Eric Bogatin's Blog: What I Learned This Month

In the last few years, the focus of Bogatin Enterprises has been almost exclusively signal integrity education. This is through our live classes, lectures and publications.

Our mission is to accelerate engineers up the learning curve to enable them to “get to the right answer faster.” We do this through three general themes in all of our activities: understanding the principles, applying analysis techniques to explore design space with “virtual prototypes” and leveraging commercial measurement and simulation tools.

Combined, we find this is an efficient process to transform complexity into practical design solutions.

Other than a little kibitzing over the phone or after classes, we do not do consulting. While we are never at a loss when asked our opinion, sometimes problems require more than a superficial analysis. This is when we recommend other experts in the industry whose mission is providing expert advice and services to help you solve your problem or achieve your design goal.

For anyone looking for consulting assistance, I’ve created a new page on my blog with a list of recommend consultants. If you need help in your current project, you’ll want to contact the experts I list here.

“There is no such thing as a free launch”, Scott McMorrow, President of Teraspeed Consulting Group LLC is fond of saying. It is offered more for effect than truth, considering that one of his specialties is engineering transparent launches.

Teraspeed Consulting was founded in 2002 to “Enable clients in the design and implementation of extreme performance systems.” Their staff has more than 120 years of collective design experience in measuring, analyzing and designing high speed systems.

The techniques they pioneered span from DC to 50 GHz, covering 3D electromagnetic simulation to VNA and TDR de-embedding and calibration techniques measurements. Just as important are the tricks and methods needed to get good correlation between simulation and measurement.

Scott has found that a key ingredient to successful simulation-to-measurement correlation is accurate materials characterization, so this has become an important element in the engineering services Teraspeed offers.

They specialize in the following services, each spanning the DC to 50 GHz range::

• Correlation between electromagnetic solver and measurements
• Interconnect model correlation
• Material property measurement and modeling
• RF test launch design

GigaCon connector system engineered by Teraspeed for transparent launch and the measured 50 Gbps eye for this system.

If your project involves data rates above 10 Gbps, you will not be successful by accident. Cost effective systems require that you do everything right. If you are looking for help navigating the complex trail through the maze of Gigabit design, I recommend Teraspeed as a guide.

This question comes up in almost every advanced class I teach: what are the limits to FR4?

Like almost every important question in signal integrity, the answer always stars with “…it depends.”

The next step is to “put in the numbers” using analysis tools, based on all the assumptions and conditions for the specifics that should be considered.

In a long differential channel, if we do everything right, like no stubs anywhere, no asymmetry anywhere, no cross talk and no impedance discontinuities anywhere, the limitation for the highest data rate a channel can support is set by the signal to noise ratio (SNR) at the receiver.

While there are theoretical evaluations based on Shannon’s Information Theory about a channel’s information carrying capacity, its – 3dB bandwidth and the SNR at the receiver, there is an alternative analysis based on practical considerations.

If everything is done right in the channel, the fundamental limit to the data rate it will support will be set by the frequency dependent attenuation and how much signal is required for an acceptable eye . It’s not just the attenuation, it’s the frequency dependent attenuation. If we have roughly a linearly decreasing attenuation with frequency, much of this can be compensated using equalization techniques such as CTLE (continuous time linear equalization), FFE (feed forward equalization) or DFE (decision feedback equalization).

Typical high performance specs offer a limit of about –25 dB attenuation at the Nyquist frequency as the practical limit to what can be recovered in a usable eye. However, my buddies who work with optimized TRX equalization techniques tell me that if all the more than 10,000 coefficients available for the three equalization techniques are optimized perfectly, it may be possible to recover a usable eye with –40 dB attenuation at the Nyquist frequency.

Now we can ask, how far and at what frequency can you go in an FR4 interconnect and still have less than –40 dB attenuation? This is a simple analysis, which we go through in our S-parameters for SI (SPSI) class and Advanced Gigabit-differential Channel Design (AGCD) class. The result is a simple relationship between the length of the interconnect, in inches and the highest data rate, in Gbps, below which the attenuation will be less than –40 dB and an acceptable eye can be recovered. This relationship is:

This assumes the attenuation is limited to just dielectric loss and no conductor loss, which is the ultimate best that can be done. There is a distance-bandwidth trade off. This is fundamental and is the driver for transitioning to fiber optic connections at either high data rates or long distances. The boundary of when photons are more cost effective than electrons is set by this relationship.

Generally, the closer you get to this fundamental limits, the more expensive it becomes to implement a solution in copper and the more cost effective the solution may be in optical interconnect.

For example, in a 40 inch backplane, the ultimate limit to copper is about 20 Gbps. It is probably not practical to achieve 28 Gbps in a 40 inch backplane using a pulse amplitude modulation of two levels (PAM2), with an FR4 type material even with wide copper traces. Data rates above 20 Gbps using copper interconnects will require a lower loss laminate.

This estimate is not so far off from what is actually measured. Here are examples of the measured insertion loss for different length transmission lines in FR4 interconnects using wide conductors.

For the 40 inch interconnect, the frequency at which the insertion loss is larger than – 40 dB is about 10 GHz. This suggests the possibility of sending data at about 20 Gbps through this interconnect, close to what we estimated.

What’s the limit to copper interconnects in backplane applications? It depends. As a rough starting place, doing everything right, FR4 interconnects will limit out at about 20 Gbps in 40 inch backplanes. For higher data rates, and to have better margins, lower loss laminates will be in your future. It may be a possible to implement 40 Gbps backplanes in copper using suitable low loss materials.

There will be a limit to copper where it becomes more cost effective to switch to optical interconnects. I remember the days when folks suggested this limit was 2.5 Gbps. Then practical solutions in copper were developed. Then the limit was touted as 5 Gbps. But this was overcome. Then I heard the limit was 10 Gbps, but cost effective solutions were found.

As the cost of higher data rate copper channels goes up and the cost of optical channels comes down, they will cross and optical interconnects for 40 inches will be cost effective. I think this day is still in the future. To paraphrase Mark Twain, “the reports of copper’s death are exaggerated.”

I don’t usually write pieces in this blog that are not directly related to signal integrity, but I recently saw a TED talk on battery storage technology that I think should get more visibility.

Prof Donald Sadoway, from MIT, presented a talk on “The Missing Link to Renewable Energy.” Of course, he says, what’s needed for large scale power production from wind and solar and wave and other renewable sources, is a cost effective, scalable and efficient way of storing the energy for later use.

Prof Sadoway developed a radically different “liquid metal” battery technology. It’s based on Magnesium as the top, negative electrode, Antimony as the bottom, positive electrode and a magnesium chloride salt as the electrolyte.

What’s unusual about this battery is that these ingredients are heated to their melting point, 700 deg C, and their density difference naturally separates them into three different components.  There is no assembly, no moving parts. It’s just a battery during the discharge cycle and an energy storage device during the charging cycle.

Sadoway suggests this battery technology is scalable and provides a high energy density, efficient way of storing large amounts of energy to distribute to the power grid. He and MIT colleagues created a separate company to commercialize this new technology, LMBC.

In addition to his research, he is an engaging professor. Last year, I sat in on his Introduction to Solid State Chemistry class through MIT’s Open CourseWare program.

In our S-parameters for SI (SPSI) class, we identify four different commonly occurring patterns in the return and insertion loss of S-parameters from interconnects. One of these patterns is sharp dips in the insertion loss, such as shown to the left.

The chief characteristic of this pattern is the presence of narrow peaks, with a Full Width, at Half Max (FWHM) that is very small compared to the center frequency of the dip.

In general, if this dip were due to coupling to some resonant structure, and it had a narrow absorption spectrum like this, we would judge the Q of the resonator as the ratio of the center frequency to the FWHM, Q = Fcenter/FWHM.

In the example shown here, the Q is about 1.75 GHz/0.1 GHz = 17. Anything over a Q of 10 about is considered a “high-Q” resonance. Generally, these high-Q dips are caused by coupling to a floating metal structure nearby. This can be an adjacent “guard” trace, a “shield”, thieving metal, or even to a pair of planes a signal via has passed through.

The center frequency of each dip corresponds to the resonant frequency of the floating metal. The resonant frequency is the frequency at which you can it a multiple of 1/2 a wavelength between the reflecting ends. As a rough estimate, when the metal is embedded in an FR4 type material, and both ends are open, the resonant frequency is roughly 3 GHz/Len[inches]. If the resonator length is 6 inches the resonances should start at about 500 MHz, which we see they do in this case above.

The Q is related to the damping- the losses from the conductor and dielectric. The tighter the coupling, the more energy couples over and the deeper the dips.

This is one of the reasons why it can be dangerous to have floating metal, like a copper pour, adjacent to signal lines. Even if there are shorting vias to a ground plane, there can still be resonances in the plane, based on fitting a half a wave between the shorting vias.

However, if one end of the floating metal is terminated with a resistor, it may damp some of the resonances and dramatically reduce the Q and the impact from the dip.

This is also why sometimes guard traces cause more harm than good if not implemented correctly.

When signals transition through plane pair cavities, they can couple to the plane resonances and suck out a large fraction of the signal’s energy at specific frequencies. Where does this energy go?- into the cavity, available to couple into other signal lines and appear as via to via cross talk.

For more details about high-Q resonances in insertion loss, to try your own simulations of coupling to high-Q resonances in our hands on labs, and to learn more about the other three common patterns in insertion and return loss, check out the SPSI class and schedule, posted on www.beTheSignal.com.

If you want to accelerate up the signal integrity learning curve, check out our other classes.

Thank Alexander Graham Bell (1847-1922) for the introduction of the dB. Though best known for the invention of the telephone, he was even better know in his day for his research in studying the deaf and quantifying the sensation of hearing.

He noticed that our sensation of hearing is not linear with the power in a wave, but scales with the log of the power of the wave. Bell created a perceived loudness scale based on the log of the acoustic power in a sound wave.

For historical reasons, when we take the log of the ratio of powers, we refer to the units as Bels. Even though this is in reference to Alexander Bell, we drop one of the ”l”s and just call it the Bel scale. A Bel is ALWAYS the log of the ratio of two powers.

The threshold of hearing (TOH) is about 10^-12 W/m² of sound intensity. A normal conversation is about 10^-6 W/m². On the Bel scale, the conversation would be rated as log(10^-6/10^-12) = 6 Bels.

On the Bel scale, a value of 1 means a power is 10¹ or 10x higher than the reference base. A value of 3 Bels means the power is 10³ or 1000x higher than the reference base . Historically, we have come to use the Bel scale to measure all powers, such as light intensity and radio power, relative to some baseline value.

In general, the Bel scale is not very large. For example, the entire range of hearing goes from the TOH to about 10⁴ W/m², where the ear drum is perforated, or a total of 16 Bels. For such a large range of sensations, 16 is just not a very large number.

This is why it has become conventional to use not Bels but deciBels as the scale. A deci means 1/10th, so there are 10 deciBels in 1 Bel. We abbreviate this as dB. This means that we can write any power in terms of is dB value, relative to a reference level as: Power_in_dB = 10 x log(P/P₀). The factor of 10 is to convert the value in Bels into deciBels.

This sets the range of hearing to start at 0 dB at the TOH to 160 dB as damaging. More examples of sound levels can be found here.

A Saturn V Apollo rocket launch generated sound levels of 135 dB 1 mile away from the launch pad.

But, if we want to measure a quantity that is NOT a power, such as the amplitude of a wave, like a voltage or current, we can’t use the dB scale. It is only used for the log of the ratio of powers.

The work around is that if we want to measure the ratio of two voltages in dB, we actually measure the ratio of the powers in the waves. The power in a wave is the square of the amplitude. So, when we measure the ratio of two voltages in dB, we are really measuring the ratio of the powers in the voltages.

For example, an S-parameter is really the ratio of two amplitudes, not powers. When we calculate the magnitude of the S-parameter in dB, we use the factor of 20:

Sometimes it is confusing to figure out is the quantity we are looking at a power or an amplitude. For example, we often will see impedance measured in dBOhms. Is impedance an amplitude or a power? It turns out it is an amplitude. If you want to convert an impedance from dBOhms into Ohms, you need to use the factor of 20: Z = 10^(Z_dB/20) .

As long as you keep in mind that dB is ALWAYS the log of the ratio of powers, it’s pretty clear how to interpret the results.

For handy reference, keep in mind that a –3 dB drop in power means the power decreased by 50%. The amplitude decreased to only 70% of its initial value.

When you see a drop in amplitude of 50%, this is a drop in power of –6 db.

A signal that drops off by a factor of 10 in amplitude with each decade, linearly decreasing with frequency, for example, has a drop of a factor of 100 in power per decade, or –20 dB per decade.

Capacitance is the efficiency of storing a charge difference between two conductors at the expense of the voltage between them. A high capacitance means there is a lot of charge stored per volt between the conductors. This is described by the definition, C = Q/V. If the definition requires two conductors, what does it mean to talk about the capacitance of one conductor?

If you put some excess charge on a conductor, sitting in space, it will rise to a new voltage, compared to any other place measured as the reference. It will have a capacitance, the ratio of the charge added to its change in voltage.

It’s difficult to calculate the voltage generated on an isolated conductor except for simple geometries, like a sphere. The case of two concentric spheres is a classical problem in all freshmen EM classes. A great explanation is found here.

We start with two concentric spheres. In this geometry, one sphere is inside the other. The capacitance of this configuration can be easily calculated and is

Suppose we make the outer sphere bigger and bigger, effectively moving it farther and farther away. The value of b gets larger and larger and 1/b goes to zero. If the outer sphere is more than 10 x the radius of the inner sphere, the value of 1/b is less than 10% the value of of 1/a and has only a small impact. In this extreme case, when the outer sphere is very far away- like to the floor, or the walls of the room, the capacitance of the inner sphere, to any metal far away, is related to the size of the smaller sphere, a.

The capacitance of a small, isolated sphere is just 4 x pi x epsilon zero x a. Using values of 0.225 pF/inch for epsilon zero, the capacitance of a sphere, with radius a is: C in pF = 1.4 x D, with D the diameter of the sphere in inches.

This is a startling result. It says that a piece of metal floating in space has a capacitance to any far away surface and it is roughly related to its diameter. If it is other than a sphere, it is a little hard to calculate, so to use the luxury of a simple estimate, we have to assume it is a spherical shape.

For example, if we have a cable sticking out from a computer that is 3 inches long, maybe its equivalent to a sphere with a diameter of about 1 inch. By nature of its size, it will have a capacitance to any other surface, far away, of about 2 pF.

This is a very good estimate of the capacitance between the shield of a cable to the floor. It’s the fringe electric fields of external cables to the floor that is the return path for common currents on the cable. It’s the impedance of this path that usually determines how much common current flows on the cable shield.

If there is 2 pF of fringe field capacitance, at 100 MHz, the impedance is roughly 1 kOhm. If the ground bounce noise on a plane, that drives the common currents, is just 100 mV, the common currents will be on the order of 0.1 v/1k Ohm = 100 uA. It only takes 3 uA of common current to fail an FCC class B certification test so we see how easy it is for ground bounce to cause EMC problems.

In the last few months, I’ve had occasion to participate in a number of question and answer events.

On Jan 26, 2012, I hosted the first online Chat with Printed Circuit University. In the hour and a half live session, I answered about 20 questions, all of which were recorded and posted.

What most participants did not know was that at almost the moment the chat room opened, I had a water pipe burst in my basement and I was rushing between my computer to quickly read a question and furiously type an answer, to finding the main water shut off valve in the house, mopping up the floor and finding the number for an emergency plumber. This was one occasion I was glad the chat was only by written word and not a video feed!

At the most recent DesignCon 2012, I moderated a panel discussion, “Ask the experts,… anything goes.” We had seven industry experts field questions from an audience of about 75 sitting around us on the show floor in the ChipHead Theater. In our brief 45 minutes together, we covered questions about return currents to the future of copper vs optical interconnects.

In the months of January and February, I taught a total of 14 different classes around the world, in Switzerland, Germany, the States, Malaysia, Singapore and China, and visited with over 800 students. After each class, I was always inundated with students hungry for answers to their specific questions.

I usually receive a dozen emails each week from former students or folks who read my book and still have a question. While I try to answer each note, I am finding that many of the questions are similar.

I’ve decide to introduce a new feature in my blog which will be Frequency Asked Questions (FAQs). I’ve created a new static page on my blog which will be the running list of questions folks send to me and I will select specific questions every so often to answer in my blog. When I post an answer, I will link it to the question on the static page.

I invite you to submit your questions to me at DoctorIsIn@beTheSignal.com and I will add it to my list and try to make a point of answering it for you. I am going to keep the question source anonymous so you should feel free to ask anything you want. The better I can understand your question, the better I will be able to answer it.

I’m giving some thought to creating some sort of office hours which might be a Google+ video chat room or some other live video chat event. If you have some suggestions, drop me a note: DoctorIsIn@beTheSignal.com

Hope to see you in one of my upcoming classes.

Even though we’ve provided signal integrity training classes for more than 20 years, we are constantly evolving them based on the changing needs of the industry and feedback from our customers, our students.

Our most successful experiment has been the introduction of hands on labs to all of our classes. These are based on three different tools which we’ve arranged to give to all of our students.

QUCS is the easiest to use SPICE-like circuit simulator I’ve ever found. We provide the software and all the lab exercises using this tool.

Mentor’s HyperLynx is the most popular advanced circuit simulator with integrated field solver. Recently Mentor has announced cloud access to HyperLynx. Through special arrangement, we give our students access to their cloud server and the special labs we’ve created that run on this server.

LeCroy’s SI Studio is a powerful signal analyzer which has an S-parameter viewer, a signal synthesizer, a channel simulator and clock recovery algorithms which can implement FFE, DFE and CTLE algorithms. Additional analysis tools can be applied to extract useful parameters from the eye, such as jitter decomposition.

By special arrangement with Mom and Dad at LeCroy, we give a fully licensed version of SI Studio to all students who attend our classes. This software tool has a $5,000 list price.

Starting in 2012, all students to any of our classes will receive:

• A color copy of each slide in the handouts
• An e-book copy of Signal and Power Integrity Simplified viewable on ANY device
• A copy of the QUCS software and the QUCS hands on labs
• Access to the Mentor Graphics cloud server and the HyperLynx hands on labs
• A licensed copy of the LeCroy SI Studio software and the SI Studio hands on labs
• Breakfast, snacks and lunch
• A certificate of completion

Check out the schedule of classes and all the course details on our web site.

Standing room only crowd at Eric Bogatin’s Speed Training Session, photo courtesy of Jeremy Graef.

DesignCon 2012 has come and gone, leaving in its wake a core dump of new and useful information that can be immediately applied to help solve signal integrity problems at the “bleeding edge” of bandwidth and data rate. Over the next few weeks, I will post a series of summary and review columns about what I learned at this DesignCon.

Let me start this series with one of my session, the Speed Training Event, How Return Loss Gets its Ripples. If you want a copy of the slides, you can download them here. If you missed the event, I covered this topic in a recent webinar on Reading S-parameters like a book. You can view the recorded webinar here. 

As an experiment, the speed training event was held on the show floor at the Chip Head Theater. Seating was limited to the first seventy folks, and the crowd spilled over into the aisles.

The theme of this presentation was to illuminate the basic, fundamental mechanism that leads to the ripples in all measured or simulated return loss plots. What is it about the interconnect structures under consideration that cause this distinctive feature, and why do ripples appear sometimes in insertion loss, but not other times?

The punch line is that it is all about the interference between the reflected waves from the ends of the interconnect- wherever there  is an impedance mismatch. In a uniform transmission line, this is usually at the ends of the line, where it connects to the 50 Ohms of the ports.

When the waves reflecting from the front interface and the back interface combine at the receiver, they will either constructively or destructively add together, depending on the total path length.

When the interconnect length is an even multiple of a quarter of a wave, they subtract and there is a minimum of reflected signal. When they are an odd multiple of a quarter of a wave, the reflections from the front of the interconnect and the back of the interconnect add and the reflected signal, the return loss, is a maximum.

The strength of the min and max signals depends on how large the impedance mismatch is, at that frequency.

If return loss and insertion loss are important properties of interconnects for your applications, you might want to check out the S-parameters for SI class I am teaching, now scheduled for Longmont, CO and San Jose CA in the next few months.

Hope to see you there!