[SI-LIST] Re: Skin Effect Phase 2

• From: "Ransom Stephens" <ransom@xxxxxxxxxxxxxxxx>
• To: <si-list@xxxxxxxxxxxxx>
• Date: Tue, 12 Jun 2012 14:51:11 -0700
```You're free to use the Bessel function formulation - just keep your
perfectly cylindrical conductor straight and infinite.

> -----Original Message-----
> From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx]
> On Behalf Of Doug Brooks
> Sent: Tuesday, June 12, 2012 2:32 PM
> To: rhaller@xxxxxxxxxxxxx; vachkumar@xxxxxxxxx
> Cc: si-list@xxxxxxxxxxxxx
> Subject: [SI-LIST] Skin Effect Phase 2
>
> Thanks for sending this link.
>
> The following is in no way an indictment re how we handle skin effect
> calculations. It's just that as I look further into it, I'm a little
> surprised at how many approximations we make.
>
> Consider the following:
>
> 1. We hypothesize a thing called the skin depth, which we can define
> with some implied precision.
>
> 2. Then we assume the current density is uniform from the surface
> down to the skin depth. This allows us to then calculate the
> cross-sectional area of the conductor where this assumed current is
> flowing, allowing us to then infer the increased resistance of the
> conductor. Except.......... the current does not flow that way.
>
> 3. We assume the current density is following an exponential curve.
> We conveniently define this (normalized) curve as J =
> (1/sd)*e^(-d/sd). This allows us to calculate the normalized current
> density at the skin depth as J=1/(e*sd). Except this doesn't fit, either.
>
> 4. We have defined three curves under which we can calculate the
> area: (a) a rectangle of uniform current density (J) through out the
> conductor, (b) a rectangle of uniform current density (J/(e*sd)) down
> to the skin depth, and (c) an exponential curve. If each truly
> represents the situation accurately, the (normalized) area under each
> of these curves equals 1.0, o0r at least equal each other. But in
> fact, the area under the exponential curve does not. It is very close
> for sd<<conductor radius, but the error goes up the deeper the skin
> depth. (It is still true, however, that this error is small, less
> than a couple of percent.)
>
> So the skin effect calculations we make are models of the skin effect
> based on assumptions. Probably very good assumptions. But
> nevertheless, they are not exact calculations. Is it too much to
> expect that some exact calculations exist, or is this the best we can
> do with our current knowledge and capabilities?
>
> Doug Brooks
>
>
>
>
> At 05:56 AM 6/12/2012, Robert Haller wrote:
> >I had the pleasure if working with Mike Tsuk (PHD) at DEC who did his
> >thesis on Skin effect and supported all our EM tools.  When I left DEC
> his
> >parting gift to me was a very concise table comparing skin depth versus
> >frequency which I find invaluable (and published with his permission).
> You
> >can find this table in a paper I wrote comparing lossy versus lossless
> >T-line simulation results.
> >I keep his table on the wall of my cube to refresh my memory how dramatic
> >the skin effect is at high frequencies. Regards and hopefully you will
> >
> >At 1 MHz ~ skin depth is 2.5 mils
> >At 100 Mhz ~ skin depth is .26 mils
> >At 1 Ghz ~ skin depth is .08 mils
> >At 10G ~ skin depth is 26 uinches
> >
> >
> >Regards
> >Bob
> >
> >
> >-----Original Message-----
> >From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx]
> >On Behalf Of Vachan
> >Sent: Monday, June 04, 2012 1:33 PM
> >To: dbrooks7@xxxxxxxxxxxxxxx
> >Cc: si-list@xxxxxxxxxxxxx
> >Subject: [SI-LIST] Re: Skin Effect question
> >
> >I think that is the point of defining a skin depth - An exponential
> >current density is mathematically equivalent to an approximation where
> you
> >assume uniform current density just below the surface (up to 1 skin
> >depth), and then the current density suddenly drops to 0.
> >On Sun, Jun 3, 2012 at 7:44 PM, Doug Brooks
> ><dbrooks7@xxxxxxxxxxxxxxx>wrote:
> >
> > > This question relates to skin effect.
> > > Consider a current density function with (surface density) Io=8 and
> > > skin depth = .125, unity radius.
> > >
> > > consider the current density function y=8*e^(-x/.125) integrate the
> > > area under this function between 0=<x=<1. The answer is
> > > .9997 (according to the tool I am using!)
> > >
> > > Consider the rectangle formed by the points 0,0, 0,8, .125,8, .125,0
> > > (Note that x=.125 [i.e. at the skin depth] is where the exponent of e
> > > in the current density function is -1.) the area under this rectangle
> > > is 1.0  (same as the area under the current density function.)
> > >
> > > Here is my question. Is this a fortunate coincidence or can this
> > > identity be proven mathematically?
> > >
> > >
> > > Doug has a new e-mail address  dbrooks7@xxxxxxxxxxxxxxx check out the
> > > free resources at http://www.ultracad.com
> > >
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> >
> >
> >--
> >Vachan
> >
> >
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