[SI-LIST] Re: conductor losses
- From: wolfgang.maichen@xxxxxxxxxxxx
- To: "Saoer Sinaga" <saoer.sinaga@xxxxxxxxx>
- Date: Fri, 27 Jun 2008 09:03:36 -0700
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
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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
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