 Today our 35th lecture is on non sinusoidal oscillators. We had earlier in the 34th lecture discussed about the speed trigger circuit and we had seen how the speed trigger or regenerative comparator can be used for a variety of application as a mixed mode circuit. Pulse width modulation that is the basic speed trigger is having regenerative positive feedback we saw this is represented as an inverting type of speed trigger with the hysteresis inside so actual hysteresis of this is going to be looking like this this is V naught this is VI and the amount of hysteresis can be controlled by R1 by R1 plus R2 which will be called as beta so this when it is this can be only at plus VS or minus VS not any intermediate point whatever be the input so this particular thing is going to be plus or minus beta VS plus or minus beta VS so this was the speed trigger that was used as inverting another one topology which is called non inverting speed trigger that is the input and the ground for example they get interchange this earlier input is grounded now so the feedback retains its regenerative action only the input now is fed here output is taken here so this is what the inverting the non inverting speed trigger represented by this kind of symbol without this inversion okay and its characteristic is the something like this this is V naught and this is VI so how these speed triggers can be used for FM generation is another basic principle that we have this comparator regenerative comparator one feeds here a triangular waveform and this here a reference waveform then you get here okay based on what the V reference is a square wave or a rectangular wave rectangular wave has a duty cycle which can be made to be proportional to the reference so the duty cycle generator or FM or FSK generator has this kind of characteristic is half into 1 minus VR into 1 minus beta by VP is the peak of the square input so this is beta R1 by R1 present so using this one can design a class D power amplifier DC to DC converter etc based on this then it can also be used for FM generation okay when this VR is varied according to nodio signal that is FM if it is digital data once and zeros DC changes from one value to another then it is the FSK generation it can be used for that now a stable and multivibrator function generation so this is another important use of these mid trigger so we are now taking this inverting type of mid trigger here with beta equal to R1 by R1 plus R2 that is the amount of voltage fed back and this is either at plus VS or minus VS so this is changing state at this point when VI corresponds to this plus or minus beta VS so what happens let us assume that initially at plus VS so initially at plus VS so the capacitor is going to start charging from zero so it is going towards plus VS if this connection is made so the input now sees a voltage which is exponentially increasing because of the charging of the capacitor with the time constant equal to R into C so this exponentially increasing voltage it sign to reach plus VS but as soon as it becomes equal to beta VS same as this beta VS change of state has to occur from plus to minus so now the capacitor is seeing minus VS and it is discharging at the same time constant RC so it will be discharging towards minus VS as soon as it reaches minus beta VS this is at plus beta VS again it changes back to plus VS so this will keep on happening as this toggles from plus VS to minus VS this will toggle from beta VS to minus beta VS so the capacitor will be charging and discharging continuously so it is going to acquire this beta VS again so these two time durations are the same because the capacitor is going to be having a voltage of beta VS to minus beta VS that is twice beta VS in a time let us call this half time period because these two times are same this is the time period so this is half time period so charging and discharging take the same amount of time because they are the same time constant RC and acquiring the same voltage of 2 beta VS within that time T by 2 so you can consider this portion for example the capacitor is trying to charge up to plus beta VS it would have gone on like this so the voltage applied is minus beta VS plus VS which is VS into 1 plus beta that is the voltage applied and in T by 2 it is acquiring the voltage of 2 beta VS so this equation is the charging of capacitor when a voltage is applied across it is the total voltage applied this is the voltage it acquires within that time T vector so this gives you T equal to 2 RC log 1 plus beta by 1 minus beta and F is nothing but 1 over T so this is a function generator or a stable multivibrator which gives a exponential increase and exponential decreasing wave form if the time interval is very short this can be considered linear and it is a triangular wave form here you get a square wave form with frequency equal to 1 by T both of the same frequency so this is simulated for R1 equal to R2 beta equal to half so beta equal to half in this case so 2 RC log 1 plus beta 1 plus half by 1 minus half is log 3 so that is the time period see T T equal to 2 into R is 1 key C is 1 micro farad log this comes out to be roughly equal to 2 RC log 3 right which is equal to 2.2 milliseconds 1 over T is 454 hertz so this simulation exactly tell us with the expected results so this is beta VS so in this case beta is half and VS is 10 volts even the VS is 10 volts the op amp used is TL 0 TL 0 A2 okay so when 10 volts supply is used it is going only up to about 8 volts okay minus 8 volts so that is why the square wave amplitude is limited by the ability of the op amp to give the highest output as 8 and minus 8 when 10 volts supply is used and correspondingly this voltage is 8 by 2 which is 4 volts so the amplitude gets fixed the frequency gets fixed and please note that the frequency is independent of the amplitude of supply voltage magnitude of supply voltage yes so that is the advantage of the simple circuit this has no need for the substituted amplitude stabilization schemes that become necessary in the case of sinusoidal oscillators so very simple thing what is now done is in simulation 2 right the this voltage is shifted to a reference value this particular thing is sort of grounded so grounded the plus supply only minus supply is there so this is single supply utility of the same circuit so this is made 0 this is minus 20 and the V reference is minus 10 so beta is still half for that it is again plotted you can see here the same frequency and the same swing okay for the square wave as well as the exponential wave occurs okay so the value of this remains the same it is 2 RC log 3 so frequency is same as before what has now happened is there is an offset okay around which these things are toggling that means minus 10 volts is the offset around which this is toggling as before plus 4 okay minus 10 minus 10 minus 4 okay so the that is the minus 10 plus 8 okay minus 10 minus 8 this will be minus 10 plus 4 minus 10 minus 4 so the frequency remains the same so even with single supply we can get the same kind of waveform both for the square wave and the exponential wave and direct application of this is a non-off temperature controller so again this trigger is right there R1 and R2 to control the hysteresis beta that controls the extent of hysteresis around VR into 1 minus beta so let us consider this that this is a heater coil which is switched on or off depending upon whether the temperature has reached what is called the set point temperature this particular point is called set point temperature it is going to be in terms of the voltage at this point so this diode is a temperature sensor which we had explained earlier in diode applications so it is forward biased okay so minus vs is applied to R to it so it is forward biased this voltage is typically say minus point 7 volts so as the temperature increases the characteristic we have told that delta VBE or delta V diode by delta T is negative and it is almost constant at minus 2.5 millivolts per degree centigrade that is the diode forward drop temperature coefficient so this voltage V gamma actually or the cut in voltage of the diode this keeps decreasing for the same current okay the forward voltage decreases at this rate 2.5 millivolts per degree centigrade so it is a negative temperature that means V gamma becomes less in magnetism so since we are biasing it in this fanner the voltage V gamma magnitude when it is reducing it is becoming less negative that is it is going towards positive so when the temperature is at room temperature it is the highest magnitude okay and as temperature increases it becomes less and less in magnitude okay so the voltage okay is let us say becoming less negative as temperature increases okay that characteristic is obtained okay for this a stable multivibrator action this is the kind of hysteresis it has because you are using negative voltages and negative reference just like the example that we had shown earlier in this case so it is all in one quadrant negative voltages okay for both x axis and y axis so we use a MOSFET as a switch here right so actually the thing is located somewhere here initially okay so that it is on it heats up the coil and this voltage is going to become less negative in magnet so it is moving in this direction so at some point it is going to change state okay and it is coming over to this so that means it is going to be switched off becomes less than the threshold voltage here it is greater than the threshold voltage so this is an on off control which is adopting the same principle of charging the capacitor however this is nothing but the thermal time constant for it to reach the set above the set point temperature okay and then it is switched off so it starts cooling and then the it is coming towards okay value which is okay below the set point temperature right if this is the room temperature this is the set point temperature right so this is coming below the set point temperature like that it will go on so this is nothing but an stable multivibrator designed to incorporate the temperature controller so these are the deviations around the set point so we have this deviating by delta T on either side of set point temperature so this is delta T on this side and delta T on this side that is determined by the hysteresis so this is the hysteresis bringing about fluctuation around the set point so depending upon the accuracy with which we want this to be set right this particular delta T can be varying and delta T is directly proportional to beta okay so now monostable multivibrator action we just connect a diode across the capacitor then what happens is this particular structure has now one stable state that is why it is called monostable stable state what is it let us assume that it is plus vs so when plus vs is here this capacitor tries to charge up to plus vs with RC time constant but as soon as it reaches V gamma this diode conducts and never allows it to charge above V gamma so at that point of time this is placed into plus vs and this particular thing is at plus beta vs so the voltage effectively across the op amp or the comparator is positive here more positive here so this state is a stable state we have assumed it to be at plus vs because it is at a large positive voltage so now what is done is a trigger pulse comes momentarily it comes and makes this voltage immediately go to a negative value more negative than this so the moment that goes to a negative value or a value less than V gamma this immediately goes to minus vs so this is the trigger point so the capacitor now is seeing a voltage which is minus beta times vs so it will charge with the time constant RC up to minus vs but as soon as it reaches this voltage reaches minus beta vs it will come back to the stable state of plus vs so it has changed the state to minus vs at this point and after a time duration T let us call it the delay it has come back to plus vs again it will go on like this remaining until the next trigger pulse is applied so let us say it is applied arbitrary at this point then it will again generate a pulse width of T and then come back to plus vs so this can be used as a timer application where any process actually starts at this point and ends at okay after time T so once such timer IC which is very popular is LM 555 cost about 0.48 but that contains two comparators here just using one comparator one can also build this sort of timer so this particular thing is again this time duration T can be evaluated this way the voltage applied is let us say this is V gamma and it is going on up to minus vs so effective voltage is vs plus V gamma 1 minus e to power minus T by RC that is the time the voltage across by across the capacitor at that time is okay this twice that is beta times vs okay plus V gamma that is the voltage acquired by the capacitor so T is equal to T is equal to RC log 1 by roughly 1 plus 1 minus beta we can ignore V gamma compared to beta vs that is what is simulated beta is again kept as half and T is nothing but RC log 2 so that comes out to be 0.693 milliseconds so this has been tried with the trigger pulse coming at a rate of 100 hertz so this is the point where the trigger pulse has appeared so it has gone from V gamma to minus beta vs and that is T again after this it has to discharge and it will keep on up to this but at this point the diode comes into picture and holds the voltage at V gamma across the capacitor so the next trigger pulse has to come only after this has reached this state that is the limitation of the frequency of triggering okay so the time T is equal to RC log 2 is exactly fixed so industrial timers make use of this principle for actually generating a fixed time duration function generator so we have here the inverting non inverting type of non inverting type of Schmitt trigger we have seen inverting type of Schmitt trigger being used for function generation suppose we replace it with the non inverting type of Schmitt trigger which we have discussed earlier in the last class with an integrator which is again near ideal we had used earlier R and C which is a rough approximation to an integration operation so we are using this as an ideal integrator of amp so what happens to this a stable multivibrator let us see so once again output of this can be either plus vs or minus vs so it is pumping in a current of vs by R into this and this voltage across this is going to change linearly so this voltage is going to be 0 here and therefore it is minus vs by RC into T so that means for plus vs we have a linearly decreasing voltage here as soon as this voltage reaches a value such that for plus vs here this should become equal to 0 that means it should take on a minus vs okay so the voltage at this point is continuously changing when it is plus vs here it is vs into R1 okay plus V0 prime into R2 by R1 plus R2 that is the voltage at that point that when it becomes equal to 0 this changes state from plus to minus so what is that voltage V0 prime can be from this equal to minus vs into R1 by R2 so as soon as it reaches minus vs into R1 by R2 this changes state from plus to minus so this will now change slope from minus vs by RC into T to plus vs by RC into so this will linearly increase this way so as soon as it reaches plus vs into R1 by R2 again this minus will change over to plus this way it will go on this time duration is T by 2 this also is T by 2 so in a time T by 2 it is changing at a rate of vs by RC into T by 2 it is acquiring a voltage of twice vs into R1 by R2 so again the time period T is independent of vs because vs vs get cancelled and T becomes equal to 4 R1 by R2 okay into RC so here we get a triangular wave output here you get a square wave output of this frequency F equal to 1 by T so this is what is derived here can see that this is changing from minus R1 by R2 into vs 2 plus R1 by R2 into vs at a rate vs by RC again discharge is at the same rate but negative vs by RC so frequency is R2 by 4 RC into R1 so this is what is shown here in simulation R equal to R1 equal to 1K R2 is equal to 2.2K reason why we have chosen R2 to be now different is because in the case of this kind of variation R1 by R2 if it is less than 1 only this scheme will work if R1 by R2 is greater than 1 the voltage here has to go above the maximum limit possible for the Schmitt trigger output okay which is not going to make it toggle at all so R1 by R2 in this case has to be less than 1 in order to make it toggle and continue with this kind of generation so this is something that has to be remembered so we made R2 safely equal to 2.2K so this particular thing has now resulted in this is vs into R1 R1 is 1K by 2.2 times the maximum which is 8 volts okay and this is minus 8 by 2.2 this is plus 8 and this is minus 8 so the time period is 1.82 or milliseconds F naught is 550 hertz now let us say we have put here an asymmetrical voltage that is this is V asymmetry what does it change in terms of symmetry earlier the current of charging and current of discharging of the capacitor C was the same in magnitude it was changing direction from vs by R to minus vs by R the moment you put a VA here this is changing between plus or minus vs because it is the Schmitt trigger output so the current here while charging is vs minus VA by R this is charging that means the voltage at that point here is changing as vs minus VA by RC into T so it is negative so it is minus so this is the slope vs minus VA by RC and in the other direction this is minus vs this is VA so the total current in this direction is vs plus VA by R so that means actually it is increased okay that means it will take less time to come to this which is because it is slope is higher vs plus VA by RC into T plus so if there is an asymmetric causing voltage here which is positive then this slope is lower than this slope so we get a short tooth at this point of course this will become a rectangular view so this will be at plus vs all the time and at minus vs for less time so rectangular view here and a short tooth here is what you get because of asymmetry taken an asymmetry voltage of 5 volts are actually I think so for 10 volts supply we have taken an asymmetry of 5 volts so and shown you the result of asymmetry so we have seen here vs minus VA by RC into T1 is the same voltage from here to here the voltage changes remaining the same as before 2 R1 by R2 into vs so T1 changes however because the rate of charging and discharging are different now so T1 and T2 are different T1 plus T2 is now T so T1 is this and T2 is this from these equations and T1 plus T2 is this so we get a short tooth generation here so asymmetry is 5 volts as I told you the charging is occurring at a faster rate so it takes less time discharging occurs at a slower rate takes more time and this is the short tooth with VA changing over to minus 5 we have now charging taking more time discharge takes less time the short tooth is of this time so by merely changing the asymmetry voltage VA one can actually get the different types of short tooth waveforms from this function generator so this function generator essentially can be used for triangular waveform at this point and square waveform at this point this triangular waveform is converted okay using a diode function generator which we had discussed earlier which can convert a triangle to a sine wave triangular to sine wave converter we have discussed complete design of this in the earlier lectures so here you get a sine wave of the same frequency f equal to 1 over T so these are the important functions necessary for testing okay in a test lab this is a test oscillator okay which is one of the cheapest oscillators available in laboratories today all over the world so ICs are available which use these principles okay we will come to that later at the end so now we will convert this into okay function generator with offset if you now put instead of bringing about asymmetry we are putting an offset voltage here we offset so this ground is lifted and offset voltage is put here then what happens is as far as the triangular waveform is concerned it remains the same as before because the charging and discharging remain the same okay because this is grounded now so with this offset here what can only happen is this output waveform of the triangle is offset by certain amount okay so that is what is being shown here now so with an offset okay this triangular waveform which was swinging around 0 has got shifted to a positive voltage okay so because of an offset of 1 volt introduced there so this offset can create a problem sometimes because if it is too much this particular thing will be getting distorted because it cannot go above 8 volts here so the offset should be such that the triangular waveform is produced only within this thing that is possible for the Schmitt trigger output now this function generator can be simply converted to a VCO which is an important block again in communication systems VCO is nothing but FM generator or FSK generator so this particular Schmitt trigger is followed by now not an ordinary integrator but an integrator preceded by a multiplier this kind of conversion we have done also in the case of voltage control filter converting a double integrator loop into a voltage control filter or oscillator was done by replacing the integrator by multiplier followed by an integrator. So this multiplier followed by an integrator is ahhh going to make us a current here which was earlier simply VI by R or plus minus this VI was only changing between plus and minus VS it is either plus VS or minus VS so what happens here when you multiply with VC this will become plus minus VS divided by 10 which is the reference voltage for the multiplier into VC so the current in this which was earlier VS by R in this direction or this direction is now going to change to VS by 10 R okay into VC plus or minus okay so it is going to change in the same direction but you can think of this as modifying the original R as 10 R by VC that means all those ahh frequency and time period get modified simply by this factor that is earlier we had this as R2 by R1 into 4 RC here as F so now this R is going to be replaced by R into 10 by VC which results in VC by 40 RC into R2 by R1 so it becomes a linear VCO and if you now find out the sensitivity of the VCO which is defined as delta F by delta VC this becomes simply since it is linear it becomes constant equal to R2 by 40 RC into R1 or it can be also written as F divided by VC hers per volt this is an important parameter associated with a linear VCO it is non-linear you have to find out at the coefficient frequency of oscillation this look so VCO is an important building block in a phase lock loop which we will discuss which we have already discussed earlier this is strictly speaking not really a phase it is a frequency lock loop will hence forth call this phase lock loop we have discussed it as something that we had used in the filter for self tuning of the filter for locking on to for example pi by 2 phase shift here this block VCO is an important building block in a feedback system that is called frequency lock loop so the VC voltage control filter VCF is replaced by VCO there becomes an independent system generating a frequency of oscillation dependent upon the control voltage function generator is an oscillator which produces square wave triangular wave rectangular wave with specific duty cycle and shock okay also it can produce a saw tooth okay can also output sine wave by converting the triangular wave to sine wave using diode function generator the VCO circuit that was discussed earlier okay which is available as an IC XR 2206 or LM 566 but this function generator is very popular as test oscillator chip which is used in almost all laboratory function generators okay for test purposes now FSK generation how to do FSK generation so we can actually use this VCO and modulate it at modulation simply means that we are now connecting at this point VC 2 positive voltages one indicating one digital one another indicating digital zero then it becomes a FSK generator so this is high this is low both have to be positive right so this gives high frequency this gives low frequency this is what is used in modems okay for modulating the frequency next instead of the square wave applied as VC one applies a DC with a sine wave superimposed so that it gets now modulated continuously the frequency is slowly becoming highest and slowly becoming lowest like that it goes on this is nothing but FM generation so at this point okay at this particular voltage it is the carrier frequency okay and it is more than the carrier frequency it is less than the carrier frequency here so that is depicted for the triangle also that way for the sine wave also it same kind of characteristic exist and therefore you can take the output at the sine wave output and it will be FM generation so these are the characteristic features of this IC XR 2206 and it is continued here you can see the sensitivity sweep range 2001 so 566 is the TIIC which is capable of being used as a VCO now the limitations due to the op amp rise or the comparator rise time and fall time will not permit it to be used for very high frequencies it will be more so with op amps being used as comparator here the limitation is due to slew rate right. So if slew rate is known right you know that see from plus VS to minus VS the op amp is going to rise at slew rate okay and therefore the voltage twice VS divided by row if row is the slew rate of the op amp that is the time taken for as rise time in the case of op amp which is going to make it too slow right so if it is for example 1 volt per microsecond okay and VS is let us say 10 volts so this will be 20 divided by 1 okay so that is the rise time okay 20 volts per microsecond that is 20 microseconds it is going to take which is going to result in the rise time being too large in the case of actual comparator the rise time is going to be pretty small and therefore it can be used for very high frequencies okay so the accuracy of the frequency also is better with comparators okay so it can typically be used up to megahertz very easily with full output swing possible whereas this is limited to few kilohertz okay as plus minus 10 volts amplitude because of this fundamental limitation so we have seen how op amp should not be used as comparators comparators are used in mostly open loop or positive feedback and they do not have any frequency compensating capacitor put like the ones used in popular general purpose op amp with frequency compensation that fundamentally limits the frequency of operation it makes it very slow so comparator like 311 etc are fast comparators there are no capacitors added there is no need for them because it is never used in negative feedback thank you very much.