# Re: [SI-LIST] : skin effect

From: Andreas Cangellaris ([email protected])
Date: Thu Aug 31 2000 - 21:41:22 PDT

Gentlemen,

Greetings!

I second Michael Tsuk's opinion. His explanation of the reasons
why FDTD is the wrong approach to use for the quantification
of skin effect on resistance is excellent!

Michael has contributed some of the most effective methods for
extracting frequency-dependent resistance as a search in the relevant
literature will convince you.

Andreas Cangellaris
University of Illinois

----- Original Message -----
From: Tsuk, Michael <[email protected]>
To: <[email protected]>
Sent: Thursday, August 31, 2000 12:56 PM
Subject: RE: [SI-LIST] : skin effect

> Mike Khusid wrote:
>
> > My favorite way to solve a skin effect problem is an FDTD (finite
> > difference time domain) solver which can actually use Maxwell
> > equations directly and avoid approximations done to derive the
> > aforementioned skin effect formula. Practically any FDTD solver
> > can solve for current distribution inside a real conductor and
> > calculate the resulting skin effect loss.
>
> I'm sorry, I can't think of a *worse* computational technique to solve
skin
> effect problems than FDTD! In order to model, say, the skin effect in
> copper at 1GHz, you'd need cells no more than say a fourth the size of the
> skin depth, which is about 0.08 mils. So to do a 6 mil by 1.4 mil line,
say
> 4 mils above a ground plane, you'd need at least 900 cells wide by 400
cells
> high. And you'd want to do a significant length of etch, at 50000 cells
per
> inch. At 25 bytes per cell, minimum, you're talking 450 GB of storage per
> inch of etch! (You could use 2D FDTD, reducing the memory requirements
> significantly. But then you'd be making the kind of approximations you're
> trying to avoid by using a full-wave technique).
>
> But the real problem is the timestep. The Courant condition would force
> you, with 0.02 mil cells, to a timestep on the order of a femtosecond. So
> to do just one period of a 1GHz sine wave would take about a million time
> steps!
>
> Use finite elements. Use the Partial Element Equivalent Circuit method.
> Use a method of moments code with an impedance boundary condition (my
> favorite). But *please* don't use FDTD for this!
>
> --
> Michael Tsuk
> Compaq AlphaServer Product Development
> (508) 467-4621
>
>
>
> -----Original Message-----
> From: Michael Khusid [mailto:[email protected]]
> Sent: Thursday, August 31, 2000 3:03 PM
> To: 'Clewell, Craig W'; 'Muhammad S. Sagarwala';
> [email protected]
> Subject: RE: [SI-LIST] : skin effect
>
>
> Craig,
>
> The formula Ray and you are referring to
> skin depth = sqrt(2/(omega * mu * sigma))
> indeed seems to be geometry independant, but that's where the catch is.
>
> This formula is derived from a current/electric field penetration if an
> electromagnetic wave is normally incident on the half-infinite slab of
> homogenious material (metal in this case). This would normally be a
> viewpoint of microwave textbooks.
>
> There are two gotchas going to high speed digital world. First, in the
> stripline the propagation of field is parallel to the metal, not
> perpendicular. Second, the thickness of metal comparable to field
> penetration depth changes the current distribution, and thus, the skin
> effect. What a digital designer ultimately cares for is an increased
> resistance of the stripline at high frequencies, and that can be
determined
> from the current distribution.
>
> My favorite way to solve a skin effect problem is an FDTD (finite
difference
> time domain) solver which can actually use Maxwell equations directly and
> avoid approximations done to derive the aforementioned skin effect
formula.
> Practically any FDTD solver can solve for current distribution inside a
real
> conductor and calculate the resulting skin effect loss.
>
> Mike Khusid
>
>
> > -----Original Message-----
> > From: Clewell, Craig W [mailto:[email protected]]
> > Sent: Thursday, August 31, 2000 2:24 PM
> > To: 'Muhammad S. Sagarwala'; [email protected]
> > Subject: RE: [SI-LIST] : skin effect
> >
> >
> >
> > Funny thing....I was under the impression that the skin depth was
> > "frequency" and "material" dependant not geometry dependant.
> > I would be
> > curious to know what data your boss has that says different.
> >
> > Craig
> >
> > -----Original Message-----
> > From: Muhammad S. Sagarwala [mailto:[email protected]]
> > Sent: Thursday, August 31, 2000 12:45 PM
> > To: [email protected]
> > Subject: [SI-LIST] : skin effect
> >
> >
> > Hello Si Gurus,
> >
> > I just had an interesting discussion with my boss on "skin
> > effect on pcb
> > traces".
> > I was of the opinion that increasing the trace thickness from
> > 1/2 oz. to
> > 1oz. would help reduce the
> > skin effect but according to him skin effect does not reduce
> > significantly
> > with the increase in trace thickness.
> > He was of the opinion ( and also had some data to back him
> > up) that skin
> > effect is more dependent on the
> > width of the trace.
> >
> > I always thought that if one increases the overall perimeter
> > of the pcb
> > trace - regardless of whether it is done by
> > increasing the width or increasing the thickness - the skin
> > effect would
> > reduce. I would appreciate if somebody
> > could come up with a better explanation...
> >
> >
> > p.s.: when we talked about pcb traces we were talking about
> > striplines in
> > particular...
> >
> >
> >
> >
> >
> > Design Engineer
> > Schlumberger SABER
> > Ph. (408) 586 7065
> > Fax (408) 586 4668
> >
> >
> >
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