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

Michael Tsuk ([email protected])
Tue, 03 Aug 1999 15:41:34 -0700

Dmitri Kuznetsov writes:

> 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 may model certain cases rather well, as for example an "infinite"
reference plane. The DC inductance will be quite large in that case.

However, a better model in my opinion uses something like:

R(f) + j 2 Pi f L(f) = j 2 Pi f Lhf + sqrt(Rdc^2 + j 2 Rs^2 f)

If I've done my math right, this has the right behavior for R at low and
high frequencies, and L at low frequencies is finite. I believe it also
requires no frequency-response correction.

The main problem with this formulation is still that the low-frequency
limit
of L is incorrect. The only way to solve this is to calculate Ldc and
it to the Wline definition. This is most important if one is modeling
structures which are much smaller than the skin depth at the frequencies
of
interest (i.e. on-chip inductance).

I am currently working with Prof. Kotiuga at Boston University on better
understanding skin-effect modeling for time-domain simulation. Very
interesting stuff!

```--
Michael Tsuk
Compaq AlphaServer Product Development
(978) 493-0479

-----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 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
frequencies.

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.

Regards,
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 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
> 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
>