[SI-LIST] Re: Prepreg dielectric constant and thickness: what actual values to use?

Scott,
>Average Er is just that, an average of the two materials.  A trace will 
>see an average of the two dielectric constants of the prepreg material 
>above and/or below it.  Use a simple average for the volume.

The situation outlined in the previous post (core and prepreg have 
different eps_r) is case 2 of my post below, so the average you have to 
take is not the arithmetic average - the material with larger eps_r "soaks 
up" more of the electric field and thus has a stronger contribution - same 
case as a microstrip line (where the second dielectric is air).


Actually, in the general case, determining the effective dielectric 
constant of a mixture of two components (e.g. glass and resin in the case 
of a typical PCB material) is non-trivial. I ran into that a while ago and 
at first was a bit surprised to find there are several different widely 
used mixing formulas with contradicting results. The reason becomes 
clearer when as a simple thought experiment you picture a planar capacitor 
consisting of a brick of dielectric between two metal planes. The 
dielectric consists of two sub-blocks with different dielectric constants. 
For simplicity, assume a volume ratio of 1:1 (so each material makes up 
half of the block's volume). If the two sub-blocks are arranged side by 
side (relative to the electric field, so the interface between the two 
blocks is parallel to the field lines), you have a parallel combination of 
two capacitors (neglecting fringing fields). But if you have them stacked 
on top of each other (assuming same outer dimensions, i.e. plate area and 
spacing, of the capacitor), you get a series combination of two 
capacitors.

Assuming a capacitor plate spacing of d, and a total capacitor area A; 
dielectric constants eps_r_1 and eps_r_2:

case 1: each capacitor has area A/2 and spacing d. Parallel combination 
-->

C_tot_1 = eps_0 * eps_r_1 * (A/2) / d + eps_0 * eps_r_2 * (A/2) / d

case 2: each capacitor has area A and spacing d/2. Series combination -->

1/C_tot_2 = 1/(eps_0 * eps_r_1 * A/(d/2)) + 1/(eps_0 * eps_r_2 * A/(d/2))

As anybody can easily see, those two cases produce quite different results 
unless eps_1 is equal to eps_2. The only difference between the cases is 
the distribution of the dielectrics, not their dielectric constants or 
their volume ratio. The mismatch gets worse the more different eps_r_1 is 
from eps_r_2. In a real, fine-grained mixture the effective eps_r is 
somewhere between those two cases, but you can't really tell where without 
knowing the spatial distribution of the two components. For accurate 
results you'd need to enter that distribution into a 3D field solver...

For more details see e.g. 

Stuart O. Nelson
"Density-Permittivity Relationships for Powdered and Granular Materials"
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 54, NO. 5, 
OCTOBER 2005, pp. 2033

or

Kimmo Kärkkäinen, Ari Sihvola, and Keijo Nikoskinen
"Analysis of a Three-Dimensional Dielectric Mixture with Finite Difference 
Method"
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 39, NO. 5, MAY 
2001.


Wolfgang









Scott McMorrow <scott@xxxxxxxxxxxxx> 
Sent by: si-list-bounce@xxxxxxxxxxxxx
05/21/2009 06:33 AM

To
Marc Battyani <marc.battyani@xxxxxxxxxxxxxxxxxx>
cc
si-list <si-list@xxxxxxxxxxxxx>
Subject
[SI-LIST] Re: Prepreg dielectric constant and thickness: what actual 
values to use?






Marc

The problem is one of volume displacement.  Prepreg flows and fills in 
the space between traces on a copper layer.  So, the final thickness of 
a layer of one or multiple prepreg sheets is variable.  For example, if 
prepreg is placed between two solid ground planes, there is nothing to 
fill, therefore no change in thickness - except for the small amount of 
material that is squeezed out the edges of the board during the press 
process.

If prepreg is placed between a ground plane and a trace layer, then 
there will be no filling on the solid ground plane layer, but there will 
be filling of the space between the traces on the trace layer. 
Thickness will be dependent upon the volume change in material that 
flows in between the traces, and the density of traces in any area of 
the board.  If prepreg is placed between two trace layers, then more of 
the material will flow, decreasing the spacing even further.

Average Er is just that, an average of the two materials.  A trace will 
see an average of the two dielectric constants of the prepreg material 
above and/or below it.  Use a simple average for the volume.

best regards,

Scott

-- 
Scott McMorrow
Teraspeed Consulting Group LLC
121 North River Drive
Narragansett, RI 02882
(401) 284-1827 Business
(401) 284-1840 Fax

http://www.teraspeed.com



Marc Battyani wrote:
>  Hi,
> When you specify a stackup the thicknesses of the cores are well defined 
but
> the for the prepreg layers it's less obvious. So when using one or 
several
> prepreg sheets do you just use and add the basic thicknesses or is there 
a
> correction to make?
>
> For the dielectric constant of those materials, when you have 4.3-4.5 @ 
1MHz
> and 3.8-4.0 @ 1GHz what value should we use as a basis for the 
simulations
> for 125MHz HSTL or 200MHz SSTL for instance?
>
> Thanks,
>
> Marc
>
>
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-- 
Scott McMorrow
Teraspeed Consulting Group LLC
121 North River Drive
Narragansett, RI 02882
(401) 284-1827 Business
(401) 284-1840 Fax

http://www.teraspeed.com

Teraspeed® is the registered service mark of
Teraspeed Consulting Group LLC

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