If the frequency is high enough so that the skin depth is not an
appreciable portion of the conductor thickness, does the signal
really know or care whether the surface radius is finite (i.e., round
conductor) or infinite (i.e., flat conductor)?
Paul Levin
Xyratex
Ray Anderson wrote:
> Please correct me if I am wrong, but as I understand Dmitri's
> comments, the present implementation (99.2) of the W element is correct only
> for cylindrical conductors and not those of rectangular (or other arbritrary)
> cross section as are commonly used for interconnect purposes.
>
> This makes sense in that the Rs number derived by a field solver
> is geometry dependent (i.e. that portion contributed to by the proximity
> effect current crowding). The W element must make some assumptions on the
> geometry. Apparently, the assumption is that the conductor has a cylindrical
> cross section, however I feel even this leaves the proximity of the
> cyclindrical member to adjacent planes and adjacent conductors unaccounted
> for.
>
> So if we have a need to model a circuit comprised of non-
> cylindrical cross section conductors at relatively low frequencies
> as well as high (say a fast risetime pulse train with low rep rate)
> can the W element be used to obtain accurate simulation results?
>
> It seems to me that even though the mathematics of the
> W element are said to be correct, that the constraints imposed
> by the cross section assumption and neglect of the proximity
> effect current crowding render the element's accuracy to be
> dubious for real world applications.
>
> The above is not meant to be critical of the W element's
> developers or owners, but just an attempt to really understand
> the limitations of the implementation and to determine a region
> of validity for it's use.
>
> Does anyone have any comments and/or ideas on what might
> possibly be done (short of the vendor re-writing the W element code)
> to ameliorate the short comings such as predistorting the R values
> fed to the element or whatever ??? There are a limited number of
> "knobs" to turn to effect the W elements behavior so this may be
> a challenging problem. It kind of seems that any 'predistortion'
> of the R values to accound for different cross sections and proximity
> consideration would probably be valid a some spot frequency at
> best, and would not be a true broadband solution.
>
> As I prefaced my comments/questions, if I misconstrued
> Dmitri's comments, please correct me.
>
>
> Ray Anderson
>
> Sun Microsystems Inc.
>
> >
> > 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: vdm@viewlogic.com
> > 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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