 Today in lecture 12 will be discussing the static characteristic of feedback system. So let us see what we have done in the lecture 11 previous lecture we had considered the basic aspect of negative feedback and positive feedback in the last year last lecture. What is the major advantage of negative feedback in systems that is desensitization of the active device parameter in the performance factors of the feedback system. And the second important function is to generate an inverse function okay given a specific function it may be a non-linear function right. So to generate an inverse function right we put it in a feedback loop okay and that can facilitate generation of inverse function. So these two are the main advantages of negative feedback and a variety of applications emerge out of it. Feedback output follows the feedback output follows the input that is the basic idea that we get when the loop gain is very large compared to one. So this is an important basic principle that the feedback output always follows the input in any feedback negative feedback system with loop gain much greater than one. That means error at the point of determination of the error okay in a feedback system the error tends to 0 as loop gain tends to infinity. The resultant effect we have voltage follower application in electrical engineering current follower or these are called buffer stages acting as power amplifiers. So whose performance in terms of transfer parameter since it is equal to 1 is independent of all the parameters used in the loop okay. So frequency follower phase follower so these are the variety of applications we have discussed in the previous class right. This is in what is called encoder decoder kind of loop that we have formulated which is very useful in again a variety of applications in communications. Square router from a square FM detector from an FM generator D to A converter from A to D converters are the resulting functions in signal processing that emerge out of feedback negative feedback. So today we will be discussing the effect of offset in feedback systems. Let us say G1 represents the sensitivity factor of a block that we are considering or G1 is the transfer function of the system. So X naught is equal to G1 into XES that is if we have a block that is made up of G1 this is what we are considering G2 is the feedback system this is X naught this is XI XES. So this is the error so we have seen that this G1 block has its output which is nothing but XES times G1 if there is an offset what happens is X naught is not equal to just this into the input plus some factor which is independent of the input okay this factor which is independent of input in this case XES okay is called an offset this can arise in any system okay. So it is still a linear system so in a linear system if the output is having a factor which is independent of input it is called offset okay and what happens to the offset that is introduced at the output okay to the system. So we are now having this system XI is the same input okay XF is the feedback output which is X naught times G2 let us consider this is also linear like this okay but does not have any offset here so offset is present only in this we are considering that is considered as an additive okay signal at the output this is the XO offset. So we have here this output now coming as X offset plus the output of the ideal block without any offset. So XES into G1 emerges here so this is XES into G1 so this X offset gets added here okay so this X naught is going to be XES into G1 plus X offset so that is what is written so we have here XI minus G2 into X naught okay so we have input to this as XI minus X naught G2 into G1 that is what is emerging here plus X offset okay is equal to X naught. So what happens X naught now becomes equal to G1 into XI by 1 plus G1 G2 this is the result of negative feedback now so we can see here that we got back the original relationship for the transfer so XI is G1 into 1 plus G1 G2 so if G1 G2 is much greater than 1 this is nothing but XI by G2 this is the inverse function okay plus X offset and if G1 G2 is very large this gets reduced to 0 this tends to 0 that means offset at the output okay of a feedback system is the original offset okay transfer feedback divided by the loop gain roughly so this is what we can now understand in terms of offset getting reduced considerably so this can be thought of as another input coming there so whatever input comes even if it is noise for example that gets reduced by loop gain so offset is a sort of component which can create noise because offset if it is a constant value independent of time okay can always be subtracted whereas what happens is the offset is dependent upon temperature and time etc so it drifts it changes with respect to time and that gets confused with the signal that comes into the picture right. So it gets added to the signal and therefore it might cause the effect of low frequency noise very low frequency noise okay so this is also getting eliminated in a negative feedback system by loop gain by a factor of loop gain okay now nonlinearity you are supposed to have a linear system okay and what happens to the nonlinearity with practically is there in most of the systems right so the nonlinear effect can also be thought of as an effect that is introducing noise okay unwanted component at the output you can treat it this way also right so it also gets reduced that is in principle what happens in negative feedback but we will mathematically establish this nonlinearity and particularly the most important nonlinearity that we have to understand in system design first okay is the saturation analytic most of the systems okay maybe linear up to a certain range okay of input and thereafter the output gets saturated what is the saturation saturation simply means there is no change in output in that region for a change in input no change in input for further changes okay no change in output okay for further changes in input that means delta X naught by delta XES for example okay is going to no change in output for further changes in input that is called saturation input output relationship of G1 and G2 can be nonlinear therefore so how do we tackle this system in terms of linear analysis so we have to make what is called a piecewise linear approximation to nonlinearity so in general G1 is going to be a function of the input itself okay or G2 is going to be a function of its own input which may be X naught in this case so that is what is meant by nonlinearity most common nonlinearity saturation and it is the odd symmetric saturation effect that we are considering that means a thing goes into saturation it may be linear here okay on either side okay in a symmetric manner let us consider that kind of nonlinearity okay output is saturated the feedback loop gets broken now when any of the blocks inside a feedback system go to saturation then the loop gain goes to 0 so in saturation state the loop gain goes to 0 so what happens is that the feedback gets broken the dynamic range of the input signal over which the feedback effect exists is what is called the lock range of the feedback loop okay where for example output of the feedback okay tracks with the input that happens only as long as the thing is within the limits of saturation that we call as may be lock range of the feedback this is an important concept that we have to understand in feedback so saturation nonlinearity for small changes around a cohescent value now cohescent becomes important that means operating point at which the system is functioning is an important aspect of nonlinear systems that we have to consider and then assume it to be linear only over a small range around the operating point the for a path gain now the gain function may be approximated as this also called sensitivity around that point okay operating point so this sensitivity so output parameter may be different from the input parameter so that is why we have instead of gain function we call it a sensitivity factor in general when the output is of a different parameter compared to input saturation may be modeled as normally hyperbolic tan function so that is when XI is large it saturates okay positive it saturates at a positive level and negative it saturates at a negative level okay so X naught therefore is modeled as G 1 0 that strictly speaking the factor which is linear this is the linear term output is linearly related to input then the nonlinear terms so they are there is no square okay because it is all symmetric so cube minus right so what happens is that it is linear over a certain range around 0 and then the first thing that comes into picture is the cubic term contribution then the fifth order so as you go further and further in XES magnitude the higher and higher all the contributions become more and more dominant and that is how the output saturates so delta X naught by delta XS itself that is the slope itself is a function of its input so this is odd symmetric this will be even symmetric okay that is what is happening the slope is even symmetric that is modeled here this is the hyperbolic tan function saturating okay at this point and this point okay on the other side and this is this slope of this okay from a maximum value at X equal to 0 okay it is going to 0 on either side symmetrically so this is the typical nature of most of the blocks that are used in systems so study of saturation can be done by making use of for example the hyperbolic tan function in general we can study it using piecewise linear approximation to nonlinearity negative feedback system and saturation that is consider this it is assumed that G2 is linear and there is no output offset okay if saturation is simplified to include only the third order term now okay that means you are having a mild amount of saturation coming about only due to the first nonlinearity that is the third order term in saturation symmetric saturation so X naught therefore is equal to G10 into XI minus G2 into X naught that is XCS okay into 1 by factorial 3 which is 6 G10 into XCS cube so X naught now is equal to G10 XI by 1 plus G10 G2 this what is already known to us and what happens here you can see G10 by 1 plus G10 G2 into XCS cube so when the cubic nonlinearity has small contribution to this linearity then we can assume that rest of the higher order terms go faster to 0 okay so XCS cube is nothing but XI by G10 G2 whole cube that means G10 G2 the loop gain when it is large the error due to the nonlinearity goes to 0 very fast because of the loop gain being very high compared to 1 that the cubic of that loop gain is going to be huge quantity that means it becomes almost linear because you can neglect the contribution due to this nonlinearity so that is what is mentioned in this slide so that is demonstrated very clearly by the macro model now the significance of macro model is understood by you here we had already discussed how the nonlinearity can be modelled as piecewise linear approximation so here we have G1 stage which is V in voltage amplifier okay which is 100 times V in as the voltage source here voltage control voltage source with gain equal to 100 and then we have a voltage limitation at the output caused by a macro model so the power supply limitation okay of an actual amplifier brings about this limitation and you see how that has been brought about here artificially in the model okay using devices which may not be there in the actual amplifier at all this limitation comes about due to power supply so that has been modelled as a diode in series with 10 volts supply here this has been modelled at the output with a diode in the reverse direction and the minus 10 volts here okay so what happens with this effect right we have a gain of 100 for this stage which is coming about as a linear relationship that means slope is 100 this is the output of the amplifier and this is the input and then it goes abruptly to saturation okay at 10 volts positive on that side and minus 10 volts negative on this side that has been modelled then we have put another voltage control voltage source with gain equal to 1 so that this becomes a voltage control voltage source which is simulating a characteristic of an amplifier with gain linear in this range okay that means it is linear all the way up to okay this 20 volts okay this 10 volts by 100 here which is okay 0.1 volt is minus 0.1 volt 10 volts by 100 110.1 so that is the linear range of the amplifier that I am using in a feedback loop so this feedback loop has G2 equal to 1 by 10 what is 1 by 1 plus 9 1 by 10 so there is G1 equal to 100 okay G2 equal to G10 equal to 100 G2 equal to 1 over 10 so the actual gain of the amplifier because this output the input follows the I mean output follows the input so this voltage is also VI and this voltage automatically becomes 10 times VI because of the attenuation factor here 1 by 10. So actually it has been designed for an amplifier of gain 10 and the system saturates at plus minus 10 volts that is what is depicted here and you can see what is called the static characteristic of the feedback amplifier so the feedback amplifier also goes to saturation at the same point as 10 volts and 10 volts however the voltage range over which it is linear now is going to be this change which is 20 volts okay 20 volts divided by 10 okay that is 2 volts that is 1 plus minus 1 volt this is the range so this is what happens this range minus 1 this range is plus 1 so within this range it is going to be linear perfectly linear so you can see here the input limit to saturation that is the lock range of my stage the range of input okay is going to be plus minus 1 volt within which it is going to be linear. So this is demonstrated by applying a signal low frequency 1000 hertz okay to the amplifier and you will notice that it has gone into saturation as plus 10 volts and this is at minus 10 volts so the output does not change as the input is changing so it is getting distorted okay because of saturation limits so we should confine our input to plus minus 1 volt in order to avoid this okay. Now feedback system within offset so what I have done is that I have made the limit of saturation change from symmetric value of plus minus 10 volts to 0 to 20 volts so this is bringing about the saturation at 0 and the other one is at 20 volts so obviously the operating point of this at the input should now change from 0 to an offset voltage of about 1 volt so we have to have a 1 volt operating point around which the signal can equally swing on either side so that is the effect of offset in a system that is input itself should be offset suitably in order to gain advantage of the maximum dynamic range of the feedback system okay. So the dynamic range has remain the same as before that is 20 volts peak to peak however in order to gain advantage of the dynamic range of 20 volts one has to operate the system at an input voltage of 1 volt or the output cohescent of 1 into 10 that is 10 volts. So the input should have a cohescent of 1 volt output will then have a cohescent of 10 volts so you can symmetrically swing on either side of the cohescent for this particular system. So you can see the piece wise linear approximation now to non-linear systems what is done is G2 is taken in this example as 1 G1 is as before 100 over a range of input which is plus minus 50 millivolts from 50 millivolts to 550 millivolts it has a gain of 10 that means the gain is changing instead of continuously changing we are changing it piece wise okay. Then for a range of 550 and above it has gone to saturation gain is 0. So the slope is 0 so the slope is 100 initially changes to 10 and slowly changes to 0 there beyond this point and what happens to this kind of non-linearity which is an approximation to hyperbolic 10 non-linearity and that is modeled now again you have a voltage control voltage source with gain equal to 100 and then you have put an attenuator here okay so the attenuation is going to be initially 1K okay none of this diodes conduct okay initially okay and therefore the output is open so gain of 100 appears at the odd then this 100 is simply transferred to this as 100 because we are using a buffer stage here of in the gain. So the model is now depicting a non-linearity which is we can be drawn here gain of 100 then gain of 10 then gain of 0 right. So this is the model the voltage control voltage source is having okay that is simulated by these piece wise linear approximations the diode resistor scheme that is put in full feedback output is completely feedback that means feedback amplifier gain is 1 because output is fully feedback. So V naught by VI is 1 so what happens now this is the transfer characteristic of the feedback amplifier now you can see that it is almost linear okay fully right all the way up to saturation point okay the error is extremely small you can not visibly see this actual characteristic of output versus input of the voltage control voltage source okay is given here this is gain of 100 is gain of 10 and 0 so it is actually non-linear over the entire region okay. So this is its input and that is the output and that input in a feedback is almost not visible at all as far as the transfer characteristic is concerned that is how it gets the attribute of reducing distortion in feedback. So this is what is the input signal now is applied okay 1000 hertz as before okay this is the input and it is 10 times the input is going almost all the way up to 10 volts and is perfectly linear right now input is changed over to value such that output goes to saturation so output is getting saturated at plus 10 volts and this is at minus 10 volts but before that it is still almost faithfully reproducing the sine wave that means in spite of the change in gain from 0 to 500 5 to 10 it is 10 okay we have a almost faithful reproduction of the signal but of course since the gain goes to 0 here there is distortion appearing there. Now let us consider the lock range of a system with multiplier put in feedback of an amplifier. So G2 in this case is nothing but this V naught is getting multiplied by VC by 10 here so the transfer function of this multiplier under this case when VC is the control voltage so this is acting as a voltage controlled amplifier the gain is directly proportional to the control voltage here so VC by 10 so multiplier in the feedback path causes it to become a divider and therefore what happens here this is VC V naught by 10 multiplication so VI becomes equal to VC V naught by 10 output follows the input okay feedback output follows the input so we have V naught equal to 10 VI by VC this is valid along as VC is positive VC has to be positive because there should be no change of sign here because change of sign is here so that overall lip gain is negative and it is negative feedback okay that means VC should be from 0 and above. However okay up to 10 volts the multiplier function thereafter multiplier saturates that means this whole thing has its transfer parameter going to 0 of beyond any of these 2 inputs going to 10 volts so the limitation is put by the multiplier for its input as VC from 0 to 10 volts okay so 0 to 10 volts is the range for VC within which it can function okay that is corresponding to the lock range here and corresponding to which what is the range of VI for which this can function okay obviously range for VI is such that output of the multiplier can go to plus minus 10 volts okay and therefore VI range is still equal to plus minus 10 volts however VC range here okay is 0 to 10 volts so the lock range will be corresponding to VC being 0 to 10 volts again at 0 output goes to infinity so it should be above 0 okay it can be equal to 10 volts at which point full output is fed back to the input it is acting as a voltage follower otherwise it will be acting as a non-inverting amplifier which is greater than 1 it gain greater than 1 square rotor now in feedback so we have now VI equal to V naught squared by 10 here so VI is equal to V naught squared by 10 so because of the squaring operation here right there is no meaning to the sign here therefore it is always going to be positive voltage here okay so that means actually VI has to be always greater than 0 for this to be satisfied because V naught squared is always positive V naught squared by 10 is always positive VI has to be restricted to okay should be greater than 0 obviously since this is the output of the multiplier it should be less than 10 volts so VI limit now comes as the lock range comes as 0 to 10 volts for VI for this loop to function properly with the loop gain becoming greater than much greater than 1 so then only it can function and then only it can function as a square root so now this is a DC feedback loop here and it has a DC limit on the VI as lock range we have now consider this this is nothing but a comparator for DC here so V reference if it is applied here and this is R minus V reference is what should be developed here because this is at 0 this should be at 0 this is the current comparator okay of DC so output will be inverse of input that means if this is V ref minus V reference this will be positive V reference because you are putting a square here this has to remain positive okay DC because of the square operation in the feedback loop okay so this will be a square rooting operation here if you consider V reference in relation to this output but it is a DC to AC converter here this DC is converted to AC here okay this is a DC to AC converter and AC to DC converter okay in loop okay so we have a DC to AC converter in loop with AC to DC converter so we have a DC controlling the magnitude of AC here peak magnitude of AC because this is VP sin omega T this is VC so this will be VC by 10 VP sin omega T so V naught is equal to VPO and VPO is controlled by this VC so that is why I say that this is a DC to AC converter okay and this AC is converted by squaring operation to a DC and filtering okay so this is a AC to DC converter so this is the DC gain stage okay this is G1 okay so what happens if this DC remains constant then this should remain constant okay positive it should be same as V reference here this should reproduce V reference here if it is working satisfactorily and that is equal to VPO squared by 20 because VPO squared by 10 into sin squared omega T is VPO squared by 10 into 1 minus cos 2 omega T so this gets removed by the filter and the DC corresponds to VPO squared by 20 okay so that is how we get this so VPO gets of this AC gets fixed as square root of V reference into 20 so this is the result of this kind of feedback loop so where does it function satisfactorily that is what we are going to discuss so the lock range therefore is going to be a range where you can look at it here this is a multiplier so when this is VC the gain of this stage is this VC by 10 VC can be at most equal to 10 volts VC max so if you are expecting an output corresponding to let us say VP sin omega T and this VP sin omega T can only be attenuated by VC becoming less than 10 volts because VP equal to 10 volts VC equal to 10 volts corresponding to gain of 1 so this particular multiplier can only give you again which is less than 1 and VC cannot be negative because then the feedback loop will be positive feedback so in order to make the feedback loop gain negative okay we have to maintain VC positive throughout so that 0 to 10 volts is the range over which VC can change okay what is the result of this that means you cannot expect an output okay which is greater than 10 volts to be obtained here so when VP is 0 for example when VP is 0 nothing appears at the output as far as this is concerned so at that point of time what happens to this this is 0 this is 0 and minus V reference is applied this simply goes to saturation it is a high gain stage the feedback loop is broken because the gain function of this is 0 so this minus V reference brings about a negative voltage here which forces this output to go to positive saturation right so may be plus 10 volts let us say so this gain is initially at 1 value so output simply gets reproduced at the input until this DC voltage becomes equal to V reference this is what is going to happen because this is going to have a negative voltage all the time here maintaining it in saturation so that is what is seen in this characteristic so let us say we have made V reference equal to 0.8 initially corresponding to which the square root of 20 times V reference is going to be 4 volts so that is the magnitude at which the output of the multiplier is going to remain okay is going to remain constant at 4 volts until the voltage at the output of the squaring device goes to this value okay the control voltage is going to be remaining at 10 volts and therefore the gain of the multiplier is going to be 1 so output follows the input okay and thereafter output remains constant at 4 volts all the way up to 10 volts because that is the limitation by the multiplier so multiplier cannot have anything operating beyond 10 volts it goes to saturation. So this is the range of locking of this AGC system or ABC system okay this is where output voltage of the AC remains constant at 4 volts it begins at 4 volts okay and then goes on remaining constant at 4 volts up to VP of 10 volts from 4 volts to 10 volts is the lock range if you make square root of 20 times V reference equal to for example 2 volts right so that is if you put V reference of 0.2 square root of this VPO becomes equal to 2 volts so this whole thing remains the multiplier gain remains constant at 1 all the way up to this 2 volts thereafter it remains constant at 2 volts for higher voltage again lock range becomes smaller okay so this is demonstrated clearly by this experiment here so this is corresponding to VP equal to 8 volts so output can be now 4 volts okay because maximum gain of the multiplier is 1 so it has to only attenuate so it will maintain it easily at 4 volts you can see that 8 volts is the input and 4 volts is the output and control voltage is at 5 volts so this is the simulation result now VP is same to 10 volts again the control voltage is brought to 4 volts automatically okay you can see it is at 4 volts and the peak value of output of the multiplier remains at 4 volts so exactly it is followed okay the theory is followed exactly by the practical simulation now VP is made less than 4 volts it has to function at the maximum gain multiplier at is 1 so you can see that output is very nearly equal to the input this gone slightly that is control voltage now goes to the saturation so you can see it has gone slightly above 10 volts okay about 12.6 volts so that is why the gain is slightly greater than 1 okay multiplier is an ideal multiplier that is no limitation on the multiplier that has been put in the model so it has gone slightly above 1 gain of 1 so that is what has been reproduced and the DC voltage has gone to saturation as far as the up amp is concerned so this is demonstrating clearly that it is working outside the lock range now we can consider a trans resistance amplifier cascaded to a trans conductance amplifier resulting in a current controlled current up amp with gain equal to 1000 let us say so we have taken a trans resistance amplifier of 100 K trans resistance and 10 millisiemens is the trans conductance resultant effect is the gain okay initially is 1000 into 10 and it is made to go to saturation the trans resistance amplifier since output is voltage is made to go to saturation at plus minus 10 volts what is the resultant effect of this on the lock range of the system and this is a current follower so the full current is fed back to the input this output current is fed back this is the load let us say so output current is fed back so what happens this voltage gets limited to 10 volts and that 10 volts get transmitted to the output as 10 millisiemens times 10 volts okay which is 100 milli sort of amperes so the limitation of this is for currents plus minus 100 milli amperes okay is the lock range. So this is a place where voltage gets converted to current and current gets converted back to voltage so voltage to current converter current voltage converter the lock range becomes that of current okay so it is demonstrated here the transfer characteristic of output current and input current so you can see that it has gone to saturation okay at about 100 milli amperes this is the top dotted thing is 120 so 100 milli amperes is limiting range on this side also minus 100 milli amperes because the voltage limitation has been set at plus minus 10 volts so this is the voltage limitation V3 is plotted there and this is the current limitation at the input so this is the lock range. So that is demonstrated in the simulation as shown in figure so you can see what is applied is 12 milli ampere sin omega 3 is applied obviously it is going beyond saturation so it gets limited by saturation you can see some voltage is getting limited at 10 volts and current is getting limited at 100 milli amperes in the operation. So we have an F2 V converter and VTF converter earlier we had seen now voltage to current to voltage okay converter and C and D limitation on lock range here F2 V and VTF for the lock range okay is coming about because of voltages okay going to some saturation states in terms of input frequency input frequency lock range okay comes about. So because of again the limitation of the blocks within the loop they are going to have saturation a multiplier we had seen if you make it as a face detector the face detector has this kind of characteristic we had seen if this is VPI sin omega IT okay this is VP naught okay this is going to be sin omega naught okay which is going to be equal to omega IT plus phi okay. So that is a phase shift okay frequency locking occurs output frequency follows the input frequency that we have already established because voltage loop okay within the system so voltage loop within the system okay acts as a voltage follower there okay V delta V naught by delta VI is same as delta phi naught by delta PI okay is going to be the same as delta phi naught by delta T is omega naught by omega I so any phase lock loop the frequency is locked okay output frequency same as input frequency okay once the frequency are same then there can be a phase time dependent phase also here so this is a phase detector and we have established that the phase detector output average corresponds to VP I VP naught by 20 cos phi there will be another term which is cos 2 omega IT plus phi which is a high frequency term which gets eliminated by the low pass filter only the average term gets selected. So what is the nature of this phi versus the average will be a sort of cosine waveform that means it is going to 0 on either side of this pi by 2 and we have established earlier that when this BC is 0 okay when this incoming frequency is same as 10000 hertz that is the output frequency the phase shift gets adjusted cos phi gets adjusted so that cos phi is 0 that means phi is pi by 2 this is where the locking occurs when the incoming frequency is same as free running frequency of the system okay corresponding to VC equal to 0 in this case. So the characteristic of phase detector is that it goes to saturation gradually it is maximum at pi by 2 the sensitivity this if you call as sensitivity of the phase detector KBD what is it delta V average by delta phi is equal to KPD that in this case is nothing but VP I VP O by 20 sin phi and value of this is okay equal to VP I VP O by 20 okay cos sin phi at omega I is same as omega naught Q. So this is the sensitivity maximum sensitivity at this point it gradually goes to 0 okay as it goes to 0 phase and pi phase. So that means the lock range is this particular thing within which the phase can vary from pi by 2 to pi by 2 on this side and pi by 2 on it cannot almost go to pi by 2 because it is gradually approaching 0 sensitivity. So that is the limit of saturation here so that comes as a lock range limit within the phase lock loop okay. So that will be nothing but pi by 2 in a linear phase lock loop it is going to be the maximum DC here where in your eye that into okay KVCO okay is the limit. So maximum DC that this can give as average okay that into KVCO is the lock range. So pi by in a linear VCO and a linear phase detector it will be KPD into pi by 2 maximum voltage into KVCO is the lock range. If you put an amplifier with gain A naught that A naught also comes in the picture here. So the lock range of this systems is dependent upon okay the saturation range of each one of the blocks whichever is lower is the one that limits the lock range okay that is the conclusion that we can make in this gain distortion effect will be considering perhaps as quantity effect so we can put Xi as sine omega t and see how different from sine wave it is going to be at the output in terms of distortion factor this particular thing will be discussing in the next class right. So noise we have already discussed is an additional input at the output okay just like offset and that also gets reduced because of feedback by loop gain. So this is the conclusion that we have made okay static characteristic of negative feedback system has been discussed distortion in terms of distortion reduction linearity noise reduction effect of saturation dynamic range of the system where it works as proper feedback system called lock range dynamic characteristic of feedback loop will be the topic of next lecture.