188N. Intro. to RF power amplifiers

okay we are going to talk a little bit about in power amplifiers we did talk about output stages while back and we talked about Class A Class A B Class B and we've kind of touched upon Class C amplifiers but we're thinking about as an output stage more than anything else now what we are going to be doing today is more focusing on power amplifiers that are intended mostly for RF applications so gender generating high frequency signals at certain frequency or set of frequency ranges and they are producing this power with reasonable efficiency so efficiency is one of the parameters that's important when you are making power amplifiers and output stages and things of that sort and the reason as we discussed before is that it basically sets the amount of total energy that you spend a good degree because that's the most powerful hungry stage in your amplifier chain usually because the one that has the most power so the cookie question is that how do we do this so the focus today would be a little bit about more mostly on RF power amplifiers and it's an introduction to that and with a fair amount of focus on switching power amplifiers although we are going to be talking about non switching linear ones along the way so before we start talking about specific topologies and things of that sort there are certain rules and relationships that matter in power amplifiers and there are certain ways kind of like a spectrum if you think about a power amplifier they really form a spectrum if you think about purely linear one Class A where you bias two stage they did it operation point it at a point where you have the largest rate of linear operation meaning that you're trying to be avoiding turning off of turning the transistor off or putting it into triode or saturation if it's a BJT or something like that and then that would be Class A she's on the left of the spectrum that you're looking at and then as we saw before you can go to Class B where you basically turn the transistor on for half of the cycle so your current is basically on for half of the cycle where the voltage is going through so you basically presumably have two transistors that provide this one or or in a resonant circuit that captures the energy during the time of the transistors on and through its resonance behavior produces the voltage that's mostly sinusoidal so we can do this either as a resonant circuit or you can do it as a double driven stage where half of the current is driven on each side for half of the cycle so you can see in this plot that usually by the rate in these all this plus that we're going to see here the voltage is red and current is blue just just so that sometimes you don't have them label explicitly and then the other end of the spectrum is basically when you can make make it more and more switching now let's ask this question from ourselves the energy that's lost on the transistor itself the power on the transistor is primarily determined by the product of the current in the transistor let's say if it's a MOSFET the drain source current the drain current and the drain source voltage right with my definition power is the product of the voltage and the current so when that's a power that turns into what it turns into heat right because that basically it's a transistor up that's the power that's dissipated in the transistor if you're trying to maximize efficiency one of the things that you want to do at least if you're trying to minimize the loss in the transistor itself what do we need to do ideally we want to make this product zero right well one way to make this product zero is having one of these parameters being identically zero which is useless because then you would have no power output but the other thing is to create two waveforms whose product is zero while they're independently non zero so the idea here is that if you want to have maximum with the minimum amount of loss in the active device in the transistor you want to have wave forms that look more like like the wave forms on the right meaning that your voltage is nonzero when the current is zero and the current is non zero when the voltage is zero right and in this way you the product of those two will leave zero at least theoretically if you can make these ideal wave forms and it would be zero and that means that the power dissipated in the transistor will be minimized or zero if they were theoretically zero and that would imply that you can actually then then you are limited by other losses in the circuit for example if you have a resonant circuit or things of that sort the energy loss in those matters now what happens in this spectrum I mean these are some points along the spectrum of things is that there's a trade-off between efficiency and any errors at least the linear it's straight linear straight-up linearity meaning that if you put a sinusoidal waveform input how sinusoidal how much the output deviates from an sinusoid so an ideal linear circuit would produce another sinusoid that's amplified in power a nonlinear example of a nonlinear circuit would be one where you basically have like a square wave coming out or some other wave form right but that's what we mean by linearity in this context so as you can see when you move to the left you have more linearity in gain and when you move to the right you have more efficiency before the reasons that we discussed there are a couple of scaling four laws for power amplifiers that are interesting to discuss but to do that let's have a simple model for a switching power amplifier now if you think about a switching power amplifier and a few and abstractly we want to create something that has non overlapping voltages and currents right as we discussed earlier to produce the mean amount of loss now if you use a switch as shown on the lower left here what you will see is that if you had an ideal switch and some mechanism let's say a very large inductor to maintain a constant DC current there called RF chokes sometimes to produce this current then by turning the switch on and off you can presumably produce some sort of a waveform here and through a passive network what we call the output Network you can convert it to the waveform that desired output voltage now the voltages we are showing here the red voltage here is the voltage across the transistor across the switch not the output voltage you want the output voltage to be close to a sinusoid so we're talking the voltages and currents shown in this plot on the lower on the upper left are the voltages and currents across the switch itself as shown in the picture now the problem of approaching power amplifier design really to the first order is designing that passive network in such a way that it produces the desirable waveforms voltages and currents on the left side why'd it draw it delivers load to the output so it's a network synthesis problem in that sense in general that's right it's a passive Network synthesis problem now the question is that there are many many different approaches to do now there are if you think about the simple there are several scaling there are couple of scaling rules account we call them way for from scaling rules now one is if you had something let's say you had you already had a VDC DC voltage across that but now if you scale the DC voltage by factor lamp lambda right yeah if you scale it by a factor of lambda the question is like what would happen to the waveforms in currents and voltages now if you're using a switching amplifier although it's a highly nonlinear device because it's reaching turning and on and off this scaling rule holds exactly which means that both your current and voltage would proportionately scale if you increase your lambda so you will get the same exact work remains the same and your switch properties don't change the waveforms will remain exactly the same they would just be both current and voltage with scale up proportionately the useful thing to remember when you're designing amplifiers another thing that's interesting is it a blip there picture on the right which is the impedance exclaiming the impedance scaling tells you that if you actually now tuck the impedance that you had and scale the impedance by factor of lambda right as you make that impedance larger your current will go down but the voltage remains the same so scaling of the impedance if you take that impedance network and scale it would only change the current and we reduced increasing that will result in reduced current but will not change the voltages across this network I mean this may seem obvious and simple but they apply properly they can be like a provide additional insight okay so now if you think about it depending there's a there's another spectrum there's another of kind of range of variations in a transistor in a power amplifier you can have the same through the scaling laws that we talked about you could think about having designed a certain kind of amplifier with a certain width current voltage a current and voltage waveforms with certain current or voltage waveforms as shown here let's say in this case they're non overlapping so there are good designs there's a pretty efficient and scaling we can actually have ones that you scale the current down and voltage up so just basically make the voltage is larger or current smaller while maintaining the general shape of course you do that if you move to the if you have more current and less voltage and to the right you have more more more voltage and less current right again this is somewhat of an obvious statement but why does this matter it matters because the choice of the devices you're designing with determines where in the spectrum you will land so for example let's say you're using some RF gallium nitride transistors for your design that have high breakdown voltages let's say your transistor has a breakdown voltage of 50 volts right then you would your design should be more towards the right because you have the ability to have of what large voltage swing and you want to minimize your currents because you want to minimize the other I squared R losses in the circuit and all those things right so for that you would be moving more to the right of the spectrum now let's say you're using very small scale CMOS transistors right let's say you're using CMOS transistor with a breakdown voltage of like 1 volt then if you are trying to deliver the same amount of power then you would have to operate more on the left which means that you need to be operating in situates create situations and we'll discuss this in a lot more detail in practical settings where you need to produce large currents and small voltages and that's scaling matters the way you think about that ok now for a from a transit now if you start to talk about the transistor technology now there are several figures of merits or demerits depending on which one we're talking about for different kinds of amplifiers so if you're making a linear power amplifier as shown as a for example on the upper left that cyan box what you see here is that you have a transistor and a tuned load right you have a parallel RC LC network and some RF chokes to provide some DC currents right now the question is that how do you biases if you're using it as a linear amplifier you want to make sure that your device remains in the lid let's say if it's a MOSFET it remains in the pinch-off region or if it's a bipolar transistor it remains in the forward active region so there are two voltages that determine the boundaries of this limit region right on the lure and this voltage where you transition from let's say tryout to pinch off right we call this the knee voltage week' because that looks like a knee right Benton and then on the right hand side you have the breakdown voltage vbk okay and then these two basically determine the bout range that you can operate and you can see that even if you lose the perfect load line a linear load language would correspond to a linear amplifier Class A amplifier for example then the maximum efficiency you can get is given but it's proportional to the 1 minus V K over V B K divided by 1 plus V cave over V B and we saw this in the lecture earlier on we did this derivation or something along these lines so this but however this number this V K / v BK or this equivalent ADA that we showed here is the parameter that would be used to evaluate given transistor technology right say okay what is the best efficiency I can possibly get from this if everything else were perfect now for switching power amplifiers will introduce two figures of Merit really that very important one in a twist and if you have two fingers Americans are two different scenarios now in a switching power amplifier the actual switch more look looks more like the picture on the upper right right what you have here is that you have it's an ideal switch it has an own resistance and you have a capacitance associated with it which will be present when you have when the transistors off right and so and when it's on so if you look at this if you scale the transistor up basically meaning you take the transistor and and take another copy of it and put it note for note parallel right what would you do to these parameters or on would be half right and C on would be C out would be doubled but there's one thing that doesn't change which is the product of these two the RC product so RC product is independent of the size of the transistor and therefore can serve as a figure of really dim demerit because you want it to be as small as possible right now if you for situation like this where so this is a scenario where your capacitance limited meaning that the transistor size is limited by the maximum C out you can tolerate now what why would you have a tolerance why would you have a limit on C out well it's a choice of that passive network that follows the transistor switch right so we said that we are going to make this network of Z impedance Network Z afterwards that could we can synthesize and that would determine how the transistor works and and and and and how the amplifier waveforms will look like so that we can tolerate certain amount of capacitors because that capacitors becomes part of that Network right if you make it to the certain design and then you put the gigantic capacitor and its input the network has changed and therefore it will not perform as you experiment so that's what we mean by capacitance to limit now in this scenario the losses are really determined by our on CL and the loss will be proportional to this product that this R on C our product times F because that's the number of times you switch and you charge and discharge your network and the total power of course the more power you have the more loss you have because it's proportionate right I mean if you're using losing 10% of it 10% of one watt is smaller than 10% of 10 watts right okay so so that's the figure of Merit for the device so if you what if you have a transistor if you want to evaluate it in this scenario the first number we look at is or on C out now there's a second scenario which is basically when you have gained limited system in this case basically meaning that you do size of the transistor is limited by how much power you are providing to the input and this is an important parameters if you're looking at the power added efficiency as opposed to just pure drain efficiency now the difference between these two is that the drain efficiency is the ratio of the output power to the DC power that the amplifier draws right but I can make a device I can suggest a device to you that has hundred percent draining efficiency which is a wire because the drain efficiency doesn't take into account the input power it in fact can have even hunt more than hundred percent because you know you have provided more power at the output then you're drawing from the VDD right so so the drain efficiency in that sense is not a very good metric I mean this is an absurd example obviously but now there's another metric which is the power added efficiency which basically takes the input power - into account right and it's basically it takes both the power output power and input power okay in this scenario you can't care about how much power you drive into your amplifier meaning that you need to have in your amplifier right so if you have an amplifier that has very little gain it means that yes you can maybe you can generate a lot of power at the output but you need to drive it with almost as much power at the input which defeats the purpose so in those scenarios where your gain limited then the figure of Merit that changes so the losses would be proportional to this parameter where basically you have the our on and our gate both matter and the quality factor of the gate the are just determine the gate in the input network which is consisting of there on the gate series resistance and the capacitance of the gate now this this is a different scenario and in this case you your figure may slightly changes so you'd usually evaluate both of these things so now now that we've understood these things the next step is how does the weight how do the waveforms look like as we go through the spectrum of the amplification in different classes I'm not a huge fan of naming the different classes with different letters and things of that sort but that's a convention so we stick with it but in general they're just basically it's a continuum of things and it's probably more like any other continuum it's more defined as opposed to defining it I mean it's convenient to define colors by their names but then different people have different resolutions there's another way to define colors is by wavelength right which is very quantitative and repeatable and a cure but so we are defining their colors by names here so if you think about so let's start with this the more linear amplifier so let's say you have a Class A so what you have for a Class A amplifier is a load line that looks more on the one like on the one on the left so you can see that if you have the IV characteristic curves that you look like this a Class A amplifier moves from between the breakdown voltage and the knee voltage and tries to stay in this region and if you look at the waveforms associated with that then you will have a continuous waveform on the cottage and current in that case so as you transition took for example Class A B as the load line becomes more and more bent to transition into Class A B and the load line becomes more steep and then for Class B you have a load line look that looks like the one in blue which corresponds to the waveforms that are shown on the right hand side and you can see that your current is on four half of the cycle the voltage is basically more or less sinusoidal and then if you go beyond that if you make your duty cycle less than hundred eighty degrees less than fifty percent then you basically are venturing into the realm of Class C the so-called Class C which again corresponds to even a steeper load line with a larger knee so basically you're transitioning between the right and that green dot on the right hands right-hand side of that x-axis on the left and the green the other green dot on the top where the knee happens right so you have this transition that's kind of less linear and you're transitioning between those two points that's basically as you're operating your operation point moving now this is when you don't overdrive your amplifier if you overdrive your amplifier meaning that your input is larger than expected your currents will start behaving in this funny way as you can see on the right-hand side so what you see is that your current instead of being this kind of like a single bell-shaped loop they go up and then there's a little dip in the middle and they come back down and the reason for that dip in the middle can be better understood by looking at the plot on the left and that orange overdrive part of the curve which basically means that you're now going into the transistor is going to a triode region or saturation for bipolar transistor and what happens is that you just overdrive it it starts the voltage across it significantly drop so it doesn't start drawing that much current and the load line instead of going up it goes back down which corresponds to a smaller current as seen in that by that orange dip in the middle and that's that's something that you see a lot in amplifiers if you overdrive them in the waveforms of the current and if you see that that's a telltale sign of an over driven amplifier so now if you look at these stages so these are these classes again the waveforms are shown here on the right hand side so if you look at it for example in the plot the four plots on the right hand side you have Class A where the input current and voltages are both kind of more or less sinusoidal looking now as you go to class a B the current starts becoming more and more saturated on the bottom hitting zero more frequently Class B is where basically you're mostly you're off for half the current that off for half of the cycle and Class C is when that duty cycle is even going below 50% right so these are the typical waveforms that you will see in these classes and as you can imagine this is a continuum you're just like naming and then any convention it's kind of a funny thing because Class A is a point on that line Class A B is a big line big part of the line Class B is again a point and then you have C which is like another part of the continuum but again it is what it is okay so now how about other switching amplifiers the concept of switching amplifiers so this is like an examples of class your class F so here the idea here is that you're doing more waveform engineering right you're trying to design the desired waveform so this conceptually what you see on the left hand side is what for example could be a class F amplifier now the class F amplifier the idea of a class F amplifier is that if you look at it in this example in this again conceptually the way it's shown there's a bunch of parallel branches that series branches in shunt and a bunch of parallel or LC branches in series right so what do they do the see that they're series LC branches in shunt like the one that's A to F knot and for F knot in this case our are going to be short circuited at least or closed or have a very low impedance at those frequencies right so in this case a second and fourth harmonic you're controlling your short circuiting this so and then once the series the parallel ones that's three F knot and five F naught are going to be open circuited at those particular frequencies right so what you're doing you're short-circuiting in parallel at those even harmonics so what does this do if you think about this it they would affect the voltage and currents right at even odd harmonic now imagine for a second forget about this and imagine that if you wanted to create a voltage waveform that was a square wave what would you do a square wave with a 50% duty cycle would have only odd harmonics right and it would if you have the odd harmonics in the right proportion you can actually create an in the right phase you actually create a waveform that's an X square wave now why do we do for example would you care about a square wave voltage because if you have a if you could generate this I mean this is an idealized waveform obviously in practice they wouldn't would never look like that thing is that but if you could do that it allows you to get to the maximum voltage operate very close to the knee voltage or breakdown voltage sorry not the knee voltage the breakdown voltage and stay there so as a if you have something that Peaks close to the breakdown voltage you are limited by that peak but your voltage would not be optimum because at other points it will be less than the peak but this way you can keep it as close to the peak for as long as you want for as long as possible right and this is a useful property it's for example so so you can do a form engineer and then associated current waveforms would be the ones as I've shown here now this is our class F this is a classic and the other two the challenge one of the major challenges with a class F is that this capacitance this CS this capacitance of the two switch CS for switch state is going to actually cause you a lot of trouble how so because if you think about it this these networks only operate as as that idealized short and open network when that capacitance is zero when it's driven with an ideal switch this capacitance becomes part of this network and then therefore the limits how large you can make your your transistor which basically their limits how much power you can generate so this is one of the major challenges in class F amplifier what to do with that capacitor because in theory it looks very nice as soon as you attach a real transistor to it it doesn't work as nicely anymore now there are each one of these classes has an inverse what do we mean by inverse which is shown as D to the power of negative 1 and f to the power of negative 1 by inverse we mean that the voltages and current waveforms are switched so what looked like a voltage control voltage waveform becomes the current waveform and what looked like a current waveform becomes a voltage waveform so now the question is that how can you make something whose current waveform looks flat like that and the voltage has that other shape and this is actually in a way easier because for example if you differential what we did with a balance properly to load you can actually create this kind of current now this is useful because of certain things that we'll see in next which is another class of amplified Class E which is an interesting class so this is this is a perfect example of intelligent synthesis of the network right so this was done by actually a father and son it's a famous paper by SoCal and SoCal that introduced this class II stage and it's very interesting because they designed it they went through analytically designed in an LC network that would produce not only this non overlapping waveforms but it also has what it what we call the zero voltage switching which basically means that you switch at the time that the voltage is zero which put at and they try to also control the slope of the voltage so not only they control the value of the control the slope which would have an impact in terms of the capacity of discharging losses or things of that sort so it's even more optimized and this waveform is is nice now the most useful thing about Class E is that it this capacitor is part of that network design so that the design allows actually includes that capacitor so whatever you design for you can allow for a certain amount of capacitor and that capacitance becomes part of that network and you just account and you in your network that they actually explicitly place there you place the difference whatever extra capacitance you need to get to that total capacitance that you need and this is a very useful property so now the interesting question is that is there a way to combine for example this good property of Class E and some of those interesting waveform engineering other engineer away from engineering aspects of a class F and an example of that is what we call the class E over F odd sometimes people call class EF it really should be pronounced e over F because it's an F inverse combined with an e not a regular F so the and that's why there's a slash it's really a division it's e over F or should be e F to the minus 1 and odd meaning that we only do the harmonic control on the all harmonics on in the class F and this basically this topology on the left allows you to do that basically it allows you to absorb the CSS these capacitors the switch capacitors and it also allows you to create waveforms that are non zero of Z zero voltage switching so in principle it allows you to also operate at higher currents with a given voltage now all of these can be actually summarized in this table here so this is like the summary of all these results what each one of these classes allow and things of that sort and an examples of the efficiencies would be what is what what do you do with these capacitances and all those things and the output versus load product the power output power versus x load product and then output power and breakdown voltage products so so that's actually an interesting thing and then you can look at them a little bit more deeply if you really wanted to and then you can also do some wave overtone control right I mean this is the other interesting thing that's controllable the path that you take actually the trajectory that you take for the current and and the operation point you can actually control it either to be on a straight line or have some sort of a hysteresis in practice because of the capacitor and the in this allows it to do some sort of a waveform control so now having said all of these things as a background now let's look into some practical questions about design of power amplifiers in particularly in CMOS now why would why are we making RF power amplifier in CMOS because if you look at the typical radio now radio this radios happen everywhere right I mean you have a cellular phone you have Wi-Fi receiver you have Bluetooth you have all sorts of system that also some other system that use radio transmission and a radio transmitter and receiver in short a radio transceiver consists of you typically looks like that the concept is that you have an RF transmitter an RF receiver usually have a separate power amplifier that norm Nek in many cases if the power levels are high is not implemented in silicon CMOS and then you have the baseband processing in the microprocessor and now a lot of this is basically what we call a single chip radio if you could make a decent CMOS power amplifier one of the long-term things you could do you could integrate all of that into one chip CMOS chip raid a single chip CMOS radio and then eventually for even for high power system you could have a single chip cell phone or single chip radio or things of that sort and these are kind of happening right now and it would be more and more of that of course for low power system it's already happened right if you have a Bluetooth to bluetooth the entire system is on on on a chip if you have a cellular phone or things of that sort then it may not be still I mean some of them are happening and have happened in various forms so why do we want to see most power amplifier there are very various reasons CMOS technology is very low cost in volume because you can actually make it we talked about the economics of this along a while back and the economics of it is basically such that it allows you to make it in large volume with large wafers you get very low cost so cost is important especially things that have a large you sell a large number of them there's a lot of capacity for integrated for making these things and also you can integrate with other things and do a lot of on chip systems some of the challenges are basically addressed with these integration issues integration discussion and then the question is that can we take a power amplifier so if you look at some of the standard power amplifier for higher power generation system they look like that more or less there's a module there's some external passive components there is a semiconductor die sometimes a gallium arsenide some some compounds that other kind of succumb pound semiconductor and you want to see if you can convert it into a single chip device that sits in the same standard package and integrated fully so now for doing that of course what are the issues so we have to think about what are the challenges that you deal with the biggest challenge perhaps in CMOS for getting making high power systems is a low breakdown voltage right CMOS transistors the way are very fast and you make them very numerous you can make in practically unlimited number of them on a chip but it comes at a cost the cost is that you make them smaller and smaller which makes them puny and puny or which basically means that they have a smaller and smaller breakdown voltages that's the scaling that's the concept of scaling we talked about this when we were talking about device physics now so that's one of the challenges we have to do the other thing is that if you to make it fully integrated meaning that all of the elements are on the same chip for it to be repeatable all those things one of the other things that you have on chip inductors for example spiral inductors and all those things but they're low quality factor basically mean they're they're very lossy because it's a very thin layer of metal and it's one layer or a couple of layers and then you basic that you can actually use for this I mean there are more layers but the thick layers are really top layers there are also other kinetic problems you have if you want to have those inductors for example RF choke AC blocks things of that if you use the classical topologies like this you have to run into all of these problems so how do you deal with this now before we turn this talk about how to deal with this let's focus a little bit on the first issue of the breakdown voltage and and do a little of a deeper dive into the device physics mechanisms involved there are multiple breakdown mechanisms so let's talk about them one at a time the first breakdown voltage so that we will talk about three general category of the breakdown issues one is what we call the gate oxide breakdown so if you look at a typical transistor which is shown on the upper left corner and if you look at the voltage across the channel we talked about this again when we talked about the transistor MOSFET transistor while back you see that actually the voltage across the channel which is this red curve goes slowly in the channel and when once you get to the pinch off region most of a lot of good chunk of the voltage is dropped across there so you have a small region where you have a large voltage across which means that basically electrons startx or charge carriers if it's a P FET will be holes if you'll start basically accelerating from the edge of the channel towards the edge of the drain now they start excited because they're subject to a large field and then accelerate there and then they hit the drain where there's out the impact cross-section is pretty large so they would basically be all of a sudden stopping there so now this is a challenge this area is where a lot of things will happen as we will see now one of the breakdown mechanism is basically if you if you think about this this gate oxide by the way the other way to make the transistors good and fast is to make this really really thin this is several atomic levels levels thick maybe like three atoms or three layers of silicon atoms thick right in a in a state-of-the-art transistor so you can imagine that actually what that can happens that if you have like too much of a large too much of Motorz difference between this gate and the drain then at that point you can have a breakdown and that can if there's a current flowing for example all of a sudden you can actually have caused a catastrophic damage and irreversible damage so basically at some point you voltage exceeds something you just basically charge passes through current passes damages the oxide and the transistor is done it's a probabilistic effect right it's like like a lightning happening right where does it happen when does it happen depends certain conditions are more conducive to attend and others and it's determined by the quality of the gate oxide at this point which is very interesting because it ties into the next one in the light of that acceleration inside the depletion region so now the second mechanism is the hot carrier degradation is that again as we said the electrons start accelerating and particularly in that region and they will have more impacts in areas close to the vicinity of the gate and drain where they where they are coming close to each other now we saw that that's where you usually experience a larger voltage difference right if you look at the previous plot if you remember the voltages basically here this is the voltage the voltage difference between the gate which is the green voltage and the red which is the drain voltage so this is highest here and this is where you have all these hot carriers coming in and having impact and they can be even so hot that you can actually really secondary carrier some of these electrons can get actually stuck in the gate ox in the oxide itself balance and get scattered and get and get trapped charges there it can change the properties of the transistor slowly because of the stretch trap jaw or it can expedite the catastrophic gate breakdown itself so it's generally a slow degradation initially because you have more and more gradual degradation of the drain region but at some point it can also lead to a catastrophic gate failure there's a third mechanism which is interesting which is what we call punch through which is basically when the depletion region associated with the drain and source right actually start meeting the only reason under normal circumstances off okay there's you're current between drain and source is that you have two back-to-back diodes right you have an NPN I mean in a MOSFET right the source and drain and and the gate the gate there the channel area is is p-type normally before it's inverted and what happens is that if you apply large enough voltage depletion regions will extend and start meeting and getting close which basically means that there's a potential barrier lowering and this will exhibit itself like this part this changes in the IV characteristics on the right hand side you will see that once you go beyond a certain limit all of a sudden current starts pushing up that's the current that's going through the bulk that has nothing to do with the MOSFET that surface channel on the MOSFET is just going through the bottom now this mechanism in and of itself is not a cat it's not a destructive mechanism right it's just a guy I mean just a current flowing through the bulk now but so heat it can actually damage the transistor and can also accelerate the hot carrier effects so there are all these breakdown mechanism so we need to really think about what we are doing with the transistor to overcome these things there are other methods to deal with these things as well but let's focus on on these three for that now so if let's go to the topologies of the power amplifier different ways so the idea here the question is that how do we generate large enough power how do we make create large power using MOSFETs that have low breakdown voltages so let's start with some basic topology so this is the most basic topology is the one shown on the upper left here in this one so you have some sort of an inductor or choke that provides a DC current then you have the transistor operating at some sort of a switch turning it on and off and you have some network following it right now if you look at the waveforms associated with it you can see where different kinds of breakdown voltages would be important right for example you see that the gate the drain voltage the red curve and the gate voltage which is the green curve are going to be that have the largest difference at the minimum of the input voltage and the maximum or the output right as it's swinging of course the inverting stage so the drain voltage is going to be highest when the input gate voltages the Loess and this is where you are stressing that the drain gate drain gate oxide the most so that's where you are that now the hot carrier effects on the other hand are significant when you have both voltage and current right because you have and that's basically these like orange bands where the hot carrier is most pronounced the damage of the hot carrier will be happening there and also the punch through will be happening at the time where that excursion is the largest so this is the kind of the stage that you're dealing with and then you're limited by how much voltage you can tolerate so at some point basically if you say if I say okay I have a maximum gate breakdown voltage of 3 volts it means that this voltage cannot exceed that and it's it's not even a number like that but what happens is that it's usually specified in terms of the life right now life time of the transistor expectation of the lifetime of the transistor in terms of the voltage you apply so you can basically increase the voltage by point one involved and the lifetime of the transistor will degrade by a factor of 10 for example but it's it's still it's not a statistical analysis and those that information is usually present in the available from proper boundaries so so this is one basic topology so what can we do from a topological on the circuit standpoint to overcome some of these things the idea would be essentially all of these ideas are based on one thing can you find a way to break they've split these voltages among multiple stages instead of having one transistor carrying all the burden if you have a large number of them larger number of them that you can basically they can share the burden each one of them can carry a little bit of the burden then you can do it so basically going again from the mindset of going from the big elephant to the army of ants right is that understand so what are the things you could do is this kind of alternative concept of bridge right a bridge amplifier the bridge amplifier the way it's shown here consists of an N mass and a PMO's so if you can have an N Mo's and P Mo's and then both of them basically drive so what happens is that this voltage if it's let's called V bat or VDD the average output voltage will be halfway through and the N FET and pivot are kind of like all more more or less if properly designed will split this their share of the voltage excursion voltage swing and that way each one of them experiences about half of that so it reduces the voltage stretch by a factor of 2x the problem is that P masses are not generally as good as the end masses in MOS transistors primarily because of the fact that the holes are not as mobile as electrons and this is it and then you have to also have the right drive voltage for these things the DC voltages and all those thing which is doable I mean but it's some extra thing to worry about and the voltage swing also is reduced because now your maximum voltage is V bad not you know V back to V bat or even 3 V bat in the case of a class II or something like that because in those cases where you have an inductor like the previous example let's connect sent the DC is centered around VDD and therefore you can actually go above be bad in that case and you go quite a bit you can go actually above that quite a bit now what else can we do to overcome this thing if let's say if you already have a voltage supply that's large but you're trying to use transistors MOSFET transistors that are capable of only handling certain minimum amount of it not a very large amount of voltage right so what the other thing you could do you could say you know what I'll make a DC to DC converter I'll take the DC voltage I make it converter a buck converter or you know whatever you want to the different kind is about covers so that basically is switching converter a DC to DC converter I'll take one of our voltage I have and I convert it to whatever voltage I need and then I Drive my amplifier with this this is kind of like one of those trivial solutions right this is that this is an if it was patents this would be a quintessential example of obvious Ness right taking things that exist and put them together which is fine I mean a lot of engineering is that but that's okay but but it just so and the other problem with this is that this introduces other problems first of all this guy this DC DC DC converter itself will have some loss it's not going to be perfect then when you're just doing switching a lot of time you're introduced witching noise that you have to think about filtering and things of that so because that could get into your RF chain it's or modulating your RF signal let's create superior signals it usually requires a large inductor that cannot be integrated on chip that inductor will have to be off which kind of now starts defeating the purpose of doing everything on chip and all now nevertheless there are scenarios where this is the useful thing to do the good thing it does it actually allows it to modulate the amplitude to if you need it to do that if you can well the question is how fast can you do this but you can allow provide some amplitude modulation you remember we had the scaling rule in the very beginning and if you scale the VDD or the power amplifier but a factor of lambda up and down we could scale the voltages and currents and therefore scale the power so by controlling this voltage you can scale the power in general with the power amplifier switching power amplifiers you can scale control their power by scaling the voltage so now the other alternative which is quite interesting it's using a cascode now the idea using a cascode is that again you have two transistors but now this time you have two nfit which are faster and you can actually drive them in such a way that they are going to be shared splitting the total voltage swings so they say in this example you can see that for example this mid voltage between the two casco the VD one is shown with the orange level and if you look at it each one of these drain source voltages experiencing pretty much half of the voltage color:string of the other one right and what this allows is that by controlling this which has code you can actually adjust it in such a way that you split the voltage between the two of them and get a better performance in terms of the voltages so now of course there are other things you have now two transistors in series so your own resistance is twice so you have to make these transistors larger which means that now you will have more capacitances associated with that but this is actually pretty decent example the other thing that you can do is basically what we call the stacking of amplifiers so you can make any kind of amplifier so any of the select of the triangles on the left hand side the four that are shown here or stack and each one of them is really essentially what is for each one of them is it can be a complex amplify it can be a cascode amplifier itself it can be any kind of topology but you can now have them the Dre the vote that the VCC VDD of the supply voltage award can be the ground of the other one so in you see they are stacked so they share the same DC current but the DC voltage is split among them and if you properly design it and it's easier said than done to do that and I will talk about that briefly in a second you can actually have the voltage divided in in this example an equal quarter so you get quarter of the V bath on each one of them and these voltages would be at one corner of about one half about 3/4 v bat and v bat of this intermediate node and this is an example of how that was done in one of the earlier papers published but so here's a stick key the key is that the challenge with these things is that the interaction between the power amplifiers this power amplifier start interacting because there are some fluctuations in one there's some coupling of ära from one to the other one and that interaction can create create all sorts of very complex very interesting and sometimes very difficult to handle dynamics of control so this intermediate voltages need to be well controlled if you want to do that so now let's say let's look at the practical example right let's say we are trying to make a power amplifier see most power amplifier to drive a 50 ohm load for a given amount of power now generally speaking if you look at the power amplifier it has some sort of a supply connection as it's shown here and you have a harmonic and waveform control which is basically the way for engineering part of the thing there is some impedance transformation symbolically shown as a transformer here it doesn't happen always a transformer gave me an LC network or RLC Network a lot of times it is and then you have the load so let's look at a typical it's a basic example let's say you have a supply voltage of 1.8 volt for the sake of argument right and let's say your transistors so basically and and then let's say you're trying to deliver power with this supply voltage let's say your transistor can handle twice as much voltage as a breakdown voltage so let's say your transistor can handle 3 point 6 volts which is pretty high for small MOSFETs but let's just should even use this even using this example you will see how pronounced the issue is so if I were - just take this amplifier and make like a standard analog amplifier like the ones that we output stages that we drove and even if you allow it to go above VDD by a factor of two by biasing it with an inductor in the middle and then letting it go above and below the maximum voltage doing that you will have is Z from 0 to 3 point 6 volts roughly first-order and the amplitude is going to be 1.8 volts for that sinusoid that goes from 0 to 360 right the amplitude is 1.8 volts so what is the power deliver to a 50 ohm load if you connect a 50 ohm load here what do we get you guys we did you get the 1.8 volt divided by V DD v square divided by 2 R right and if you do the calculations for this voltage and this 50 ohm you get 32 milliwatts so if you were to directly drive with a load okay we call this P direct with that power supply you get about 30 millivolts delivered that's the maximum power you can deliver now let's say you if you wanted to deliver couple Watts right let's say you wanted to deliver 2.8 watts of power to a 50 ohm load now if you wanted to do that with direct drive what is the voltage swing this is a basic calculation you just solve for V in V squared over 2 R them equal the power right which is basically this equation so your voltage swing with plus/minus 16.7 so the voltage swings has to be more than 34 volts clearly this transistor cannot handle a mass transit mass transistor cannot now if you confused a for example gallium nitride transistor it can but then you can't integrate it with the rest of your CMOS transistors or things of that it would cost a lot more but yeah so so you can see the problem right so this ratio of the power that you want to deliver to the power that you can redirect they will deliver without impedance transformation given a voltage swing it's called power enhancement ratio and we'll talk about it more explicitly and it's an important parameter so we call the power enhancement ratio because you want to enhance it from 3430 milliwatts to whatever 2.8 Watts so how do we do that well we do impedance transformation there are different ways to the impedance transformation for example symbolically shown on a well it's not somalis a schematically shown on the left as a resonant match you can have single or multiple stage of resonance matches like an LC matches and each one of them does an impedance transformation in LC match or on the right hand side with a magnetic transformer you can actually achieve that so let's look at the number and look at the equation a little bit more carefully and see what they tell us so imagine that you have this impedance a single-stage impedance transformation LC transformer and see how that performs again it's a pretty straightforward circuit it's an inductor capacitor and let's say you have it let's assume that you only lost source of losses coming from your inductor and it has some loss that can be modeled as some serious resistance right and that that's captured by some quality factor so for the inductor you can have a quality factor to find a Q insured for short for that inductor and then if you have a quality factor for an inductor and you the impedance transformation of this thing which will be RL or load divided by RN is QM squared of the network divided +1 the passive efficiency the ratio of the power delivered to the load to the power that goes in is basically determined by 1 minus qm / ql and so basically and then that the power enhancement ratio or PE R is the ratio of P out to what we get from a 50 ohm load so this is basically the denominator P 50 ohm is the power that your transistor would deliver directly to a 50 ohm load without this network and now if you put this network and you of course get more power because now you've done impedance transformation that ratio is basically you can easily show it's a product of the ADA and are the efficiency and the transformation ratio now the interesting thing is shown here if you look at the efficiency of the passive network this just this are else that this RL network right or RLC Network sorry this the single stage impedance transformation Network and plot it for vs. power enhancement ratios that you would need for different values of quality factor of the inductor this shows something remarkably I mean it is it's something striking actually this is the equation that's being plotted so I can actually solve for a pretty straightforward calculation it's a pretty calculation you can do it it's on the right basically it's shown what ADA is so this is what you see so in the example that we talked about like the ratio of 2.8 Watts to 34 milliwatts so it's a power enhancement ratio of like 8090 right so if you look at it at power enhancement ratio of AD and inductor Q of 10 it says that your passive network alone even if you had ideal transistor we'd have an efficient you cannot have an efficiency higher than 10 percent it means that you can you will lose a lot of power now if you have a Q of 50 the situation would be different that that power has been ratio I mean it can be close to 80% maximum efficiency of the pure passive network nothing else it'll just dad LC so this is important this means that you cannot I mean if in this examples we encountered if you want to make a water level power amplifier in CMOS with transistors that have breakdown voltages of a couple of volts you are in this power enhancement ratios of like 100 or so range and if you're trying to make an unzip in matching Network you have quality factors that are in the range of 10 and 15 and therefore it sounds like it's an impossible task or is it ok well there are a couple of things first of all is that the path what we calculated was for a single stage LC transformer it transformation Network you can have multi stage you can say you know what the problem arises from the fact that you're trying to do too much in too few steps in that example one if you want to do to achieve something more efficiently you probably ought to do it in more gradual steps so instead of doing all of that impedance transformation in one step have multiple steps if for each one of them do that there's a little of impedance transformation and you can improve it and that is true you can actually improve it so if you take that do that and find the optimum number of stages that would give you the best power efficiency for a given power enhancement ratio you get this curve this these curves are a little you can see they're not as they don't drop as precipitously as the other one but still they're not pretty they're not that good so at the power enhancement of a ratio of 100 and a Q of 10 then it says the passive network efficiencies little bit over fifty percent so that's still a lot of power loss just purely in your passive Network right so the question is that is there another way to think about this now conceptually when you're doing this thing you're doing it what we call a resonance match resonant right so it's a resonant match resonance match means basically that this is an example shown on the left hand side you have an inductor and a capacitor in the load and they're in resonant now if you look at the currents and voltages what you see here is that inductor current and voltage are both high right so they both inductor current and inductor voltage are high at the same time which means that there's there's also a large amount of energy stored in the inductor so if you look at the energy stored in an inductor in this example of seven and one conversion almost day is like forty nine volts volt amps now restricted power per seconds now if you think about this now that if you and if you compare it to a transformer in a transformer on one side you have large voltage and small current or large due to small voltage and large current and on the other side you have a large voltage and small current so the magnetizing part of the inductor which happens in the transformer is storing a lot less energy in fact a factor of seven in this example now if you're storing less energy in your circuit resonant circuit for a given quality factor considering the fact that called a factor is the ratio of the energy store to the energy dissipated per cycle if your quality factor is fixed it means that the energy dissipated per cycle is also reduced by the same factor so that's why using a transformer where there's a large transformation ratio magnetic transformer has a fundamental advantage compared to an LC now if you do that I think if using magnetic transformer you can actually derive the efficiency in terms of this power enhancement ratio and other parameters it's a little bit more elaborate calculation all those things and it's shown here but in you can you get some improvement the improvement may not be as large it's not exactly a proportional one like that that simplified example that you should but it's a relatively decent one now left if you look at it now it depends what in the example that we talked about if you're trying to make the 33 DBM power out between the 2 min 2 watts and use 1/2 bridge circuit then what you're talking about is that your transformation ratio should be a factor of n the transformer ratio is n of 8 now if you think about this there are certain scenarios if you want to just do a transformer like that if you just were to make that transformer the primary and secondary inductors would look very strange because in this example the primary inductor the secondary inductor would have would be four nano Henry inductor which is a relatively normal value for unship and doctors but the primary inductor would be 63 Pico Henry's and again it's possible to make a 63 Pico Henry inductor on chip but coupling them effectively to a four nano Henry inductor is very difficult so the large disparity is significant now if you were to do this instead of 33 DBM for 15 DB L n becomes 1 and they both become the same value which is kind of like a relatively straightforward transformer to me so there's another problem still to make to solve right which is basically now even if you wanted to do even if you could do you know if you wanted to do the transformer making really good transformers on chip at least the 1 2 want the transformers with one single input and single output in this format it's difficult so there are other issues with this also that there are the ground inductance and all those things when you have the matching network when you're on ships you have wire bonds or solder bumps and you have to think about the ground wire bonds and the supply wire bonds or supply bump and those would also impact your overall performance quite a bit so the question is that can we come up with a way to solve this problem so for example if you wanted to reduce the bond inductance right so yes you could you could see you may come back and say well use many multiple bonds right the problem here is that if you try to do that then the mutual inductance between them starts luring them all so if you to to wire bonds in pairs next to each other the inductance is not going to be half very that 0.9 because of the mutual inductance between them now you can use it a lot and you can get some reduction but it's kind of like a brute force solution that's not really that effective anyway right the other thing is actually for example if you use a differential drive at least as far as the odd harmonics are concerned right that node becomes a virtual grout and for all the harmonics and same thing with the VVD so that way allows you to that allows you to at least take care of some of the harmonics with whatever impedance you have on your ground and VDD so and that leads to some sort of it and you can basically in principle say I can use some sort of a class EF u over F design where you basically have a wire bond connection or you know sort of I saw the ball and then you can have a differential one and if he gets over overcome some of these problems now the other problem for the differential one is that yes the differential is fine but a lot of times your output needs to be provided as a single ended output for a variety of reasons sometimes your load your antenna is design whatever you're driving is designed as a single ended load a lot of times you don't want to kind of like have multiple lines routed on your chip the same way you want to go to ground play on one end and have it one line distributed as opposed to two so you need some sort of a balanced it converts the balanced to the unbalanced and hence it's called talent and there are different ways you can actually have some LC balance like the one on short shown on the right hand side or you can actually use some sort of a transformer based one that's shown on the left hand side for example and you get good thing about is that if you have some sort of an inductor like that you could actually use a transformer and the other side of it can be about now but still we haven't solved basic problem the basic problem is that how can you make high quality factor inductors that are coupled to each other magnetically and they're small enough but they're magnetically strongly coupled right because we saw that before what level amplifiers we needed something like that so one of the things that you can think about is that if you've compared a loop inductor with a line inductor if you could connect to it right which one has a higher inductance so if in other words let me specify the problem more clearly let's say you have a piece of wire and then you take this piece of wire and turn it to a single loop and the inductance of this single wire from one end to the other compare that with the inductance of the loop which one has a higher inductance and the answer somewhat maybe counter-intuitively for some people some some people is that the straight line has a higher inductance for today and you may say wait a second where is that what how about this like spiral we do the loops and all those things we learn all of those things that you know we make seller noise and all those things to get more inductance and the answer is yes solenoids have multiple turns that's why their inductance goes up because it's mutual between the adjacent turns that helps it another way to see this is that if you have for example two wires that are carrying current and they are going in opposite directions which is what's happening in the loop the mutual inductance of these things actually is reducing the inductance and one way to see that is that if you bring them very close to each other in the end the magnetic fields cancel there's no magnetic energy stored into space anyway so if you could use this slab inductor which is basically a straight line they would be better because then you can actually either force given inductance you can make them shorter and have the left loss also they don't have current crowning things of that sort and there would be nice but the problem is you cannot connect to them properly how do you connect them if you put a transistor here and a transistor there then they are not going to be connected to each other because you need an extra wire and then that defeats the purpose so the questa keys that is there a way of taking these slab inductors and driving them in such a way that you get the same effect and take advantage of that and also you need to be magnetically coupling to them and the answer is putting them in a circle so now if you think about this if you take these multiples in this case four of these slab inductors and for example look on the one on the plot that they figure on the right-hand side and look at the slab let's say on the right-hand side of that plot you have two transistor on the top and bottom that driving it out of a it's kind of out of phase asymmetrically and in this case you have a speedy DeeDee is connected in the middle which is the virtual ground so this is going basically that that slab is basically going up and down like this now what you do is that if you put them in a loop then the next slab is also going up and down but out of phase with that so if these are the two slabs they're going like this with respect to each other in terms of voltage and therefore of them but I can't do it I don't have four hands so now the other interesting thing is that now that they can actually connect the transistors and the ground would be connected in between the adjacent transistors because that would also be the same way a virtual ground as the connection between these two adjacent transistors whoo that bit the same way for the capacitor instead of connecting the capacitor between the two ends of the slab you can take the same capacitor and connect it across two adjacent slabs without now physically close to each other so you can actually make a good connection and the event and from the perspective of the capacitor the voltage it sees on this other end is the same exact thing that it would have seen on the other end of the slab so from the capacitors perspective it can't distinguish these two voltages by substitution right and what happens is that this architecture allows it to have a this is like an engine right now now it's kind of like you're driving it it's a pretty strong engine it's going around now what you need is some sort of a transmission to take this and get it out and connect it to the to their tires right for example and that would be the secondary which is shown here so the second risk taking this is magnetically coupling to this engine that's going around that's kind of circular so there's an AC current circulating back and forth in this thing and you make now you put a secondary loop here that takes that and magnetically couples that and then couples it to the load and this is what we call a distributed active transformer it's distributed because it's not in one place it's active because if every part of it is driven and they're driven in multiple parts and they can couple to the output and one another way to think about this is that you can think about each side of this thing the part with the primary slab in the secondary slab as I want to 1 transformer and you have a 1 to 1 transformer there where you under primaries you're driving the in the primaries of these things independently the structure that we discussed but the secondary's of them are put in series which allows them to add the voltages so now you can the primary you can have a much lower voltage that your transistors can tolerate because they're driven independently they're driven in parallel ready primaries are in parallel if you think about it but your secondaries are in series which allows you to add the voltage and generate that like 3040 volts voltage that you generate here and drive the output with that now that's not a problem because there are no active transistors on the secondary it's just a piece of metal and that can drive the 50 ohm load and drive the power that you need to now you'll need to also think about how what you do about your input matching your different ways to do this is one of the early ways of doing that which basically you can see you can have another one and if you need an input inductor for matching you can actually place it between the two adjacent transistor as opposed to across a full slab and you can get structures looking like that you will need some distribution network to get the power to these things these are just demonstration these are not wire bonds this is like they look like what was just showing where the connected connection is to avoid making the plot even more complex you if you haven't single ended input you want to convert it to a differential you need another balance at the input and then that's basically something that looks like this so this was the first demonstration of this distributed active transformer producing a couple watts of power at 2.4 gigahertz and you can see the different element these are the primaries the thick ones are the primary slabs there's a thinner one the secondary slab inside there is a distribution network these are the inductors for the input matching and this is the input ballot and then there are some variations that happen later so this is another this is the distributed active transformer of that that this is another example of that it's not clear on this picture but anyway so it's a it's another kind of dat structure that produces like again 2.8 watts that came from the example that I gave and if you want to see actually how the performance looks like so this is these are the powers of the alpha power gain and PAE of that particular amplifier it's quite broadband if you look at it it's quite better now you don't have to do it in square setting only you could have as many of them as you want another example fun example is that you can actually make an octagonal one you can make any kind of like polygon an octagonal one will have eight cores to drive it in there are a series so this is an example of an octagonal design that was done with different kind of distribution network this is a picture of that die made with that octagonal design and different people see different things in this some see a ferris wheel some people see a turtle this is the head this is the body some see some people see a carpets I don't know what you see anyway now and it can be done quite well so if you perform performance wise this is very good and compares quite favorably to other things that we're done in similar technologies at the same time now the other thing is that now if you want to really turn it into an actual part that goes into your cell phone for example if your earlier dates where this was done many years ago for gsm/gprs example so you have for example in this case you need it for band power amplifier so you need it a power amplifier that covers the two lower band 850 megahertz and 900 megahertz and in a higher band which basically covers the 1800 and 1900 megahertz 1.8 1.9 gigahertz and runs off of a lithium at that I am battery full full power control it can can it can tolerate load mismatch and things of that sort and so if you can do that if you did the problem here is that you have power supply limits so if you make it at the standard way so this is the standard way just like drawn record rectangle as opposed to a square so you have four cores and you have the primary and secondary now of course if you look at this you will suffer from a breakdown issue because if your voltage is 3 point 6 volts or higher for example then you put your phone on a charger the voltage would be higher now this these transistors cannot withstand it so the idea here is to use a double concentric design so the double concentric design is it's shown here and it takes a couple of there's a couple of interesting points about to know about it so here you have two primary two sets of two primary loops as opposed to what and each one of them of course each quarter as if you notice compared to the previous case is for another cast code as opposed to a single differential pair so that doubles the amount of voltage they can withstand but now you have two primaries right but these two primaries are so from a driving perspective they are operating independently but from a DC perspective they are placed in a very interesting way they're stacked if you think about look at the VDD if the villain is for the outer primary those four points now the ground for the outer primaries are the best comments that that's become a source point of this outer differential pairs right this normally would have gone to ground at this point but now instead of going to ground is serving as the VDD of the inner primary loop right you can see that the ground of this guy this guy the despairs this course is basically connected to midpoint of these inductors the slab inductors of the inside primary so these primaries are now stacked so which means that the voltage the three point six volt or higher voltage is divided between them so each one of them experienced only half of that sees one point eight volts supply of that and now each one of them splits that using a cascode between two transistors each transistor on average sees point nine volts of this voltage so but now they contribute power to that they're both coupled to the secondary right in parallel so both of the magnetically couple and they are driven in phase so they basically produce each one that produces half of the total power that's coupled to the secondary which is between sandwiched between them the darker can like a red burgundy color and then that's fit to the output so this allows you to withstand the voltage none of course you need additional thing you need to have some sort of a power control because you know in an actual power amplifier you need to be able to do power control each one of them has some biasing control that's the central bias there's a sense and feedback there's a sensor here that detects the power there's a feedback loop that controls this and controls the power and adjust them accordingly so there's and there's a lot more sophistication in law in that and this was actually became a commercial product that was sold in large volumes but this is a picture of it and basically this stick on the right hand side of it you can see the lobe and that 800 900 megahertz one and then the one on the left is the high band and 1.8 1.9 gigahertz example and these are some of the performance measures basically shows that the noise performance is good the spectral you know that time the temporal the temporal their spectral and temporal masks meet this requirements it can withstand various kinds of load mismatch so if your load is not exactly 50 50 ohm it can still produce power it doesn't blow up doesn't do all sorts of crazy things it is very well controlled over different battery voltages or supply voltage from 2.9 volt to 5 volts you can see the power control loop is very stable and does it just control it to within like 0.51 or point 15 dB and then the power control the power output versus the control which is pretty well behaved and monotonic it's quite reliable many millions of hours of reliability test at it was done the reliability tests on amplifiers on power amplifiers in particular is very interesting you'd get a large number of them and then you have an elevated temperature an elevated voltage and their formulas that translate them to additional utility time so if you use for example if you do 2 million hours of device hours of testing which basically means that you have a large number of devices that are testing in parallel and you can accelerate that and you do it and then accelerate at higher temperature and higher voltage you can accelerate it testing which allows it to check the test the long term reliability of these devices and these we're quite reliable and predictable so that's one of their ass but that's an example of a design that leads from a conceptual design to something that actually is a product ok now there are other things we talked about linearity right in the power amplifiers and we can talk a little bit about that and going forward just briefly some of the issues with linearity is that dark we said I mean the way phones become more and more nonlinear if you remember the discussion that we had and the interesting thing is that the exact device characteristic is less important than the switching power amplifier it's really kind of like the overall behavior now there are a couple different as a very introductory discussion of this there are two different kinds of non-linearity and to show you the difference I want to show you an illustrative example so these two pictures show the two different kind of non-linearity but one on the Left I would call a static non-linearity one on the right called dynamic linearity now the static non-linearity is that if you have a non maravene v out and this is a modulated waveform that's what this voice look look what it looks like that so you have a modulator and the blue curve is the envelope of a modulated signal so basically this is a two tone this is a beating tone right coming in and what you see is the envelope of the actual carrier is pretty moving pretty fast when it's going to a device with static non-linearity basically it has a nonlinear V in V out here first now you put it through that through an amplifier switching amplifier well and there's no dynamics involved in it and you what you see is that there's a one-to-one correspondence between the input and output voltage it's not linear so you take that envelope and you turn it into something that looks different right now there's something else now if there's dynamics associated if there's some delay and lag and memory in the system you can put that the same input in but the output would look different now you can see that there's no symmetry versus the middle of the waveform which means that there's some buildup for example what can you do that a no time constant in the circuits right and biasing network can do that a capacitance somewhere a thermal behavior if the device is heating up so that's it's going up it's different from the when it's going down there many many things that can produce this kind of dynamic non-linearity and interesting me enough of course if you have in if you look at it in the spectrum you I didn't want to have your spectrum confined to a limited band that you have access to for a variety of reasons you don't want to be creating noise for other people and you don't want to be spilling over in other people so you want to create create some sort of a clean waveform that looks like that blue curve right now the green one is what comes out when you put it through this nonlinear system that's the product problem it not the power amplifier but what we called a spectral regrowth so you can see that you know that this these parts that were clean went through the cement one when they go through the non-linearity it's basically you can think about the inter modulation between components within the spectrum that you're transmitting different components are talking or interacting with each other and that inter Mars would appear outside the bath and these are in some other people's bad so other people don't like it so you need to get rid of them or minimize them so the question is that isn't there a way first off before we even talk about how is there a way to correct for those non linearities in particular well the static ones it's kind of straightforward I mean if you think about it this conceptually if you know that you have a certain kind of nonlinear transfer function V in V R you can apply the inverse function to the input right and instead of applying a waveform that you wanted to create you apply it through the inverse function and apply that thing and then it will produce to write out the question is that how do you fix it online can it can the dynamic one can be even corrected and the interesting thing is that the answer is yes and this goes back again to waveform engineering right is so what you see here on the right on the top right what you see is the original dynamic non-linearity the blue one is the input and the green is the envelope of the output which is what what is damage in a spectrum and the spectrum is shown on the left so the spectrum of the blue is there there's a color correspondence between the per spectral plot on the left and the temporal plots the time domain plots on the right so you can see that uh none corrected you put that modulated signal in you get that green envelope which is asymmetrical now but the interesting thing is that there exists that other second blue one which is not doesn't correspond to this spectrum that you can put under lower right that you can put at the input and it to produce the output that you do require so but you can see that's also asymmetrical so you produce you make you design the input in such a way that it will produce the desired output now how do you come up with this thing is a more interesting discussion and again we are not going to be able to have to have time to go into it but there's some kind of like interesting ways of creating a network that has some certain kind of dynamics itself and one of those things is basically creating the preamp pre-distortion waveform based on a system with memory so for example you can also make a tap delay line structure with non-linearity that has various elements of the input signal delayed and then added with different weights and different nonlinearities which allows you to produce that kind of input call it a generalized on linear memory pre-distortion that you put into the amplifier and that can produce the output that you want and that would give you the kind of correction so that's a very very introductory discussion of power amplifiers there's a lot more and a lot of interesting architectures which we didn't talk about our power mixers power Dax things of that sort power mixers is basically when you're doing your up conversion mixer where you're doing the power combining and you do it in a binary weighted fashion you can actually add them or you can have a power DAC where basically you can have different power amplifiers with different powers combining together and you're just doing a digital of conversion you're basically depending on which ones you turn on and which ones you turn off your basically have a power digital to analog converter whose output is a power at the frequency of interest control like that there are lots of different variations on this thing that you're not talking about today but hopefully that would give you a little bit of an introduction as a starting point to think about power amplifiers okay any questions all right

Channel: Ali Hajimiri

Views: 27,647

Rating: 4.9380531 out of 5

Keywords: CMOS, PA, power amplifiers, silicon power amplifier, Distributed active transformer, DAT, Axiom, Class A, Class B, Class C, Class D, Class E, Class F, Class EF, Class E/F, Class E/Fodd, linearization, predistortion, power combining, transformers, LC match, RF amplifiers, mm-wave, microwave, cell phone, wifi, 5G

Id: 8GLpBE5n5Cw

Length: 79min 13sec (4753 seconds)

Published: Sun Aug 04 2019