Hello, and thank you for joining us for today's Teledyne LeCroy webinar on the impact of power rail noise on clock jitter presented by Dr. Eric Bogatin. A few housekeeping items before we begin. To keep us running on time, we will hold questions and answers at the end of the webinar, but feel free to submit your questions as they come up using the question section of your control panel, which should be to the right of your screen.



  

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Again, thank you for joining Teledyne LeCroy today for our webinar on the impact of power rail noise on clock jitter presented by Dr. Eric Bogatin. LeCroy was founded by Alabama native Walter LeCroy in 1964. Our origins were in high speed digitizers for particle physics research.



  

Our corporate headquarters is in Chestnut Ridge, New York, but we have sales and service offices all over the United States as well as the rest of the world. We started as an oscilloscope manufacturer focusing on physical layer tests and have branched out into protocol analysis through several compatible acquisitions. In 2012, LeCroy was acquired by Teledyne Technologies, and we were renamed Teledyne LeCroy. A little bit about our presenter, Dr. Bogatin, founded Bogatin Enterprises in 1992, which we acquired in 2011. He has produced over 200 hours of training material for the Teledyne LeCroy Signal Integrity Academy and has written over 17 books. Eric teaches at the University of Colorado in Boulder in the Department of Electrical and Computer Engineering and also currently holds the position of technical editor for the Signal Integrity Journal. We know that there are a lot of demands on your time and appreciate you joining us today.



  

I'll now hand things over to Eric to begin. Hey. Thanks for that great introduction, and thanks everybody for joining us today on our webinar. We're going to talk about the impact of power rail noise on clock jitter.



  

We have a lot to cover in a short period of time, so let's get started, and let me walk you through what we're going to be talking about today. We're going to spend time talking a little bit about jitter in general and distinguish jitter in data and jitter in clocks. And then I'm going to walk you through how we go about measuring jitter in clocks. I'm going to introduce you to some of the best measurement practices.



  

And along the way, I'm also going to show you some of the artifacts to watch out for and what to pay attention to in your circuit that you're measuring the jitter in and the interactions with the scope. And then once we have a robust way of measuring jitter, we're going to look at some of the analysis of the jitter. We're going to use statistics, we use histograms, we'll look at variations in the jitter. And using that technique, we're going to look at how to measure the sensitivity of the jitter to, in this particular case, a power rail voltage.



  

And if we understand what that sensitivity is, then if we look at the noise on the power rail, we'll have an idea of what the impact is going to be on the jitter, and vice versa. And then we'll pull everything together. Well, let's get started. And in particular, I wanted to spend just a couple minutes distinguishing this idea of jitter in clocks and jitter in data because they're similar, but they're also different.



  

And if you're familiar with analyzing jitter in data, some of the techniques we'll use, but some of them won't apply. There's a distinction between the source of jitter and how we measure jitter in data versus in clocks. We define the jitter a little differently in data and clocks, and I'm going to walk you through very, very briefly how we define jitter in data, and then we'll look at jitter in clocks. We even measure jitter slightly differently.



  

And of course, in a clock, there's no data dependent jitter because the data pattern is always the same. It's not varying. And so that's an important distinction. And, of course, in data, especially if it's NRZ data, one of the important features that influences the jitter that we see is the clock data recovery circuitry, and that has in an element like a local oscillator and a PLL, which can be influenced by external forces.



  

Some of the features of the root causes of jitter in data don't necessarily apply to clocks, but there are also some similarities. We'll see that we can measure both the jitter in data and the jitter in clocks with the scope, time domain based measurements, and we'll see that some of the same external forces that influence jitter in data will influence jitter in clocks as well. And sometimes that sensitivity is similar. Let's just spend a minute looking at how we define jitter in data.



  

Of course remember that when we have a high speed serial link, oftentimes we don't have an external clock to compare the data pattern with the synchronous clock. Instead, the clock is embedded in the data. And one of the first steps we have to do in looking at high speed serial link data is to kind of de-embed the clock. That's part of the clock data recovery circuitry.



  

And so after we get that clock synthesized locally, after de-embedding it from the data, then we use that synthesized clock to compare the arrival time of the edges of the data. And we define the jitter of the data in terms of the difference in arrival time between what we measure in the data edge and what we measure in the synthesized clock edge. And that synthesized clock edge is the expected arrival time. And so when we look at data and we look at the jitter in data, we define the jitter in terms of this term time interval error (TIE).





And the time interval error is the difference in arrival time between the edge of the data and the edge of that synthesized clock, which is the expected arrival time. And so if we have a data pattern and we've extracted the clock that's embedded in that data pattern, and we use that synthesized local clock in order to measure the expected arrival time of each edge, we can literally look at each edge, compare the time interval error for each edge, and now we have this new pattern of the TIE, the time interval error, and that becomes our jitter. That is a direct measure of the jitter, and then we can do a lot of analysis with that jitter.



  

It's this time interval error track that variation in the TIE for each edge of the data that describes fundamentally the jitter in the data compared to the local extracted synthesized clock that's embedded in the data. And so it's possible then to develop an algorithm to take the data, extract the clock, compare the clock edges with the data edges, get that time interval error, and now we can do statistics on it. And that's how everything about jitter in data is really derived. That's what it's like for looking at jitter in data.



  

Looking at jitter in clocks is actually a little simpler than that because in a clock we have a repetitive pattern. We don't have to synthesize a local clock using clock data recovery. We have the actual data itself. And so we can look at the variation either in the frequency or the period.



  

They both have exactly the same information. In fact, the period is a more fundamental measurement in the time domain because it's a time interval. To measure the period in a clock is relatively simple. We just measure the time at which we see the edge pass a reference level going up, and then we pass on the falling edge, and we look at the next rising edge, and we measure that time interval.



  

And so we get the time interval for the edge crossing, the same voltage level. Jitter in the clock then is the variation in the period from cycle to cycle. Oftentimes, especially if we're doing measurements in the frequency domain, we'll measure the jitter in the period in terms of the phase. And if we know the noise in the period, the variation in the period, then the phase is literally just what fraction of a cycle that jitter is, and times 63 or if we're doing cycles, or 2 pi if we're measuring the phase noise in radians.



  

So fundamentally, if we measure the period in the time domain and the variation of the period, that noise in the period, then we can convert that to whatever form that we want. The measurement really comes down to measuring the absolute period of each cycle, recording that, and measuring it cycle to cycle. That variation in that period becomes a measure of the jitter. And once we measure the period of the clock cycle to cycle, and we get that track of how the period varies from cycle to cycle, then we can do analysis of it.



  

We can look at the statistics, we can do the histograms, and I'm going to walk you through how we actually go about doing this. Now, another really important feature of the variation of the period is the spectrum of the period. We're not going to talk about the spectrum in the webinar today because I want to tease you with that for a future webinar. We have a series of webinars coming up that are going to be discussing spectral analysis of real time signals.



  

And in one of the future webinars, we're going to be talking about the spectrum of the jitter and its impact from the spectrum of the power, a very important technique to identify some of the sources of jitter. But today, we're going to look at some of the other signatures of the statistics of the jitter and relate that to some of the features of the voltage noise on the power rail. The voltage noise on the power rail is just one of the external forces that can affect jitter. If we have a robust way of measuring jitter, then we'll be able to use that to look at the impact and the sensitivity of other features in the environment that can affect the period.



  

Now along the way, one of the things I want to introduce you to is best measurement practices. And a lot of best measurement practices are really about what I call situational awareness. Situational awareness is being aware of the features of your system you're measuring, the signals coming from it, and the features of your instrument that includes the cabling and the probes and the connectors all the way into the scope and all the other features going on inside the scope. So we can think about how is the measurement system affecting the measurements of the device you're measuring and the signals coming from that device.



  

The better we understand that entire system of the device, the connections, the cables, and the instrument, the better we can watch out for and avoid potential artifacts. And I'm going to show you a couple of these. To illustrate these principles, I'm going to introduce you to a very simple clock as our example. This is a ring oscillator.



  

And a ring oscillator is composed of an odd number of inverters in series. And you can kind of get the idea. If we have an odd number, then whatever the output is over here, that's going to be the output at the input. That's going to change state here and change state and change state, change state, change state.



  

Ah, it's a changed state. It's going to come out over here and change state. And if we have an odd number of inverters in series, then we're going to go through this constant changing of states. And the period, the time it takes to go through half a cycle, input to the output to change state, to make half a cycle is 5 propagation delays, and to do an entire cycle, or in other words the period, is going to be 2 of those cycles.



  

And so the period is roughly equal to 10 times the propagation delay of each one of the gates. And of course the frequency is 1 over the period. And so the frequency of the ring oscillator depends on the number of inverters that we have in series and their individual propagation delay. Now this particular ring oscillator we're going to use is using just a simple, you know, hex inverter.



  

If you look at the specs for it though, you know, the specs, like typical specs, are incredibly vague. The propagation delay listed, at the 5 V that we're going to use is 1.5 ns to 10 ns. That's a factor of like 6 or 7 in the propagation delay.



  

That means that the expected frequency is going to vary somewhere between 10 MHz and 66 MHz according to the spec. How can you possibly design a system based on a spec that is that wide? And of course the reason it's that wide is because the suppliers want to have a wide enough margin so that, depending on the process that they're implementing and what the parts come out that they'll get a high yield. If they use a narrow propagation spec then their yield is going to take a hit.



  

And so we suffer the consequence of that by not having a very robust parameter to design our system. And that's why sometimes we just have to buy evaluation boards or buy samples to characterize them, and why, you know, using a ring oscillator for a device that we don't have control of the process is not a very robust way of defining an important performance metric. For this particular ring oscillator, you can see the implementation right here. This circuit was designed and built by one of my graduate students, Chaithra Suresh.



  

This is her first year as a graduate student here at University of Colorado in Boulder. She's in the embedded systems engineering program, and she is, ace designer. She designed this particular 2 layer board to minimize the noise that will be generated. We still have residual noise, but it's fundamentally related to the package.



  

Not much we can do about that. This is a 2 layer board. All the high speed signals are contained on the board, and we're just going to use the signals coming off the board and a simple, solderless breadboard in order to make it easy to connect to power and to the signals, with the scope. And that makes it easy to make some changes.



  

The other instrument that we're using today is the Teledyne LeCroy WavePro HD. The instrument that I have here, it's 4 channel. We're going to use a couple of the channels. It's an 8 GHz bandwidth, analog front end, 12 bit vertical resolution.



  

We'll be using up to 20 GS/s, so keep in mind that's 50 ps as the interval between samples. That's a really important feature of our instrument to be aware of, and I'll show you the impact of it, and also the fundamental jitter in the clock base inside the scope. In this particular scope it's 60 fs. When we're trying to measure jitter, which is all about the variation in arrival time, knowing what the intrinsic limit of the scope is really important.



  

And so if you're not using a WavePro HD, using another scope, you want to, as part of situational awareness, you want to find out what are these parameters? What is going on inside your scope to understand how close to the properties of the device under test might those properties of the scope be? The first step in thinking about the scope is, you know, I always recommend, hey, when you're trying to do a new kind of measurement, you always want to measure, or when you're doing a, using a new simulation tool, you always want to measure or simulate something that you know. And that gives you a feel for the properties of the simulation tool or the performance of your scope.



  

And so I'm just going to show you this measurement, and then we're going to, I'm going to bring you into my lab here and we're going to look at some other measurements. But the first thing that I wanted to look at was, well, just how good is the time base? This is not a measure of the jitter, but a measure of the accuracy of the time base. Now, looking at jitter, it's not really about absolute accuracy; it's about the relative precision of measuring the time interval from cycle to cycle.



  

But part of that is the absolute accuracy of the scope's time base. And so I grabbed a function generator, and this particular function generator, it goes up to 30 MHz, got a sine wave. Now the rated spec for this synthesized sine wave is a part per 1000000 absolute accuracy. And so here is the measurement on the scope of that 30 MHz signal, and I'll show you how we set this up, and I'll show you what the measurements are.



  

But basically, I set it up the same way we're going to do today in the lab. And here is that sine wave we're measuring. It's a plus or minus, 2.5 or about 5 V peak to peak kind of signal.



  

And here is the frequency that we measure. So fundamentally, because we're measuring in the time domain, we measure the period of that signal, 0 crossing time intervals. We measure that period, we invert that, and that is the frequency. And we do that cycle to cycle to cycle.



  

And you can see that the frequency that we measure, the average value over, oh, let's see, that's 10000 cycles that we've taken here, the average value is 30.000028 MHz. Pretty darn close to the 30 MHz, specification accuracy of the source. And so when you put in the numbers, and here's what we measure as the frequency, the accuracy of our source is about a ppm, and the accuracy that we measure, just this quick measure, is 10 ppm.



  

So we can see that the absolute accuracy of the scope, pretty darn good. On top of that is that 50 or 60 fs of intrinsic jitter in the synthesized clock in the time base. So with that as our starting place, now I'm going to bring you into the lab and we're going to take a look at measuring jitter in a clock and how we, once we establish the statistics of it and how that jitter is affected by external factors. So I'm bringing you here into my lab.



  

Here we are. I've got the camera going here. And, we've got the ring oscillator here. We've got it powered on.



  

You've got the little light here. We've got an external 5 V on it. We're going to look at the output voltage on this pin over here, compared to a ground. Now all the high frequency signals are done on the small breakout board.



  

All we're doing is picking off the signals coming off over here. We're going to take a look at the signal on our scope. Now I'm going to tilt the camera back here so you can see the setup here. A little awkward here.



  

There's my scope over there. And instead of trying to squint and see the screen through the camera, because our scope is a Windows PC. I'm running TeamViewer on the scope and TeamViewer on my laptop, and so I can literally show you the screen and also control the scope from my screen. So that's what we're going to do in order for you to be able to see the signal.



  

Now we're going to take a look at that signal initially. Remember rule number 9, what we expect to see is a ring oscillator. It's got 5 inverters. It's going to be roughly in the 10 MHz to 66 MHz kind of range.



  

I'm going to guess it's going to be on the high end. Let's take a look at what we see on the scope. So here is the scope. Now whenever you start out with the scope beginning of the day, especially if you have multiple people in the lab using it, you'll never know what state it was left in.



  

And so always a good habit is to use the default setup. So it gets it into a state you're familiar with and then you can start from there. Or if you have been working on the scope before, you save a LabNotebook and you can bring up that LabNotebook and that will recover the exact same state at which you left the scope. Because I have a lot of students that are using the scope, not sure what the state was they left it in, I'm going to push the default setup.



  

It's not the auto setup. I don't recommend using that. It's the default setup, and that brings the scope into the, a standard, default condition. So push the button, there we are, and here we go.



  

Now, I personally like to see the display as a tandem display. It's a personal preference. I don't have anything plugged into channel 1. Instead, the clock signal is actually plugged into channel 2.



  

So I'm going to turn off channel 1. We're going to look at channel 2. I'm going to zoom out the time base. There we go.



  

Now, again, I also like to see it over on this side, so I'm just going to move that signal over to this side. And, let's see, it should be about a 5 V signal. Oh, and I want to trigger the scope on channel 2. So we move the signal over to channel 2.



  

There's our little caret for the trigger level. Boy, that's not exactly what I expected. It's going all over the place. In fact, I expected something like a 5 V signal, but gosh, there's something else going on.



  

How come? Well, that's because, again, default case, this is why we walk it through, we should be using 50 ohms because I'm seeing the reflections in the cable. So move to 50 ohms, and there we go. Ah, that looks a lot better.



  

I'm going to adjust the trigger level, move it down toward the middle, and now we can zoom out a little bit more, And there's our clock signal. Now, nice sharp edges, the little bit of variation we see on the top and the bottom, that is the noise in the package. Not much we can do about that. In other future webinars, we're going to walk through this kind of noise.



  

This is the power rail noise in the package, and this is the ground bounce noise in the package. And I'll show you how we measure it and how we know that's what the source of the noise is. But for looking at it as a clock, it's perfectly fine because we're going to be using the edges that contain most of the information. One of the first questions I want to know is, hey, what's the rise time?



  

And so I'm going to expand, and we're going to take a look at what that rise time is. So I'm going to zoom in on the edge, and let's see. We have nanosecond per division, and that rise time is, you know, a little bit more than a nanosecond, 1 or 1.5 ns, something like that. Once we have an idea of what it is, we can have the scope measure it for us, roughly about 1.5 ns.



  

While we're doing that, again, situational awareness, be aware of the condition for the scope. So we're sampling at 20 GS/s over here. We want to keep that, we want to maintain that. And so I'm going to come over here and in setting up the scope, I'm going to tell it, hey, I want a sample rate fixed.



  

I'm fixing the sample rate. I want it to be 20 GS/s so that we have the highest resolution. We'll see the impact of that in a moment. We can also get a rough idea of what the period is.



  

Let's see. So we go through the beginning, the middle of the we go through the middle of the rising edge here. We go 1, 2, 3, about 4 divisions, and then we see it going up again a little bit more than 4. That's 5 ns of division.



  

That's 20, maybe 21 ns is the period. So the frequency, whenever that is about 48 MHz, is roughly the period. Given those rough estimates, we can now use the scope to measure those for us. So I'm going to turn on parameters.



  

Let's see how I'm going to use my parameters. Personally, I like using statistics, and we're going to see the importance of that here for today. Now let's see. I want to measure the rise time first, so I'm going to select this parameter.



  

I want it to come from C2, which is the channel that has the clock in it. And I want to measure not the amplitude, but I want a horizontal measurement, and that's going to be, the rise time. And so let's see. Here's rise time.



  

Okay. And, hey, I estimated about 1.5 ns, and sure enough, we're getting about 1.4 ns as the rise time. The second metric I want is the frequency. Of course, it's going to measure the period first and then get the frequency.



  

So let's also go from channel 2 into frequency. Hey, 48 MHz, just about what I estimated. And now let's add the period, because that's the one that has most of the valuable information that we're going to use to get the jitter. So I'm going to create another parameter, and, let's see, I want this one, this is parameter 3, also coming from channel 2, I want that to be the period.



  

And so here we go, here's the period. And now we can see, hey, it's about, I estimate about 21 ns, 20.7. Here's the average value, 20.788, you know, pretty stable, depends on the number of cycles that we've got, and then here's the important term, here's the standard deviation.



  

So 6 ps of variation in that period. The number you want to pay attention to, that 6 ps to kind of think about the artifacts introduced, is the sample rate, which is, 20 GS/s. So that's every 50 ps we're taking another measurement, and we're measuring a variation of 6 ps. That means that, when we look at that rise time, which is about 1.3,



  

1.4 ns, and we're sampling at 0.05 ns, we've got something like 20, 25 points per rise time. And to get that 6 ps or sub 6 ps resolution, in order to see the variation, we're doing interpolation between the individual data points. The second term to be aware of is, okay, this 6 ps, how close to the edge of the fundamental jitter in our scope are we?



  

Remember the scope jitter is 60 fs, so we're well away from the fundamental limits in this scope. And so this is probably a pretty real number. It may be close to the edge of what we can measure, and I have to say I've looked at a number of different clocks trying to find a low jitter clock. I see a lot of variation.



  

I haven't found a clock that has jitter less than about 5 ps, and I think that's more about the clocks that I'm using than about the scope itself. So I think this is a real number, and we'll see the impact of some of the features in the scope. Now this is measuring 1 cycle, and then it's going to take another acquisition, another acquisition, another acquisition. I want to see the variation of this period over a long period of time.



  

And so I'm going to increase the time base, and every cycle we're going to be measuring that period. So let's increase the time base. Remember, I set it for keeping the acquisition time constant. So if we increase the time base, we're going to collect more points, and that's going to take longer in order to do the analysis.



  

So it's going to be a balance of how many points, how long that time interval, and what our sample rate is. So let's increase the timebase, and as we increase the timebase, we're at 50 ns per division, Pay attention to we're still at 20 GS/s, we're at 10000 samples here, we'll go up some more, we'll go up some more, we'll go up some more, we'll go up some more. Wow. We're at a 1000000 samples, and we're still acquiring the data, doing that measurement of the period at each point, displaying that information here, and doing that in real time.



  

So we're going to go up one more click. So we're at 4 mega samples, still at 20 GS/s. And I find somewhere in the order of 2000000 to 4000000 samples is a good buffer size that gives us a nice time interval. If we increase the time interval more, we get more points, but it just takes longer to do the analysis, and so I want to show you in real time some of the variation.



  

So we're at 4000000 cycles, we're calculating the period, and look, we're still at about 6 ps as the standard deviation of the variation in the period. So that's 6 ps out of 20 ns, so we're at about a 0.03% variation in the period. Now that we're on this 200 ?s full scale setting, we can't see the data anymore. We can't see what that waveform looks like.



  

And so I'm going to zoom in just a little bit here in the middle, and we're going to grab a zoomed version of that data. So here is that zoomed version. We're looking at, that's in zoom 2. And we'll keep it the zoom 2, so it's kind of the pink color here.



  

We'll keep it on. And now I'm going to adjust the scale so it brings it on scale. And then to do that, let's see, the vertical scale, we use the same scale that we've got the measurement on. We're at 1 V per division.



  

There we are. And we're going to change the offset here. We're going to center this at 0. There it is.



  

And now we're going to zoom out. So we're going to change the horizontal scale. We'll also center this at 0. And now we're going to zoom out, in order to see that data in more detail.



  

Okay. So we're taking the data in real time, we're taking 4000000 points, we've got the data in the background here in that grayed out region, and now superimposed is each cycle, and that gives us a sense of what the data is doing. And now we can see, well here is the period. We're measuring this on every single one of those cycles in each acquisition and then updating it. And you can see that, here's the information.



  

Now we're ready to do some of the statistics on this data. Here's the information that we want to act on, and really the most important information is the period and the variation in that period. So what we want to do is first look at the track. The track is the value of the period for each cycle plotted in real time along with the data.



  

So let's take a look at that. So we come over here to our measurement. We're going to look at the track, that's the variation. Let's see, we're already using zoom 2.



  

Let's use zoom 1, to describe the track. So here is the track. This is the measured period for each cycle plotted over the same time period as the data coming in. So if I just superimpose them here, as the data comes in and we've got our 200 ?s full scale, that means if the period is about 20 ns and we've got 100 ?s, that's 5000 cycles we're measuring, and we're plotting each, the period of each one of those cycles here, versus time in the vertical scale.



  

And you can see the variation, the scale is 10 ps per division. Now just eyeballing it, we estimated about 6 ps as kind of the standard deviation at 10 ps per division. You know, it kind of sort of matches that. It's consistent.



  

But you know, it sure would be nice to see the histogram of the variation in the period cycle to cycle. So let's turn on the histogram. So I'm going to click to turn on the histogram, and let's see, we've got that in that track. Let's use, let's use the, the F3, in order to store the histogram.



  

So here is the histogram, and here it is displayed, and we're going to change a couple of the features on it. So personally, I like, you know, only 1000 points. That's not enough. I mean, we're taking so much data - 5000 per acquisition. So let's change this to, again, I find about 20000 values in each histogram is a reasonable compromise to give us a nice distribution, and we're taking it pretty fast. So there we are.



  

And we're going to automatically center it, which it already is. We have it set up here to automatically find the center and adjust the scale. And we're at 10 ps per division. And let's see, so we have 100 bins, so over this whole interval here of 100 ps, we have 100 bins, so that's 1 ps per bin.



  

And sure enough, here's the 10 ps. Remember, we're measuring a standard deviation of 6 ps, and a standard deviation really only makes sense if we have a Gaussian distribution, and you can see that's a pretty darn good Gaussian distribution. If the cause of the jitter in our clock is random causes, we'd expect a Gaussian distribution, and that 6 ps is a good measure of it. So that's roughly around here.



  

And you know what, that's a pretty darn good match to our full width half max for the Gaussian distribution. So everything seems to be consistent. We've got a Gaussian distribution in the jitter. We've got about 6 ps.



  

Now we have a metric of the jitter. Here is that track of that jitter. We can do statistics on it. We can look for patterns.



  

In a later video we're going to look at the spectrum of this jitter as well, and compare that to the fingerprint of the spectrum of other noise sources. One of the first measures of the impact of the jitter that we're going to look at is the sample rate. Remember, we're at 20 GS/s and we're at 6 ps as the RMS. Let's see what happens if we change that sample rate.



  

This is part of situational awareness. This is part of investigating scope on our measurement. So we've got a fixed sample rate. Let's decrease that.



  

Let's go to 10. So remember that number, 6 ps at 20. Here we are at 10 GS/s, and I'm going to start over, clear the sweeps. We've GS/s.



  

And I'm going to start over, clear the sweeps. We start over again, and we're at, about 5.8, about close to that 6 ps, not much change. We go to 5 GS/s.



  

Not much change. We're at 6.1 ps. I go to 2.5 GS/s. So remember, that's about 400 ps per interval, and remember we get about 1.5 ns as the rise time.



  

So we're looking at, oh, about 3 or 4, points per rise time, and we're able to interpolate pretty well. Look at that. 6.5 ps as the standard deviation.



  

Let's go down some more. So we're at 1 Gsample, per second. So that means 1 ns. And that means we really, gosh, we can't even measure the rise time very well.



  

We can see the; here's our zoomed image. We can see the signal, but you can see the individual data points on that edge. We can't get a good measure of that rise. And look, our histogram is grossly distorted, and our RMS is really high. So that says don't use a Gsample per second, it's way too short a time interval.



  

In fact, we didn't see a whole lot of variation from about 5 GS/s, or in other words about 200 ps. We need a few points per edge in order to do an accurate interpolation of where the 0 crossing time is. And so that gives us confidence that, hey, you know what, 20 GS/s is below the threshold at which the sample rate is affecting the measurement. So we have confidence in the quality of the measurement at 20 GS/s.



  

Important artifact to watch out for. Now let's take a look at the sensitivity of this jitter on external forces, and in particular we're going to look at the voltage sensitivity of the power rail. We're going to look at the sensitivity of the jitter on the ring oscillator from the voltage variation on the power rail. And to do that, I'm going to connect the power rail to a function generator.



  

And that's going to generate a nice, square wave. It's going to have a, that's going to generate the DC voltage level for the power rail, about 5 V. And we're going to modulate that by, you know, a few 100 mV on top of that. We're going to look at how the period is affected by that voltage.



  

And, of course, we expect some variation because, of course, the propagation delay depends on the voltage. The higher the voltage, the faster the gates are going to switch. The shorter the propagationally, the shorter the period, the higher the frequency. And so we're going to see kind of an inverse relationship.



  

A higher voltage means a shorter period. A lower voltage means a longer period. And we'll measure that sensitivity. And that's why voltage noise, that is unintentional variation on the power rail, voltage noise is going to affect the period because of that sensitivity.



  

If we measure that sensitivity, we'll know how much period noise to expect given the voltage noise on the power rail. So I've got a function generator, and in channel 3 of the scope, we're going to measure that voltage in the function generator. We're going to set it up, and then we're going to drive our device with that voltage. So here's our scope again, and we're going to look at channel 3, and that's going to be the voltage from the function generator.



  

So let's turn on channel 3. We're going to turn that trace on, and I'm going to put it over on this side. And, again, because we're looking at the voltage on the power rail, I'm going to use 1 M? input. We're going to look at small voltages.



  

So I literally just have a direct connection to the function generator. It's going to be low frequency stuff. We're going to use the 1 M? input. And now let's increase the scale so we can see it.



  

It's a 5 V DC level with a little bit of modulation on top of it. And sure enough, there it is. I'm going to move it down so we can see that modulation in a little bit more detail. So there is the 5 V level, a little bit of modulation.



  

Now we're going to expand the voltage scale so we can see that. And there is the variation. Now, I've got the output, the sync output of the function generator going to the external trigger of the scope, and so let's trigger the scope now on that modulation. So I'm going to go to the trigger, I'm going to go to the source being external.



  

And now we can see it synced up, and we're measuring the signal coming off of the function generator. This is now going to be the DC voltage or the power rail that we apply to our device. I'm going to switch out the power source that was coming from our nice DC supply, and now we're going to take it from the function generator. Okay, and now we're driving the oscillator with the function generator.



  

-oh, what happened to our signal? So let's go back and adjust the scale a little bit. So we've got an offset here. I'm going to go back to 0.



  

I'm going to zoom back in. My gosh, look, the voltage has dropped. I mean, it was 5 V. And now when I connected it in, we're down to, you know, a little like 3.5 V.



  

What happened? Part of situational awareness is thinking about our device under test and the rest of the system and what's going on and how consistent that is with the measurements. So let's go back to the slides for a second, and I'm going to show you what's going on with our system. So here is kind of a simplified, equivalent circuit model for the system.



  

Here's our function generator. Every voltage source can be thought of to first order at least as a Thevenin voltage with a Thevenin resistance. And here's our device under test. This is the little ring oscillator circuit.



  

Well, that ring oscillator represents a current load or resistive load to the power supply, and so here's the equivalent circuit. This resistor, the Thevenin resistance in most function generators, is about 50 ?. That means when I attach a load to it, if that load is on that order, we're going to have a voltage divider and the voltage on the rail is actually reduced quite a bit. In order to use the function generator with this load, I have to up the voltage over here in order to arrange for the voltage across the power rail to be that 5 V.



  

So that's our next step is by monitoring the voltage, I'm going to adjust the offset voltage and then the modulation so we get the modulated signal across the load. So let's go ahead and do that. So here is the scope, measurement. And to help me kind of measure what that average voltage is across the load, that's in channel 3, I'm going to create a new parameter.



  

And that new parameter, I'm going to set that as, see, coming from channel 3, and I want that to be the average or the mean. That's a vertical measurement. So I want it to be the mean value for that voltage. So here's that DC voltage.



  

It's about 3.3 V. And you can see this is where, looking at the signal coming in, it's still oscillating. There it is oscillating. Of course it's not, we're not triggering it, we're triggering on the 10 kHz sync signal coming out of the function generator.



  

But you can see that waveform, it's an okay waveform. We're getting some jitter, coming out here, pretty large jitter, 31 ps, and you can see, gee, there's some variation in that jitter. Wow, we're already seeing the impact of voltage noise and voltage behavior on the jitter. Well, let's up that voltage to 5 V, and let's modulate that waveform.



  

So we're going to change the offset, and we're going to go up to whatever offset we need to give us 5 V. And so we're reading the average value, and there we go. So we got about a little bit over 5 V here. And now I want to change the offset, in order to get us about, plus or minus 100 mV or about 100 mV peak to peak as the modulation.



  

So I'm going to bring this down to the center, and now I'm going to expand on that, and we'll go to, let's use 100 mV per division. -oh. Gosh. Can you see that?



  

Look at all of that noise. This is the high frequency noise that the ring oscillator is created on the power rail. That's because we've got this as the ring oscillator transitions, we've got the changing load given the 50 ? of the source and the changing load. That's generating voltage noise.



  

Look, we're on 100 mV of variation. That variation is swamping the modulation that we want to see. How do we get around that problem? Well, remember it's a measurement problem, and so we're going to take advantage of a feature in the scope to filter out that very high frequency.



  

Remember, that's about 48 MHz, almost 50 MHz of a first harmonic and then noise above that. That's all coming from the noise on the power rail. And just to demonstrate that, we're going to trigger on the ring oscillator. So now we're triggering on the ring oscillator, and now let's zoom in to see the noise on the power rail that it's really synchronous with the ring oscillator.



  

So we come over here and we're going to zoom in on the time base, and we'll move that ring oscillator coming out here. And now you can see here is the ring oscillator and here is the noise on the power rail that is coincident with the, and synchronous with the ring oscillator. So this is clearly pollution noise from the ring oscillator on the power rail. And when I'm using my function generator to modulate the voltage on the power rail, to see that modulated voltage, I want to filter all that out.



  

I want to look at the low frequency components. Our function generator is modulating at 10 kHz. That's the square wave signal that I want to see, and so I want to filter out all this 50 MHz stuff. And so here's how we're going to do it.



  

First, let's go back to the timescale that we had. So we're at 200 ?s full scale. We want to filter that out. And the way we're going to filter it out is we're going to create a little math function.



  

So we're going to filter that voltage noise on the power rail. So we're going to add a little math function here. Let's see, we want it to be the voltage on the power rail, and the function that we want is we're going to add a filter to it. So let's see, here's a filter.



  

We're going to do a simple low pass filter. We want to filter out that 50 MHz signal, and so the filter that we're going to use is going to be, I like Butterworth as a really standard one, we don't have to do anything fancy, we're going to use a fourth order, really common, and the cutoff frequency, if I make this, so our noise is at 50 MHz, we're going to modulate the power rail at 10 kHz, So if I use a low pass filter with a pole frequency of about 1 MHz, that should eliminate all of the high frequency noise and let through our 10 kHz modulated voltage noise. So let's make this 1 MHz.



  

So it's 1 MHz. And now, this is going to be the signal coming through. So let's move everybody over. Here is that low frequency voltage noise on the power rail.



  

And to see that a little more clearly, now that we've got an idea of what's going on, we're going to change the scope trigger to trigger on the function generator so we see that modulation. So we go back to the scope and the trigger. We're going to make the source now the external. So we trigger on it.



  

And now you can see that pattern. But wait a minute. I'm going to move that up in the middle. Let's zoom in.



  

We're already at 100 mV per division. Wait a minute. Remember, we had set the amplitude to 100 mV peak to peak, and yet we've got a lot less than that, and it's not a square wave. It's not much of a square wave.



  

What's going on? In fact, if I were to kind of zoom out on this, that's not much of a square wave. It looks like a triangle wave, and it's a pretty low amplitude. Here's 20 mV per division.



  

Of course, you know, while we're looking at this, we can see that, gosh, you know, the jitter and that noise are pretty darn coincident. And so we can see right off that there's a definite connection between the voltage on the power rail that we're measuring here directly and the jitter. We see the low, the high frequency jitter, this is the random jitter, and that's being modulated inversely with the voltage noise on the power rail, exactly like we expected. How come it's not the square wave that we expected to see?



  

And that's because we have on this package, we have a decoupling capacitor over here, so about 10 ?F. And remember, we've got a 50 ? source driving that square wave into the power rail, and across the power rail we have 10 ?F of capacitance. That 50 ? and the 10 ?F makes a 0.5 ms time constant. And so we're seeing the voltage increase on the capacitor as the RC charging that capacitor.



  

At 10 kHz we have a 100 ?s as the period, and we see that here. And that means that we have 50 ?s as half that period, but wait a minute, the time constant is 500 ?s, and so we're only going to see the very beginning part of the charging of the RC. Again, situational awareness, being aware of what we got. If we use our device with no decoupling capacitor then we would be able to see the square wave variation.



  

But even this we can still use. Let's increase the square wave amplitude. So now we have a little bit more voltage, and you can see the modulation of the voltage on the power rail and the jitter in the clock. And we can read literally off the front screen, we've got about 20, 40, 60, 80 mV of peak to peak voltage noise.



  

And if we click and highlight, we've got about 50 ps per division. So we've got about 1, 2, 3 divisions. That's about 150 ps of jitter, and so you can see we have a 150 ps of jitter for about 80 mV of peak to peak of voltage variation, and that corresponds to about 2 ps per mV of jitter sensitivity. Now we have a direct measure of the jitter sensitivity of our ring oscillator.



  

It's about 2 ps per mV of voltage rail noise. If we know what the voltage noise on the power rail is, we can get an idea of how much jitter and the impact on jitter we expect to see. I've got another power supply that has a little bit more noise on it. Let's take a look at that.



  

I've just plugged in another power supply to the ring oscillator. It's an AC to DC converter, and you can see that it's generating some periodic variation in the jitter as well. It's also on the same order of about 10 kHz. This is the switching frequency of the switch mode power supply in this converter.



  

And you can see that the peak to peak value of that modulation, oh, we're looking at something in about 2 divisions here. That's 20 ps. And remember our sensitivity of about 2 ps per mV, about 10 mV of voltage noise on the power rail on, after the low pass filter. Well, we expect about 10 mV of noise on the power rail, and sure enough, you can see, if I expand the scale just a tad here, so we are at 10 mV per division, and you can see, again, just about 10 mV peak to peak voltage noise on the power rail.



  

And so you can see in this technique we've taken advantage of many of the features of the scope in order to quickly and simply measure the jitter in the clock, the variation of the jitter with voltage on the power rail, and the jitter sensitivity to voltage noise, and now looking at an external power supply that has, voltage noise on it, and measuring the voltage noise on the rail, and being able to roughly predict how much voltage noise we're seeing for the amount of jitter, that we measure. So let's wrap everything up here. We're basically out of time. I just wanted to illustrate for you in this webinar how we measure jitter in clocks using that precision timing of the period, and it's the variation of the period from cycle to cycle that is the jitter in the clock.



  

And we saw that when we minimize the external forces, that clock jitter in this case is mostly Gaussian, and the standard deviation is a good metric of the clock jitter. And once we establish a simple way of measuring the clock jitter using the track of the period, we're able to modulate some of the external forces, in this case the voltage on the

power rail, and measure the sensitivity of the clock jitter to that power rail voltage. We took advantage of a lot of features on the scope to simplify these measurements in real time. We took advantage of using parameters to get the period, getting the statistics from that, the standard deviation.



  

We were able to generate the histograms to look at the distribution. We could look at the tracking that gave us the pattern or the signature, the fingerprint of the jitter variation, and we can compare that to the fingerprint of other features, in this case, the power rail voltage. And we also took advantage of, in this case, the low pass filtering to eliminate the high frequency noise so that we can see the underlying modulation of the voltage on the power rail in order to look at the voltage, to look at the jitter in the clock. And we also, I purposely, used a couple of features in our system that produced artifacts so that we could be aware of those artifacts and practice situational awareness.



  

These are the kinds of consistency tests we always want to be doing in order to gain confidence in the measurements so that we can use our scopes for answering those important, so what questions and have confidence in the results. Now, in this presentation today I used our WavePro HD scope. Whichever scope you use, be aware of the important figures of merit of the scope to see how they affect the measurement of the device under test. And then finally, I want to bring your attention also to all the other webinars that we have.



  

Today, we focus on this very specific feature of jitter. There are a lot more topics of jitter that we can cover. We have other webinars on demand about jitter that you'll

be able to browse through, going to our events, landing page.

And we'll be talking more about spectral analysis of signals and jitter in later webinars.



  

And then finally, you'll want to download a copy of MAUI Studio to your PC. We have built in a function generator, and all the measurements that we did here in terms of looking at, period, looking at the statistics, doing the tracking, doing the filtering, all of those features you can practice with using the version of the MAUI Studio that'll run on your PC. And with that, I'm going to turn it over to questions, and thank you very much for your time today. Okay.



  

Let's see. I'm hoping you can hear me. Is that okay, Hilary? Yep. We can. Okay.



  

Good deal. So, we've got a lot of questions that have come in. I only have a couple minutes to answer the questions right now, and so I'm going to take a couple of them. And rest assured, we have the list of questions.



  

I'm going to take those questions. I'm going to type out my answers, and then Hilary is going to post these, you know, kind of frequently asked questions on the landing page for this webinar. And you'll get a link, in an email with the link to the recording, the handouts if you didn't already, grab them, and also the questions. So let's get started.



  

I'll answer a couple of these. Let's see. Here's a question. Hitesh is asking, when you measure phase noise, why is it specified for band of frequency, like 12 kHz to 20 MHz?



  

Well, we didn't really talk about the spectrum of the jitter, and we're going to do that actually in another webinar. When you look at the spectrum of the jitter, you're going to see some frequency variation. If nothing else, if it's random, you'll see a flat spectrum. Maybe it'll have a little 1/f noise.



  

So it'll be with some noise for this kind of a pink spectrum, and so you'll be able to see the specific features in the spectrum. And if there are, because of either internal noise or external noise, there may be some peaks in that spectrum. And so, because of the spectral variation, we sometimes refer to the value of the jitter or the jitter density in different frequency ranges. So that's a common metric, and we'll have, be sure to include that in one of our future webinars.



  

Okay. So someone was very observant, and he and Shiva says, hey. When I looked at the clock signal that was measured by the scope, it was only a 4 V amplitude. I thought it was supposed to be a 5 V amplitude.



  

Well, okay. You have a very sharp eye. Yeah. It was supposed to be a 5 V amplitude.



  

The reason was only 4 V is twofold. One is, there was noise on top of the signal, and so you have to be careful where you look at, what that voltage is. It was actually about 4.3, 4.4V.



  

That difference, though, in why it wasn't 5 V, is related to the voltage drop on the output transistor, the p channel that was turning on and driving the signal. So that was just a little bit of voltage drop on the rails for the output driver. But, you know, those are the kind of questions you want to be asking. Those are important consistency tests that we always want to be looking at to verify to make sure that it's not something else.



  

It's a more serious problem. Let's see. Another question from Talal, is the rise time in the scope from 10-90 or 20-80? Very good question.



  

Always want to be aware of which one of those it is. For these particular measurements, because it was a nice kind of linear edge, I was using a 10-90 rise time as a figure of merit. And, because it didn't, the rise time itself didn't affect the period. It wasn't too important whether it was 10-90 or 20-80. But in this case, it was a 10-90 rise time.



  

Let's see. Okay. So Usman is asking, I'm just wondering, to measure a 48 MHz signal, why do we need 20 GS/s? Okay.



  

So that is a very good question because we're not trying to measure the frequency per se. What we want is the period, so it's not a question of the kind of bandwidth of the signal. We're not looking to see, okay, you know, if it's you know, depending on the rise time is the fifth harmonic or is the bandwidth of the measurement high enough to see that 1.5 ns rise time signal.



  

The real issue is the resolution of the rising edge, and we saw that when we use 20 GS/s, the sample rate was 50 ps. If our edge is relatively linear in the middle where we're looking at that switching threshold, if it's real relatively linear, then the time resolution isn't so important because we're interpolating where that edge is. And if it's a linear edge, then as long as we have, you know, a few points along that edge that define it, we can interpolate where the center of that transition is. But we saw that, gosh, when we went to, at about 5 GS/s, that meant 200 ps per sample interval.



  

That was enough resolution. We could get a good interpolation of where the center crossing is. But if we went to a slower data rate, 2.5 or even 1 Gsample second, that lower data rate, we could not interpolate very accurately where the center crossing is.



  

And so that's why situational awareness, being aware of the feature being aware of the features of the scope, and in this particular case, the sample rate of the scope is really important because that's going to tell us our ability to resolve where that 0 crossing is. And if we have a nice linear, ramping edge near the center, then the exact number of points we have is important to all give the same interpolated, rhizome, and that's exactly what we saw. And so if it's free, if it doesn't cost anything and you have it, hey. Why not use that higher sample rate?



  

Just gives us that little bit of extra margin. But you always want to be aware of what is that minimum sample rate you need so the sample rate does not create an artifact in interpreting where that 0 crossing is. Okay. Okay.



  

I'm going to call the clock. You're going to pull the hook out? Pull the plug. Yep.



  

So, everyone, thank you so much for joining us. Like, Eric said, we will go ahead and transcribe all the questions. He'll give us answers. We'll post it on the same page as the recording, and for those of you who asked, this was recorded.



  

We will send out a copy of the on demand and the slides within the next 24-48 hours. You'll get an email from me automatically. There's nothing you need to do to get that. If you come up with any other questions, please go ahead and email us.



  

And as Eric mentioned, this is going to sort of kick off the first in a new power integrity related series, so check out your upcoming emails. I'll be sharing the details on that and we appreciate all of you, your time and attention. Stay safe out there, healthy, and enjoy the rest of your day. Thanks, Eric.



  

Okay. Thanks, Hilary. Thanks, everybody, for joining us today. Bye bye.