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

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 signal’s path from source to load. Wouldn’t life be different if speaking nicely (or shouting) at an underperforming circuit would spring it to life? (Though the application of warm air to drive out moisture can help, as long as it’s dry, hot air.)

Feedback Facts
I’m not referring to electrical feedback, but process feedback. PCB fabricators will look at process measurements and adjust process parameters to optimise yields; this saves cost and time, and produces a better product for lower material cost over time. Trace width dielectric separation, glass-to-resin ratios, datasheet values, and measurements can all go into the mix when feeding back production measurement values to tailor transmission line characteristics to get better yields on the next build.

Fudge
Why the mention of this sugary sweet yet addictive substance? Sometimes the feedback from measurement doesn’t correlate as expected; there is always a good reason for this, but until you know the root cause it can be tempting to “what if?” a hard-to-measure parameter from the datasheet that wasn’t correct. Then the temptation is to “fudge” the results of the correlation by adjusting said tricky-to-measure parameter. Perhaps a more professional term would be to apply “goal seeking” or “empirical” correction. But this comes with a warning, as often noted by Polar’s signal integrity product manager Neil Chamberlain, “Occasionally a little fudge tastes very good, but too much fudge can make you feel quite ill.” The same is true with measurement correlation. Goal seeking—“fudging”—the results can actually be a very powerful tool, provided you have a good enough knowledge of the physics and the range over which goal seeking is reasonable.

How Much is Reasonable?
Sometimes a process engineer with an impedance correlation problem will microsection and find an inexplicable variation between the modelled and measured value of characteristic impedance. A microsection or two is all it takes to confirm geometries of the line and the dielectric separation of the planes. So, the temptation to enforce correlation is to take the only electrical characteristic that’s not easy to measure and “goal seek it” to the correct value; that mystery characteristic is the dielectric constant.

Our technical staff has uncovered situations where the “goal seeking” of dielectric constant, commonly called Er, has gone way beyond the realistic limits of Er for a given material. Why should that be? Well, Er value could be part of the correlation but more often there are several parameters, each having leverage over the gap between measured and modelled. If a PCB fabricator goal-seeks outside of these limits, their customer may well raise eyebrows that the figure landed on is unachievable.

I have some personal experience with fabricators who are maybe new to the fabrication of transmission lines, goal seeking an Er of less than 2.0 on an FR-4 stripline. Given that the resin has an Er of 3.0 or thereabouts, and the glass of 6.0, then no amount of excess resin or resin starvation in FR-4 will get anywhere near 2, which is the Er of a pure PTFE material. It is also worth recalling that Z_O varies as 1/sq. root Er, so relatively large changes are needed in Er to effect small changes in modelled impedance. Line width and dielectric separation have a much larger effect.

Whilst on the subject of dielectric constant, many PCB engineers who may not have an electrical background obsess over Er at frequency. It’s a bit trickier to measure Er than Z_O, but once you have a suitable coupon and the correct tools (in this case, a short line, long line coupon with Polar Atlas software driving an Anritsu VectorStar VNA), you can use the phase delay per unit length to get a very accurate measurement of transmission line effective Er vs frequency. In Figure 1, you can see that above 1 GHz or so, the variation is absolutely minimal. Higher-loss substrates will see more variation, but surprisingly less than you expect.

Historically, with wider trace transmission lines, TDR measurement of impedance was a simple exercise of reading off the impedance from the TDR reflection, and the reflection over the whole coupon was flat. However, with fine lines, the traces exhibit an upward drift primarily from series resistance of the narrow trace. This upward drift must be removed by DC resistance compensation or launch point extrapolation before attempting correlation. Without correcting the Z_O measurement for resistive effects, correlation will be poor, and if Er is used as a variable to correct the correlation then a false value for Er will be the result.

Conclusion
Whatever you are measuring or modelling it is important that you learn enough about the limits within the modelling tools’ operation, and the physical limits of the “invisible” properties of the materials in the sample under test. Without background knowledge and intuition based on the knowledge and the careful application of measurement and modelling it can be easy to be seduced into correcting the wrong variable.

This column originally appeared in the October 2021 issue of Design007 Magazine.