[SI-LIST] Re: Using W-element in HSPICE

john lipsius wrote:

> 
> and Zij = sqrt[ (R+jwL)/(G+jwC) ]     i,j = 1,2     w=2*pi*freq ,
> 


The above is only valid for the scalar case.  For two or more lines, you 
have to use matrix math, e.g.

Zc = (R+jwL)*inverse(sqrt((G+jwC)*(R+jwL)))

where "inverse()" is the matrix inverse and "sqrt()" is the matrix 
square root.  This is valid for any number or lines, and can easily be 
implemented in matlab or something similar.  Just make sure that you are 
  doing everything at the matrix level, including the square root, i.e. 
"sqrtm()" in matlab.  It's worth noting that for the symmetric, 2-line 
case you are working on, the inverse and square root can be computed 
analytically, so you can get closed-form scalar equations for each 
element of Z if you work out the matrix math longhand.


> where the RLGC have subscripts "ij", too, and are what you input to the model.
> Careful.... from what I can understand, the W-element G, C matrices' are what 
> avanti
> calls "Maxwellian", so that the ii diagonal elements are actually the sum of 
> the ii and the
> |ij elements| (abs value) for i=const. So, to get C11 in the above for Z11 
> you'd have to
> take C11-|C12| from the model matrix.   But, you better verify this.


To apply the above equation, you do want to use the "Maxwellian" 
matrices, so there's no need to alter the G or C matrices.

You can find this and additional information in "Analysis of 
Multiconductor Transmission Lines" by Clayton R. Paul.  You may want to 
verify my algebra while you're at it...

   -- Steve

-------------------------------------------
Steven D. Corey, Ph.D.
Time Domain Analysis Systems, Inc.
"The Interconnect Modeling Company."
http://www.tdasystems.com

email: steve@xxxxxxxxxxxxxx
phone: (503) 246-2272
fax:   (503) 246-2282
-------------------------------------------


> 
> 
> ----- Original Message -----
> From: <Patrick_Carrier@xxxxxxxx>
> To: <whizplayer@xxxxxxxxx>; <Patrick_Carrier@xxxxxxxx>; 
> <Michael_Greim@xxxxxxxx>;
> <si-list@xxxxxxxxxxxxx>
> Sent: Wednesday, May 29, 2002 4:33 PM
> Subject: [SI-LIST] Re: Using W-element in HSPICE
> 
> 
> 
>>I do not know those formulas.
>>I think odd-mode impedance is a function of twice the single-ended impedance
>>minus twice Z12 or something like that.  So you'd have to get your impedance
>>numbers for the above formula from using your Rs, Ls, Gs, and Cs.
>>Honestly I don't know.  Perhaps someone on the SI-lIST could lend some
>>knowledge....  ;-)
>>
>>--Pat
>>
>>-----Original Message-----
>>From: Bob Patel [mailto:whizplayer@xxxxxxxxx]
>>Sent: Wednesday, May 29, 2002 6:24 PM
>>To: Patrick_Carrier@xxxxxxxxxxxxxxxxx; Michael_Greim@xxxxxxxxxxxxxxxxx;
>>si-list@xxxxxxxxxxxxx
>>Subject: RE: [SI-LIST] Re: Using W-element in HSPICE
>>
>>
>>Hi! PAtrick, Thanks for the reply. Michael did correct
>>the statements for the broadside & edge coupled
>>structure.
>>So, if I wanted the RLGC for differential from the
>>extracted RLGC , you mentioned it would require some
>>math. Are there some analyitical formulas that apply
>>or is it something I have to write in say matlab.
>>Thanks
>>Bob
>>--- Patrick_Carrier@xxxxxxxx wrote:
>>
>>>Bob--
>>>Your RLGC information from the W-element will be
>>>extracted regardless of
>>>what stimulus you apply to it.  In other words, the
>>>RLGC information is
>>>strictly a function of geometry and material
>>>properties (with the exception
>>>of your frequency-dependent losses, which have a
>>>calculated value that is
>>>multiplied by a frequency).
>>>
>>>So, to answer your question, the stimulus does NOT
>>>matter for what goes into
>>>your .RLGC file, if you have selected that option in
>>>the field solver
>>>definition to extract R,L,G, and C parameters.
>>>
>>>However, if you are using the W-element right in
>>>your deck, you need to
>>>apply a negative stimulus on one side and a positive
>>>one on the other side.
>>>This will give you the proper output waveform, but
>>>will not effect the
>>>numbers that go into the .RLGC file, if you are
>>>creating one.
>>>
>>>I know APSIM RLGC puts out a differential impedance
>>>for the pair, and you
>>>can get that from the W-element as well but you need
>>>to do quite a bit of
>>>math with the outputted RLGCs...
>>>
>>>Hope this helps.
>>>And since your traces are on the same layer
>>>(coplanar), I believe they are
>>>considered edge-coupled.  Broadside-coupled traces
>>>sit above one another on
>>>different layers, with their broad sides facing one
>>>another.
>>>
>>>--Pat
>>>
>>>-----Original Message-----
>>>From: Bob Patel [mailto:whizplayer@xxxxxxxxx]
>>>Sent: Wednesday, May 29, 2002 4:50 PM
>>>To: Michael_Greim@xxxxxxxxxxxxxxxxx;
>>>si-list@xxxxxxxxxxxxx
>>>Subject: [SI-LIST] Re: Using W-element in HSPICE
>>>
>>>
>>>
>>>Hi! On item 3 I meant broadside coupled traces.
>>>Thanks
>>>Bob
>>>--- Michael_Greim@xxxxxxxx wrote:
>>>
>>>>On item three that sure looks edge coupled
>>>>to me.  Is that what you meant?
>>>>
>>>>MG
>>>>
>>>>-----Original Message-----
>>>>From: Bob Patel [mailto:whizplayer@xxxxxxxxx]
>>>>Sent: Wednesday, May 29, 2002 4:15 PM
>>>>To: si_list
>>>>Subject: [SI-LIST] Using W-element in HSPICE
>>>>
>>>>
>>>>
>>>>Hi!
>>>>I had looked up the past archives on this subject
>>>>pertaining to the definition of differential
>>>>
>>>pairs.
>>>
>>>>I
>>>>had additional questions as to
>>>>1)if I am extracting the RLGC for a diff pair do I
>>>>apply the stimulus to one node only. And if YES
>>>>
>>>then
>>>
>>>>shouldn't I excite both the nodes differentially
>>>>i.e.
>>>>positive going to one node and inverting to the
>>>>other.
>>>>2)Also when defining the stimulus does the
>>>>
>>>stimulus
>>>
>>>>have to represent the source of the frequency of
>>>>interest i.e. the RLGC will be extracted based on
>>>>the
>>>>pulse source. e.g. at 2.5GHz the pulse source is
>>>>(3.3
>>>>0 100ps 50p 50p 150p 400p)
>>>>3)When defining the model statement for the
>>>>broadside
>>>>coupled pair
>>>>+ CONDUCTOR = ( MATERIAL=copper, SHAPE=rect,
>>>>ORIGIN=(0, 7.2mil) )
>>>>+ CONDUCTOR = ( MATERIAL=copper, SHAPE=rect,
>>>>ORIGIN=(17mil, 7.2mil
>>>>i.e. the traces are 6mil above the gnd plane and
>>>>
>>>are
>>>
>>>>separated by 11mil & are 1.2mil thick. Is this
>>>>correct?
>>>>Thanks in advance.
>>>>Bob
>>>>
>>>>__________________________________________________
>>>>Do You Yahoo!?
>>>>Yahoo! - Official partner of 2002 FIFA World Cup
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>>>>
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>>Yahoo! - Official partner of 2002 FIFA World Cup
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