Re: [SI-LIST] : Proposal: Rs correlation/collaboration for W-Elements

Dmitri Kuznetsov (
Mon, 02 Aug 1999 12:01:43 -0700

I agree with Richard, the really important factor is accuracy of Rs and
Gd values. As they are multiplied by frequency, a small error makes a
huge difference. But for a given Rs and Gd, my algorithm in W element
will give you mathematically accurate answer.

I would like to comment on the Sqrt(f)*(1+j)*Rs skin-effect equation
introduced in Hspice 99.2. It has mathematically correct imaginary
part, and does not require frequency-response correction. But this
equation is only valid for cylindrical conductors and only at higher

This skin-effect equation produces the corresponding inductive component
Ls(f)=Rs/(2*Pi*Sqrt(f)). Thus, the inductance becomes infinite at dc.
This substantially alters the waveforms especially when Rs is large.

This was the reason I used Rs*Sqrt(f) in W element. This equation gives
asymptotically correct loss, and I was restoring the correct imaginary
part for any, not just cylindrical, configuration by applying
frequency-response correction.

Dmitri Kuznetsov

Dmitri Kuznetsov, Ph.D.
Principal Engineer

ViewLogic Systems, Inc. e-mail:
1369 Del Norte Rd. Tel: (805)278-6824
Camarillo, CA 93010 Fax: (805)988-8259

"Mellitz, Richard" wrote:
> 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>>
> ------------------------------------------------------------------------
> Name: Mathcad - ms_loss_eq.pdf
> Mathcad - ms_loss_eq.pdf Type: Acrobat (application/pdf)
> Encoding: base64

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