What I Learned this Month

I’ve been teaching signal integrity for more than 20 years and keep getting asked the same questions over and over again. That’s one reason I wrote my text book, Signal and Power Integrity- Simplified.

I read so many on-line forums where engineers- both novices and very experienced, ask some very important fundamental questions, and the responders struggle or muddle through the answers.

I tried to include the answers to many of these questions in my book. Here is a short list of 20 questions which are answered in detail in my text book. If you puzzle over some of these signal integrity questions, you might find it instructive to browse through my text book.

1. Why are signal integrity problems only going to get worse as we progress on Moore’s Law? (section 1.7)
2. Why is the bandwidth of a signal related to 0.35/RT? (section 2.10)
3. What is the origin of the rule of thumb that the bandwidth of a clock signal is roughly the 5th harmonic of the clock frequency? What are the underlying assumptions? (section 2.13)
4. What is the difference between a “real” component and an “ideal” circuit element and why is this distinction important? (section 3.3)
5. What is sheet resistance and why is this an incredibly useful figure of merit? (section 4.5)
6. Why is the capacitance of a simple, short wire hanging in space about 2 pF? (section 5.2)
7. What really is inductance and how is it influenced by physical design? (section 6.3)
8. What is ground bounce and how can I reduce it? (section 6.7)
9. Why does current in a conductor re-distribute at high frequency? (section 6.16)
10. What does characteristic impedance really mean? (section 7.9)
11. How does return current really flow in a transmission line? (section 7.13)
12. How does return current flow from one plane to another when the signal transitions through a via? (section 7.14)
13. Why are there reflections? (section 8.2)
14. Do corners cause reflections and when should I care? (section 8.16)
15. Where does dissipation factor and dielectric loss come from? (section 9.6)
16. Why are the capacitance matrix elements sometimes negative? (section 10.6)
17. What is differential impedance and how is it different from odd mode impedance? (section 11.7)
18. Why is there no far end cross talk in stripline? (section 11.11)
19. Why are there always ripples in return loss and sometimes in insertion loss? (12.11)
20. What is spreading inductance and why is this important? (section 13.14)

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.”

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.