# Delay Line SI Puzzler

-December 08, 2013

For more than 20 years, papers have been published demonstrating that the shape of a delay line influences its delay. Now there is a beautiful video demonstrating this effect.

Even though she's a Caltech graduate (I'm am MIT graduate), Heidi Barnes, a senior applications engineer with Agilent Technologies, put together a wonderful animation of the advancing phase of a wave through delay lines of equal length with different shapes. See the short video below.

In this example, a 5GHz sine wave goes through two delay lines, each 33mm long if unwound. This is a total delay of about 200psec. The color-coded current density is plotted in time, showing how the zero phase points advance through the two interconnects. This still from the video (Figure 1) shows the position of the zero phase points at the same instant in time.

Figure 1. Time delay shift in delay lines of equal length.

Even though the zero phase points enter each delay line at exactly the same time, the one going through the serpentine line comes out 12 psec earlier than the one going through the switchback line. This is about 5 percent off from the naive prediction.

Knowing the serpentine line will be a little faster than predicted, it's easy to add an extra length to match it to any fixed delay. When the serpentine line is made a little longer (Figure 2), the delays are perfectly matched, as shown below.

Figure 2. When the serpentine line is lengthened by 12psec, the delays are perfectly matched.

Barnes says in the video that, since this is an electromagnetic effect, accurately predicting the delay for interconnects requires an electromagnetic simulation, rather than just a uniform transmission line circuit simulation. This raises a question: Why is there a delay difference, just based on the shape of the traces? She and I have been going back and forth on the possible root cause and how to test our theories.

Rather than hogging all the fun for ourselves, we decided to throw this puzzle out to you, the EDN community. To play this game, you must not only propose a root cause, but suggest a consistency test to support your explanation.

In so many cases of root cause analysis, you can never prove you have the right explanation. All you can do is look at tests that verify the consistency of the explanation. This is illustrated by something I learned in college. A physician should not say, "I have cured this man." Rather, the physician should say, "Under my care, this man did not die." Likewise, scientists (or engineers) should not say, "I have explained this." Rather, they should say, "I have presented an explanation, the absurdity of which cannot be conclusively demonstrated."

What is your explanation for the delay difference based on shape, and what should Barnes try simulating next to support your explanation?

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