Q & A on "A Simple Via Experiment"

This morning I read your award-winning (congrats on that) paper “A Simple Via Experiment”.
Nice work. Thanks for challenging my notion of ground stitching vias.
A couple questions arise:
Question 1:
In Eq 19 the two radii are not defined. I’m assuming R=antipad_radius and r=barrel_radius. Correct?
Question 2:
At the top of page 6 (in 2.1) you assert that the results are relevant at 3x frequencies because the dimensions used are 3x larger than typical. Why? This doesn’t immediately connect in my thinking. Perhaps you’re looking at it in terms of wavelengths?
This point was stated a little imprecisely in the paper, and I was able to clarify it in the webinar. The point I was trying to make was that the dielectric thickness, center conductor diameter and antipad diameter used in the baseline structure were all three times the corresponding dimensions used in most PC boards. Thus, any electrical behavior that is a function of the ratio between the PC board dimension and wavelength will scale according to this factor.

For example, Figure 14 on page 21 predicts that the distribution of magnetic field strength will be a function of frequency and, examining the equations themselves in more detail, the magnetic field strength distribution is a direct function of the radius to wavelength ratio (kr). Thus, although Figure 14 plots distributions up to 20 GHz for the experimental structure, users of these results should associate the 20 GHz distribution with a 60 GHz real world frequency because their structures are so much smaller.

The one dimension which does not scale to a broader frequency band is the overall size of the dielectric disk. Although the diameter of this disk is the largest width Radio Shack thinks their customers will need, most PC boards are much larger. Thus, the ground cavity resonances for a typical PC board will be more closely spaced, irregularly spaced, and narrower than those observed in our baseline test structure.

Like you, I’ve been fascinated lately to come across a variety of structures in which SDD21 is way less then SCC21. This has been stretching my intuition, yet happens when we leave the nice world of 2D t-lines.