**From:** Ray Anderson (*raymonda@ha1mpk-mail.eng.sun.com*)

**Date:** Thu Aug 31 2000 - 12:56:58 PDT

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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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**Next message:**Tsuk, Michael: "RE: [SI-LIST] : skin effect"**Previous message:**C Deibele: "Re: [SI-LIST] : skin effect"**Maybe in reply to:**C Deibele: "[SI-LIST] : skin effect"**Next in thread:**Tsuk, Michael: "RE: [SI-LIST] : skin effect"

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