# Re: [SI-LIST] : 20-H Rule and Self-Resonant Frequency of Power Planes

From: [email protected]
Date: Fri Mar 31 2000 - 16:19:29 PST

Response to SI inquiry of 3/30/00, Re: [SI-LIST] : 20-H Rule and
Self-Resonant Frequency of Power Planes

Sorry, guys, although I'm always open to newfound knowledge, my first
reaction to raising the PCB self-resonance by a factor of two to three times
is "horse pucky!"

Assuming a 12-inch PCB, the only possible support I see for the claim in
Mark's book would be the observance of surface/external waves (using air as
the dielectric) which would exhibit a fundamental frequency of about 492 MHz,
and support higher harmonics of same. Or perhaps a unique situation where a
surrounding enclosure reflected radiated emissions at a higher harmonic of
the PCB and added to the resonance strength. Let's look at two approaches...

First:
Consider a 12-inch PCB (i.e., its longest dimension). For c = 2.998E8 m/s =
9.836E8 ft/s and FR-4 with a relative dielectric constant of 4.5, the basic
fundamental resonance of a pair of ground/power planes with interplanar
excitation would be 231.8 MHz (ignoring any edge setback of the planes).

When the PCB is stuffed with components at reasonable density, the added
capacitance of the many necessary vias alone reduces the board resonances by
a factor of two to four based on the added interplanar distributed
capacitance. So the example PCB would tend to exhibit a fundamental (half
wave) resonance in the 60 MHz to 120 MHz range, plus at harmonics of the
fundamental frequency. I have observed this phenomenon in over 40 different
designs from as many vendors over the last decade.

When one considers the influence of the (typical) myriad of 0.1 UF bypass
capacitors, their distributed capacitance impact is primarily observed below
200 MHz because of the limiting effects of self-resonance. In other words,
the reactance of their connecting inductance becomes sufficiently high to
isolate their effect from the interplane waves. Therefore, the capacitors
become only a secondary consideration on the effective Er of the dielectric
above 200 MHz.

The surface waves I alluded to earlier would treat the plane pair as a single
conducting plate; hence, the potential for exhibiting higher frequency
resonances independent of the dielectric between the planes.

Second:
Basic transmission line theory demonstrates that when the line length is
shorter than 1/4 wavelength, a shorted line will exhibit inductive reactance
(varies with frequency and length of course) and an open line will exhibit a
capacitive reactance (which I've used in many RF designs). By the same
effect, adding capacitance to an open line will make it appear longer. If we
cut back on the power plane at the edge of a PCB, the length is shortened
which will raise the self-resonant frequency of that plane a bit. However,
the fringing capacitance now added by the ground plane being longer than the
power plane will make the shortened power plane look longer. Hence, the
effective cutback (power plane length) is actually less than the magnitude of
the physical cutback, and the PCB resonances will be minimally affected.

BOTTOM LINE:
I'm either missing something or Mark is quoting a special EMC circumstance
like we have all seen and scratched our heads at.

Michael L. Conn
Owner/Principal Consultant
Mikon Consulting

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