Thank you everyone for joining Teledyne LeCroy today for our webinar on Reading S-parameters Like a Book Part 2 presented by Dr. Eric Bogatin.

A little bit about Teledyne LeCroy before we begin. We were 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 US and 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. We became part of Teledyne Technologies, and our name changed to Teledyne LeCroy.

For those of you unfamiliar with Eric Bogatin, Dr. Bogatin is now a Teledyne LeCroy fellow.

He has produced over 200 hours of training material for the Teledyne LeCroy Signal Integrity Academy while also teaching at the University of Colorado in Boulder in the engineering department and presides as technical editor of the Signal Integrity Journal. We know there are a lot of demands on your time. We appreciate you spending this hour with us. I'm now going to turn the presentation over to Eric.

Thank you for that kind introduction, and welcome to today's webinar. This is part 2 in our series of How to Read S-parameters Like a Book. Really, what I want to do is introduce you to some of the patterns that we're going to see in the insertion and the return loss, and how to see those patterns in the S-parameters and think of the interconnect structures that create those sorts of patterns. In Part 1, we introduced some of the fundamental principles of how to interpret insertion and return loss and we looked at a number of examples of measured S-parameters and how to interpret those behaviors.

In today's webinar, we're going to continue that process and we're going to look at the specific structures that give rise to dips in the insertion loss and how we interpret them in terms of resonances in the interconnects. I'm going to give you a very brief introduction to how to think about these resonances as interference patterns. We kind of touched on that in Part 1. And then we're going to look at a couple of different types of resonances that we commonly see in interconnects.

I'm going to show you about series resonances, stub resonances. We'll look at coupling to high Q structures and then I'm going to show you a couple of examples of what look like resonances in the insertion loss but really aren't resonances in the interconnects. There are other reasons why we have these structures. I call them kind of fake resonances and we'll see how when we look for these features in the S-parameters, we can then get an idea of what kind of structures and what features in those structures must be causing them. We'll finish up with a little summary and then we'll open the floor for questions.

Let's take a quick look at this idea of resonances as interference patterns and then we'll continue looking at other types of resonances.

Remember from part 1 we talked about where return loss gets its ripples and we said it was really about the interference between reflections from the front surface of the interconnect and reflections from the back surface. That was kind of a general case of a resonance that when we have a maximum in the return loss and minimum in the insertion loss that means that we have the signal that's bouncing back and forth. Every time it bounces back and forth and comes out the front they add together and we get a peak in the return loss and we see the dip in the insertion loss. That's the general case of resonances.

It is due to bounces between two or more discontinuities in the structure. They have some spatial separation and depending on how large the magnitude of the impedance discontinuity at the interfaces are determines how strong the resonances are, how deep those dips are in the insertion loss or how high the peaks are in the return loss. And we saw that the larger the impedance discontinuance at the ends, the more reflections we have at each interface, and the higher the return loss peaks and correspondingly lower insertion loss dips. It's important to keep in mind that when we talk about the resonant frequency the frequency at which the waves are bouncing back and forth inside the cavity kind of reinforcing each other so they either cancel out in the forward direction or add in the reverse direction that resonant frequency depends on the length of the interconnect and is seen as peaks in the return loss dips in the insertion loss.

Here's that first example. If the impedance difference is really small then we don't have much depth to those peaks or dips. We don't have much coming back. You don't need me to tell you of course that this is the return loss and this is the insertion loss.

The peak in the return loss that's the resonant frequency when the wave is bouncing around on the inside, reinforcing what gets reflected and canceling out what gets transmitted.

And of course if the peak is and the return loss is below roughly about -10 dB don't expect to see any impact on the insertion loss. And as we increase the impedance difference on the ends we see more reflected at the peak resonant frequency. And when it's above -10 dB we're going to expect to see that impact on the insertion loss. And then of course we have a really big impedance difference. Then we see a large reflected peak in the return loss and a correspondingly larger dip in the insertion loss. And this is what we covered in part 1 where we looked at why do we see ripples in the return loss. It's all about the resonances in the interconnect between those two discontinuities.

We're going to take this principle to the next step and I'm going to introduce you to three types of interconnect topologies or structures and the resonances that they can create. First we're going to look at series structures. That's kind of what we looked at before. We had two. We had a uniform transmission line with two discontinuities on the ends and we saw the resonance when the signal is bouncing back and forth. Well we can have more than two of course. We can have multiple discontinuities but they're still in series.

There are two kinds of cases. One is when the spacing between the discontinuities is equal. In other words they're kind of periodic. They occur at a uniform spacing. In that environment the reflections will reinforce each other at a specific frequency and enhance the magnitude of the dip and make it a narrower dip where if we have multiple discontinuities, but their spacing is kind of random, we're still going to have interference between them. But those interference patterns the ripples between the discontinuities will combine together and give us a different pattern depending on what that spacing is between the structures.

Those are series discontinuities. The principles are identical to what we've talked about, just enhanced.

The second topology is a stub topology or a shunt. We have a uniform transmission line with a small section going off from the middle. And in this environment, the resonant structure is that stub and that's going to cause again the same kind of pattern of dips in the insertion loss peaks in the return loss. But we'll see that the shape of those dips is a little different. It's because of the multiple balances in here. We'll see that it is going to be enhanced dips.

And then the third pattern that we're going to look for due to resonances are from what we call high Q structures. These are structures that there is some coupling between the uniform transmission line and there is very little loss in that structure. Once energy couples in it's going to bounce around rattle around very little energy loss and we're going to find those are very narrow frequencies at which we have the dips in the insertion loss. We're going to look for the patterns in the insertion loss and try to associate which kind of structure is causing those patterns. And I'm going to show examples of each of these. Let's start out with the first one and we'll look at resonances from series discontinuities and multiple discontinuities.

And then we'll address stubs and look at high Q structures.

What we're going to find when we look at these series resonances is that there are generally five features. We're going to see that the magnitude of the peak in the return loss depends on the impedance difference. The larger the impedance difference in those discontinuities the larger the peak in the return loss. And of course the correspondingly larger dip in the insertion loss. But of course we're only going to see that dip in the insertion loss if we have enough energy reflecting back to affect the transmitted signal and that's roughly that -10 dB point. And we reviewed that in part 1 in detail.

The first resonant frequency is going to be related to the space between the discontinuities. It's going to go 1 over the spacing. In other words, if we bring those discontinuities close together we make the spacing shorter the frequency span for the first resonance and the later resonance is going to increase. There's that inverse relationship.

If you see frequency spacings between the dips as really close together that means that they're really small frequency between them. We're going to see correspondingly longer distances between those discontinuities when we look at the physical interconnect. At a glance at how often those resonances occur in the S-parameters, we can get a rough feel for where those discontinuities must be located or how far apart they are in the actual interconnect. And we're going to see multiple resonances roughly that are they start out at the first frequency and then they're going to go to 3 times the first frequency and then 5 times and then 7 times that first frequency.

And what we'll find is when we have multiple discontinuities with different spacings, gosh, that's going to make our interpretation more difficult because we're going to see multiple periodicities. Let's take a look at this behavior. I'm going to show you first a simulation so that we can create an ideal system and then I'm going to show you what real S-parameter measurements look like and how we interpret those measurements in terms of these simple patterns.

We saw before that if we have a uniform transmission line that's a different impedance than the ports but it's uniform that the return loss is going to be pretty flat. And only if that return loss is large enough will we see an impact on the insertion loss. And from the very tight spacing for the ripples in the return loss you can tell the glass oh this must be a large structure with discontinuities far apart.

If we take another structure that's a lot shorter but a larger impedance difference from the port impedance, we're going to see a larger peak impedance. And because it's physically smaller the spacing between those peaks is going to be farther apart.

If we take a structure a composite structure that's composed of a uniform transmission line and these small large discontinuities at the ends of the transmission line we're going to see a combination of that uniform pattern kind of not exactly convolved but in a complex matrix math way a multiplication of the uniform part plus the the larger frequency spacing between the dips. And here's what that structure looks like. We see that the modulation of the tight spaced frequency S-parameters for the uniform line modulated by the very short spacing of the discontinuity and the large frequency variation that we would see for that short discontinuity. We see a combination of periodicities in the frequency response for the return loss and the corresponding insertion loss. And again it's only when the return loss is above that -10 dB point that we see an impact in the insertion loss. When we see multiple periodicities that's an indication we have multiple discontinuities.

Let's take a look at an example of this. Here's that structure that we saw. We see the two periodicities corresponding to the long uniform interconnect and those very small discontinuities and of course the small discontinuities because we're getting enhanced reflections across the middle they're giving us enhanced return loss and enhanced when we hit the resonance of those small structures.

But suppose that when we looked at the S-parameters, we didn't look at all the S-parameters. Suppose we only looked at this part of the S-parameters.

Then we would say wow look at that. The return loss is increasing with frequency. I see the modulation that I expect to see because of a large space in between discontinuities.

But look, it's increasing as we go up in frequency. What could possibly be causing that? Well we know what's causing that. It's the fact that we have two different size structures. Each one contributes a different periodicity.

But if that's all we saw it'd be hard to interpret that. And here's a perfect example of that.

This is the measured return and insertion loss for a short transmission line with discontinuities on the ends. Here's the TDR response and you can see the launch on this end and the launch on this end. You see large discontinuities and we're going to see the modulation of just the launch by itself plus the modulation of the reflections, the series resonance between those discontinuities.

And we see the increased amplitude with frequency for the return loss. That's because of the modulation of that very short discontinuity and the resonance of that short discontinuity.

And we see the impact on the insertion loss. We see that when we're below that -10 dB level hardly any impact at all on the insertion loss is when we get above that -10 dB that's when we start seeing a large impact on the insertion loss. This is a case where we are only seeing the low frequency part of the S-parameters and we're only seeing the beginning of the modulation of that short discontinuity. Now of course in this structure we have other complications.

We have this very sharp dip here at about 18 GHz and that corresponds to the circular mode of the SMA connector. Nothing we can do about that in these structures that we're measuring. It's another type of resonance and you see that the characteristic of a high return loss and a dip in the insertion loss. If we didn't have that cutoff frequency in the low cost SMA connectors we're using we would see that same periodicity in the return loss because of the short discontinuities that we have on either end.

Let's take a look at two other structures that are similar, that illustrate the principle of the spacing between the discontinuities and the impact we see in the frequency domain. Here's a short transmission line structure on a board measuring with our WavePulser 40iX. This is the structure that we saw just a moment ago. It's about an inch across.

But remember we saw those discontinuities at the launches and that gave us that longer frequency modulation.

And we see that the spacing between these ripples is relatively far apart. It's about 4 or 5 GHz between the spacing. We see the gradual increase in the return loss because it's part of an interference pattern of that short discontinuity.

If we make that structure longer, we're going to compress those ripples because of the large spacing between the discontinuities.

Here's a much longer transmission line and you can see it's a much tighter spacing between the ripples from the resonances back and forth. But you also see that gradual increase in the return loss. Now there's a convolution or additional complication of slowly varying return loss because of the short discontinuities.

And in addition we have that very sharp resonance, the 18 GHz resonance because of the SMA that we're using. We see the convolution of the two. But if we didn't have that low cost SMA and we used a high bandwidth SMA you can imagine this increasing and decreasing increasing and decreasing. We're just seeing the beginning part of it.

This is why it is so important when we're looking at S-parameters and trying to interpret them. It's important to look at all of the S-parameters and to go to as high frequency as you can to help you interpret what's going on. Let's take a look at an example. I get requests probably a couple times a month from engineers sending me their S-parameters saying, hey,

Look at my S-parameters. It has some screwy behavior. I don't understand how we can get this kind of behavior. This is an insertion loss versus frequency. How can you have this non-monotonic behavior in insertion loss?

What crazy property of the material must be giving me this frequency dependence and then suddenly I get more signal coming through rather than less at a higher frequency. How could you possibly have this kind of behavior?

Just looking at the insertion loss by itself doesn't give you a complete picture. But we've seen that if we knew what the return loss was we might be able to better interpret the insertion loss because maybe where some of this dip is not due to an attenuation in the interconnect. Maybe some of this is due to reflections from the return loss.

When we take this structure that created these S-parameters and we look at a higher frequency and we also include the return loss it's clear. This happens to be a long BNC cable. That's why we have the very tight space frequency for the ripples that says we have a long distance between the primary discontinuities but we also see some structure to it. And we look in at higher frequency and we look at the return loss, we see why we have this behavior. This sharp drop off in the insertion loss that's not due to attenuation of the cable, that's due to the fact that we're getting a huge amount of reflection from the cable because of these really screwed up launches.

And we see we have a very long space between the launches and we see we have a huge discontinuity from those launches that are giving us this periodicity in the return loss. And sure enough when we look at the TDR response here's what we see. We have huge discontinuity at the launches. There's a little bit of complex structure to them.

We may see multiple periodicities because of that structure of the launches but it's primarily the launches that are giving us this return loss modulation and in turn giving us this insertion loss dip. This large dip here is due to the large amount of return loss. The peak over here of like -3, -4 dB return loss is what's sealing all the signal in the insertion loss and the fact that because of the resonances in the connector we go through a dip in the return loss. That means we have more energy that is not being reflected back that's going to get through.

And likewise we see a peak in the return and a dip in the insertion. This complex behavior that we saw at low frequency was really due to series resonances that caused the modulation of the return loss and it's the return loss that influences the insertion loss and we can see the large discontinuities when we look in the time domain. That's why it is so important to always look at as high a frequency as practical and always look at all the S-parameters. Don't just pay attention to one S-parameter.

Let's take a look at the next type of resonance which is from a stub. And then we'll take a look at coupling to HiQ resonant structures. Let's take a look at a uniform transmission line that has a stub discontinuity in it. Here's kind of a top view of the line.

Here's a transmitter, here's the receiver. It's a 50 Ohm transmission line. There's a little branch that's sticking off to the side and if it's a short enough branch we call it a stub. And we're going to define the length of that sub either in terms of its time delay or the physical length. The time delay of course is the physical length divided by the speed of the signal material and we're assuming 6 inches/ns to get us started. Let's imagine what that signal is going to do as it travels down this uniform transmission line.

Of course I'm not showing the return path but there's an absolute return path. They're uniform transmission lines. Signal is going to see 50 50 50 50 50. Uh-oh.

It's going to see 50 this way 50 this way. It's going to see 25 and so we're going to get some signal reflecting. But at this branch point that signal, as it hits that branch, is going to split. Some is going to continue down to the receiver and some is going to head down that branch point, and it's going to travel around and sees 50 50 50 suddenly sees an open and what's it going to do when it hits the open?

It's going to reflect. And when it reflects, it comes back up sees 50 50 50 and now it sees, uh-oh, 25. It's going to split as well. Some is going to go this way back to the transmitter and some is going to go this way to the receiver.

And the wave that travels this way to the receiver it's going to have taken a longer path to go down and back, and that means that this wave that makes its way to the transmitter is going to be a different phase than this wave that made a direct path to the transmitter. And that phase delay between them is related to this path length down and up. The time delay difference between these waves is going to be twice the time delay of that stub.

When these two waves combine into the receiver they're going to interfere.

And if we have the time delay between the incident wave and the down and back reflected wave, that round-trip time is equal to half a period.

These two waves are 180 degrees out of phase. They're going to completely cancel out. We're not going to have any signal at the receiver. We're going to have hit the resonance. Well, that condition for down and back being half a period means that down is a quarter of a period or a quarter of a cycle.

And we call this occurrence at this frequency where the two waves are 180 degrees out of phase. That means that the length of this stub is exactly a quarter of a wavelength at that frequency.

And we call that dip that we're going to see in the insertion loss, we call that the quarter wave stub resonant frequency. And we can calculate what frequency that is based on when the one-way travel time the time delay of that stub is a quarter of the frequency.

When the round-trip time is half a cycle, that's when we're going to get a minimum. That means that when the time delay going down is a quarter of a cycle, we're going to have a minimum in the insertion loss, and that's the quarter-wave resonant frequency. And what's easy to calculate is that when the time delay is one quarter the period which is one over the quarter-wave resonant frequency.

And knowing what the physical length is over here and the time delay we can calculate what that resonant frequency is. A little bit of algebra that says that okay the quarter-wave sub resonant frequency is going to rise when at the frequency of 1.5 over the length with the resonant frequency in GHz. I did the translation for you based on the speed of the signal in the interconnect assuming FR4 and length is in inches.

Let's do a quick example. Suppose we have a stub that's half an inch. Maybe it's a test point coming off or maybe it is a line that's going to go to a switch and the switch happens to be open. The length is half (0.5) an inch long.

The resonant frequency is 1.5 over 0.5. That's 3 GHz. And that's when we're going to see if we look at the insertion loss we're going to see a big dip in the insertion loss. Let's take a look at it.

Here's that example. If we have our stub that is half an inch long, we expect the quarter-wave sub-resonant frequency where we have a dip at the receiver to be about 3 GHz. And here's what we would get. This is a simulation.

Here is the return loss versus frequency, and here's that dip, and darned if it isn't at 3 GHz. And it's going to be at, that's for a quarter wave, here's the 3/4 wave, here's the 5/4 wave and on.

Now when you look at this, when you look at the insertion loss and based on what we saw in one of the previous examples the first question you should ask is well wait a minute. If we don't have any energy coming to the receiver over here at 3 GHz where did it go?

Where is all that energy that we've lost at the quarter-wave sub-resonant frequency?

Well I'll give you a hint. It doesn't have anything at all to do with radiation.

It's actually really simple because when we did the analysis, we looked at the quarter-wave sub-resonant frequency, the wave going to the receiver directly from the transmitter and the wave that bounced down to the bottom and then came back again. The reason we got that dip was because these 2 waves were 180 degrees out of phase at the quarter-wave stub resonant frequency.

Well let's look and see what happens to the wave that reflects back. Because remember we have the wave that continues, in we have the wave that is launched from the transmitter. It travels down. It hits the branch point and sees 25 Ohms. That's a low impedance and what happens? We're going to get a reflection. But in reflecting from that branch point, because it's a lower impedance, we're going to have a 180-degree phase shift.

The wave that's heading back automatically a 180-degree phase shift half a cycle.

When that wave splits and part of it goes down hits the end and comes back and going down and back that is half a wavelength change a quarter down a quarter up and now it splits. Some goes this way, some goes this way. Well the wave that reflected off the front was already half a cycle phase change. The wave that goes down and back is another half a cycle phase change.

That means that these 2 waves, the wave that heads back to the receiver from the reflection and the wave that goes down and back, they both saw a 180-degree phase shift. They're both in phase. They're going to add. What we saw was a cancellation in the forward direction to the transmitter; addition is a reinforcement of the signal that heads back to the transmitter.

This is S21, we see a dip. This is S11, we're going to see a peak. And when we look at again the insertion and the return loss we ought to see a peak in the return loss. And sure enough that is exactly what we see. Here's that dip in the insertion loss and here's that corresponding peak in the return loss because of the reinforcement of the wave going back. And that's going to be an important consistency test for us when we see dips in the insertion loss to verify that it's a subresonance; we're going to want to see the peaks in the return loss. Well let's take a look at a couple of examples.

The first example that I have for you is a simple stub that we built using a little T-junction for an SMA connector.

Now remember what we're going to look for. In a stub resonance, we're going to look for the return loss increasing the insertion loss is going to show the dip. And it doesn't really matter. I'm showing an example here of single ends. We're going to see exactly the same behavior on single-ended or differential signals as long as both lines in the differential pair have a corresponding stub on them and I'll show you an example of that. Now for this structure it's not very long. It's about 3/8 of an inch long.

We would expect the quarter-wave stub resonant frequency. Now I changed it around a little bit to include the speed of the signal in the PTFE material of the SMA connector. That has a dielectric constant of 2. You put in the numbers. We expect that quarter-wave stub resonance to occur at about 5.9 GHz.

Let's take a look at the measured insertion and return loss for this structure and here it is. Again you don't need me to tell you that the teal color is the insertion loss and the yellow is the return loss. As we saw in part 1 we're always going to start return loss at a large negative dB value and insertion loss is always going to start at 0 dB. And now we see because of the presence of that stub we see that large dip at about this frequency corresponds to darned if it isn't 5.9 GHz.

That's where the dip happens at the receiver or S21 and when we look at what comes back, oh my gosh, look, we have a peak in the return loss exactly what we expect to see from a stub. And sure enough we have another resonance. This is 3 times that resonant frequency and a few more going forward. We see that classic behavior of a stub resonance.

Here's another example of a board that has a couple of via stubs in it. This is a simple board that I use in one of my classes uniform transmission line. We got discontinuities on the ends because of the launches. But here in the middle here and here are 2 vias that are just drilled through the board.

There's no connection on the other side so they're just stubs sitting there in the board. It's a 4-layer board. There's some capacitance in the capture pad and the clearance holes through those planes.

As we would expect to see a quarter wave stub resonance corresponding to those dimensions it's going to be at a little bit lower frequency because of the high capacitance of that via stub. And sure enough here is the measured insertion loss with the WavePulser 40iX.

Here's that insertion loss the monotonic drop because of the conductor and dielectric loss in the board and sure enough right here around 5 GHz is that quarter-wave stub resonant frequency. We see the dip in the insertion loss and a corresponding peak in the return loss.

And likewise we see a few more of these before we lose the insertion loss because of all the attenuation in this interconnect and the other multiple reflections.

But you can clearly see that dip in the insertion loss for the first stub resonance for those 2 vias.

We see the dip in the insertion loss. We see the peak in the return loss. And why do we have a dip in the insertion loss? That's because of the cancellation of the waves that are traveling back and forth and we see the corresponding energy that goes back to the receiver as the return loss. And here's one last example. This is a differential insertion loss measurement and this is the measurement of 2 channels in a backplane.

One channel has no via stub in its path. The via stubs have been backdrilled in this structure whereas the other channel does have the via stubs about almost a quarter of an inch long, the periodic dips in the insertion loss and the very large broad dip in the insertion loss due to that quarter wave stub resonance. Let's take a look at the third type of resonance, high Q resonances and we're going to see the signature for a high Q resonance and then we'll finish up taking a look at what I consider to be kind of the fake resonances.

Here's what I mean by a high Q resonance structure. It is any additional piece of metal nearby that might be floating, like copper fill usually is, or it could be another trace that's sitting there minding its own business, or it could be a plane cavity. Plane cavity means we have two planes that are adjacent to each other and the two planes make up a cavity. We're going to take a look at both of these.

Let's take a look at the plane cavities first. Here's what I mean. In its simplest form, here's a 4-layer board with a microstrip on top and a microstrip on the bottom down here with two planes in between. They could be two ground planes.

They could be two power planes. They could be a power and ground plane. The DC voltage isn't important. What's important is the fact that we have two pieces of metal separated by a dielectric.

When the signal's on the top layer, the return current is on the adjacent layer 2.

When the signal transitions through the signal via to the bottom layer, the return current is on layer 3 adjacent to the bottom layer. The signal traveled through the via to make a transition from the top to the bottom layer. How did the return current travel from the top plane to the bottom plane?

That is a really important question to always ask.

In this structure, there are no return vias nearby, there are no decoupling capacitors. The capacitance between the two planes isn't so much. How does the return current get from one plane to the next? And the answer is through the impedance of the two planes.

Here's what it looks like. Here's the side view. As the signal is moving in the top microstrip, it sees signal return, signal return, signal return signal return, signal return. And when it gets in this region here it's still going to go signal return, but it's going to return through the impedance of the cavity. And if the planes are close together, that impedance can be very low. That instantaneous impedance the signal sees at the beginning of this cavity that can be on the order of Ohms or less.

The return current is going to flow through that low impedance between the plane 1 and plane 2 and then continue its way along. We have a continuous return current path but that return current is now going to see the impedance of the cavity and it's going to see this waveguide. It's going to propagate down that waveguide in the circular mode of the cavity. And of course on the other side the signal is going to go signal return signal return signal return.

The return current is going to be making its way through the impedance of the cavity and the backup of the top plane. We have a continuous path for the return current but it happens to go through the cavity. And when that current hits the end of the cavity what's it going to do? It's going to reflect.

It's going to head back and we're going to hit a resonance in the cavity. We're going to trap energy in the cavity at the frequencies corresponding to the resonant frequencies of the cavity. We are exciting that cavity through the return current flowing between the two planes of the cavity to make its way from the bottom plane back up to the top plane. And here's an example of it.

Here's a 4-layer board top view. We've got some microstrip transmission lines that are going through the middle of the board. And right here in the middle of the board we've got some vias and they go to the bottom layer. Now in the vicinity of these vias the signal layers there's no other connections between the two planes.

There is a connection over here where I have the SMA connections.

The grounds of the SMAs do short the two planes together but we still have resonances in this cavity. And when that microstrip signal goes through that signal to the via down through the bottom side and then coming back out to this connection when the return current hits that cavity and bounces back and forth it's going to see resonant frequencies. It's going to see this resonant frequency where we can fit a half wave here down the 3.25 inches. It's going to see the resonance going this way when we can hit the 1.187 inch half a wavelength. And because we have the shorting vias here and here, they make up an array as well. And we're going to see a resonance when we hit that resonant frequency between the array of shorting vias at 0.8 inches. Here's the measured insertion loss from top layer to the bottom layer. We see the monotonic drop and look, we see these very sharp dips.

This one corresponds to the long length resonance.

This one corresponds to the lateral dimension and this one corresponds to the 0.8-inch space between the array of shorting vias. You can see that when we have a resonant structure and our signal passes through that resonant structure you can see how the return current excites that resonance and we see it as an energy loss in the insertion loss at those specific cavity resonances. And you can see they're relatively sharp, narrow frequencies.

Here's one more example.

In this case we're going to look at the insertion loss of a microstrip transmission line when it's adjacent to another microstrip transmission line but the ends are open.

What's going to happen? We're going to send a signal from port 1. It's going to come along here to port 2 and in traveling to port 2 there's going to be some coupling to this other line.

And when that energy gets coupled to the other line that voltage signal is going to bounce across the open on one end and the open on the other end is going to bounce back and forth. We're going to hit the resonance of that structure. And when we hit the resonance of that structure we're going to lose energy into heat.

Some of the transmitted signal is going to go into the other interconnect. It's going to bounce around and we'll lose that in the transmitted signal. And in addition as it rattles around back and forth we may see a little bit of that trapped signal coupling back onto the transmission line kind of polluting the signal on the transmission line. And yeah we'll see it at the far end but it'll be a really small amount compared to what's already there.

But when we look at the return loss because we're already looking at a small amount, that little bit of pollution that comes back we're going to see it enhancing the return loss at those resonant frequencies of the floating structure. Let's take a look at that. Here is the measured S-parameters versus frequency for looking at driving port 1 and port 2. Here again, you don't need me to tell you this is a return loss, this is an insertion loss.

And look, we see these sharp dips in the insertion loss. Those dips correspond to resonances in the floating conductor on the other side and you can see they're very sharp. And at those frequencies where we're coupling energy into the other line some of that signal couples back onto the quiet line and we see it as large peaks in the return loss. Normally, we wouldn't see much return loss.

It was a nice uniform line. We wouldn't see much return loss but because of the energy that's coupling in here and then comes back we see them as sharp peaks in the return loss corresponding to those dips in the insertion loss.

If we were to spoil the queue of that floating conductor, if we were to minimize the reflected signal back and forth so we don't get energy building up and coupling back, if we were to terminate one or both of the ends of the other line, then we would expect to completely damp out these resonances and not see them anymore. And sure enough, when I connect 50 Ohms to the two ends on the other line we still have energy coupled over there. We'll see the impact of that in a minute but we don't have the resonances that we're exciting. We damp out those resonances.

And sure enough here is this pale blue line. That is the measurement of the insertion loss of one of the lines in the two microstrip couple microstrips when the other line had 50 Ohm ports on the ends. And you can see it is completely devoid of any of those sharp dip resonances. And that's how we know that it's a high Q structure.

How do we know if we're getting coupling to a high Q structure? If we see a sharp dip in the insertion loss, it indicates the presence of a high Q structure, and that says you want to look at your structure, look at your interconnect, and look for is there any adjacent metal that we might be coupling to that's stealing some of the energy and then dissipating as heat in the dielectric and conductor loss of that resonating structure. Well so far we've talked about three kinds of resonance structures.

We talked about series structure. We talked about a stub structure. We talked about a high Q structure.

I wanted to show you a few other examples of what look like resonances but really aren't resonances. I call them fake resonances, something to pay attention to.

And then we'll summarize what we've talked about and we'll take some questions. These are two structures in particular that show these resonant-like behavior, but have nothing at all to do with resonances. We're looking at the singlet response of a microstrip and differential pair with mode conversion. And I'm going to show you how we can distinguish a fake resonance from a real resonance.

How do we know it's these two effects? We're going to look at the signature to look for in the S-parameters to distinguish these two structures.

First let's look at the insertion loss of a single-ended microstrip. Now we're only going to look at one end of the microstrip but I have two microstrips in close proximity. We already said that okay if the other one is floating we're going to see high Q resonances in this one. But suppose that we're measuring all 4 ports.

So we have 50 Ohms connected to the other ports. Let's look at the insertion loss of one of those lines. That's just S21. Here is the measured S21 versus frequency for one of the lines when he's part of a pair and we're measuring all 4 of the ports.

And you can see the insertion loss starts out at 0 dB like it should. We see the kind of monotonic drop off but then we see this really sharp dip here at about 11 GHz or so. Here's 10 GHz. Here's 12.

A little bit more than 11 GHz. It's not that 18 GHz circular mode of the low-cost SMA. There's something else going on. What could cause this resonance?

Could it be a stub resonance maybe?

Well the way to tell is we look at the return loss. Because if it's a stub resonance where we lose energy in the transmitted signal we should see it coming back in the reflected signal. Well here is the return loss S11.

Let's see. It starts out at large negative dB at low frequency, what we expect. We don't get very much reflecting. That says pretty good launch and it's below -10 dB.

And look where we lose energy in the insertion loss, we're not gaining it back in the return loss. We're still pretty low. We're below -10 dB and yet we've lost almost everything in the insertion loss. It's not a quarter-wave stub resonance.

In fact it's not a series resonance either because we don't have anything coming back to us. What could be causing this?

Where is the energy going? We send energy in at around 11 GHz.

It doesn't come through here. We don't see it come back. Where is it going? Is it going into heating up the dielectric? Is there some other place it could be going?

And the answer is, in this case, it is due to the far-end crosstalk to the adjacent line flowing down the far end of the adjacent line into port 4.

If that's what's going on if we look at port 4 S41, we gotta see the energy coming out. And sure enough here is S41.

As we lose energy in the insertion loss we gain the energy back in the far end. This is part of the behavior of a coupled microstrip. It's related to the behavior of far-end crosstalk in microstrip. We will always see this in microstrip. And depending on the amount of coupling and the coupled length that's going to determine the frequency at which we have the coupling. The longer the length the lower the frequency in which we're going to see the dip in the insertion loss and the tighter the coupling the lower the frequency we're going to see the dip. If we have loosely coupled and we see and if we have loosely coupled and short microstrips then we're going to see this dip in the insertion loss push to higher frequency and we may not even see it.

The way we tell that it's due to the microstrip behavior is number one if we have coupled microstrip expect to see this behavior. And number 2 the energy we lost we better see it in S41.

And now comes the last kind of fake resonance and that's related to mode conversion. Remember what causes mode conversion? It is any asymmetry between the signals on the P and the N line.

Remember we start out with a perfect differential signal going down our transmission line. It's going to hit on line 1 and line 2. The perfect differential signal means that the two waves are exactly out of phase 180 degrees out of phase and they have exactly the same amplitude. That's the pure differential signal because there's no common signal component.

Anything that affects one line and not the other either affects the amplitude of that of one line and not the other or the phase of one line and not the other is going to cause these two waves to change.

They will be different. They will not be exactly the same amplitude and 180 degrees out of phase. There's going to be some phase shift between them or some amplitude difference when we add them up to look at the common suddenly what was zero common signal over here suddenly has some amount of common signal over here.

And if for example the asymmetry was a time delay difference you can imagine that if I shift them to be exactly half a cycle where they were 180 out of phase and I shift it half a cycle they're going to be completely in phase. That means there's no differential component anymore. I'm going to see a dip in the differential component. If we have a constant time delay difference between the path of those two signals on the N and the P lines if there's a constant time delay difference a time we call that a length skew between the two lines then at some frequency where I have half a wave difference in length between the two lines at that frequency I'm going to turn that differential signal into completely common signal and no differential signal left.

I'm going to see a very small amount of differential insertion loss and that is exactly what we see. In red is the differential insertion loss and at that frequency where the time delayed difference between the two lines of it is exactly half a cycle that's when I turned all of the differential signal going in into common signal. There's no differential signal coming out. I see a dip in that insertion loss.

Where did that signal go? It did not go back as reflected differential signal. I'm not going to see it in SDD11. Where did it go?

It went into mode converted common signal. I have to look at the SCD21. This is differential in on port 1 common out on port 2. And sure enough here's where all that energy went.

It went into the common signal coming out. And that's the signature. That's how we're going to tell we have mode conversion in a differential pair. If you see a sharp dip in the differential insertion loss and you're wondering is that a stub resonance?

You would look first at the SDD11. Nothing would be coming back. It's not there. The next place you would look is SCD21 and sure enough that's where it is.

That's an indication that we really have mode conversion going on and there's a length skew between the two lines.

Well let me just summarize what we've covered so far. We've covered a lot of material here. We said look for dips in the insertion loss. That is a common feature that we're going to see in many interconnect structures.

What causes those dips? If we have broad dips they're due to a serious resonance.

And if we have multiple serious discontinuities they're going to have multiple resonances that can be relatively complex interference patterns hard to decipher just looking at it by eye. That's where we want to look at TDR response.

And remember keep in mind that we will only see the dips in the insertion loss if we have peaks in the return loss greater than about -10 dB.

When we have a sharp dip in the insertion loss it could be due to a quarter wave stub resonance and to confirm that we want to look at peaks in the return loss. If we see a peak in the return loss at the same frequency we see the dip in the insertion loss that's an indication of potential stub resonance. This says look at your interconnect for those structures.

And if we have a very sharp dip in the insertion loss that may indicate coupling to some high Q resonator some other piece of metal nearby that's floating some cavity nearby that is extended to planes in close proximity. If you see those sharp dips at some frequency based on the frequency you can back out what the length of that resonance structure is and that will give you a hint of what to look for in your interconnect.

And then finally we also showed a couple of features in the insertion loss that look like dips but they're not due to resonances.

They have their own mechanism.

We saw the two of them that were related to single-ended microstrip and mode conversion in a differential pair and we want to confirm those features by looking at the S41 in microstrip and the mode conversion term for the differential pair. With that thank you very much for your attention today. I want to also mention to you that we have plenty more of these webinars available. You go to our website teledynelecroy.comevents and you'll see the listing of all the upcoming webinars and other events that we're doing as well as the recorded ones.

You go to the upper right corner click on view on demand and you'll see all of the webinars that we've done over the years that are available for free viewing. And then finally also recommend you take a look at MAUI Studio. You can download your own copy of MAUI Studio which is basically the software interface to our scopes and you can run that on your PC. With that I'm going to throw the floor back for questions.

Again thank you very much for joining us today and hope to join you guys on future webinars.

Okay. Alright. Thanks Eric. We have a lot of questions.

We're not going to have time to review them. I wouldn't even know where to get started. What we'll do is what we've done the last couple times we'll transcribe them. We'll put them up on the website with the recording.

If you think of any other questions, go ahead and email them to me or to Eric and we'll get you answers right away. We do appreciate you coming on. For those of you who are asking, the slides are available in the handout. They'll also be sent out to you via email when I send out a link to the recording.

If you watch the recording your colleagues watch the recording and you have more questions again you guys have my email hilary.lustig@teledyne.com. You have Eric's. You can reach out to us. And Eric's next webinar will be taking place on March 17th so take a look at your emails for that. We also have a webinar on TDR and S-parameters coming up March 4th.

Thanks again for joining us. For those of us on the East Coast in the United States stay warm.

And for everyone else stay safe and stay healthy. Thanks so much. Have a great day.