# The Pulse: Fitting Physics to Fact

Driving down cost has always been the goal of modern engineering. The phenomenal reduction in manufacturing cost we’ve enjoyed over the past 50 years is primarily the outcome of engineers whose goal it is to make a good, affordable product. Economic cost-effective production benefits us all, including consumers, defense, aerospace, and automotive sectors.

Composites
Composite materials are incredibly versatile; they blend the characteristics of the component parts and are engineered to result in a product with the benefits of both the composite parts with few of the disadvantages of the individual constituents. In our PCB world, the use of composites gives access to PCB substrates with as many or as few layers as desired and with a wide variety of flavors, from low cost to high reliability and high speed, whilst at the same time juggling the safety and regulatory challenges of the available fire-retardant properties.

Statistics
At a large scale, many of the variations of composite materials, from an electrical perspective, are small enough to be dismissed, but with feature dimensions and interconnect geometries shrinking, it’s important to be aware of the inherent variation of the electrical properties of the substrate. These have been dealt with in much detail by the many authors of this column. However, the result for designers of inherent electrical differences distributed in the substrate is that as a designer you must look at the statistical effect on your design. How much variation is there and how much is that likely to affect prop delay, impedance, or insertion loss over a typical production run?

Monte Carlo Gives a Reality Check
It is easy to focus on one parameter and how that will impact the desired electrical characteristic, however, a far better approach is to set a tolerance for each primary dimension which may impact the circuit, then run a Monte Carlo analysis. This allows you to simulate a production run. I have used characteristic impedance of a 93-ohm differential pair in this example, but the Monte Carlo holds true for any characteristic which is impacted by a number of factors. In this example (Figure 1), I set each raw material dimension a 10% tolerance, and then simulated building 250 PCB transmission lines with a normally distributed, randomly selected set of parameters. This gives a far better impression of how production will vary over a batch of boards rather than simply focusing on one or two characteristic dimensions or looking at the worst case. It does allow you to experiment with which a particular dimension should be more tightly controlled to achieve a higher yield.

Figure 1 demonstrates that with a 10% tolerance on every characteristic over a production run, the majority of impedance results will fall well within 5-6%, but there will be outliers just out of the 10%.

In Figure 2 you can see that in this simulation the tightening of the trace separation specs significantly tightened the distribution with a significant peak on the nominal.

In Figure 3, purely for illustration, I pushed the dielectric constant tolerance out to an exaggerated ±20% and the more benign effects of Er, having only a 1 square root effect, show a minimal flattening when compared with the 10% illustration in Figure 1. These three illustrations demonstrate how a signal integrity engineer needs to balance the material properties of a base material with varying constituent properties and use statistics to see whether there is the potential for good yields based on the simulation. Making a good yielding design from materials which have inherent variability is one of the key areas where a design or SI engineer can add value to the production process and ensure a product is either profitable—if commercial—or within budget for contractual purposes.

When the Going Gets Rough
In the first part of this column, I looked at how an understanding of statistics helps maximise yields when working with composite materials. But copper is not a composite; it is a “pure” element. However, in high frequency designs the signal largely moves to the surface of the copper, and here it engages with the surface finish. For boards to be useful they must bond and survive assembly, possibly some rework, and then the environment that they will be used in.

This means that the copper must bond sufficiently to the epoxy in the prepreg to ensure that the board does not delaminate during either assembly or its working life. If you are using Gigabit speeds, then you will know that the roughness impacts insertion loss. The complex nature of electroplated surfaces means that it is far from practical to field solve the EM fields and associated losses at the surface, so empirical models are used to make predictions of loss owing to skin effect which are “good enough” for the SI engineer to work with when considering the loss budget.

Chemistry suppliers are gradually improving the pre-treatments in use to permit the use of ever smoother copper, which is easing this modelling situation, but most designs need to take care of roughness modelling. Designers new to the subject may think that they can obtain all the roughness data they need from a datasheet. However, more seasoned professionals will know that, depending on the stackup and the drill arrangements, only some of the surfaces are as in the datasheet; some will be pre-treated for bonding, and others will be plated as part of the plated through-hole process. This adds a layer of electrodeposited copper on the foil or core material and awareness of the stackup and the PCB fabrication process. It also adds the knowledge that maybe one fabricator prefers one approach over another and that for good modelling the SI engineer needs an understanding of both the specified materials and the stackup, as well as the approach of the fabricator. It’s not as simple as sitting in a darkened room studying datasheets.

Conclusion
Good use of modelling tools, a knowledge of PCB fabrication, and, even better, a close relationship with your fabricator perhaps will help you answer why “the laws of physics” don’t always seem to apply. The fact is that they do, but the materials we use and the geometries that are used mean that SI engineers, PCB designers, and PCB technologists need to know how material composition and interaction with the PCB fabrication process will impact a successful design. With careful use of simulation, your chances of a high yielding reliable design are increased whilst at the same time reducing your need for repeated prototype builds.

This column originally appeared in the November 2022 issue of Design007 Magazine.

# The Pulse: Fitting Physics to Fact

11-28-2022

In an ideal world you would use “perfect” materials that behave in a truly predictable way, but the realities of engineering mean that compromise is always needed—and so the desire of the purist for “absolute perfection” has to be balanced with the skill of the engineer in designing product to be “good enough” for the specific application.

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# The Pulse: Field Solver Finesse for Modelling Transmission Lines

07-28-2022

When I-Connect007 asked me to contribute for this issue on field solvers, I wondered what more could be added to this extensively discussed subject, but as a supplier and developer of field solvers, Polar still gets asked the same questions both by experienced customers who are perhaps exposed to a new scenario and, as is most welcome, by new entrants to the industry.

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# The Pulse: Using Touchstone Files to Build Measurement Confidence

04-21-2022

Measuring PCB insertion loss can be time consuming, and the probes and cables tend to be significantly more costly (and delicate) than those used for characteristic impedance measurement. Nonetheless, given the high capital investment required for test systems, cables, and probes—and the design of the test vehicles themselves—wouldn’t it be nice if you could have a way of looking at your expected results before you put a test probe to a PCB?

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# The Pulse: Fake Fudged Facts—Using Software to Get the Right High-Speed Answer

10-21-2021

In the science of high-speed signalling, the signals obey the laws of physics, so when a design won’t work or meet a specification, no amount of psychological persuasion will smooth the signals path from source to load. Wouldn’t life be different if by speaking nicely—or shouting—at an underperforming circuit that it springs to life.

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# The Pulse: PCB Design Education—What ‘They’ Don’t Tell You

08-17-2021

For a new designer entering this space for the first time it can be quite an eye opener (no wordplay intended) to discover just how many different disciplines are involved in turning a good design into a fit for purpose PCB.

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# The Pulse: Simulating Stackup and Signal Integrity

04-22-2021

Civil engineer Isambard Kingdom Brunel set a high bar for simulation and modelling—to reduce the number of prototypes and predict the safety margins for structural loads.

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# The Pulse: Don’t Ignore DC Trace Resistance

12-16-2020

Time flies! But the laws of physics don’t. Martyn Gaudion focuses on how important it is becoming to take DC trace resistance into account when measuring and specifying thin copper traces.

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# The Pulse: Application Notes—Advice for Authors

07-27-2020

Application notes are the key to shedding light on new topics or new products and software tools in an easily digestible form. As both a consumer and an author many application notes, Martyn Gaudion explores various types and how to approach them.

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# The Pulse: Communicating Materials From Design to PCB Fabrication

05-12-2020

Designer and fabricator communication—especially for high-speed PCBs—should be a bidirectional “thing.” It is so easy for a designer to say, “Just build this,” and hand over a challenging design to a fabricator who could have performed better with some preliminary conversation or dialog before placing the order. Martyn Gaudion explores communicating materials from PCB design to fabrication.

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# The Pulse: Modelled, Measured, Mindful—Closing the SI Loop

07-18-2019

In this woolly world where high-speed signals enter a transmission line with a well-defined shape and emerge at the receiving end eroded and distorted—and at the limits of interpretation by the receiver—it is well worth running simulation to look at the various levers that can be figuratively pulled to help the pulse arrive in a reasonable shape. At speeds up to 2 or 3 GHz, it usually suffices to ensure the transmission line impedance matches the driver and receiver. And a field solver makes light work of the calculation. But push the frequency higher, and other factors come into play.

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# The Pulse: The Rough Road to Revelation

03-07-2018

Several years ago, an unsuspecting French yachtsman moored his yacht to the railings of the local harbour. For a very nervous full tide cycle, he awaited to see if the cleats would pull out of the glass fiber hull. Fortunately, the glass held. A yachtsman at high tide isn’t too worried about whether the seabed is rough or smooth, but at low tide, the concern about a sandy or rocky seabed is altogether different. With PCBs, the move to low-loss laminates exposes a similar situation.

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# The Pulse: Tangential Thoughts--Loss Tangent Values

12-06-2017

Numbers are fascinating things, and the way they are presented can influence our thinking far more than we would like to admit, with \$15.99 seeming like a much better deal than \$16. Likewise, a salary of \$60,000 sounds better than one of \$0.061 million, even though the latter is a larger number. Our brain has been programmed to suppress the importance of numbers to the right of the decimal point. Such is the case with the loss tangent of materials. It is a tiny number and so to our minds looks insignificant, but it has a directly proportional effect on the energy loss suffered by a dielectric.

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# Vias, Modeling, and Signal Integrity

12-05-2016

Remember that good modeling can’t fix a bad design. The model can tell you where a design is weak, but if you have committed your design to product, the model can only tell you how it behaves. Some less experienced designers seem to think a better model will fix something that doesn’t work; it won’t. It will only reassure you that the design was bad in the first place.

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# Impedance Control, Revisited

06-10-2015

The positives for new fabricators and designers lie in the fact that, even though impedance control may be new to them, there is a wealth of information available. Some of this information is common sense and some is a little counterintuitive. So, this month I’d like to go back to the fundamentals, and even if you are an experienced hand at the subject, it can be worth revisiting the basics from time to time.

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# I3: Incident, Instantaneous, Impedance

03-11-2015

In my December 2013 column, I discussed “rooting out the root cause” and how sometimes, the real root cause is hidden when digging for the solution to a problem. In that column, I described how sometimes in an attempt to better correlate measured impedance with modelled impedance, fabricators were tempted to “goal seek” the dielectric constant to reduce the gap between predicted and measured impedance.

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# Tolerant of Tolerance?

03-30-2014

Wouldn’t life be great if everything fit together perfectly? There would be no need for tolerance. However, for that to be the case, everything would need to be ideal and without variation...

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# Rooting Out the Root Cause

08-31-2013

When your measured trace impedance is significantly different from the calculated/modeled trace impedance, be careful before jumping to conclusions.

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# Changing, Yet Changeless

01-16-2013

Like the whack-a-mole game where the moles keep popping up at random after being knocked back into their holes, the same old questions about technical hurdles surrounding signal integrity continue to surface as technology advances.

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# Repeatability, Reproducibility and Rising Frequency: The R3 Predicament

08-29-2012

One of the more popular editions of The Pulse in 2011 was the article "Transmission Lines - a Voyage From DC." Starting again from DC and working through the frequency bands, Martyn Gaudion looks at what is realistic to achieve and where economic compromises may need to be made.

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# Transmission Lines – a Voyage From Dc – No, Not Washington ...Part 2

08-01-2011

In the second part of this two-part article we continue on our voyage through a transmission line from DC onwards and upwards through the frequency spectrum, step by step exploring the characteristics from very low to ultra high frequencies.

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# Transmission Lines – a Voyage From DC – No, Not Washington, Part 1

07-01-2011

In this two-part article I'd like to join you on a voyage through a transmission line from DC onwards and upwards through the frequency spectrum. In Part 1 we trace the impedance from infinity at DC to the GHz region where it reaches the steady state value of its characteristic impedance.

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# Crosshatching Compromise

06-16-2011

Sometimes engineering results in some uncomfortable compromises; this is often the case with PCBs as the mathematical methods used by the modelling tools are based on "ideal" physical properties of materials rather than the actual physical materials in use.

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# Correlation, Communication, Calibration

05-31-2011

At ElectroTest Expo at Bletchley Park, UK, Martyn Gaudion noticed the extent to which some technologies change, while the overall concepts do not. Prospective customers still ask exactly the same questions as they did 50 years ago: “What’s the bandwidth? Will it work in my application? How accurate?” Followed by the predictable, “How much does it cost?”

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# When Is a 10ghz Transmission Line Not a 10ghz Transmission Line?

03-13-2011

'Just as in life, in electronics the only certainty is uncertainty.' -- John Allen Paulos

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# Regional Differences – a Voyage of Glass Reinforcement

01-13-2011

Why bulk Er is not the same as local Er

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# The Pulse: Laminates Losses and Line Length, Part II

12-20-2010

In the last edition of "The Pulse," we began a discussion on how a modern field solver can help choose the most cost-effective material for a high-frequency application. Last month we looked briefly at the effects of line length and dielectric losses and this month we focus on copper losses; all three are primary drivers for losses.

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# The Pulse: Laminates Losses and Line Length, Part I

12-01-2010

The EE creating the "platform spec" and the PCB fabricator responsible for its realisation face an array of materials with a mix of choices: From ease of processing to reliability requirements and signal integrity. For then next two months, "The Pulse" will focus on signal integrity, describing how to use field solvers to select the best materials when trading cost versus SI performance.

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# Signal Integrity – the ‘S’ Words

10-01-2010

Three words, or rather, phrases are in the process of entering the vernacular of the PCB industry, albeit one phrase is already familiar, but taking on a different meaning. All start with S and all relate in one way or another to signal integrity.

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# All Set to Measure Differential Insertion Loss?

09-13-2010

This column discusses the gradual adaptation necessary for PCB fabricators as more and more silicon families drive the industry toward the requirement for in house measurement of insertion loss.

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# Zen and the Art of Accurate Impedance Measurement* – With Apologies to Prisi

08-12-2010

In his 1974 philosophical novel "Zen and the art of Motorcycle maintenance” Robert M. Prisig contrasts his regular and ongoing daily approach to motorcycle maintenance with his friend's alternate view of leaving well alone between annual service center based maintenance. What has this got to do with accurate impedance measurement you may ask? Please read on to discover more…

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# New Column: The Pulse

07-14-2010

Polar Instruments CEO Martyn Gaudion will be exploring a number of themes. A major SI topic that is set to grow is the emergence of new silicon families designed to push traditional materials into the multi-gigahertz arena. These new chipsets lift transmission speeds up to a point where signal losses rather than reflections become the predominant concern from an SI perspective.

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