字幕表 動画を再生する 英語字幕をプリント so in this week we shall be starting with some discussions on low power design ah as you know designing a circuits for low power has become so much very important in the present day scenario and it also affects the way vlsi chips are designed and also in particular the physical design process the so called back end design of the vlsi chips the way they are done today some techniques and some rules you can say design rules are incorporated at various stages of the design so that out final product the chip consumes less power ok so that is the topic of our discussion today low power vlsi design so as i said power consumption is ah very big challenge perhaps the most important challenge in modern day vlsi design which is pushing performance to a secondary level the primary reason is that almost all the devices we use today they are portable in nature other then of course the desktops which sit on our tables this portable devices all run on battery power ok you think of our mobile phones our laptops our notebooks our tabs everything these are the devices which we use they all get the energy from the battery that is built inside it so if you can design the circuits that get embedded into these devices in a way that they consume less power or energy whatever you call so the battery life of the devices tend to increase which is extremely desirable from the users prospective ok so there have been various works and strategies that have been proposed over the years which try to reduce the power dissipation so we sometime say that we have added a fourth dimension to the design process what are the other three dimensions lets see you see this is a typical picture that will find in several places in some textbooks also traditionally in this seventies and eighties area and delay were the most important parameters so when someone try to design a circuit a chip the primary emphasis was how much less area is occupied by my circuits on the chip on the silicon floor and what is the maximum speed so we try to reduce the delay [vocalized-noise] now often this area and delay are mutually conflicting so some typical figure of merits were ah proposed and used one of them was the product of area and delay square a d square so there there there are number of such have a matrix which you are used and proposed so you can have a figure of merit but as the circuits started to become more and more complex so what happened was that you see area and delay were not the only parameters now after a chip is manufactured mean one very important task of the designers or you can say the text engineers was to ensure that the chip does not contain any apparent fabrication defects so the chip needs to go through a process of testing more the complexity increases in a chip the task of the testing becomes more and more difficult so there has to be some design rules like the design for testibility techniques that where discussed earlier those have to be incorporated or embedded in the design process itself so that whatever circuits we design they are easily testable so thats why we say that in the eighties and nineties this third axis of this in this diagram testability came into the picture but now two thousand onwards with the advent of battery operated mobile devices portable devices power as become a very important fourth parameter in this design space so not only we have to address area delay and testability also you have to address this power consumption issue ok fine so let us look at some of the terminologies so in a typical chip which in todays technology is normally built using c mos technology so we say that power is dissipated whenever there is a current flowing from the power supply which you called the v dd to the ground so power is drawn from the voltage source and this source i mean sources of these currents can be various these we shall be seeing subsequently but let us look at how we typically measure the power so i shall be explaining this very clearly so we distinguish between instantaneous power energy and average power so how are they defined see instantaneous power is defined simple by the product of the current and the voltage the current flowing from v dd to ground we call it as i dd this is a function of time t multiplied by the voltage v dd now instantaneous power does not give us a very clear picture of means how much our battery is getting drain because it may so happen that sometimes the instantaneous power is very high but over long period of time we are consuming very low power means our currents is very less ok so some sort of average is more meaningful instead of the power drawn at a particular point in time ok so we talk about energy so how is the energy defined so i shall be explaining these terminologies graphically very shortly this energy is defined as the integral of the instantaneous power over a period of time let say capital t zero to t what is the sum of the instantaneous power drawn that aggregation is defined as the energy this is how you define ok and of course you are computing this energy over a time period t so if you calculate the average simply divide this e by t you get the average power so normally when we evaluate the power consumption of a circuit or a device or a chip we talk about the energy or the average power now let us see with the help of a diagram how these three things are related so let us show a typical diagram this is the access of time and here we show the instantaneous power consumption which means the the product of the current and the voltage lets say we [vocalized-noise] the value of p t varies with time like this lets say so we are interested to measure the power between time zero and capital t now just recalling the definitions for a particular value of t lets say here so if we try to see what is the corresponding value of p t it is here this is the value of the instantaneous power i p instantaneous power at this particular time lets say t i right now if i want to calculate the energy so energy as i said is the integral of pt from zero to capital t so so what is the physical interpretation of the integral integral means the area under this curve so this total area under the curve this is defined as the energy that is integral pt dt between zero and t now if you just take the average energy over this time p t [vocalized-noise] it is energy is varying so possible the average will be somewhere here you show it as a straight line so this will give you the average power p avg now as i said p average can be computed by dividing the energy divide with this time t so we understand this p average is this level that means the height of this rectangle and energy is the total area height multiplied by the width and width is capital t so if we divide this area by capital t you will be getting this height that means p average ok so diagrammatically i am showing you the difference between instantaneous power the energy and the average power ok so let us come back so talking about [vocalized-noise] power dissipation in a typical c mos circuit we can classify the power dissipation into three types very broadly dynamic short circuit and static so we shall see what are the sources of these different kinds of powers and what are the typical methods that are adopted to reduce the effects of these ok so we shall see this subsequently let us start with dynamic power well [vocalized-noise] as the name implies dynamic power is something which is depending on the dynamics of the circuits what is the definition of dynamics something which changes with time so dynamics power by its definition means whenever some signals in the circuits are changing those changes cause some dissipation of power that is basically what is meant by dynamics power dissipation so lets try to understand this so basically dynamics power is required for what purpose for charging and discharging load capacitances with transistor switch so let us look at very simple example of a c mos inverter so here i have a p mos transistor and n mos transistor this is my input let say a and this is my output lets say f so f is given by the complement of a and this is v dd now what i am saying is that this output as i said earlier may be driving the inputs of other gates so we can equivalently assume that it is driving a load capacitance lets say the load capacitance is c so lets say when the value of a switches from zero to one lets say the value of f will be switching from one to zero similarly when a switches back to zero the value of f will again switch to one now whenever this output node f changes from high to low and low to high what does this mean whenever it is changing from high to low this means c is getting discharged and whenever it is rising from low to high we say c is getting charged ok now in this circuits the discharging path of the capacitor is this through the pull down transistor and the charging path of the capacitor is this through the pull up transistor so as you know in a c mos circuit depending on the value of a so either the pull up or the pull down one of the networks is conducting so depending on that this c will be either discharging or it will be charging now every time there is a charging discharging of a capacitor it will consume ah power because you recall the basic definition from circuit theory current is defined as c dv d t so you can define the current flowing as the product of the capacitor and the rate of change of voltage so whenever there is a this kind of charging discharging going on there will be a current flowing and the product of currents and voltage will be the power consumption ok fine so let us come back to this slide [vocalized-noise] so i have ah just shown in one cycle we can have a rising output and also falling output right so whenever there is a rising output that means the output node is getting charged charge means what the capacitor is getting charge to v dd so what is the total charge charge is the product of capacitance and voltage so c multiplied by v dd this much charge is required to charge the output node to v dd similarly when the output goes to zero the load capacitor needs to discharge to ground right now it can so happen that lets say we are considering a certain time period t right now within this time period t the output f may be going up and going down several times this may so happen depending on the behavior of the circuit now if this kind of thing happens which means in the same interval of time t the capacitor is getting charged and discharged multiple number of times see charging discharging charging discharging charging discharging ok so if i define a parameter f sw this is the frequency of switching then within a time period t so if you multiple t with f sw this will be number of switching that is taking place within this time period t the product of the time and the frequency of switching this you can call as the frequency of switching sw right fine so this already i have ah explained that if the frequency of output switching is f sw that charging and discharging cycle will be repeating so many times over a time interval t ok now let us see that how we can calculate the average dynamic power in a circuit now our assumption is that we have a circuit like this where there is a period time t and the inputs are changing at some rate so i am again showing that picture that i am concentrating my calculation within a time period of t and within the time period t the input or the output [vocalized-noise] whatever we call in inverter both will be the same will be changing certain number of times so i am calling it as the frequency of switch right fine now let us look at this calculation so how do we calculate the dynamic power this is actually the average power consumption so whenever the output ah is switching so between time zero and t i simple multiple the current with the voltages this is the definition of the instantaneous power you integrate it over a time t you get the energy take the average you get the average power ok since v dd is a constant you take it out so you have an expression like this so let us see how from here i get this so we get an expression like this i am just to working this out so you get v dd divided by t integral zero to t current d t fine now let us make an observation so our observation is the value of current is defined as the product of the capacitance and the rate of change of voltage so if you take this into account so i dd tdt becomes c dv so i can write it as v dd by t integral c dv now the independent variable is v so what will be the range of v see i am working from zero to t so this will be from zero to what something i am writing a question mark here because you see a within this time t as i said charging and discharging will take place multiple number of times right multiple number of [vocalized-noise] so far each charging i can say each charging the voltages is going from zero to approximately v dd in the load capacitor and for discharging it is the reverse v dd back to zero now in each such cycle i can write it like this v dd by t see c dv is nothing but c into v now since this charging upto v dd so for every charging it will be c into v dd not only this how many times it is charging within this period t it is charging if s w multiplied by t times as i said so f sw multiplied by t this will give you at how many times this charging and discharging is taking place within this time period t so you will have to multiple this by this t into f sw this will give you the total value of the integrate see here basically this integral you are separating out between these each of these segments one two three so thats why if you just add them out there are so many such segments you multiple this by this right so how much this comes to if you make a simplification c v dd square capital t cancels out and f sw this is the final expression for dynamics power right ok so in this expression also this same thing is shown finally the value of the dynamics power is this and the point to observe here is that the dynamics power is proportional to load capacitance so to reduce it you can try and reduce the value of c proportional to square of v dd so if it is possible to reduce the supply voltage that will also be good and of course proportional to the signal switching frequency so if you can reduce the frequency that will also result in less dynamics power ok now taking the concept of dynamic power one step forward let us define something called an activity factor now see in the previous expression we talked about this f sw which was the frequency of switching of the input or the output signals right now here we are talking about the clock frequency f is our clock frequency now we are trying to relate this f sw with f by multiplying it with the parameter alpha which is defined as the activity factor you see some signal can change state at a rate which is at most equal to the clock frequency because it is the clock the edges of the clock that defines the various events in a circuits but all edges of the clock need not result in a change in the signal state so only a fraction of the clock edges will actually result in an activity that will result in consumption of dynamics power so we define something called an activity factor which if we multiplied by the frequency we get f sw this is how we just estimate f sw now if you are directly connecting the clock with the gate input so the input as well as the output will be changing at every edge of the clock so there we say alpha equal to one but if the gate output switches once per clock cycles see once per clock cycle means or in every clock cycle the clock is transiting twice low to high and high to low i am saying that the output is changing once for every two transitions of the clock so here the activity factor is defined as half and we have something was c mos dynamics gates i have not talked about it c mos dynamics gates are something like this say you can implement ah [vocalized-noise] this is a p type transistor so you see in a dynamics c mos dynamics logic we are not using many transistors in the pull up this is the output this is a nor nor gate so here in the [vocalized-noise] pull up network we are using very few number of time here only one and you see you are using a clock phi one and phi two it is like a two face clock so how it works let me just briefly tell you lets say phi one s running like this and phi two is running like this they are non overlapping right so when phi one equal to one phi one bar will be zero and this will be conducting so it is here so the output load capacitance will be here this is your c so it is during this period when phi one is high you call this stage as the precharge stage during this period phi two is zero so this transistor is off so capacitance if getting charged through v dd this is the precharge state but when phi is two this part then phi one is back to zero so this transistors is off the capacitor was already charged the phi two is high means this is conducting now depending on a and b this capacitor can discharge or may not discharge so we call this as the compute phase so depending on the phases of phi one and phi two you can alternate so depending on the value of a and b the output value may change it may not change while [vocalized-noise] in every cycle worst case it can change twice during precharge state it can go from zero to high again during compute state it can go back to from high to low right so this is actually mentioned here that for a c mos dynamics gate switching takes place either zero to two times for an average of alpha equal to half because two times per cycle means alpha equal to one zero means zero so average is half but for c mos static gates conventional c mos gates ah the activity factor is very much dependent on the design the typical value is around point one so if you take the activity factor into account our dynamics power equation changes to this square you replace f sw by alpha into f right so alpha is also a factor here now we look at short circuit power short circuit power this is some kind of power dissipation in a c mos gate when the signals transitions are taking place because they are periodically for very small amount of time both n mos and p mos networks can be conducting this is also called as the crowbar current and in modern day designs this short circuit power can consume so means of the tune of ah twenty percent