[SI-LIST] Re: Prepreg dielectric constant and thickness: what actual values to use?
- From: Scott McMorrow <scott@xxxxxxxxxxxxx>
- To: wolfgang.maichen@xxxxxxxxxxxx
- Date: Thu, 21 May 2009 13:08:04 -0400
Wolfgang,
You are absolutely correct. In reality, to perform a thorough analysis
you would need to also separate each dielectric into it's constituent
parts, epoxy and glass fiber. For differential pairs with edge
coupling, there is a significant divergence in Er, since epoxy may
squeeze through to fill the interstitial void, whereas fiberglass will
be generally constrained to the layers above or below the traces. This
will reduce the edge coupling coefficients, since epoxy has a much lower
Er than glass.
Scott
wolfgang.maichen@xxxxxxxxxxxx wrote:
> 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
Teraspeed® is the registered service mark of
Teraspeed Consulting Group LLC
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