Hello, your doubt is justified, the simple formula indeed violates causality and as a result will also produce incorrect simulation results. The problem is that it neglects the change in internal inductance. Well above skin effect onset (i.e. in the region where the skin depth is small against the conductore diameter or thickness), you can approximate this with the classic formula R_AC = (1 + j) x k_skin x sqrt(f) = k_skin x sqrt(s/PI) where j is the imaginary unit (sqrt(-1)), s is the Laplace parameter 2 x PI x f x j, k_skin is yout fit parameter, and of course PI=3.14... In essence, this corresponds to a resistive part that increases with sqrt(f), in series with an internal inductance L_int that decreases with sqrt(f) (so the inductive reactance 2*PI*j*f*L increases with sqrt(f)). As said above, this formula breaks down at low frequencies, it would predict zero resistance (in even worse, infinite internal inductance) there. In his last book Howard Johnson gives a simple approximation formula to extend this formula towards DC (with R_DC being the DC resistance), although I have to admit I did not yet check how well this fares in terms of causality: R_total = sqrt(R_DC^2 + R_AC^2) Hope that helps! Wolfgang "Saoer Sinaga" <saoer.sinaga@xxxxxxxxx> Sent by: si-list-bounce@xxxxxxxxxxxxx 06/27/2008 06:04 AM To si-list@xxxxxxxxxxxxx cc Subject [SI-LIST] conductor losses Hi all, Some approximate the resistance of a conductor with the following formula R( f ) = R_DC + R_AC*sqrt( f ). But I read some where, R_AC*sqrt( f ) violates the causality and passivity. I also found a formula to approximate the conductor loss of a plane R( f ) = R_DC + sqrt( j * 2 pi * f * mu / sigma). Question: Can I also use the same formula for e.g. via ? many thanks, Saoer Sinaga NXP ------------------------------------------------------------------ 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 technical documents are available at: http://www.si-list.net List archives are viewable at: //www.freelists.org/archives/si-list or at our remote archives: http://groups.yahoo.com/group/si-list/messages 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 technical documents are available at: http://www.si-list.net List archives are viewable at: //www.freelists.org/archives/si-list or at our remote archives: http://groups.yahoo.com/group/si-list/messages Old (prior to June 6, 2001) list archives are viewable at: http://www.qsl.net/wb6tpu