RE: [SI-LIST] : Proposal: Rs correlation/collaboration for W-Elem

Mellitz, Richard ([email protected])
Mon, 2 Aug 1999 15:17:40 -0700

I need a little clarification here. I must be thinking too slow.

Do HSPICE versions prior to 99.2 not use the Sqrt(f)*(1+j)*Rs?

Do Quad Design's W models use the Sqrt(f)*(1+j)*Rs?

If the Sqrt(f)*(1+j)*Rs are only valid for cylindrical conductors, then
should we not use W elements for microstrip and strip line or are they just
less accurate. If so, how much less and at for what frequencies?

Dmitri you said you used Rs*Sqrt(f) in the W element. Is this Rs the curve
fit coefficient for Re(rs) or the |rs|?

...Richard Mellitz

-----Original Message-----
From: Dmitri Kuznetsov [mailto:[email protected]]
Sent: Monday, August 02, 1999 3:02 PM
To: [email protected]
Subject: Re: [SI-LIST] : Proposal: Rs
correlation/collaboration for W-Elements

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
introduced in Hspice 99.2. It has mathematically correct
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
part for any, not just cylindrical, configuration by
frequency-response correction.

Dmitri Kuznetsov

Dmitri Kuznetsov, Ph.D.
Principal Engineer

ViewLogic Systems, Inc. e-mail: [email protected]
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
> 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
> 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 -
> Mathcad - ms_loss_eq.pdf Type: Acrobat
> Encoding: base64

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