 Today we are going to have our 37th lecture on frequency lock loop. Let us just consider what we have already done in the last class that is the 36th lecture on phase lock loop. We consider the true phase lock loop is something that has only the phase lock to a specific value phase difference between input and its output is locked to a specific frequency I mean at a given frequency to a specific value of phase shift of for say for example 90 degrees quadrature irrespective of the incoming frequency it is only locked to 90 degree phase shift that is what is truly called a phase lock loop which is what is commonly used in tuning filters or obtaining multiphase signal from a single phase. So this phase lock loop we have seen how it can be converted into by a minor modification of replacing the voltage controlled phase generator by VCO an independent oscillator in the loop. So into a frequency lock loop which is now popularly called as phase lock loop the other phase lock is even though used for tuning is not all that popular. Now we saw that that particular phase lock loop true phase lock loop is a first order system if it is an integral control system and it becomes a second order if the comparator that is used within the op amp used within in the integral control as a finite gain management product. So basically it is an integral control system for locking to phase. Now today we will see all about the frequency lock loop so as I already explained what is common to both these loops is the phase detector which is at present we are using the multiplier low pass filter configuration for the phase detection and if you want to increase the loop gain you can put an amplifier with KA as the gain amplifier gain and it is compared with the V reference here and that error is amplified. So ultimately just like any other control loop integral proportional PID control we have this steady state error coming to 0 if the loop gain is very large that means this voltage sets itself to V reference V reference is 0 then we have seen that cos phi V average at this point okay has to be 0 which means phi should be pi by 2 that aspect is followed here also okay. So it is the same topology except that this voltage control phase generator is replaced by VCO where KVCO is the sensitivity factor of the VCO which is now becoming part of the loop gain. So let us see what happens in this case in terms of understanding the frequency locking we know that omega not by omega I we have shown okay is equal to delta phi not by delta phi I here okay the phase difference is phi if this is delta phi I and this is delta phi not we know that in this phase lock loop we have this as KPD divided by 1 plus S by omega LP and omega LP is 1 by RC so and then this has KA as the amplification factor here and then this is KVCP this whole thing forms the loop gain. So 1 by 1 plus 1 over loop gain is what is equal to delta phi not by delta phi I if this is delta phi not this is delta phi I and if that is divided by delta T common then by definition delta phi not by delta T is omega not and delta phi I by delta T is omega I rate of change of phase is frequency reading frequency. So this is how we are proving that in the case of frequency as input and frequency as output okay output frequency is going to follow the input frequency that is why this is a frequency follower or phase lock loop or frequency lock loop. So that is how we have to discuss the first effect in terms of whenever frequency change occurs to a small extent we have to consider it as a change in phase and say that output phase change is going to be same as input phase change and that is why output frequency is going to be equal to input frequency and the transfer function for omega not by omega is also 1 by 1 plus 1 over G R this is how we indirectly show that phase lock loop like this in this case is a frequency lock loop okay. So omega not by omega I now we have shown is delta phi not by delta phi I is equal to 1 by 1 plus 1 over G L what is this G L. So as far as the phase detector is concerned it takes on the same sensitivity factor KPD okay it is converting phase to a voltage with the help of the low pass filter whose transfer function is this and amplifier is concerned it is KA only that part of VCO since VCO is something that converts the DC voltage input to a frequency this is not defined as KVCO and what we are interested in as far as phase detector is concerned it is delta phi not okay which is of interest to us. So delta phi not that check place because the frequency is delta phi not by delta omega not okay delta omega not by delta AC. So change of phase with respect to frequency okay this is nothing but 1 over yes integration so that means the this is nothing but KVCO. So VCO can be represented when the output is a change in phase okay by KVCO by S as the transfer function. So that is what is done here KVCO by S is the transfer function of the VCO when output change in phase is what is considered okay. So the overall loop gain therefore is KPD KA KVCO which is called the DC loop gain GLO but please remember that this is not a ratio this is nothing but a frequency in dimension radians per second. So that divided by S is a ratio that into 1 plus S by omega LP of here. So this whole thing in this GLO is what is called the DC loop gain of the phase lock loop KPD KA into KDC. So omega LP equal to 1 over RC in each case 1 by 1 plus 1 over loop gain is now going to come as S by GLO into 1 plus S by omega LP. So 1 by 1 plus S by GLO plus S square by GLO into omega LP. So this is a second order system 1 by 1 plus S by omega n natural frequency of the system into cube of the system plus S by omega n square. So the PLL the basic PLL as against the through PLL that we have discussed earlier is a second order system whereas the basic PLL earlier considered was the first order system. And the omega natural frequency of the PLL is square root of GLO into omega LP comparing it and quality factor is by comparison root of GLO by omega LP. Normally the GLO is made very high compared to omega LP and therefore Q of the PLL is essentially a high Q system. So just like any other control system which we had considered earlier we might have to introduce a zero in the transfer function okay or the low pass filter such that this Q can be brought down to manageable value of 1 or so okay. So the design of the entire system is following exactly same as that of the amplifier feedback amplifier or any feedback system. Once you consider it in terms of a phase following acts. So let us now consider the lock range of this PLL. When VI input voltage is zero nothing is applied to the input just ground it okay that is let us go back to the loop. So here the input is not connected then what happens this multiplier so if one input is zero theoretically output has to be zero that means nothing happens here other than remaining in whatever state earlier it was or quiescent state okay and this will remain at a quiescent state. So VC is at a certain quiescent state okay by design so let us say it is at VCQ. So the output frequency is going to be something corresponding to this VCQ which is called omega naught Q let us say. So if it is having an output frequency of omega naught Q only one input is applied the other input is not applied so the multiplier output is zero if there is some feed through it will be some component of omega naught coming through okay but the low pass filter will eliminate it. So nothing happens here this continues to remain at the quiescent state of VCQ that is called the free running frequency of the PLL. So that is what is stated here VI equal to zero VC is equal to VCQ output of the linear VCO it is not VCO this is nothing but VCO is an AC signal with frequency of KVCO into VCQ if it is a linear VCO and that is omega naught Q this frequency is called the free running frequency of the PLL FLL and depends upon the gain of the amplifier it is input offset okay and V reference etc. of the amplifier input. So quiescent state of the FLL is defined as VI equal to zero and VC in the operating range. So VCQ setting the VCQ okay such that it is free running at the desirable frequency we will just see what the desirable frequency of free running should be later is called tuning the PLL. So setting a desirable omega naught Q is called tuning the PLL this can be done by setting the VCQ value or setting the value of R and C that determines the free running frequency of the VCO output of the VCO once again VCO has to be VP some VP dash omega naught QT as well as phi okay. So this is the quiescent state of existence okay now what is lock range is what we are going to consider V average is VP VP dash by 20 cos phi and therefore now if we apply an input voltage omega that is input frequency omega I equal to omega naught Q. So what is now happening is apply omega I equal to omega naught Q. So that is what is done then the output frequency can be VP dash omega naught QT plus phi it has to be that continuing to be that because incoming frequency is same as omega naught Q. So what can happen only the phase shift can be something different. So if phi is the phase shift now we have omega I equal to omega naught Q and omega naught equal to omega naught Q but with the phase shift of phi omega naught QT plus phi VP dash sin. So this is sin omega naught QT VP. So the incoming frequency corresponds to VP sin omega naught QT omega naught corresponds to VP dash sin omega naught QT plus phi. So the frequency has remained the same as incoming frequency we have only the phase shift then output average is going to be of the low pass filter VP VP dash by 20 cos phi this but this has to be 0 because the frequency should remain same as omega naught Q okay it should not change for it not to change nothing should change at the input of the VCO that means input of the VCO should be at VCQ that means actually this average should have no effect at the output of the amplifier that means cos VP VP dash by 20 cos phi should be 0 or cos phi should automatically get adjusted to pi by 2. Now let us see what happens when omega I changes away from omega I is not equal to omega naught Q but close to omega naught Q it can be higher or lower and VC should change around VCQ by an amount equal to omega naught Q minus omega I by KVCO that is by definition the linear VCO. So omega naught Q minus omega I is the change in frequency that is brought about at the output because output frequency should be same as input frequency. So omega naught Q minus omega I by KVCO is the change in voltage above VCQ or below VCQ depending upon whether omega I is higher or lower than omega naught Q input to the amplifier therefore should change by omega naught Q minus omega I by KVCO into KA the DC gain of the amplifier phase change in V average can be at most be KPD into pi by 2 if it is a linear phase detector. So by definition the phase can change around pi by 2 on one side up to pi on the other side up to 0 that means the extent of total change on either side of pi by 2 pi by 2 is the cohescent phase. So this pi by 2 has to change can change all the way up to pi that means by an extent of pi by 2 on this side and pi by 2 on the other side okay. So KPD into pi by 2 is the maximum change that the linear phase detector is capable of sustaining okay on either side of the cohescent. So that means this KPD into pi by 2 should be equal to omega naught Q minus the limit of omega I on either side so that is called the lock range that omega L which is KVCO KPD KA into pi by 2 KPD into pi by 2 into KVCO into KA which is nothing but GLO this we have called as the DC loop gain into pi by 2. So that is called the lock range there is nothing but the DC loop gain into pi by 2 this is under the circumstance that the amplifier does not go to saturation before that and VCO continues to act as a linear VCO all the way up to that range without any problem in such a situation the maximum ever okay lock range is going to be this if it is a linear phase detector. So this is the best one can have as the lock range on either side of the let us say free running frequency okay. So once again KPD into pi by 2 is in our case VP dash by thin if VP is the input incoming frequency magnitude sine wave and VP dash is the output that is square wave and VP dash is the output square wave. So both are assumed to be square wave because it is a linear phase detector we have a CO. So VP VP dash by thin is the maximum value. So remember that the lock range depends upon the magnitude of VP VP dash for the linear phase detector for a change of maximum phase shift of plus minus pi by 2 around pi by 2 this is what I have explained amplifier input gets this as the maximum input change right. So KA into VP VP dash by 10 is the amplifier output change and therefore VCO change will be that into KVCO okay around F naught Q. So F naught Q plus or minus KA into VP VP dash by 10 into KVCO okay or it is nothing but okay the delta FL is going to be plus minus KA KPD KVCO pi by 2 GLO into pi by 2 which is the lock range around F naught Q. So an example has been chosen here the lock range is given above if VCO can oscillate in that range if the amplifier does not saturate then that is the maximum lock range. So in our case let us say we have chosen okay VCQ of 10 by 2 5 volts that is because in our arrangement okay we have made the VCO okay this amplifier is removed okay we are just having no amplifier put there we can make the loop gain high by increasing the KVCO and KPD and controlling the VP VP dash. So this is the actual PLL that we are trying out so 5K attenuator has been put okay so this 10 volts DC is going to have a quiescent voltage here of 5 volts 5K 5K so 5 volts is the quiescent voltage this is our VCQ okay and this is going to the VCO that has been designed just in the lecture on VCO we have formulated this Schmitt trigger 2.2K and 1K okay R2 is 2.2K R1 is 1K and frequency of oscillation of this F naught Q is going to be VCQ by 40 RC into R2 by R1 this is 2.2K this is 1K this R is 1K this C is 0.1 micro farad with all this this whole thing has been designed so this will give you sort of F naught Q of 2.75 kilo hertz at VCQ of 5 volts so this is the example that we have tried we can see here F naught Q is equal to VCQ by 40 RC into R2 by R1 so this becomes F naught Q as 2.75 kilo hertz for the example that we have chosen and what is done is VC as VCQ cos 5 has to be 0 so 5 has to be 5 by 2 so if I now apply Fi equal to 2.75 kilo hertz the phase shift good it automatically adjust itself to pi by 2 so that cos 5 is 0 so this is what is done okay and delta FL is calculated VP dash by 10 okay that is the maximum change okay of DC from VCQ that can occur okay at the output of the phase detector average right its input is VP dash by 10 okay and that into half because there is an attenuator there so this also gets attenuated in the loop so essentially the KPD is going to be halved here and then applied to the VCO so that into KVCO is the lock range into KVCO is the lock range so you have KVCO as 2.2 okay by 40 into RC so it is 2.34 by calculation so the lock range is 2.75 kilo hertz plus or minus 2.34 kilo hertz which is 5.09 kilo hertz okay 2.41 kilo hertz okay that is the range so this is what is done VI equal to 0 input is connected to ground then output frequency happens to be 2.75 kilo hertz that is what it is output frequency is 2.5 and the quiescent voltage you can see here is nothing but 5 volts slightly less than 5 volts right so this is the situation of the quiescent condition right you can measure the output frequency is close to 2.75 kilo hertz now what is happening is Fi is going to be made equal to F naught Q so what should happen the phase shift should automatically adjust itself to be 90 degree so we have this input adjusted to 10 volts square wave that is the input waveform 10 volts square wave and this is the output waveform of the VCO okay and you can see that these are exactly in quadrature with one another 90 degree phase shift so you can see this as the phase locked at 90 degrees pi by 2 and you have the 2 omega component at the output of the low pass filter as expected durable triangular waveform charging and discharging okay and causing an average which is close to the quiescent state okay so earlier when it was a DC it was just flat here and you can see that this is remaining at the same level okay as the quiescent but now it is phase locked okay now what is bad news Fi is changed away from the quiescent frequency of 2.75 kilo hertz so what happens then is what is described here so it is changed to 1.9 kilo hertz from 2.75 kilo hertz it has now gone over to 1.9 less okay than the quiescent so automatically you can see from the quiescent value of 5 volts it has gone down but it is still double the frequency which is appearing at the output of the low pass filter and this phase change you can see earlier it was 90 degree now it is trying to go out of phase away from 90 degrees right so that is the change in phase that means it is trying to go out of phase because ultimately if it goes to this this will be 180 degree right so it is going towards pi on this side so this is the output frequency right so we have purposely made this output different from the input to show the distinct difference between output and input waveforms and we have applied I think 10 volt supply so whereas the op amp cannot go all the way up to 10 volts it goes up to about some 8.5 volts also now the frequency is changed to still lower to 1.2 kilo hertz so it goes further down the DC so the control voltage is keeping on changing to change the output frequency to the same value as the input frequency and the phase shift now again goes towards pi more towards pi okay this is the input waveform this is the output so you can see it is going towards pi almost close to pi so 1.2 kilo hertz 1.1 just gone out of log you can see no longer is it a double the frequency right there is just not in sync with the incoming that is the output incoming frequency is totally different from the free running frequency it goes back to the free running frequency and this is the variation this is the bit frequency that is produced okay that is nothing but omega i minus omega naught q bit frequency which is the output of the low pass filter that is you can very clearly see that it is not any longer DC with double the frequency okay so this is the incoming frequency which is much lower than the free running frequency so this goes back to the free running frequency and now the incoming frequency is above the free running frequency 2.75 is the free running frequency and 3.5 is the frequency kilo hertz is the frequency of the input so you can again see the beautiful locking and it has gone above 5 volts again this is the frequency riding over the average which is close to 7.5 volts and you can find out the frequency of oscillation which is close to the incoming frequency of 3.5 kilo hertz exactly it is in synchronization with the incoming frequency now locking is taking place what has happened to the phase shift now it is coming to be in phase from the 90 degree cohescent it is coming to be in phase going towards 0 phase right output input sorry input and output so again at fi equal to 3.6 kilo hertz this is 3.5 just 3.6 kilo hertz it has gone out of lock so this is again the beat frequency it has come back to the free running frequency right and it is producing the beat frequency around the free running frequency this way and then this is the incoming waveform so you can see the FM kind of thing right now that is what happens in the capture rate let us dwell on this for some time so what has happened this is our VC okay the input to the VCO or the output of the low pass filter here okay is what is given here versus incoming frequency so when the incoming frequency is same as the free running frequency this is at VCQ VC is at VCQ so this is the operating point so there this is omega naught Q corresponding to VCQ and this is nothing but KVCO okay 1 over KVCO so if you are now changing giving an input which is same as omega naught Q it will be VCO input will be at VCQ so if it is higher then this is the change in DC that is produced which corresponds to omega i minus omega naught Q that is the change okay in frequency divided by KVCO so the slope of this is 1 over KVCO so it will go on like this all the way up to the lock range then go out of lock this is what we saw and on the other side it will go on all the way up to this and go out of lock so first you have to start with omega equal to omega naught Q to achieve this so if it is going out of lock then once it goes out of lock right this is continuing to free run at omega naught Q right so this has come down okay so just let us consider omega i either much greater than omega naught Q or omega i much less than omega naught Q this whole thing was the lock range if you start with omega equal to omega naught Q go all the way up to this and without getting lost okay loss of lock come back okay you can go all the way so you can keep swinging from here to here without any problem as long as you are not going out of lock but suppose you go out of lock is free running at omega naught Q now if the frequency is in this range beyond the lock range obviously omega i minus omega naught Q or omega naught Q minus omega i okay both these frequencies are much greater than the omega lp please understand this both this omega i minus omega naught Q and omega naught Q minus omega i both these are much greater than omega lp that means these components correspond to high frequency so whether you are starting at this point or at this point the difference in frequency corresponds to a frequency which is much greater than omega lp then what happens no output change can occur in the low pass no output can change that because low pass filter cutoff frequency is such that it will not allowing any change that means VCO is going to continue to free run at omega naught Q so catch cannot take place this is the phenomena of catch we are discussing that we have discussed lock range as the range where you start with omega equal to omega naught Q and go on either side of this where the lock is maintained but now we are considering a frequency beyond the lock range and if omega i minus omega naught Q is much greater than omega lp until this difference in frequency okay which is the average okay becomes low enough to let something happen at the output of the low pass filter VCO won't change okay so the capture phenomena is going to take place mostly depending upon the low pass filter cutoff frequency that is the low pass filter cutoff frequency is very low the capture range is very low around omega naught that means until capture takes place okay and lock occurs okay thereafter omega naught is always following omega i okay and the low pass filter will let that lock all the way up to this limit of lock range on either side so this is the capture phenomena capture takes place then lock continues until it goes out of flow on this side again until you come close to omega naught Q okay such that the low pass filter lets something out so that okay the VCO starts swinging until it captures the incoming frequency and the locking continues all the way up to the limit of the lock range on this side so this way it comes captures keeps the lock and goes out of flow again on this side captures so capture range is this range of frequencies so first for it to lock it has to come within the capture range then it can lock and maintain itself in the lock range okay so please remember this capture range is always less than the lock range so we are now trying to establish mathematically by making drastic approximations how the capture range can be roughly evaluated so closely follow what I am trying to explain omega naught Q minus omega i if it is close enough to omega LP then output of the low pass filter if the input to that is assumed to be assigned way which is not the case really because this is an assumption drastic assumption in order to simplify the analysis so if it is assigned way of magnitude VP sin omega naught Q minus omega it and that is the only component low frequency component which having some effect at the output of the low pass filter so what happens to this this frequency so this gets attenuated but if you call this as delta omega by square root of 1 plus delta omega CR square because that is the low pass filter 1 by 1 plus SCR S is equal to j omega what is j omega j omega is now the difference in frequency component delta omega okay so this is replaced by j delta omega so that gets attenuated by this and it will get subjected to some phase that we are not bothered however the sin wave says that the peak magnitude of change at the output of the V average is going to be VP divided by square root of this going to be attenuated by this much okay now this is going to be the input to the VCO around VCQ so the VCO frequency is going to change from omega naught Q by plus minus this VP divided by square root of 1 plus delta omega CCR square okay into KA into KVCO so that is clear that by definition so this whole thing okay is going to be equal to the limit if this particular swing of VCO is such that it can at least at some point of time become equal to the incoming frequency the probability of capture is hiding so this is the maximum swing around omega naught Q that can take place so when the maximum swing reaches the incoming frequency that is when capture can take place probability of capture is high if you consider that then that is the capture range omega I minus omega naught Q is the delta omega C limit this delta omega is also delta omega C so this is what the capture range is VP is strictly speaking nothing but KPD into pi by 2 the maximum DC voltage that can on either side of coefficient occur that is what we have defined earlier so this is nothing but the lock range as we had earlier defined so this delta omega C is therefore plus minus the lock range divided by GL naught into pi by 2 is the lock range divided by square root of 1 plus capture range square into CR square so if let us say delta omega C square into C square R square which is strictly speaking nothing but omega LP okay 1 over CR is omega LP so this if it is much greater than 1 this one can be ignored then delta omega C square is equal to delta omega L into omega LP or capture range is simply square root of lock range into omega LP it depends upon omega LP and therefore capture range is nothing but square root of lock range into omega LP if this assumption is valid can assume that this is so and then evaluate it this way and check whether this is so or not that is easier otherwise you have to solve a quadratic equation here okay now the process of capture or capture time this is more complex so it is again consider we see versus time so when a signal comes within the capture range how the capture takes place is that means let us consider that it is at omega naught Q and an input frequency which is within the capture range is applied as a step input at the input of the PLL a step frequency change then how does the capture take place so at t equal to 0 what happens is that omega I okay minus omega naught Q is the instantaneous frequency that is found here so that instantaneous frequency change at the output of the low pass filter or input of the VCO keeps producing a DC progressively going towards another value corresponding to which the frequency is omega I so this is the new value of DC finally settling down at the output of the low pass filter or input of the VCO so that is the settling DC voltage but how the DC voltage is generated is that omega I minus omega naught keeps on changing omega naught keeps on getting adjusted okay so that it produces a DC progressively going towards the final value so that means this area is minimal and this area is okay large okay so that instantaneously the frequency change occurs this way in order to produce a DC on this side okay this time for it to change from this cohescent to the final value is called the capture time 90% of that okay so from 10% of this to 90% is the capture time that also depends upon the low pass filter capacitor and time constant now coming to the application of the PLL so VCO is nothing but the FM generator or FSK generator this is the FM generator or FSK generator so this is going to the transmission line and being received here and applied to the phase detector amplifier plus low pass filter and VCO so according to us if this is an FM this will be the same FM okay so this is the FM so if the carrier is no this is an important thing being received here at a certain value then we have to tune our VCO said that omega naught Q of this is equal to the omega carrier then we have the maximum deviation possible around omega naught Q because the phase shift can change all the way from pi by 2 to 0 to pi okay so that means tuning the PLL in malls tuning the VCO said that the carrier frequency corresponds to the omega naught Q then what happens here is that this being put in the feedback globe in order to produce the same FM as this this should have generated the modulating frequency at the input so we have here FM detected or FSK detected output so this is a sine wave of certain frequency the sine wave of same frequency with same deviation has to be produced here so we have recovered the modulating frequency at this point so FM detection can be so we have seen this happening in our system design lecture on how a feedback can perform the inverse function so if it is a FM generator which is put in the feedback part it actually does FM detection so this is demonstrated here you can see that input FM generator is a square wave of amplitude 250 hertz and we have the of naught Q of the whole system okay at 2.75 kilo hertz the previous example to that we have applied the same VCO here with the modulating frequency here which is nothing but a square wave in this case sorry sine wave in this case so of I think we have applied a sine wave here so of frequency 250 hertz low enough so that this is the modulating input and this is the output you can see the amplitudes are the same okay so if it is low enough the amplitudes will be the same okay that means actually speaking if you consider F naught by Fi it is going to be 1 but it can peak and come down that means the rate of change of phase should be occurring or frequency should be occurring at the frequency much less than the natural frequency of the system which is nothing but okay omega n is root of DC loop gain into the what is that the lock range sorry it is nothing but that into the omega LP this we have shown earlier please check that much before we have shown here root of GL naught into omega LP is the natural frequency so the rate of change of frequency okay that is the omega m that we have applied should be low enough compared to omega n that is the requirement for it to be acting as a frequency follower otherwise distortion will occur okay this is an important function of the phase lock loop in FM detection or FSK detection right it could be a square wave again it will produce the square wave exactly okay with little bit of distortion because of the low pass filter transmission line so this is what is done what is signal conditioning here actually this is what is called a repeater station we have a transmission line carrying the microwave signal from one station to another but before that it accumulates lot of noise okay as it comes through the microwave line and gets distorted because of the transmission line characteristic so you have to restore the signal to noise increase the signal to noise ratio so you just put a PLL here so that you take the output of the VCO this is the VCO output here so it is the same FM or FSK that is transmitted in the transmission line that is received here and but restored in strength that means power and devoid of the additional noise okay it can further go to a greater distance okay if you have the repeater station so this is called signal conditioning is another important application of the PLL so you can have many such PLLs containing the different what is that data from different modems put together received here and restored to higher level of power and devoid of noise retransmitted frequency synthesis is what is called as the primary application of the PLL which was first used by the microwave people because they had difficulty in generating stable frequency sources at that high frequency so they had to start with crystal frequency and go on to higher frequencies so that required the help of efficient multipliers frequency multipliers so this is what comes into picture let us say we have frequency counter here divide by n counter this is easily designed and available so this Fi comes here as Fi by n this is the input frequency to the PLL which also contains a VCO cascaded with another counter divide by m counter let us say so this is going to be I mean the new VCO which is the earlier VCO with a divide by m counter which is programmable okay then we have this frequency divided by m becoming equal to Fi by n this frequency is tracked by this output in this PLL okay so output frequency same as input frequency and this frequency divided by m okay is what is equal to Fi by n so this frequency is nothing but Fi into m by n so we have f output okay divided by m equal to Fi by n so f output is m by n into Fi so the such an easy technique of multiplying by an integer m and dividing by an integer n you can get any non integer value for m by n so theoretically you can synthesize highly accurate output frequencies using this but efficiently you can do it okay for any frequency by incorporating multiplication and frequency translation together to form a complete accurate frequency synthesis how do you do frequency translation the simple omega i is the input omega naught is the output this response to omega i minus omega naught omega i plus omega naught is got rid of by the low pass filter and if you have an input frequency of delta omega shift that is to be achieved this output will be omega i minus omega naught plus or minus we do not know delta omega any one of this can be sustained any one only can be sustained that is if one of this becomes equal to 0 that is DC that is ultimately what the low pass filter let us out only DC then that is this state that means omega i can be omega naught can be either equal to omega i okay plus delta omega or omega i minus delta omega that means it can achieve a highly accurate shift in frequency by delta omega so it is one of these components that is sustained as DC so this is the frequency translation loop combined with frequency multiplication it becomes a powerful tool to synthesize accurately okay frequency components for use in transmitters and receivers speed control motors this is the important application in the present day speed controls here it is nothing but the PLL this is the reference oscillator divided by n counter just as before so you can get any frequency as let us say f reference f reference by n so then we have a phase detector here as before then the loop filter and the power driver the motor field winding so that the speed can be controlled okay this outputs a set of pulses how is it done you have a motor rotor connected to a disc this shaft is connected to a disc with perforations here at the circumference of the disc equidistant that should be done so this is done by photolithography this is called optical taco these are available okay you put let us say what is called as opto opto coupler it is nothing but a light emitting diode with the photo transistor in a package so this produces nothing but a set of pulses as the light gets caught by the opto coupler right it produces pulses and number of pulses produced per second based on the rotation of the motor will be equivalent to nothing but a VCO right voltage controlled oscillator here so this again forms a phase lock loop and the current the speed drives etc are controlled essentially by a frequency reference which is much better than voltage reference okay and potential divider arrangement is a very stable input okay and the future electronics will be most probably shifting from voltage or current reference to frequency or time references so this one such block which is using the principle of phase locking okay for speed control application so AM detection also can be carried out in a similar fashion so what is done here is that the AM okay comes through limiter so that amplitude modulation and noise is removed so essentially it has the carrier frequency and this gets applied to the phase detector comes out right amplifier plus low pass filter and then the VCO so VCO now has the carrier frequency right this shifted in phase cause there will be a in quadrature if omega naught q same as the carrier right there will be a phase shift of pi by 2 so if there is a phase shift of pi by 2 and then we multiply okay then nothing is detected cause one is sin phi another is cos phi so whereas we want this to go into the multiplier after a phase shift preferably of 90 degrees so that this is cos omega t and this also is cos omega t cos squared omega t okay so it produces an average corresponding to the detected signal AM detection is possible low pass filter is put so that the double the frequency component is removed only the low frequency component corresponding to the modulating signal is allowed so this is the AM detection scheme so essentially it is a frequency selective AM detection right so it removes the noise here okay and then generate the carrier with the in phase component okay otherwise it is quadrature phase and then multiplies again to detect the AM the synchronous detection synchronization is again the obvious application in television and the other receivers particularly television receivers video receivers okay we have the synchronization pulses necessary horizontal and vertical those can be recovered okay from the signal composite video signal okay using PLLs okay so in conclusion this block PLL is an important block which is essential in present day electronic system understanding clock recovery also is done that is a digital PLL because the phase detector need not be necessarily the analog multiplier it can be an XOR gate okay and edge detection can be done in order to find out the phase okay so those digital PLLs and delay lock loop is equivalent to the true PLL that we discussed earlier these are the ones which are coming to picture in the present day era of packet switching and clock recovery thank you very much.