 kinds of noise and this morning and we discussed that there are noises of variety kinds, short noise, Johnson noise, then there are Geo noise and of course one of the noise I said I will talk about is popcorn noise and of course the finally we will derive some expression for KT by C noise okay. So these are some noises of interest or the first among them is called short noise. This noise occurs due to quantum nature of electron flow through a potential barrier like a PN junction or a metal semiconductor junctions. The carriers actually exhibit average rate which is average means DC of crossing the barrier but individual carriers can have random motion. So on average there may be number crossing the barrier but an individual ones will have different probability of crossing okay. In above equation the short noise equation which is ion is the current, is the current noise source is 2QID delta F and in the above equation ID is the forward current of the device which you are, barrier about which you are talking about and delta F is the bandwidth of noise measurement. One can see from the expression that the short noise is related to the forward current by root of ID but there is no term which is KT temperature dependent and therefore short noise is normally temperature, normally I will someday show you that it is also to some extent function of temperature but very small dependency. In MOSFET particularly where you are worried about MOSFET noise one of the noise short noise is seen not in saturated MOS transistor but more so in the sub threshold region where current is e to the power QE by KT kinds and there MOSFET do show some kind of a short noise otherwise most of the time MOSFET do not show any short noise. So the first noise in the list which I said is the short noise and I repeat it is essentially randomness in carrier motion across a barrier though average there is a DC value available. The short noise I say is dominant only in the many of the bipolar devices why because there is also the dependencies e to the power QV by KT. So any relation GM is like QIC by KT in the case of sub threshold current GM is again QID by KT. So wherever that GM is only a function of I and temperature those cases short noise is observed okay. Otherwise short noise is not seen in a normal MOSFET operations neither in linear nor in saturation. The second noise of interest is the Johnson noise which is very popular known as thermal noise and any random carrier motion may be due to the drift diffusion you get a RMS noise power and that can be expressed as the noise spectral power is SNF which is taken from a frequency of F1 to F2 KT is the thermal energy and then it gives you a spectral density of KT into delta F. And obviously since the SNF is proportional to T this is thermally dependent noise so larger the temperature larger is the noise component. Typically for example if you are looking for a resistor where random motion of carriers constitutes the that is mobility fluctuations or variations carriers move through a by drift or diffusion then we can see this can be modeled as a noiseless resistor and in series to it there is a noise source which is related to the resistor noise okay. Now the spectral density it can be also written as Vn square by R which is KT delta F and if I connect it is Vn square KT R into delta F where Vn is the noise voltage and if it is expressed in RMS and per hertz if you calculate then the noise voltage Jonson noise or thermal noise is expressed as 4 KT R so now you can see from here the noise voltage of a resistor is a function of temperature and function of the resistor value itself. If I see a Vn square and if Vn square is something to do with the resistor what is the current in this? Ion square will be Vn square by R square Vn by R is the current average noise current is essentially equal to square of that is Vn square by R square and that is called current noise source. So why I am showing you this is Thevenin's equivalent the other could be Nordens equivalent. The current noise therefore is Ion square it is actually Ion square bar slightly long square nature that is bar average value of that so which is Vn square by R square and if I replace Vn square then I get 4 KT by R or 4 KT into G where G is the conductance which is 1 by R. So I can replace a voltage source noise source by current noise source by multiplying it by relative whatever resistance I see through which this current noise current flows okay. I am looking into this term in the mass transistor which what is the thing flowing through the ideas so a current is flowing through there so I would like to replace noise current source is there rather than voltage current says and except at the input source where I may use Vn square terms. The next noise of interest is called 1 upon F noise or also called popularly flicker noise okay this also is a very popular name whatever statement I have written here I may preface it with saying all these are strong conjectures there is no real proof to prove that the following things actually relate to 1 upon F okay and therefore interesting because no one actually proves it that is correct okay. So with any other thing also I can prove it is 1 by F okay therefore take it little pinch of salt but that is what most people agree that this is what it may be and it is as I said this noise was also invented in 1923 by Mr. Johnson okay particularly he was working on vacuum tubes there were no semiconductor device done okay what he says or what is the statement made is due to number of fluctuations occurring due to defects contaminants and interface state density one observes 1 upon F noise in the case of mass transistor the silicon and silicon dioxide or any other insulator has an interface which is between insulator and semiconductor and the current transport is at the surface of this interface is that correct but in source and drain you have an interface where the carriers are actually moving okay. So any change in interface density will change the what is called relaxed and time associated with this and since there is a time associated with recombinations there surface recombinations variation there leads to a noise component and this noise is found to be inversely proportioned to frequency. So larger the frequency smaller is the output if you really plot 1 upon F noise okay I call it 1 upon F noise versus F it is something like this it actually exponentially goes down but in real life this because there is some show the if you are only taking interface it actually goes like this. So there is no reason to believe that it follows exactly 1 upon F noise linearly the exponential is such this that it also closes near to the linear side. So it is somewhere one does not know which is the real cause any fluctuation there can be mobility fluctuation there can be density fluctuation carriers carriers can be number may change okay so any defect contaminant or interface states can lead to 1 upon F noise and therefore in mass transistor in specific two noises of interest to us one of course is the thermal noise because very early why thermal noise cause transistor essentially is a voltage control resistor since it is a resistor it shows thermal noise and the other noise possibly because of the phenomena of interface state it is specific it will show 1 upon F noise okay so exact method of I say is unknown there are almost people say there is a professor of course is no known now you are at University of Minnesota his name is Eldert Mender Zeal there is a book on noise phenomena in materials or semiconductors 600 odd pages only on noise okay any device you create anything you say next few months this old man will work and actually find noise for that new one okay. So that is what Wender Zeal was called Mr. Moibs okay and why I know him so much because my PLD guide was worked under him at Minnesota so that is why he is my grand guide okay so I must make some noise for him okay because he was not one there another Wender Wendell it was also the other guy but Wender Zeal was one of the two guides he had okay so 1 upon F noise is going to stick there in respect to because of the mass so you find in a bipolar this neither is not as dominant as in the case of MOSFET the one upon F noise comes in the bipolar in the base transport only because there is a fluctuation in base but that is comparatively much weaker in amplitudes compared to MOS one upon F noises okay so if you are looking for MOS circuits you do not neglect one upon F noise if you are using bipolar then do not leave short noise because that is not here in the case of MOSFET okay is that okay so the next of course is generation recombination noise in any semiconductor or devices there is a statistical variation of numbers as they move because all the transport phenomena is basically random motion diffusion for example it is a random event so any statistical number variation which has a lines available with it this leads to a noise which is popularly known in their literature as random telegraph noise why this word came can you anyone suggest why this name was GR noise were earlier called RTN I do not know whether yeah he knows when the earlier times when the you are sending messages k MOS code so there was a switch which did that that a something would be made and tack-tack-tack so every time switch was this so depending on the pressure reports it could change the actual later which it will be received the other end okay so it was therefore it was called that it is fluctuation numbers therefore it was given a name telegraph noise one of the method of measuring the interface states or rather variation is what is called as post office noise measurements which actually measures RTNs okay the MOS physics in a process of his knowledge measurement okay MOS physics in a pressure bossy you can make use of the measurement system okay the last noise in your second if you ask me I will explain you much more there because this is more device theory interesting theory okay the last noise of interest which is also very popularly in communications is called bus noise and as I said it looks like a con when bumps out so it is called popcorns okay so it is called popcorn noise and in a MOSFET channel currents because of the switching signals going through there is a bus noise available and this burst noise is essentially called popcorn noise okay you see essentially because the modulation of channel currents because when you switch okay you can see when there this happens there are two phenomena of what we call capture and emissions of the carriers and depending on their emission time constants and capture rates the cross section of the capture where it is going to capture because the defects including interface states they show some kind of fluctuations and these are found to be one upon F square kind therefore they was called a popcorn noise okay it pops up okay so these are some noise they are few more but some other day these are relevant for us so I thought at least I should talk about our requirements but in design we damn care about so much about popcorns because they are one upon us came in they died on very fast okay so we say that most region of interest this may not be of that relevant but it is not so true that it is not relevant it is so let us look to the noise due to components I will come back and say all same thing which I started with noise as a theory two things of interest to me this noise due to components a statement which I could have made earlier but I now want to make there are two types of man noise we worry about one of course is man made noise we are most famous for it okay that is signal coupling or substrate coupling in the mix signal or finite PSRR these are essentially called man made noise okay decoder system you create and possible methods of elimination this morning I already said fully differential system probably can help and one of the method of reducing this man made noise is to properly lay out the circuits since we are not done layout so far when I do layout I show I will give a name of layout method is called common centroid method okay so we will come back to layout and discuss it why common centroids okay and at that time I would say yeah this layout taking care helps you to reduce noise in particular and this is very important in real logic real implementation of layouts on chips okay so this is relevant of course if you do this and properly do this you can contain noise to a great extent the other one which is not really so called I call it man made not due to the system I am making is essentially electronic noise due to devices which is inherent with the way we work on that okay so this we already some way discussed okay now this we are not discussed very much but sigma the substrate coupling I will talk to you later maybe I can show you right here what essentially substrate noise is about you have a an n-channel device let us say sitting here in a substrate and this area is for analog this whole area is digital this is analog area please remember any such circuit here will be constantly connected to this substrate through digital means capacity coupling is that clear switch you do 1 0 1 0 so this substrate also gets 1 0s on that but that this analog area is sitting on the same substrate which may have equivalent of resistance sometimes capacitance so this change here is essentially getting transferred to analog in respect to whether you wanted you do not want it this is called substrate noise coupling okay this because of the digital part your analog parts keep receiving switch noises okay and that is something which is relevant in all mixed signal design so one method is you put it too far away so that it dies down however too far away is the problem that means you will not do anything that area is wasted or to reduce some kind of you put a guard ring as we shall see later to protect it from the actual gain occurring there okay can damp down by something so there are ways of reducing substrate couplings but there is always will be a substrate coupling any mixed signal chip okay it can be minimized but cannot be made 0 okay so this analog sitting in digital is the major cause please remember analog does not inject as much noise because it is DC it is some kind of a constant value averaging thing this is running at now gigahertz on off okay and that creates hell of coupling noise to the other analog parts okay and that particularly PSRR is the one which is heard maximum because of if opium is being used here okay and in turn therefore even CMRR gets hurt okay variations so these issues which I thought are not relevant so I must say that yeah substrate coupling is taken care in actual designs signal coupling do not bring lines closer because they may have common capacitive coupling okay it is called mutual two lines there is a capacitance to the substrate but there is a capacitance lateral between the two metal lines which are sitting on insulator oxide so two metal lines sitting on oxide may couple themselves okay which is the cause of signal couplings crosstalk as I said and there is because of the noise the maximum allowed power supply rejection may not may get exceed because the noise may over read that okay these are called man made okay so let us look for electronic noise that the other noise are relevant I already said the electronic noise in devices and circuits minimum detectable process signal is limited because of the noise noise directly show straight up between power dissipation and speed and now this is the reason why I actually brought the sheet here why we are worried okay low noise requirements dictates the use of large capacitors okay larger the capacitor KT by C noise is minimum and large GM okay both leads to higher power dissipation in digital CDV by DT dynamic power in analog GM by C is itself creating large powers with scale down technology the power supply voltage also decreases thus reducing the SNRs okay hence design of a low power low voltage and our precision circuit has a strong dependence on electronic noise and current era we are work mostly in 0.18 0.25 micron processes though they are short channel but not so short you will be working on 65 45 30 to 20 to 16 11 9 7 0 so since if at all you work in devices and circuits if at all those who work may find it that this design is now becoming more noise dependent earlier their values of the power supply as 5 volt this is in millivolts so damn care now the noise is actually hundreds of millivolts and your VT is 200 millivolt you are very close to where you should not be okay and therefore up now noise issues are more relevant in designs as they were not so early relevant in earlier technologies so most of our designs are where analog we do only on 0.18 0.25 some students may be working on 0.13 okay and some smarter may be working on 90 nanometers but no one is working on 30 to 28 or 22 nanometer process because we do not have tools forget about the other we do not have tools to do that okay so this all statement is homework okay okay so as I said you that electronic noise is an relevant part now of today and therefore you should pay lot of attention please remember C increase is not very much agreed but that actually changes the bandwidth and it also improves or other increases the power dissipation in our open design you must have seen I have already specified or a cascade design amplifier I said this is the maximum power allowed for you to dissipate okay so that is the budget is called thermal budget once you have given this you cannot exceed that how do I decide the thermal budget for a chip I had discussed earlier just think of it how do I decide this is the power I will allow you to dissipate correct so there is a issue which is called thermal resistance is actually delta T by delta P change in temperature with change in power is called thermal resistance so from the junction to the substrate down to the heatsink how much is the thermal resistance I can have which will allow me max and temperature rises maximum given to me not more than 125 degree centigrade or not less than minus 55 degree whichever the range meal standard wants within that range for given theta of those layers you are using there are one or two or three in series so calculate R is equal to real by a similar equivalent for thermal you can calculate fine thermal resistance with this three thermal total with what temperature you allow P is fixed okay so once P is fixed then you know how many vertical lines in your chip will have so you actually divide now power so much in milliamps here so much milliamps here so into V is the power okay so that is called allocation so first thing when you start designing a chip is the power allocation they do allocate the power okay so some things even if you can do better because you say no no I cannot put all the power here I will do some more other things so many designs please take it that a statement here that the actual may when you do it you will have to do much more thinking how much so the performance may not be the best but there is a performance otherwise there is no performance also okay and therefore when asked to worry how much power you will be allowed per arm okay like in defam so much microns current so much VDD each arm is so much so you know you are allocated that 10,000 defams are going on now you calculate how much power I am allocating to them okay so the game is actually know how much is power to be allotted okay so please do not think it that I am just talking some more it is a very relevant thing and therefore I must know the thermal issues very clearly because it decided by the power at hand in some way coming to the realities I would like to calculate thermal noise due to resistors a typical resistor can have either a current source noise or a voltage source noise if you have a you write a current source here then it is iron square this is 4 kT by R M square per hertz okay and now one interesting thing is if I have two resistors resistors okay then if I want to calculate noise due to this so what I say this this is noise less resistor shunted by its currents noise current source the another current resistor with its own current source noise