From: Ray Anderson ([email protected])
Date: Thu Aug 31 2000 - 12:56:58 PDT
As a couple of kind souls have pointed out offline,
I made a math error in my first posting today
regarding skin effect.
.7 mils is .0007 inch not .007 inch DUH!
So the calculated skin depth of .002 mm
turns out to be of more significance since
the line is real .018 mm thick, not .18 mm.
----------------
| ----------- |
| | | |
| | a |b|
| | | |
| ----------- |
----------------
However, despite my math error (of which I retain copyright)
I think my original argument holds.
Consider the above diagram. The annular region "b" is of
skin depth "t" in thickness.
The interior region "a" is effectively out of the picture
at high frequencies as the current for the most part
concentrates in region "b".
The total loss of the conductor is a comprised of
the copper losses (simply a resistance based on the
cross section area of the conductor) and frequency dependent
losses (skin effect) (these are per unit length losses)
and dielectric losses (and radiation losses to I suppose).
To complicate matters further, the simple skin effect
equation found in most texts doesn't include corrections
for geometry dependent "proximity effect", which due to
current crowding, caused by adjacent current return paths
in non-symmetrical geometries, causes the frequency dependent
losses to increase because the entire area of region "b" in the
diagram is not utilized 100% by the current in some situations.
We know that skin effect loss is supposed to scale with
sqrt(f) and it does except when the proximity effect is
significant (due to non-symmetrical geometries) in which
case the sqrt(f) relation ceases to be the controlling function.
This is a major cause of error in most simulator t-line models.
Note that the proximity effect is most noticeable in on-chip
t-line situations due to the aspect ratios and spacings involved,
and usually isn't too much of a concern in most pcb level situations.
Anyway, the point I was trying to make was that as long
as the "skin depths" on both sides of the conductor
are not thick enough to merge together and consume the
entire conductor (effectively removing region "a") then
increasing the conductor thickness will have little effect
on the skin-effect losses, though it will have marked effect
on the DC losses. Increasing the width of the conductor
ameliorates the effects of the skin-effect losses as well
as reducing the copper losses. (but can increase dielectric
losses somewhat in some situations.....)
-Ray Anderson
Sun Microsystems
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