John Miles said:
One thing that bugs me about your post is that you spend a lot of time
talking about "capacitance." Nobody cares about capacitance. The
only important quantities are the reactances, and those vary with
frequency.
When a person speaks of "capacitance" at high frequencies, what is really
meant is "the impedance of the structure is less (usually significantly
less) than the impedance of the related signal lines".
A trace's characteristic impedance might be 50 or 110 ohms or whatever on
L1, relative to the ground plane on L2, but the impedance from any geometry
in L2 (disparate pours, or a slot in a single pour, etc.) relative to the
(solid or overlapping) ground plane on L3 beneath it results in a
vanishingly small impedance (< 10 ohms) between those pours/planes for
"most" higher frequencies.
For lower frequencies (where the induced wave has had a chance to bounce
around the bounds of the pour a few times), the inductance of vias, traces
and packages comes into play and bypass caps take over. As a result, the
impedance of the pour may vary quite a bit with frequency, and you may get
unlucky with particular combinations of pour shapes, and where the bypass
caps are placed on them (i.e., avoid harmonically related spacings to
prevent bypasses enhancing nodes at some resonant frequency), but for the
most part, with random placement, you'll have good luck that any resonances
that occur will still be low impdance.
Note that a trace crossing a slot in a single pour is identical to it
crossing separate pours, as long as the frequency is higher than the quarter
wave length to the nearest corner of the slot -- until the energy reaches
the end of the slot, it doesn't "know" that it actually IS a slot, or just
another gap.
Terms like "not much" don't help when your interplane C turns out to
be more effective at coupling than at bypassing. And if slot antennas
don't terrify you, you're either really good at your job, really bad
at it, or working on something uninteresting.
A slot antenna, roughly speaking, looks like an inductance (defined by the
flux that goes through the enclosed slot area) parallel with a capacitance
(the capacitance of the sides of the slot to each other, roughly), limited
by the Q of copper and radiation resistance. If L is small and C is large
(which are both true when a slot is underlaid by a contiguous ground plane),
then even for very high Q (which is unlikely, because the inductive Q will
be poor with so much shielding), the impedance of the resonant tank thus
formed can still be very small. Though the resonance will be detectable, it
need not be significant in relation to digital signals (e.g., <20 ohms
versus a ~100 ohm trace crossing it), or in regards to EMC (harder to define
a quantity, admittedly may be more stringent than mere signal quality
requires).
In short, if you make a really bad antenna, it should come as no surprise
that it doesn't necessarily radiate much of significance, nor will it
likewise have any significant effect on circuit operation. It will still be
there, and be detectable through suitable means, but principles aren't as
important as real result.
The dynamics will be there, but even without significant damping, it needn't
necessarily be an automatic failure. This is important to remember: I'm
pretty sure this is one error Tesla himself made -- resonant circuits simply
do not charge up continuously for all time; all real tanks contain a
dissipative element, which acts to suppress the resonance and spread it out.
Tim