 Today we are having the 38th lecture in the last class we had started with discussion about phase lock loop which is strictly speaking a frequency lock loop and discuss some of the applications at the end. Today we will go into further details about the design of this so called PLL or FLL. So we had seen that frequency follower is a phase follower we had actually earlier the true PLL having a VCP that was getting replaced by a VCO which is an independent oscillator controlled by a control voltage in the loop itself okay. So the omega I is the input and we can consider this in terms of initially when this signal is not applied as having a VCQ here which corresponds to an omega not Q here and this being connected to nothing this PLL has now a free running frequency this is called the free running frequency which can be set by adjusting the VCO parameters so that changes both KVCO which is called the sensitivity of the VCO okay which is nothing but delta omega not by delta VC. So the VCQ makes this free run at omega not Q and nothing comes out of this low pass filter of even if there is a feed through okay. So output remains continues to remain at VCQ and at which point if one now feeds an input here corresponding to omega I equal to omega not Q again nothing should happen however this has a component of twice omega not Q at that point and a DC component so the DC component corresponds to cos Phi because there is likely to be a phase shift of Phi between this component and this component. So that cos Phi should be also going to zero so that VC remains at VCQ and therefore the phase shift case adjusted automatically to Pi by 2 so Phi becomes equal to Pi by 2 for this. So it is now phase locked okay to Pi by 2 so a phase follower frequency follower is naturally a phase follower the phase detector does not know whether it is the frequency that is varying or the phase that is changing right. So it just follows the phase delta Phi not by delta Phi I therefore is equal to 1 by 1 plus 1 over loop gain and the loop gain is made up of these components it has DC component which is KPD then KA and KVCO that is what is called DC loop gain and then it has component here corresponding to low pass filter so the actual loop gain is nothing but GLO which is KPD KVCO KA divided by this transfer function 1 plus S by omega LP where omega LP is equal to 1 by RC. So if you substitute this as 1 over GL here you get S by GL not plus S squared by GL not omega LP. So this is what is called the natural frequency squared of the system and this is what is called omega N into Q okay and therefore the omega N into Q okay will be equated to GL not so we have this Q equal to root of GL not by omega LP for this. Omega N being equal to square root of GL not into omega LP. So these are the equations governing the phase following action delta Phi not by delta Phi I strictly should be equal to 1 if these components do not contribute much that means actually S equal to J omega here corresponds to the dynamics of the phase lock loop the static characteristic just says output phase follows the input phase output frequency is equal to input frequency that means if S equal to J omega is substituted in this what does omega corresponds to omega corresponds to the rate of change of frequency at the frequency of the change in frequency. So frequency of the change in frequency is the same as the frequency of the change in phase so it is that omega that is to be put here. So this is something that we should strictly understand very well. So once the phase locking phenomenon is understood as a linear system like this is the S equal to J omega corresponds to the frequency of the change in frequency. Okay lock range of this system is actually a static characteristic where we had change the ahhh omega incoming okay starting from omega not Q and if you plot VC it will be initially at VCQ at this point corresponding to omega not Q thereafter it is going to change on either side this way this way right keep on changing this way right. So the VCQ is going to change from VCQ to VC of corresponding value depending upon how far away from omega not Q omega I is this way or that way and at one point of time it goes out of lock again we start with omega equal to omega not Q go towards this range and it stops at this point right and comes back to the free running frequency. So this range where it goes out of lock okay on either side of omega not Q is called the lock range. And that lock range is governed by the fact that the phase shift it starts with pi by 2 here right it goes on all the way up to let us say 0 on one side and pi on the other side. So that is the lock range 0 to pi around pi by 2 is the lock range thereafter it goes out of lock if the condition is that the amplifier should not go to saturation and the VCO should function in this range satisfactorily as a linear VCO. So that is the static characteristic of the PLL and again if we now do not start from omega equal to 0 and gone on either side but start with omega I at a low frequency end or high frequency end then we had you mentioned that omega I minus omega not Q itself is a component which is much greater than omega LP. So nothing happens at the output of the low pass filter nothing comes out and therefore there is no locking taking place. So when you come this way right if this is omega I equal to omega not Q one has to come pretty close to omega not Q in order to get into the locking mechanism right. So it just has to come pretty close from here all the way up to this and then it gets locked then it follows this slope which is nothing but this is nothing but omega I minus omega not Q divided by KVCO. So this is 1 over KVCO it can go on all the way up to this come down. So on this side it can go up to the lock range. So this is the lock range this is called the capture range same thing happens when omega not Q minus omega I this is what happens when omega I minus omega not this is what happens when omega not Q minus omega I is much greater than omega LP on the other side when omega I minus omega not Q is much greater than omega LP what happens is okay the other one comes like this gets captured goes on like this all the way up to this and the sort of lock on this side. So this range is the capture range it is always less than the lock range it can be controlled by the low pass filter and we had seen how capture range can be roughly got in terms of an equation which is delta omega C equal to delta omega L by square root of 1 plus delta omega C by omega LP whole square. So this is approximated under this situation if delta omega C by the omega LP is much greater than 1 this 1 can be neglected and capture ranges square root of lock range into omega LP. So otherwise you have to solve this quadratic equation to get the capture range. Next we have designed PLL and simulated is lock range capture range and it is characteristic and used it for FM detection. So let us see how it can be understood the PLL designed as a VCO with sensitivity equal to 100 hertz per volt around a quiescent frequency of 1000 this is for just demonstration amplitude of the output square wave sine wave it can be either square wave or sine wave accordingly the lock range will change the VCO is if it is a square wave or a sine wave the VCO output is taken to be 10 volts. The input to the PLL is a square wave or sine wave of amplitude 5 volts will do it for both types of waveforms. The phase detector is a multiplier VX, VY 10 followed by a low pass filter with R equal to 1 key and C equal to 1 micro this is the complete PLL circuit. So we have fixed all the parameters of the PLL so GLO is nothing but that is DC loop gain is KVCO KPDK here we have not put an amplifier so the KA is 1. So low pass filter output is directly connected to the VCO so KA is equal to 1 this is equal to 1 and KVCO we have taken 100 hertz per volt KPD is nothing but it is VP that is V average in the case of a multiplier and low pass filter V average was VP dash VP is the input peak of the sine wave VP dash is the output of the VCO VP VP dash by 20 cos 5 so delta V average by delta 5 is the KPD so that KPD is minus VP VP dash by 20 sine 5 so we are investigating at omega equal to omega naught cube to start with so phi is pi by 2 that we know so at that sine pi by 2 is that is this particular thing is delta V average sine pi by 2 is 0 and therefore this value of V average is going to be 0 that is sine pi by 2 is 1 and cos 5 is 0 so the value of the average is 0 and sine 5 is 1 and therefore this is minus VP VP dash by 20 which in our case this VP being 5 volts okay into VP dash being 10 volts by 20 is 2.5 volts per radians so with these values getting substituted we have here minus 200 pi into 2.5 equal to minus 500 pi it is indicating that is negative feedback so GLO into pi by 2 is the lock range which is 500 pi into pi by 2 which is roughly 2500 radians per second or plus minus 393 around 1000 hertz which is going to give you a lock range of 1393 hertz to 607 hertz so this is the case only if the loop gain is maintained very large in that range then the error is going to be very small okay and therefore it is going to be within this range in common practice because if it is sine 5 that is the characteristic instead of linear phase detection right linear phase detection we have seen okay will be just the sine wave is converted to square and then applied to the multiplier then this value of KPD is maintained throughout the range however if it is just a sine wave okay that is the average is a cos wave and this is a sine wave okay so that is the waveform for the phase detection I think we have to draw it more carefully so that is the sine wave so this particular thing is going to be the case okay only around this region of operation very small region we can take for granted that KPD is constant as it nears 0 or pi it goes towards 0 so most of the time if the lock range is computed with this value it is valid only for a short range within this so it is much less than this as far as the phase detector which is non-linear is concerned with a linear phase detector it can be almost reached fully okay and if you now substitute for the capture range is nothing but lock range divided by this you get this and solving this equation quadratic equation one obtains a capture range very nearly equal to 1200 radians per second here and Delta Phi naught by Delta Phi I is Omega naught by Omega I is 1 by 1 plus S by GL naught okay which is 500 pi S squared by GL naught Omega LP which is 500 pi into 1000 radians per second so Omega n of this system which has been now designed comes out to be 1414 radians per second and Q is 1.414 let us look at this system as a sort of low pass filter now it is the same characteristic as the low pass filter okay so as far as S is concerned right it is defining the dynamics of the system that is I must now have for example a step input in phase or a step change in frequency that is a frequency stage change suddenly from one value to another at the input so this is Omega I initial okay which may be Omega I equal to Omega naught Q to Omega I which is different from Omega naught Q so that is a step change in frequency it is equivalent to finding the step response of this so what should happen is if you see the control voltage it will have to change suddenly from VCQ to any value of VC as a step strictly but because of this nature that it is going to be changing in this manner. So this is the process of capture of one frequency starting from another frequency this is a step change in frequency and this should be the characteristic if it is a second order and the number of such peaks which can be counted give the value of Q okay as ringing frequency corresponds to a close thing for Omega N strictly speaking it is Omega N square root of 1 – 1 by 2 Q square this we had already understood when we discuss passive network and low pass filters second order same characteristic exists for the PLL also so let us look at that so I have just applied a step input in frequency so the frequency at the input as a change it suddenly okay from one value to another so what happens here is the DC value is going to change at the input of the VCO okay from one value to another so this is the way and you can see this particular thing peaking like this this is nothing but the ripple which is unfiltered this corresponds to 2 Omega I component so that unfiltered 2 Omega I component still exist but the DC component you can trace here is something that is well understood in terms of the filter function now it is applicable equally well in the case of the PLL okay. So this is called the step response of the PLL but is step change in frequency at the input of the PLL and this change that is observed okay is clearly observed at the input of the VCO of the PLL so when the input is a square wave of 5 volt amplitude and VCO output is a square wave of 10 volt amplitude the only difference is KPD into pi by 2 which has to be recalculated now because it is a linear phase detector so KPD into pi by 2 in this case is nothing but okay 10 into 5 this 10 volts is the VCO output 5 volts is the input to the PLL square wave input and this is corresponding to the multiplier voltage 10 volts reference voltage so this is KPD into pi by 2 that is because we had seen that earlier once we linearized the phase detector right this corresponds to the slope corresponds to let us say KPD right the KPD into pi this pi by 2 is the peak change in DC voltage on either side of VCQ. So this is nothing but KPD into pi by 2 so that is the maximum change in DC on either side of VCQ and therefore omega naught Q should be capable of changing by this into the KVCO so KPD into pi by 2 into KVCO KA being 1 okay is the lock range which is 500 hertz K because KVCO is 100 hertz okay so that multiplied by 5 volts this corresponds to 5 volts so this is 5 times 100 which is 500 hertz around 1000 hertz you can see this so this is the VCO output 10 volts plus minus 10 volts and PLL input is plus minus 5 volts square wave and the what has been done is that the arrangement of another VCO at the input of the PLL to which I am applying identical VCO okay at the input of the S law club okay so here the same VCO as put is put and I am applying a VC at that point to change the incoming frequency so at that point I have applied a voltage of VC equal to 4 volts to that VCO which is at the input and what happens so the arrangement please understand it this way we have a VCO okay here and this is VC so this is going to change this frequency from omega naught Q to omega naught Q which is 1000 plus 4 times 100 which is 400 right so 1400 corresponds to the input frequency for VC equal to 4 volts oh this is what is applied to the PLL and this same VCO is put in the feedback path so that is the macro model that we had used and we have the low pass filter one key and one micro farad okay which is getting connected to the VCO input so at this point immediately the output frequency should correspond to 1400 okay and the this should change from the coefficient to 4 volts so initial coefficient if it is 0 this will go to 4 volts so that is what has happened the phase shift is nearly 0 you can see the output and the input they are almost in phase so this has come close to the lock range on this side okay and now the same thing is repeated with VC equal to minus 3 volts that means it has been changed to okay 700 hertz as the input so then the phase shift goes close to you can see 180 degrees so phase shift is going close to 180 degrees phase shift is going close to 0 so we have almost covered the lock range this way right and thereafter okay it is going out of lock that is primarily due to the fact that the double the frequency component is still not eliminated so the voltage is still varying around the so called 3 volts so it is going all the way up to 5 volts and thereafter therefore it is going out of lock this is happening more at the lower frequency end okay than at higher frequency because they had higher frequency though pass filter filters it better so you can see the 2 omega component is smaller in amplitude whereas at lower frequencies the 2 omega component is larger in amplitude so that is restricting the lock range to ahh something close to 700 hertz on this side and close to 1400 hertz on the other side so this unfiltered ripple is responsible for restricting the lock range because once it goes out of lock it has to be recaptured so that means you have to come closer so that means this system dynamics is not ahh functioning properly so it is better to remain in lock range as long as you want to track the change in phase okay ahh change in frequency that is happening at the input to be followed at the output so these are the points that must be born in mind while designing the system okay so the lock range has been constrained even though it is a linear phase detector to ahh value which is less than what is predicted because the actual predicted lock range is 500 hertz on the lower side and all the way up to 1500 on the other side so it is restricted by the ripple that is not it completely removed by the low pass filter so this is the dynamics of the ahh phase lock loop as an FM detector or FSK detector the entire dynamic characteristic of the phase lock loop is ahh tested okay in fact if input frequency of the phase lock loop is remaining constant at a value so it is changing in steps let us say then what it means is you are testing the static characteristic of the PLL it is only when the frequency of the input is changing at a frequency it is that frequency that comes as S equal to J Omega okay then only the dynamics of the phase lock loop is getting tested so that is why in order to test the dynamics of the phase lock loop the actual input that must be applied is a FM or an FSK right so that is what is done we have put the same VCO at the input of the PLL as that is there in the ahh loop and we have made the cohescent frequency of this loop VCO same as that of the input VCO that means this is the transmitter okay which is receiving the modulating frequency and transmitting the carrier here then through the media it is restored by the receiving antenna and accepted by the PLL which is tuned to the same carrier frequency 1000 hertz as that of the transmitted frequency. So the frequency deviation is controlled by this control voltage VC so if you apply a DC here that is a fixed frequency if you apply an AC at a certain frequency Omega M then this is VC is replaced by VP sign Omega MT that means this becomes the frequency deviation what is the frequency deviation is 100 times VP in this case. So the frequency deviation can be controlled it is going to test the dynamic range the frequency deviation can be as much as the lock range if only this phase lock loop is tuned such that the cohescent frequency of the phase lock loop corresponds to the carrier then the full dynamic range of the PLL is exploited. So the phase can change from pi by 2 cohescent to pi on this side and 0 on the other side so that is important to understand it is the rate at which it changes depends upon the modulating frequency Omega M. So we have several components to be thought of there is this carrier here plus Delta Omega D sign Omega MT this is the FM that gets produced here. The carrier in this case corresponds to let us say 1000 and 100 times VC means this is the frequency deviation you see and this is the modulating frequency. So there are 3 frequency component in the incoming frequency component of an FM carrier corresponds to the cohescent voltage of a voltage follower and this corresponds to the input sign wave applied to the voltage follower right. In the case of frequency follower this is the amplitude of change of frequency this is the rate of change of frequency Omega M okay. So what should happen is the output frequency is same as input wave that means if this is an FM the same FM gets reproduced here Delta Omega D sign Omega MT if that means this is one that is Delta Phi naught by Delta Phi is exactly to one this FM that is reproduced is the same as that FM that is coming here except that if Omega naught 2 is same as carrier this will be let us say sign of this and this will be cosine there will be a 90 degree phase shape between that sign and this cosine that point clear that has to be understood well and change in frequencies will be followed exactly. However if Omega M that is the frequency that test the dynamics of the phase lock loop okay when that is increased when this is increased this change in frequency will not be same or the frequency deviation around the quiescent will not be the same it can actually be more and that is a danger because if it is more right deviating it may go out of the lock range and the system again becomes sort of no use for linear analysis. So it has to get captured and come back to the lock range right. So this is the danger that means the rate at which the frequency is changed here in the FM should be much less than the natural frequency of the system so that it is not distorted output is not distorted okay. So if you apply a step input frequency again the dynamics gets tested because this will start ringing okay at the natural frequency of the system that we have already shown here. So this is the natural frequency where it is trying to peak okay now Omega M has to be kept much less than the natural frequency of the system. So this is to be in order to be free from distortion right. So this is what is done this is now therefore the FM detected output. So because it is reproducing the modulating frequency at this component point exactly in the same fashion. So if one volt change is the peak here that same one volt change should be there if only Omega M is much less than the natural frequency okay. So what is done here this is the is getting modulated by assigned wave so you can see that this frequency is changing okay at a certain rate right and it is frequency modulated okay you can see these phase shift changing okay at times it is coming close to zero at times it is going close to pi by pi and then it crosses through pi by 2. So phase is changing continuously this is the modulating frequency okay and you can see the FM detected waveform initially it is not tracking once the lock takes place it is going on tracking the change in frequency faithfully with the same magnitude of course you have the two Omega component triple still unfiltered if one wants one can put a filter with a buffer and a filter outside the loop buffer is necessary otherwise it will interact with the loop dynamics and no question of using a second order filter because it will make the system become unstable the whole system becomes third order and becomes unstable. So one has to put another filter or better filters outside the loop to remove the two Omega component completely. So here VP has been restricted to 1 volt and the same 1 volt is detected at the same frequency of 100 hertz modulating frequency. So 1000 hertz is the carrier 100 hertz is the FM VP of that FM and the modulating frequency is 1 volt. So that it is well within the lock range when it is swinging. So VPC the carrier is 5 volts still same as before VPCO of the VCO is 10 volts these are all sine waves okay. So now FSK detection in the FSK detection it is a square wave input you can see the blue line the square wave plus minus 1 volt FM is 2.5 hertz it is still reduced so that the rise time and fall time of the square wave is reproduced smart faithfully by the FM detector. So this is still lower earlier we had taken 100 hertz at the modulating sine wave frequency here we have gone for 2.5 hertz as the frequency of FSK. So the frequency is changed in steps okay. So you have plus 1 taking it to towards 0 and minus 1 taking it towards pi for around pi by 2 the quiescent. So VPC is still 5 volts carrier amplitude VPCO is 10 volts. So that is maintained and you can see clearly the process of capture and it takes certain capture time as illustrated earlier how the capture time is going to be dependent also on the low pass filter in the dynamics. But it depends upon the whole transfer function as defined by us 1 by 1 plus S by omega naught Q plus S square by omega naught square and Q being 1.414 you can see just one peak here this we had seen earlier also please remember this. So this is what is seen so the same thing is repeated here in FSK. So this is the reproduction of the pulse information that is modulating the carrier this is the FM detected output this is the 2 omega component riding over this. Now we come to the other important application frequency translation which has been earlier discussed however now we are simulating this using an example omega i is the input omega naught is the output. So here we get omega i minus omega naught and omega i plus omega naught is being very high this is eliminated by the low pass filter ok within and it responds only to omega i minus omega naught which is the low frequency component and then there is a shift of delta omega and therefore here we cannot decide whether delta omega plus omega i minus omega naught is lower or delta omega minus omega i minus omega naught is the lower frequency component can be one of these depending upon whether we want omega naught to be higher or lower than omega i ok. So assuming that it is either this ok or this ok we get an output frequency which is omega i minus delta omega naught or omega naught is equal to omega i plus omega delta omega. So how this design is done properly is illustrated by an example again. So here we have chosen 1100 hertz to be derived ok from 1000 hertz and 100. So now we want to select 1000 plus 100 and not 1000 minus 100. So F i is equal to 1000 hertz, VP is equal to 5 volts, delta f is 100 hertz ok shift ok which is applied at the other input with VP equal to 10 volts. So now what happens is we have tuned this properly ok so this is the low pass filter output ok this is the unfiltered component at the filter. So one can see that the frequency now selected is 1100 hertz how do you select it that means the this particular VCO will have to have the what is that the omega naught Q that is free running frequency properly selected in order to select the right component. Omega naught Q has to be pretty close to this frequency that we are wanting to select. So the best way is when it is FSK detection when it is 1100 we want to select we better make the other one that we want to reject these 900 hertz we better make ok our VCO omega naught Q equal to 1100 that is the best way. So if omega naught Q is made equal to 1100 or above 1100 may be 1000 let us say 200 as long as we are sure that the lock range is good enough right. We can go from anywhere this to this as the free running frequency of the VCO that is incorporated in this loop of frequency translation. So when that is done we automatically pick the 1100 hertz which you can see here right 1100 hertz emerges as the output. This is the input frequency blue is the input frequency which is 1000 hertz and this is 1100 hertz that has been selected by the loop. Another example Fi is 1000 hertz still right. So we want to derive 100 hertz from 1000 hertz using 1000 hertz as one input and 900 hertz as the other input that means 1000 minus 900 is what is to be selected not 1000 plus 900. So that means it is easy now to make the free running frequency of the VCO close to 100 hertz within the lock range of the VCO on the PLL that is formed okay using the 2 multipliers. So once the VCO is tuned to close to 100 hertz let us say we may have made it equal to 100 hertz immediately one can see that it is getting locked you can be sure that it is getting locked because the dynamics is reproduced here that peak of about one is still existing right. So it starts okay and gets locked okay and then you can see the output is the 100 hertz okay that is selected okay when 1000 hertz is one input and 900 hertz is the other input that is frequency translation for you. So this is an important loop in frequency synthesis apart from multiplication. So that is simple you put a you affect the VCO to act as VCO with a counter okay which will count down so that it is dividing by n. So divide by m divide by n counters are put that we had illustrated in the last class okay and you can get a frequency multiplication by m divided by m that way. So coupled with frequency translation it becomes a powerful tool for exact frequency synthesis. Speed control of motors nothing but again reproduction of the PLL in terms of electrical components. So the power drive here running a motor with what I called as optical tachogenerator which is nothing but the shaft connected with a disk with slits in the circumference and an optocoupler okay which will convert the whole thing into rotation into SH series of pulses here. So omega naught output of the oscillator here which is an electrical oscillator is 2 pi into n is the rpm of the motor that by 60 revolutions per second into okay number of pulses outputted per second which is n number of slits okay. So every revolution produces n pulses so it is a pulse generator right with this frequency. So same phase detector loop filter may not be necessary because the power drive itself that is the motor itself acts as a low pass filter. So this is the speed control of motors AM detection. AM comes from the let us say antenna right and goes through a limiter so that the AM is removed here. So only the carrier is selected here right so but several carriers might just appear here. So this has to be frequency selected you know that means this is one of the way because both in FM detection and AM detection this PLL acts as a frequency selective device and selects the carrier that is corresponding to omega naught cube okay. So if you want certain carrier to be selected it is necessary to tune this omega naught cube and you select the carrier that you want to select okay at this point as omega naught cube. Now this carrier is reproduced here but only with a phase shift of 90 degrees and if this is therefore sin omega CT this will be cos omega CT. So if you multiply cos omega CT with the AM corresponding to that carrier you will still not get any output because of the phase shift of pi by 2. So there is a phase shift which is preferably pi by 2 let us say so that this becomes the same carrier in phase as the input carrier that is selected. So when you multiply it by that cos sin if this is sin this also has now become sin so you will get again once you multiply sin squared omega C okay and therefore there will be the double the carrier at this point and the demodulated output or the modulating frequency that is the AM here. So that gets detected at this point. So this is a frequency selective or synchronous detection the carrier is generated by DPL that is all that happens so that requires this kind of arrangement after that it is nothing but synchronous detection because you have been able to generate the carrier okay that is carrying the information at the receiving end that is the thing. So we have modulated the carrier amplitude modulated the carrier just by using a multiplier at the input okay. So this is also going to generate this using a multiplier here and multiplying the carrier with the modulating frequency okay the carrier has to have the modulating frequency has to have a DC okay. So if you that is the AM is generated this is the AM generator so one has let us say DC plus VP sin omega MT and this is the VP C sin omega CT. So at the output when you multiply you get the carrier plus the component corresponding to omega C plus omega M and omega C minus omega M. So this therefore is nothing but AM as long as the amplitude of VDC is greater than VP it is going to be giving you AM at the output of this that AM is supplied here and then that is what is detecting so that AM comes there and it is going through a limiter and applied to the PLL and this is the output of the PLL which just simply generates only the carrier okay. So then this carrier is being used after phase shifting by 90 degree to multiply with the AM at the receiving antenna. So what happens is this is the AM okay that is modulating frequency of the AM and this is the detected AM this is AM detection. So ICPLLs are popular IC1s are 565560 CD4046 KVCO sensitivity of one of the most popular PLL LM565 National Semiconductor KVCO is 10 kilohertz okay at F naught equal to 10 kilohertz it is 6600 hertz per volt. So 6.6 kilohertz per volt phase detector sensitivity is 0.38 volts per radians VCO maximum operating frequency is about 500 kilohertz. So this is a typical ICPLL that is available. So we have treated PLL as a control system with the same kind of activity as an AGC system or an AVC system or a voltage regulator okay. So all these control systems have the same dynamics to be understood no complicated okay issues evolved because it is a phase locked loop okay it is same as a voltage follower or a current follower or a phase follower or a frequency follower all these have the same dynamics of operation. And same ideas of frequency compensations okay that we have adopted can be adopted for these system desires. Thank you very much.