I'm in Tucson, AZ, visiting Raytheon. Digital engineer Jose Guttierez approaches me after class, wanting to know why I've suggested stitching together all of the ground planes in his board with a carpet of vias. He needs an intuitive, simple answer that will help him remember, for the rest of his career, why stitching helps.
Going to the drawing board, I sketch a two-board scenario having one connector (Figure 1). Jose recognizes in this simple configuration the obvious need for ground connections between the boards, and he knows that the multiple grounds exist to reduce crosstalk. Jose also understands, based on past experience, that the faster he goes, the more ground pins he needs.
Next, I tear off the paper from the drawing board and slowly fold it, as Figure 2 shows, producing a two-layer structure. The folded sheet now represents the top and bottom halves of a pc-board-layer stack. As Jose's eyes begin to widen, I explain that the vertical connections represent vias. The vias in this new multi-layer configuration act precisely as the connector pins in the previous picture, only smaller. Because the vias are so tiny, the crosstalk effects associated with them show up only at very high frequencies (that is, fast rise and fall times), but they are still noticeable.
Quantitatively, the 3-D rule of scaling governs the behavior of connectors and vias. Given any lossless circuit, when you scale down its physical size by a factor of 10 in all three dimensions, you get a new circuit that works precisely the same as the old circuit, only 10 times faster.
For example, a connector with pins 0.6 in. long (typical Euro-connector dimensions) and operating with 5-nsec rise and fall times requires roughly a 10-to-1 signal-to-ground-pin ratio to control crosstalk. When you shrink this geometry by a factor of 10, representing a via length of about 0.063 in. operating 10 times faster (500-psec rise and fall times), it requires the same 10-to-1 signal-to-ground-via ratio to control the amount of via crosstalk.
Jose's mouth widens into a grin of complete astonishment. Once again, a beautiful analogy has rendered a new subject, which at first seemed difficult, into an intuitive form already familiar to the student. That's a lesson I won't soon forget.