 We were last discussing about comparators and we did say that if Vn is larger than the reference or smaller than the reference output will be correspondingly plus or minus and two circuits which may be used one is inverting kind the other is non-inverting kind may have a characteristic shown here if it is a non-inverting for Vn less than 0 or smaller than V reference you will have V low at V reference when it crosses it will jump to high value which is Vh and if you do the inverting kind that is you substitute input at the V minus and put reference at the V plus the opposite will occur as state. So this idea that input when exceeds or decreases belong beyond V reference can change the state of the output from high to low is the basic feature of a comparator and I already said that this will be very sharp in what case when the gain of the comparator is very high ideally infinite but very hard into power 4 or 5 or even higher so I assume right now ideal comparators in real life there will be a slope and some adjustment has to be done but for our simplicity right now you believe the comparators are ideal why I said we do not have to do more accurately because at the end of the day it only decides the time going from low to high if the gain is not infinite it will take some finite time to reach the other level. Otherwise it is as much as saying instantaneously which normally will never occur in any system. Okay all said and done here is first of the kind of comparator which we are going to use okay the problem with which I do not know whether I have shown here if I have a normal comparator like this which has a anything below V reference or above reference state changes this is I plotted V in versus time and this is my V reference value if this is your V reference voltage and this is my V in T which is following some straight line in some sense but in real life this will not be straight line it will have some kind of noise over reading them. Now the way it will occur anytime V in crosses V reference it will switch the state is that clear if it goes above or below either case that means when it crosses here I will change when I come back again it will change the state is that one clear anytime V in crosses the V reference from lower to higher or higher to lower it will switch the state that the output if you see any time it is crossing the output V0 which what would happen actually I expected it a good straight line curve where let us at this point I would have expected something like this but now I find the noise if the amplitude of noise is not very small and whenever it crosses the reference either going from low to high or coming from high to low it will switch the state this means the noise as essentially is now actually been transferred at the output okay we do not want this to happen but it is happening okay so one of the suggestion it was done that if we do little carefully this circuit in which we would like to see that there is not one value of V reference we quickly there is one higher reference value and one lower reference value so one can cross once there so it may change but unless it comes the lower side the value it will not change the state of that correct I repeat I show you the figure so if I can make two reference value created from one single reference value where switching can from going from higher to lower to higher it may switch at one point and when come from higher to lower it will switch from some other point then the noise in between cannot change the state okay that is essentially the feature of Schmitt trigger the word which we use is Schmitt trigger here is that basic circuit which you can create for example I have a V reference and I have V in given at the V plus and there is a ground at the V minus okay I will leave it to you find out in a book or from somewhere even if you are going to ground something you should ground through some kind of a resistor what does it do even in inverting or non-inverting case the ground potential is essentially created via some resistor I can still directly ground but I do not okay think of it it is a very simple circuit issue and therefore in real life circuit even if potentially they are same there are no current passes in the open so there is no question of me saying that anything happens but their presence is some kind of essential is that clear so if you are doing some circuits in the lab which you must have already completed your lab now but you must have found that most cases we say put some resistor at the V plus to the ground before we use non-inverting circuits okay so that is basically nothing to do with our analysis but just to show you the kind of resistor I am using is identical look at this is average resistance in the V plus is R1 parallel R2 so the same resistor I have put to V minus okay this has nothing to do with how much as much as possible make it symmetric okay is that clear whatever is here substituted upstairs I mean upwards so V0 switches when V plus crosses V minus see whenever comparator change the state when V difference potential is plus or minus if we are V minus V is larger than V plus output will go low if V minus is lower than V plus output will go high this fact that means these comparison of V minus and V plus essentially decide when the switch will occur so now this V plus value we can say can be now represented as R2 upon R1 plus R2 times V reference this is a summer is that correct this is a summer circuit which kind non-inverting kind summer okay so R2 upon R1 plus R2 V reference just superposition at this point was this source like this source R2 upon R1 plus R2 time V reference plus R1 upon R1 R2 V in is essentially V plus for crossover at let us say crossing at 0 because V minus is grounded to 0 so whenever crossover occurs V plus must cross 0 so R2 V reference is R1 V in so we say now the new crossover point can be I repeat what did I say in the normal compare I want to have two separate values of switchover so how do I change those switchover points is that point clear what I am doing otherwise what was the switchover point V reference from there it was now I said okay I do not know I want to have value which I can create separately so I said okay I have another method of changing that point which is my V minus or V plus which essentially gives minus R2 by R1 time V reference is the new crossover point okay so I have moved my crossover point is that point clear to you I have I am moving in the ratio of Rs with reference your actual reference value my crossover crossover is occur where when the V plus crosses V minus is that clear but I can change V plus value now earlier it was just V reference because we are now I say okay with reference to this we will compare this fact that crossover point can be changed when the input crosses V minus is what the trick we shall use in the case of is that point clear the reference point is now modified by this ratio if they are equal then there is no question they are there it remains same otherwise it can always be shifted to any other value now I show you why I am actually trying to show you this because what is the idea I showed you what is that I was looking for that the input going from low to high should cross over at the whatever reference point I want at one crossover point but when I return it should not switch at that point it should cross over at other point okay so that whatever noise at that higher level was should not be now crossing over that point but should cross even a way point which may not because if I separate the two crossover the noise here cannot actually cross this point so I say okay I can eliminate the noise if I remove the crossover I may separate the crossover points which two crossover points I am talking one going from low to high crossing the reference the other coming from high to low input going from high to low crossing the difference those two crossover points I want to remove away from each other this is essentially the feature which Schmidt triggered why it is called trigger actually comparator itself is a trigger is that word clear comparator is essentially on off is it not it is a switch so any circuit where you want to have one input that is high input may do something and if it goes 0 it will do something else so you say I was changing the output of next circuit by putting a Schmidt trigger so it is essentially called trigger it turns on and off is that word clear why trigger so what I am now suggesting that in real life we do use Schmidt trigger in number of days in this particular area I am actually looking for Schmidt trigger oscillator we are in the oscillator area we are trying to say how can we use Smith trigger for a square wave oscillators but in turn I am also showing it can be used in variety of ways where on off is essentially required okay so here is the basic Schmidt trigger essentially a smith trigger is a comparator which is modified with a positive feedback this results in a circuit which has two stable state and therefore it is at times called by stable element or by stable multivibrator okay I repeat my ultimate aim is to see Schmidt trigger which has separate crossovers and does that create at the end some oscillator which is of what kind square wave generator we are already what kind of oscillators we have already seen genocide all earlier oscillators we say sinucide the first square wave generator what I showed you earlier simple inverters in odd numbers if you feedback then you get a square wave okay now I want to see can I use of all is inverter is how many states it gives two states so I am still using the same word switch in some sense two states by stable okay so now I say better by stable element can be created then the normal switch is the Schmidt trigger now if I have a R2 R1 and the feedback for V plus which is granted and input is given to the upper inverting kind of input then when the switch over will occur when this value will cross V plus value crosses sorry V minus value crosses V plus but there is a problem what is the problem here the V0 please remember V0 is feeding back through R2 R1 ratio to V plus but V0 is a function of V in is that point clear if I change V in I am going to change V0 if I am going to change V0 I am going to change V plus is that correct so this is some kind of a feedback going on is that correct this is also therefore sometimes called positive feedback the other term what is the name given to positive feedback regenerative positive increases now this fact since V plus is a time varying function please remember this is not constant in normal case what would have been the value whatever fixed value I did I feed back now V0 itself will change as being changes and as V0 changes V plus changes if V in is a function of T so V plus is a function of T therefore the difference potential between V minus and V plus is also varying is that point clear this is what Schmidt trigger is trying that this value is also a function of time and compared with the function of time inputs okay and then we find at that instant of time whether crossover can occur or cannot occur let us see how it occurs depending upon whether V plus is greater than V minus or V minus is greater than this output can go to VDD or to VSS is that correct if it is higher if this is higher than this what will be the output minus VSS lower value if this value is smaller than this this will go to be opposite phase okay so it will switch to the opposite side if V difference is positive output is low if V difference is negative output is high now this another thing which will do later probably this VDD may be a 5 volt 10 volt minimum any amount but in real life in digital what can be their typical values of this level you want is per square inputs maybe 1.5 volt these days it is even less than 1.5 1.2 volts at least we need at least 3.3 or 5 volt maximum these may not the comparator may behave better if it is higher voltages as the power supply because then the noise on that will be very small however the output I do not want to rise to VDD or VSS so how can I do that numbers different we have done that circuit already I have a voltage it is going to 10 volt but I do not want to rise to 10 volt I want that 3 volt stop what should I do plan use clans okay diodes so you can plan the inputs by diodes and then you actually it is going towards VDD but it will plan to some value is going to VSS will plan to some value if identical these are given it will plan to plus minus equal values is that clear this is the circuit we will show what we will do later. So that is called limiting the outputs okay so in real life I will show you the actual limit spectacles I may actually put some diodes here so that the output can be clamped to a smaller values okay however right now as a theory whatever VDD VSS down here now if V minus is V minus is V in V0 could be positive or negative depending on of course V in value and the polarity that is V difference is plus or minus will decide whether output is high or low yes I told you I am not going to tell you think of it you say laga ne ho raya chillig na kyo lagaya te toh pish toh karan ho gaya main say main aur yeh bhi actually it is not very compulsory that it should be parallel combination of same resistance but symmetry demands that it should be seen so that inverting non inverting karthi thama tension ne hai isle same litay but yaha pish toh bhi 100 ohm ka toh bhi resistance ground ke pahle laga na chahiye kyo boon pahab sushu phulhata haan usko thola sa sushya karan ke pahas pish limit karna hai sa aapne kabhi power supply yaa signal generator me dikhaw haan ek limiter laga rata hai isse jada ba toh spring loaded rata hai abhara rata hai nya haa kya kata haan chib kya andar kya load kare hain toh isko paale se hi pish karan limit kar aada toh jawab yaa aada poora nahi hai ishne aur bhi kuch haan, poora sushye kya main kya haan. Poora I am not saying that you I should not tell you all this but I thought you should start thinking in circuits why people do some things and they do not explain much ok. So, I also thought how we learn we should learn if you cannot then well I will tell you what exactly will happen ok but it not difficult to do. Pari aapko aisa book me directly nahi mila, konse book me mil sakta hain, there is a book by electronics made easy by Horowitz ok. So having told you this so it could be V o is equal to V h or V o is equal to V l could be we read your V h as f not plan. Let us say when V o is V h, V minus must be less than V plus the V o V h pegana ultah hua. So, you calculate V plus now is R 1 upon R 1 times V h as long as V minus remains less than this V 0 remains V h that is V in is less than V h. So, uska jor turn here se the V in minus a that remains high or jesei threshold ko cross krta hain, kya karenga wo lower value pe V l pe chala. So, a threshold value jo humne nikali jaan ki crossover hone wala hain what is the crossover point it is that input voltage where output swings the state from high to low or low to high that is called turnover or threshold value ok or crossover voltage. But that is not output this is the input value at which switch occurs is that correct ek semas inverter mein phichor kaun hota hai the switching threshold hai roughly kitna hota hai 0.5 nahi V dd by 2 ya right, ya right. So, waha humne adjust kya tha ki beta R jo hai ratio of n channel p channel 1 liya gaya tha beta ka isle ho V dd by 2 pe hain uska ratio change keroge to o left right way ho sakta hai. So, yehi wo hi idea thode si humne jaan bhi uska ki iska threshold point jo hai wo kaini toh bhi shift krse. So, abhi since it wa that V h this value was a function of V h is that clear this threshold was a function of because till this value output was high so this value was decided by output what is the V plus value we are getting ratio of R to upon R 1 to R 2 times V 0 if V 0 is V h the first threshold occurs at proportional to V h. However, if we were at VOL initially, yeh di hum yaha se jaar hain VOL pe the so at this is VOL please remember VOL is minus and VOH is or VH is plus. So, if I now calculate when I am reducing V in I find the new VL is R 1 upon R 1 plus 2 into VL and not VH please remember VL is a opposite sign is that VL is a minus VH is plus. So, first switchor keetar aaya plus side me aaya VH was positive to a switched here since VL is negative it switched at the negative. So, abhi kya hara hai ki if I am going from plus to minus iska yeh figure best hai jala dekhon thora sa. If I am going from minus V in towards V in plus when the output was high then what will happen it will switch over at this value VTH. However, if I am at VL and I am reducing V in it did not switch on here why because now the value of switches at VTL minus of that value is that clear clear when I went from minus V in to plus V in as V in became crossing that V plus value the state changes high to low it went through ok. Yahata V in is less than V plus so output remain high as V in exceeded V plus that is the switchor point at this point output went low this output went low and you are in the VL position now. Now you reduce your V in back where you are at much higher V in you start reducing V in back towards minus V in where were you initially at for that case at VL. So, the new switchor point will be proportion to what value in feedback it is proportion to always R1 upon R2 upon R1 plus R2 times V0 but V0 is now VL which is negative so it switches here. So, if I am going from like this I switch at this point if I am going from this side it did not switch here but it switched back from this point and when that is normally ideally kesa anatha asa anatha hysteresis but what is the advantage I will get out of hysteresis very soon seen that why I am looking for hysteresis is that point clear to you what is that Schmitt triggered rate. Because the difference of VTL and VTH is plus or minus ok the one switches at VTH the opposite when you come it switches from minus VTL ok and the gap between VTH and VTL essentially is the hysteresis voltage like magnetic curve or magnetic curve but asa anatha hysteresis voltage. So, it is a matter of decision which way you want to swing ok either use inverting comparators or use non-inverse what does that mean input upper lagana ki niche lagana aur kuch bodhi chissin ok ok. So, if we now reduce VN that is V minus you are already at the state V0 equal to VL and you are reducing it now. So, it switches over when V plus become crosses the VN V minus value versus which one ever but that value is now function of VL which is minus value. So, it has a value of VTL which is away from VTH is that correct. So, plus mein jate bakhar you switch at VTH return minus mein aate bakhar you switch at VTL. So, you create an hysteresis is that clear you create a hysteresis. So, if you are going through an ac cycle it will actually switch at 2 points now is that point clear. So, what does that trying to give you in you using a Schmitt trigger I will be able to create a nice looking for a problem we will be in shift karing a to a key bar a pulse min. So, what is the difference between here mono me to have signal there in oscillator no so that means the whatever input point is must switch out plus as a hotel and I say as a hotel that I got to be output the square where I go dick there I got go kese karing a boy Schmitt trigger is that point here. So, idea of a Schmitt trigger is that I can create two separate states okay. So, these are very much hand controlled. Okay let us say a problem is there if VH is and VL is 10 volt plus one minus 10 volt. I am asked to find this value given this value and assume that equivalent value is there and let us say R2 is T value and we also assume that VTH is equal to minus VTL why it is same because we are saying VH and VLR plus minus same value. They can also be separated okay. How do I calculate R1 either use VH or use VTH or use VTL either of them VTH is R1 upon R1 plus times VH that is given to you 2 volt VH is R1 times VH is 1 upon 20 by R1 into 10 which gives me a value of 4.2k if I use minus 2 volt here minus 10 volt I got the sign same same value either use VTL or use VTH as long as they are same it does not matter it does not. What is the design we say okay we need 4 volts this is called as 4 volts around 0 plus 2 or minus 2 which I have high volt 10 or minus 10. So, that is how you actually will hook up this value given those values you say okay put this value I should and then verify. When I put this value I do not exactly switch at plus 2 and minus 2 okay because my assumption that the comparator is ideal is not correct. So, there will be change but then what do we do you actually put a pot on R1 and keep adjusting that and at some point will come very close to it exactly 2 minus 2 but very close to it you can bring it that is how the design actually tuned fine okay its advantage that is a maths part so what is the advantage here. So, when I am actually crossing over VTL sorry VTH only then I will switch because I am going from input low to input high so crossover will only occur at this point is that clear. Please remember what I am saying I repeat I am going this is my VIN increase with a noise over reading on that. So, no switch till this point there is no switch because at this point only first time input crosses VTH VIN we are increasing till VTH it cannot change the state. So, here noise since it is not reaching VTH it is not crossing over at this point it crossed is that clear. So, at Nietzsche pulse output height how Nietzsche are there now as long as this noise does not cross VTL even if it is a larger noise going on it cannot cross over because now we are going from higher side towards lower side. So, now as now it do whatever you do till it crosses VTL it cannot reach in the state the output is that correct. So, it is that clear that is the fun of a it is possible but it is like the risky because comparators voltages if you change which can do you can then the problem with comparator open a circuit actual polarity you cannot switch because that cannot be done because it is internal chip you have no control on that if you can hook up something otherwise if you have a opamp with PN circuit I mean N channel as a load or N channel as a current mirrors and P as the driver is doable okay but that is means you are having another chip with the same chip giving VDD whatever is given you have no choice for externally you cannot do but you can use another chip which has a P defam with N loads okay that can do the opposite that is possible is that okay. So, is that advantage of Schmidt trigger is clear that it triggers at one point now okay and it eliminates noise overriding on it is that correct is that point clear. So, that is the advantage of Schmidt circuits a core circuit I will not derive it I will just show you I instead of you know this putting to be ref I mean this is a inverting kind you have been like I have been a reference. Please remember when I have been a normally a yeah yeah. I think I have been a reference potential. If I do the same analysis once again the transfer characteristics will now move away from that point okay by so much as we reference point by ratio of there is a potential called VS which is the half way switching voltage as we call VTL plus VTH minus VTL by 2 which is again R2 upon R1 times R2 is a ratio of a V plus R1 upon R1 plus R2 times P0 V plus is also created from so yeah remember this may currency theorem use only a superposition a yes a feedback a a yes a feedback a so if I do that analysis I can of course as I say you do yourself VTH and VTL could be now both positive but shifted by as much voltage is that correct by putting some positive value is that correct. So this curve itself can be moved left and right by choice of V reference do analysis please remember this is a superposition requirement is that clear only thing is both can be positive or both one can be both can be negative or if you do not do anything you put V reference 0 it is symmetric to 0 is that clear what is VS essentially is what is 0 that is 0 okay. So this is something you need at times that this crossover point need not be negative it can be positive self is that correct so by making a slight modification in Schmidt circuit I can also decide where my switchovers can be okay this is the another thing which Schmidt trigger always uses okay please this is given in our the Cedars-McBook you can read and I think they have also solved it I only written the final answers okay now we go to the final part on the Schmidt what is the all that we were doing so far as if we are only a going on now no that was not my this is usefulness I showed you many other places but the circuit which I am going to use is to be okay the circuit which I am interested in is the oscillator. So why am I did all that because to understand the operation of this I thought you should first learn the Schmidt itself okay is that point clear otherwise for this circuit I could have started here and say this is how it happens but I thought it is not fair let us say what is Schmidt and then use Schmidt trigger to create an oscillator please take a circuit actually before you draw you start drawing and then I will ask you another query. If the regenerative is not there then the crossovers cannot be fixed on one side we will fix this may few points we shall note this is your standard Schmidt trigger a input is there but this is your V minus which is your input this is your feedback for regenerative feedback and I have added two new elements RNC RNC I have also added two devices here both are Zener diodes Zener diode property if it is negative bias larger than VZ if Zener voltage is VZ negative value of any voltage closer to VZ current will be higher or lower increase very sharply but voltage will now be getting fixed to VZ if we get to positive then what will happen like a normal diode equivalently do not say exponential but as if it is rises again to a V what is VD as I put VD means cut in voltage VZ means Zener voltage so V0 sign which we have here for KITNA voltage magnitude wise VZ plus VD plus or minus depending on what V0 sign you are getting but the value at V0 will be always so total potential will be always VZ plus VD signs accordingly is that correct so what is that did you what did you see what I have done it output to climb plus or minus I repeat two separate climbs can be given to diodes need not be Zener's then okay block I may just tell you what I am saying unnecessarily making these statements any line plus so I can always climb separately at a line by two opposite direction diodes there is that clear so that is not that I cannot climb separately but I why I am not doing that okay otherwise don't think that it cannot it can always be done the way you like okay okay so how many things I change I have put a diode here I have also put a resistor R3 okay if let's say this somehow ground somewhere because of some failure somewhere that is a diode okay R3 is a limiter is that is that clear to you so this is called limiter current limiter so only is that clear to you okay so these are some issues the basic idea is to create potential at A this node where Rc is there capacitor to charge or discharge so basic idea is to create V minus which charges and discharges which is V minus which is getting compared with V plus any time it crosses those Vth Vtl value okay whenever there is nothing in the circuit put a limiter to the ground is that correct if already path exists through some resistor you don't have to want additional you do nothing you don't gain anything is that clear so in this you don't any please remember this is only a case when a terminal is directly connected to the ground that issue should be avoided it should always go through a resistor to the ground if current doesn't flow the potential doesn't change for you as in the case of open inputs so any R you put it the current doesn't change here but let's say let us say some reason this put this V0 gets to ground so the current drawn in case there is a something happens a short circuit at V0 point then we are worried is that correct so we are protected we are another shot a path the other will be protected Rc so ground but some of the case may go physically ground okay is that okay these are protections okay let's finish this abhi before we come here okay okay before we say if in this circuit what is being fed back R2 across your voltage V plus which is nothing but R2 upon R1 plus R2 times v0 yeah R2 upon R1 plus R2 okay is that okay is that okay beta is in feedback factor voltage received from the voltage v0 So, this is the voltage which is V plus across R2 V plus is that okay, minus beta V0 is that correct 2 values of V plus I can attain either plus beta V0 if V0 is positive if V0 is negative minus beta V0 is that okay, if this voltage is positive this is also positive if this potential is negative this potential is also negative is that clear. So this is 2 values of V plus I can create V plus which is plus V plus which is minus and what with I will compare with V minus, V minus is nothing but the potential across capacitor voltage across capacitor is that correct capacitor whatever voltage is nothing but your V minus okay at this node. So you have 2 nodes node A and node B this is my input node this is my output node okay is that correct. Now I say let us say now comparator is a very large gain okay very very large gain then that means what does that mean it can go to VDD and VHS full swing it can take and if that happens the voltage at V0 now you can see will reach to VZ plus VD just now we have a diode drop a Xener drop a reverse bias a forward bias is that clear to you output potential plus A so if this is positive which one is diode drop VZ1 or Z1 and Z2 is reverse bias if this is negative then this is diode drop and this is the general drop if they are identical Zener's which only on the chip you can create independently though Zener diode voltage same neither diode voltage same either V0 will be VZ plus VD which is limiting VH and VL is that correct otherwise it would have gone to VDD and VSS I do not want to go to higher voltage I want to swing it for the known amplitudes square of a care requirement is that amplitude in my hand and speed in my hand so amplitude change the voltage so what else can you do then the second Zener values of the diodes is that correct if you want a different value of swings then you should have a different Zener diodes is that clear to you okay so if VID is 0 or V minus is less than then V0 if VID is greater as a standard different comparator situation if it is difference voltage is positive then output is negative if difference voltage is negative output voltage is positive is that clear so let us start in our circuit of your circuit is okay let us say initially the capacitor is a VCT is some beta V0 okay capacitor take voltage man liya jai initial condition as VCT please remember what I am saying if this potential is higher than this potential which way the current will flow I am saying node A but B potential is higher than node A potential how the current will flow it will start charging the capacitor so initially the minus we thought if it is that minus beta value beta V0 value this will be V0 value so essentially what does it mean capacitor will start charging at node A voltage start rising as node A start rising and corresponding to this V0 value whatever V plus I was receiving VZ plus V is the ratio whenever it will cross that value is that correct initially it was minus value so this was at plus value so it starts charging okay it is charged to a higher value which crosses something like this so as soon as this become minus V0 this potential is higher than this potential so the capacitor starts discharging so whenever again switch that V minus changes lower than that VTL it will again switch over so A voltage lower has a fifth charge so point A will charge and discharge as the output voltage or beta V0 value VC value which is VN essentially crosses beta V0 value is that correct minus beta V0 so plus beta V0 that jay say threshold mela it is charged so in this case otherwise you are actually another path so that is why I said but it will draw much lower current compared to this because VZ is sinking heavy currents okay. That is why it is fixed to a VZ value. It is drawing a heavy curve. Okay. So, initially V in was at minus beta V0. So, node A voltage was lower than node B because V0 was positive. V0 was plus V0 capital value. As soon as this capacitor starts charging and reaches a threshold of beta V0, okay, whichever will occur, output will go from high to low. Initially output was high. VCA value was minus beta V0. So, it starts charging because current will flow from B to A. As VC starts charging and reaches a value of crossing the V plus value which is beta V0, switch of the output will switch in each other. But as soon as you reach minus V0, it will remain minus V0. Is that correct? The capacitors start now discharging. How long this will remain V0, minus V0 till VC crosses minus V next threshold which is minus beta V0. As soon as you reach here, switch again. Why this dotted line is showing? If you do not have a comparator, it will actually charge to V0. But here, as soon as this point reaches beta V0, it reaches threshold, then it comes down. If it comes down, then it is minus V0. So, it says minus V0 is here. As soon as it crosses here, it starts again. So, capacitor charges, discharges between what values? Minus beta V0 plus beta V0 when V plus crosses V minus switcherockers. As a output curve per square pulse. Is that correct? Square pulse. You can read book. I have only written this value, etc., is given there. Please remember initial condition is may include as minus beta V0 is the capacitor pre-charged. T is equal to 0, capacitor is pre-charged to minus beta V0. Is that clear? This is a equation. Solve this. Solve this. T is equal to T by 2. VC T is beta V0. So, beta V0 is called solved. So, I have time. 2 RCLN 1 plus beta upon 1 minus beta which is 2 RCLN 1 plus 2 R2 by R1. Is that oscillation clear to you? Because V0 changes the state, beta V0 goes from minus beta V0 plus beta which is our threshold values. So, capacitor charges to one, discharges to other. So, the output swing from high to low to high. V0 is equal to VZ plus VD. This is minus VZ plus VD. Is that clear? So, its frequency, an interesting point that I have written in the book. The period of this Schmidt oscillator is 2 RCLN 1 plus 2 R2 by R1. R2 by R1 is a feedback ratio. But it is not a function of those diode mode potentials. Amplitude helps but frequency is independent. These triggers or oscillators are generally used at low frequencies, 10 hertz to 10 to 10 kilohertz. So, RCLN can be small. So, much lower frequency, higher frequency. Why not? There is a problem in opiants or comparators its slew rate. If you want to charge it faster, you will require larger currents. Is that correct? Slew rate is called DV by DT, DV0 by DT. To increase it, you will have to increase the current. If you increase the current, you will have to draw more current from the opiants. The Gms will change from that, the poles will shift from that. So, stability can also be removed. So, you cannot enhance too high frequency from this. Typically Schmidt oscillators are used only for megahertz. What should be used for megahertz? Inverters. It is called the ring oscillators. Let us say I have 5 inverters. It is higher frequency or 3 inverters is higher frequency. If I have 3 inverters, the period will be decided by delay in 3. Larger the delay smaller is the time, 1 upon T will be the frequency. So, if we make a chain of 1, 21 inverters, then it will go to 100 megahertz. So, the higher frequency digital inverters will have a ring oscillator which has a very large number of inverters. Why we do not mind that? Because the inverter is the smallest size W by LK inverter okay. So, you put as many small area you can create very high frequency oscillators. Is that correct? Square waves. What does it call in the digital circuit? Clock. Clock generation is done through series of inverters in a binary form. Oh yes, the opposite. You are right. But it is not like that. Because C which we are adjusting is phase. You think what I said. The phase which I am adjusting with a capacitor as much as I increase, I adjust its delay. So, average delay will go down. This is what it is. I did not say it correctly. Okay. So, is that all kinds of oscillators are clear to you? What kinds we have studied so far? We are looked into RC oscillators. We are looked into LC oscillators. We are looked into ring oscillators and we finally said a Schmidt trigger oscillators. Is that correct? So, is that okay? Is that okay? Is that okay? Is that okay? Yes. is that okay. Please remember buffers are always used when you are taking from outside something and feeding to your circuits. So, in a non-inverting, inverting, it should be a follower because impedance matches. But the output low impedance is the first stage. So, for the next stage, there is a direct connection possible. Is that clear? Open can always drive an open. Is that clear? Because its input is higher, its output is lower. So, you are not loading it immediately. But if there is a circuit first, then you must go through a buffer stage. Is that clear? So, do not think that there is no buffer in between, there is no need to think about it. Low to high, always you can go. If the input is lower and your output is high, then it will load. It will change, right? If it is high and it is low, then what does it matter? So, you can directly connect all open-sync series, okay, all open-sync series. Okay, so, Schmidt triggers are very useful. This one is, comparators say with two comparators and some small counter, we can create a chip which is called timer circuit. Which number is that? 555. Timer, you will see in the book. Okay, before we quit, we will introduce a new topic. We are now interested in doing last part of our course is conversions or converters. What are we talking about converters means? Digital to analog and analog to digital. Digital to analog circuit banane ke liya, analog to digital banane ke liya, but at least A to D convert karne ke liya, we need one circuit which is very popular, which is called sample and hold. If you are dual degree students, some of you and continue to remain in micro electronics and also you take analog VLSI design course and let us say I am teaching that time that course too many all and conditions, then I will show you there is other circuit which is called hold and sample. We can I am going to say sample and hold. There I will say okay, hold and sample it. Okay, so abhi hitna kondition aapko liya mena. Okay, that is how to make chip. All that we say, test of pudding is in eating, but how puddings are made, we will only decide what test. Okay, it is a very simple circuit, ek switch hai or ek capacitor. Let us say this is input and this is output across a capacitor and switch is open. So what will be V0? Assume 0, but can be the last state, charge state of the capacitor. Initially we say when this is open, output is 0. And now I start VIN and at the same time I close the switch. Kya hoga capacitor ko kya karega ho? VIN, let us say positively charge ho raha aap bad raha hai. So it will start charging the capacitor. Sadele mena switch ban katia. Ab capacitor na kya value ho ghi? Jo ki us time T1 par jitni thi aur jab tak next switch hai. Kirtni value rehi ghi? O same rehi ghi. At second time when I switch it on, VIN to utnain time me aur kahin pohch gaya ho gha. Ab wo us value se ferese charge karna shudu karega over and above the pre state value. Is that clear? This is what essentially I am now saying. Ek example hai us na. Yeh mera VIN, half cycle ne, ko liye cycle ne. Yeh mera VIN hai, time varying. These are the instances when I am actually going to turn on the switch. Yeh wala, T1 jo hai paela. Ne, sorry, ya ontha, paela ontha to yeh capacitor jo hai, VIN will pass as it is. Please remember ideal switch ka cap property hai, resistance is 0, ideal switch. In reality there is a issue there, but right now. So if VIN is here, it will start charging to that value. Output will follow VIN charging the capacitor. So initially kya ho gaya, ki V0 toh wei hua jo VIN tha. Is that okay? So it charges to some value which is say V1, okay. Switch off kar gaya. So kya ho gaya? Till next switch on ho ne tha V1 value da, because capacitor cannot get any energy now from anywhere. Output open hai, toh wo dischar bhi ne ho sakta hai, okay. So as soon as it remain constant at some instant again I switched on the this. But at this instant of time, V kaan tha input higher value pe tha bhi. Ab ke liye time to ni rukhaga na, input toh vari hota rahega. Ab ish value ke liye ab yaha tha, toh yaha tha yaha tha, next on ho ne tha, it will again start charging to that value, jo naya value yaha tha usko pakthikap kar ke aage charge kar bhi. Jaise yaha ban kya, thir constant kar bhi. Thir on kya, thir charge kya. Equalantly saying ye aisa aisa aisa aisa kar kya. Ideally dekhaga hai to ye staircase hai. Ye close to ye kum maana jata hi hai. Can you tell me in its inner side when these two conditions are similar. When the amplitude of the signal is too high, then this is linear. O nai, sain jo hai uska ye part jo ye linear hi rata hai. Sko aur bada kar ho. Ye yaha tha ke hi nahi rata hai. To jitna high swing hoga, putna us area mo linear dikhata hai. To close to staircase leke hai ho. Iska kya matlab hua ki e di aap, this is your AC cycle, ab aisa niche bhi aata hai, jo weh ulta aana shubhunga. To ye aapka AC hai, aur ye uska equivalently discretized version hai. Aave thi is discretized value ko kisi tarah se binary ke code me convert kar dein. To we say we have converted an analog signal into digital signal. Is that principle of A to D converter is clear? Using my sample and hold which is discretized. Essentially sample hold means kya signal ko input ko kart raha hai. So jitna pass as close you will actually cut it, it will be replicating closer to the signal side. Now fast kering, is that point clear? Iska matlab hai ki aapka sample and hold should do that job faster. Aapka switch aur ye dhikta fast kar saking hai, utna hi aap equivalent digital signal create kar saking hai. Is that clear? Isko voltai fast A to D converters. So different circuits which we use essentially differentiate on what k, otherwise they all will convert analog to digital. But what will they differ from? How fast you convert? How quickly you discretize? So that it replicates close to AC signal. Okay I repeat, I have an AC signal, I am only doing I am trying to almost come closer to AC signal by jumping over it, okay. So I say equivalent aur kyonki yeh 2 states hai, yeh 01 values dikhara hai aapko. So I can say I am actually using discretization, I am some way coding digital. So that is called A to D converters, okay. Ek sample and hold jo hai, ek one of the major feature hai jo ki A to D convert kar hai. Is that correct? Why sample and hold? Okay. Ek typical aap kya rahe tha na yeh sample and hold jo hai yeh niche wala man dekhon. Yeh ek na simple circuiti hai. Pela stage kya hai? Abhi aapko bola tha. See if the second circuit has is a discrete value or some other circuit whose input impedance is not very high which like this transistor does not have, I must always feed input to this through what? A buffer, okay, follower. Yeh normal transistor kich configuration mein rakha hai main? Common grade. Aapne abhi switch koda hoon hai na digital mein. This is a simple switch, okay. Yeh control hai. One karengi to on, zero karengi to off. Transistor is turned on if V in is higher than VT, less than it is off. So I have a control signal which goes from 0 and 1, higher a lower value and allows input to charge the capacitor and hold it. Jaise mein isse off karunga, it will hold during this time through another buffer I will output it. Is that correct? So typical sample hold circuit will have two buffers in between there is a. Achha ek aisa bhi ho sakta hai. Isko kya bolte hai? Isko bolte is a CMOS. Paela to N tha na aap N and P dono laga diye complementary kar jaya to it is a CMOS switch or transmission gate. This is called transmission gate. Is that okay? So ideally a single transistor ke bada hai transmission gate laga hi. It is the care advantage. If it is only N channel it will only pass VDD minus VT. If it is a P channel it will only pass from VTP to VDD. Parallel karenge to 0 to VDD full pass karega. Okay? That is the purpose. So this is what a sample and hold circuit does. And what is the purpose of sample and hold? Is that point clear to you? Ek CMOS id a ek analog signal ko discretize karta hai aur kyunki capacitor charge hold kar raha hai ho uske upari over read hota rata equal in digital. Is that correct? So I am using a sample and hold circuit to actually discretize or digitize the analog signal. Is that correct? This is the property which I am going to use in converting an analog signal into digital signal. Different circuit like successive approximation, flash comparators, dual slope, single slope. There are many parameters. Finally, sigma deltas. All these are the different speed and different purposes to be used. Otherwise basically they all discretize. Is that correct? All they discretize. Iska karenge circuit baane rata. Iska complementary kaha a to d ka? Given a data in digital form 10110, I want to know equivalently what is its voltage. Okay? So the next block of course we will learn next time but just to name for this is digital to analog converter. In short it is called D slash A converter or more popularly called DAC. ADC bolte hain a to d converter ko or DAC bolte hain D to A converter. So we will like to see how ADCs and we will now actually as I said there are large number of ADCs and DACs. We will only do basic ADC, few of two are them and one day to A which is also very basic. Okay? Ladder method and then we will close the course.