen here that before we end we can also give an example here let us say same example okay this is say 99K and this is 1K then the current gain is 100 okay because 1 plus 99 by 1 equal to 100 with a negative value current going in this is going to be going out okay so minus 100 so these impedances do not matter at all ROA okay so if this is VI this is minus A times VI which is same as VI so this is how we compute the whole thing okay conclusion is that we have shown how starting with H matrix to get ideal G matrix which is voltage control voltage source we can design voltage amplifiers starting with G matrix okay adding G parameters of the amplifier and feedback network getting H matrix we can design current control current sources or current amplifiers we can start with Y matrix Y parameters at and which ideal Z matrix and design trans impedance amplifiers start with Z matrix late to ideal Y matrix and get trans conductance amplifiers or trans impedance amplifiers so the amplifier design procedure for feedback amplifier design is just this we can use this concept for example using human transistors so now I can tell you how using transistors in place of op amp I can design this using this as the active device okay what are the parameters of this let us say we want to design a trans impedance amplifier or trans resistance amplifier using transistors so what is the procedure we have to start with the Y matrix for this so this GIA is 0 and if you have VI here GM times VI is the current in the output so short circuit current at the output is GM times VI where VI is the input voltage so current goes in since it is equivalent circuit is for the MOSFET okay GM times VI and then we have what you call as output conductance GDS all these things we have already discussed when we discussed the MOSFET okay earlier as active device so this is GDS this is 0 this is the active device parameter okay this has to add to GS here so consistent this GL here okay and then the feedback network is GF so we have this as GL this as GS and the current at the input is IS so we can now find out the this is actually speaking GF here and this gets added to GF here this is – GF this is – GF this is – GF so actual parameter composite parameter Y parameter of this is GS plus GF – GF GM – GF okay GDS plus GL plus GF so the determinant of the matrix okay is going to be this into this – this into this so I will see that it is not having because this GF squared gets cancelled with this GF squared okay so the determinant of the matrix simply becomes okay GS plus GF into GDS plus GL plus GF plus GF into GM – GF okay so it is essentially GS okay into GDS plus GL plus GF okay plus GF into GDS plus GL plus GM into GF this actually dominates the whole scene right and good MOSFET is a device where GM is very large compared to all other conductances GM is much greater than all other GS that is how you have to build a MOS circuit if such is the case then if you now obtain the Z parameter of this composite network you will see that the Z parameter will have okay assuming that this is approximately equal to GM into GF okay if GM dominates then the whole thing is going to be divided by GDS plus GL plus GF divided by GM into GF goes towards 0 okay the other one is GS plus GF divided by GM into GF goes towards 0 this is GF GF gets cancelled 1 over GM itself okay this is approximately equal to GM because this is negligible okay so we have this 1 over GF with a negative side so this is what happens ultimately therefore this is equal to 0 0 0 and then – RF this is how we design transistor based trans resistance amplifier it is so simple as that using either MOSFET or bipolar it does not make any difference the equivalent circuit will have a modification here at the input also in the case of bipolar that is all but the procedure is exactly similar to this now similarly one can design a trans conductance amplifier by using the MOSFET or a bipolar structure what is done in such a situation is that this topology topologically this is active device and we are introducing the resistance RF as feedback resistance here so this is the topology of series at the input and series at the output so trans conductance amplifier let us say we have a finite input resistance here this can take into account the leakage etc at the input so if this is infinity then 1 over RI goes towards 0 that is all so the parameter that you have to use will be Z parameters to start with so once again you have this Z for the amplifier Z parameter is RI A for the feedback network it is RF okay and then the output it is RDS which is 1 over GDS plus RF nothing from the amplifier as far as reverse transmission is concerned but as far as feedback is concerned we have minus RF this considered as I naught this considered as I so minus RF right sorry plus RF here this considered as I naught and this will be again plus RF okay and as far as amplifier is concerned the input current is I I into RI A okay that gets multiplied by GM of the faith okay that is the current and that flows through okay that current will be fine in and it will flow through this RDS and negative voltage will appear so negative into RDS so that is the Z parameter which is minus RI A GM RDS so that means actually this is negligible okay compared to this so it is negative feedback because this into this okay in the negative sign it comes divided by this into this is the gain so the determinant of the matrix is nearly equal to RI A GM RDS into RF so that is the so that is what modifies this and you get the final Y parameter as this divided by RDS plus RF if you want to add the load resistance here you can add okay you can add the source resistance here right so RL divided by the loop gain RI A GM RDS RF so we get this as the what is that final Y parameters of the network okay again here this goes to minus this divided by the same thing and here it is RI A plus RF plus RS divided by RI A GM RDS into RF here it is nothing but 1 over RF so it is essentially equal to 0 0 0 1 over RF so even for transistors this can be applied and one can design trans conductance and trans resistance amplifiers couple these trans conductance with trans resistance you get a voltage control voltage source couple trans resistance with trans conductance you get a current control current source so that means all the four types of amplifiers can be easily realized and these are the structures which are really the integrated circuit feedback amplifiers which are used particularly no number of stages cause the order of the system to increase and make the system become unstable and therefore it is common practice to use single stage structures okay for local negative feedback topology that means trans conductance and trans resistance are a simple structures which may not give problem in terms of stability in structures therefore voltage control voltage source and current control current sources can be obtained by cascading these rather than using complex structures like pair for H and G feedback.