[SI-LIST] Re: plane RLGC Debye model

See details on the Debye's type fitting and corresponding equivalent
circuits in M.S. Sarto, A. Scarlatti, C.L. Holloway, "On the use of fitting
models for the time-domain analysis of problems with frequency-dependent
parameters" - in proc. Of 2001 IEEE International Symposium on
Electromagnetic Compatibility, v. 1, p. 588-593.
http://ieeexplore.ieee.org/Xplore/login.jsp?url=/iel5/7550/20566/00950710.pd
f?arnumber=950710 
There are no closed-form expressions for the Debye's model coefficients and,
hence, for the elements of the equivalent circuit. You have to formulate and
solve a system of linear equations to find them for a particular case
(matlab, c,...). Note, that in this case you can use pre-define real poles
distributed 1-2 poles per decade over your frequency band of interest - it
will simplify the problem.

Considering the book chapter - yes it is chapter 4. Solution of the
broadband 2D telegrapher's equations (or transmission plane equations) is
given in section 4.2.1.5 for a rectangular cavity.

Best regards,
Yuriy Shlepnev
www.simberian.com 



-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] On
Behalf Of Istvan Nagy
Sent: Saturday, November 15, 2008 2:12 PM
To: shlepnev@xxxxxxxxxxxxx; 'steve weir'
Cc: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Re: plane RLGC Debye model

hi

thanks, this answers my question, but opens a new one.
"fit it with 3-4 real poles evenly distributed over you frequency band to 
get rational approximation form"
-probably this would be the most difficoult part for me, i think. at least i

have no idea how to do it (theory, c program).
but probably its not a signal/power integrity problem already, but 
mathematics.

on chapter 7, you mean chapter 4.2.1.6, figure 4.6d ? ok, it doesnt matter.

regards,
Istvan


----- Original Message ----- 
From: "Yuriy Shlepnev" <shlepnev@xxxxxxxxxxxxx>
To: "'Istvan Nagy'" <buenos@xxxxxxxxxxx>; "'steve weir'" <weirsi@xxxxxxxxxx>
Cc: <si-list@xxxxxxxxxxxxx>
Sent: Saturday, November 15, 2008 7:48 PM
Subject: RE: [SI-LIST] Re: plane RLGC Debye model


> Istvan,
>
> If you have dielectric constant value at 1 MHz, dielectric constant at 20
> GHz may be about 10% smaller for a composite PCB material (as observed in
> multiple experiments). It may be not important for practical PDN design as
> Steve mentioned and simple 1-frequency approximation for G and C may work
> just fine. The same is valid for R and L. Though, in case of very closely
> spaces planes (with less than 5 mils distance), the effect of internal
> inductance of the metal planes in combination with the dielectric 
> dispersion
> can cause significant shifts of resonances even at lower frequencies
> important for PDN design.
> If you want to build the lattice-type equivalent circuit model valid over
> 3-4 decades in frequency and accounting for frequency variations of
> dielectric constant and internal plane inductance, it can be done with the
> broadband transmission plane model (see my paper "Transmission plane 
> models
> for parallel-plane power distribution system and signal integrity 
> analysis"
> in proceedings of 22-nd ACES symposium, 2006, p. 382-389, also available 
> at
> http://www.shlepnev.com/Publications/ACES2006c.pdf). The model is 
> validated
> with experiments in I. Novak, J. Miller Frequency-domain characterization 
> of
> power distribution networks - Artech House, 2007, chapter 7 and in J.
> Miller, G. Blando, B. Williams, I. Novak "Impact of PCB Laminate 
> Parameters
> on Suppressing Modal Resonances" - DesignCon2008.
>
> Here are possible steps to build broad-band SPICE model for PDN:
> 1) Use equation (3) from the cited ACES paper for frequency-dependent
> admittance per square Ys and fit it with 3-4 real poles evenly distributed
> over you frequency band to get rational approximation form (9)
> 2) Use equation (11) for sheet impedance of the plane pair Zs and fit it
> with 3-4 real poles to get the rational approximation form (12)
> 3) Define cell size dx and dy for your equivalent lattice model
> 4) Compute admittance of one sell as Ys*dx*dy - the rational approximation
> from step 1 immediately gives you the second Foster form of GC or RC 
> network
> for the cell node
> 5) Compute impedance of one sell as Zs*dx/dy for x-axis and as Zs*dy/dx 
> for
> y-axis - the rational approximation from step 2 immediately gives you the
> second Foster form of RL network for the x and y branches of your cell
> 6) Combine cells into a 2D equivalent circuit of the plane pair
>
> Note that the final 2D model is similar to a lumped broad-band model for a
> transmission line.
>
> Best regards,
> Yuriy Shlepnev
> www.simberian.com
>
> -----Original Message-----
> From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] 
> On
> Behalf Of Istvan Nagy
> Sent: Saturday, November 15, 2008 4:45 AM
> To: steve weir
> Cc: si-list@xxxxxxxxxxxxx
> Subject: [SI-LIST] Re: plane RLGC Debye model
>
> hi
>
> the only thing what i have is the dielectric thickness, and Er@1MHz, as
> usual. i normally dont haave measurement data.
> the simple RLGC models dont take the frequency-dependeny of the  Er into
> account, skin effect,...
> these can be described by simple equations, but how to kame a lumped model
> based on equations containing E^x... and similar things.
> at least these 2 effects should be included.
> Er(f)=Er(f0)*(jf/f0)^(-0.006366)  this gives a frequency dependency for C
> and G
> R is dependent on f because of the skin effect.
> somehow L is also dependent on frequency?
>
> because it is for a unit-cell model, it shouldnt need more then very few
> parameters, like dielectric thickness, Er(f0), f, cell size.
>
> Istvan
>
> ----- Original Message ----- 
> From: "steve weir" <weirsi@xxxxxxxxxx>
> To: "Istvan Nagy" <buenos@xxxxxxxxxxx>
> Cc: <si-list@xxxxxxxxxxxxx>
> Sent: Saturday, November 15, 2008 12:29 PM
> Subject: [SI-LIST] Re: plane RLGC Debye model
>
>
>> Istvan what data do you have?  Do you have measurements from material
>> samples?
>>
>> For most power work, it is sufficient to use a single value for tangent
>> loss.  If you get the other parameters correct, then the models will
>> tend to show slightly higher peak impedances at the modal resonances
>> than measurements out above 1GHz, but the difference is typically not
>> great.
>>
>> Steve.
>> Istvan Nagy wrote:
>>> hi
>>> how can i calculate the Ri, Li, Gi, Ci parameters for a frequency
>>> dependent unit-cell Debye RLGC model for a power/gnd plane pair? 1st
>>> order or up to 3rd order Debye model would be good.
>>> are there any equations?
>>> (Debye models introduce additional RL and GC elements into the 4 element
>>> original RLGC model to reflect the frequency-dependency, and with 
>>> staying
>
>>> with basic circuit elements, suitable for spice)
>>>
>>> i would like to make frequency dependednt spice 3f5 models (not 
>>> w-element
>
>>> model, since its not compatible with most of the spices) from arbitrary
>>> power planes, with lumped-element grid.
>>> I found application notes where in the examples they just shown the
>>> calculated values, without describing the calculation.
>>>
>>> regards,
>>> Istvan Nagy
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>>
>>
>> -- 
>> Steve Weir
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