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Apparently the W element model uses a pseudo-propagation function with the
following form.
P(f)= exp{-sqrt[ (G0+f*Gd+j*2*pi*f*C)*(R0+sqrt(f)(1+j)Rs+j*2*pi*f*L) ]*len }
(From HSPICE application note "Boosting Accuracy of W Element
for Transmission Lines with Nonzero Rs or Gd Values")
Let's assume that this is valid for some conditions. It would be nice to
know what the assumptions are.(geometry, frequency, etc.) We can talk about
the validity of the above in another thread.
I would like to make a proposal. I would like to know what various field
solvers report in regards to the above propagation function. Let's start
with a microstrip first (and only look at skin effect). The geometry
follows.
Height over ground: 0.004"
Width of conductor: 0.006"
Thickness of conductor: 0.001"
Conductivity: 0.58E8 mho/meter
Let's all use the same units for Rs. Say:
Ohms/(sqrt(Hz)*meter)
Now, A colleague of mine has supplied a formula that is used in microwave
design. I have attached a PDF file with details. (Too tough for text, TTFT
:-)), I remember foobar)
The answer, using the closed form formula for Rs is:
1.806E-03 ohms/(sqrt(Hz)*meter)
If this is the magnitude of complex Rs, then Re(Rs) would be
1.277E-03 ohms/(sqrt(Hz)*meter)
I have received sidebar results from some of you folks, but I don't want to
post other people answers. However I will compile a table of posted
results. There are issues of complex number involved. Remember I'm looking
for the Rs for the above propagation formula.
Step 2 will be to do same for a strip line geometry where:
Height over ground: 0.005"
Width of conductor: 0.0025"
Thickness of conductor: 0.0005"
Distance between ground planes: 0.0105
It would be appreciated if we could find out what "tricks" people are using
to get Rs from their field solvers.
Regards,
Richard Mellitz
Intel
<<Mathcad - ms_loss_eq.pdf>>
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