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 > >find this helpful. > > > >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 > > > >http://www.iec.org/newsletter/aug06_2/design_eng_1.html > > > >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 > > > > > > ------------------------------------------------------------------ > > > To unsubscribe from si-list: > > > si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field > > > > > > or to administer your membership from a web page, go to: > > > //www.freelists.org/webpage/si-list > > > > > > For help: > > > si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field > > > > > > > > > List forum is accessible at: > > > http://tech.groups.yahoo.com/group/si-list > > > > > > List archives are viewable at: > > > //www.freelists.org/archives/si-list > > > > > > Old (prior to June 6, 2001) list archives are viewable at: > > > http://www.qsl.net/wb6tpu > > > > > > > > > > > > > > >-- > >Vachan > > > > > >------------------------------------------------------------------ > >To unsubscribe from si-list: > >si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field > > > >or to administer your membership from a web page, go to: > >//www.freelists.org/webpage/si-list > > > >For help: > >si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field > > > > > >List forum is accessible at: > > http://tech.groups.yahoo.com/group/si-list > > > >List archives are viewable at: > > //www.freelists.org/archives/si-list > > > >Old (prior to June 6, 2001) list archives are viewable at: > > http://www.qsl.net/wb6tpu > >------------------------------------------------------------------ > >To unsubscribe from si-list: > >si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field > > > >or to administer your membership from a web page, go to: > >//www.freelists.org/webpage/si-list > > > >For help: > >si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field > > > > > >List forum is accessible at: > > http://tech.groups.yahoo.com/group/si-list > > > >List archives are viewable at: > > //www.freelists.org/archives/si-list > > > >Old (prior to June 6, 2001) list archives are viewable at: > > http://www.qsl.net/wb6tpu > > > > Check out our resources at http://www.ultracad.com > > ------------------------------------------------------------------ > To unsubscribe from si-list: > si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field > > or to administer your membership from a web page, go to: > //www.freelists.org/webpage/si-list > > For help: > si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field > > > List forum is accessible at: > http://tech.groups.yahoo.com/group/si-list > > List archives are viewable at: > //www.freelists.org/archives/si-list > > Old (prior to June 6, 2001) list archives are viewable at: > http://www.qsl.net/wb6tpu > ------------------------------------------------------------------ To unsubscribe from si-list: si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field or to administer your membership from a web page, go to: //www.freelists.org/webpage/si-list For help: si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field List forum is accessible at: http://tech.groups.yahoo.com/group/si-list List archives are viewable at: //www.freelists.org/archives/si-list Old (prior to June 6, 2001) list archives are viewable at: http://www.qsl.net/wb6tpu