RE: [SI-LIST] : Upper limit of interplane capacitance

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From: Daniel, Erik S. (Daniel.Erik@mayo.edu)
Date: Wed Jun 14 2000 - 11:34:54 PDT


Larry-

I agree with most of your comments on power plane capacitance, but I have to
disagree with one point -- dielectric loss does NOT decrease with decreased
thickness of the dielectric -- dielectric loss is independent of the
dielectric thickness in particular, and all geometrical concerns in general
(unlike skin-effect loss).

You point out that

   alpha = R/2*Z0 + G*Z0/2
   G = tan(delta)*omega*C
   
arguing that, G~C, Z0~1/sqrt(C) , so G*Z0/2 ~ sqrt(C), so reducing the
dielectric thickness increases C which increases G*Z0/2 and hence alpha.
All true except for the very last part of the statement. Reducing the
dielectric thickness also decreases L and Z0~sqrt(L). It turns out that
this cancels the contribution from the sqrt(C) factor.

To see this more clearly, I prefer to write G as follows:

   G = tan(delta)*omega / (prop velocity * Z0)
                          ^^^^^^^^^^^^^^^^^^^^
                             = 1/C
     = tan(delta)*omega*sqrt(e)/(c*Z0)

where e is the dielectric constant (real part), c is the speed of light in
vacuum, Z0 is the characteristic impedance. Using this expression, it is
clear that G*Z0 is independent of geometry. Yes, this treatment is a bit
suspect because it relies on transmission line notation when really
referring to power planes, but I maintain that dielectric loss is generally
geometry independent, unlike skin-effect loss in the surrounding conductors.

                                        - Erik

==================================================================
Erik Daniel, Ph.D. Mayo Foundation
Voice: (507) 284-1634 Guggenheim 1011B
Fax: (507) 284-9171 200 First Street SW
E-mail: daniel.erik@mayo.edu Rochester, MN 55905
==================================================================

> -----Original Message-----
> From: Larry Smith [mailto:Larry.Smith@Eng.Sun.COM]
> Sent: Wednesday, June 14, 2000 12:39 PM
> To: si-list@silab.eng.sun.com
> Subject: RE: [SI-LIST] : Upper limit of interplane capacitance
>
>
> Dr. Johnson
>
> I am glad that we completely agree on the necessity of thin dielectric
> between power planes!
>
> But, let's further consider the role of the dielectric constant. I
> don't want to discourage all the folks out there who are developing
> high K materials for pcb power planes. It is true that there are some
> time of flight issues as we raise the dielectric constant, but I don't
> think they are major.
>
> We have just about reached the "thinness" limit with FR4 woven glass
> and resin with the 2 mil Hadco BC technology. I agree that we can
> connect pairs of power planes in parallel to achieve higher
> capacitance, lower inductance and lower impedance power distribution,
> but there is a better way. It will require a new, thinner material
> between the power planes.
>
> You have asked for someone to develop materials with higher loss to
> deal with plane resonances. I believe the best material for that is a
> thin dielectric. Several suppliers have demonstrated the ability to
> build 1 mil thick dielectric cores with copper planes attached to each
> side. At least one suplier has a road map showing dielectric
> thickness
> at a fraction of a mil. They are working hard to make these
> technologies consistent with PCB manufacture. The cores would simply
> be inserted into the stackup like an FR4 core.
>
> So, how does thin dielectric increase the loss? For low loss
> transmission
> lines, the lossy propagation constant alpha = R/2*Z0 + G*Z0/2. R is
> the conductor resistance, G is the dielectric loss
> (tan(delta)*omega*C), Z0 is the impedance of the transmission line.
> The power planes are well represented an xy array of transmission
> lines. At the frequencies that we are concerned with (1 MHz
> to 5 GHz),
> R and G are dominated by skin loss and dielectric loss. R goes as
> sqrt(freq). G is proportional frequency and C. As we reduce
> the dielectric thickness, the skin losses remain the same but the
> impedance of the transmission line and goes down, thus increasing the
> first term in alpha. Z0 is in the numerator of the second term so it
> might appear that alpha is going to increase as we reduce thickness.
> But G goes as C and Z0 goes as 1/sqrt(C), so the second term of alpha
> also increases with decreasing dielectric thickness. Thin dielectric
> power planes increase the loss of the power planes, a very fortunate
> result!
>
> Attached is a (hopefully small) .pdf file that shows the simulation of
> power plane impedance vs frequency for several dielectric thicknesses.
> One AC amp is forced along the edge of our familiar 6x6 square inch
> pair of power planes. You can see the Capacitive down slope (-20 dB
> per decade) at low frequencies and can see where the plane resonances
> begin above 100 MHz. Skin effect and dielectric loss has been
> included in these simulations. Notice how the plane resonances damp
> out nicely as we simulate 1, 0.5, 0.25 and 0.1 mil thick dielectrics.
>
> A second panel is in the simulation that shows the effect of raising
> the dielectric constant between planes from 4 to 16. Notice how the
> impedance of every curve has dropped. Also notice how the damping has
> been increased for each dielectric thickness. This is because the
> impedance of the planes go as sqrt(L/C) and the dielectric
> constant has
> increased C. A reduction in plane impedance has increased
> the alpha of
> the propagation constant and reduced the magnitude of the cavity
> resonances.
>
> The first priority is to reduce the dielectric thickness because that
> reduces L as well as increases C. But if we happen to get a high
> dielectric constant in that thin material, I will definitely take it!
>
> best regards,
> Larry Smith
> Sun Microsystems
>
> > X-Sender: howiej@mail.methow.com
> > Date: Tue, 13 Jun 2000 15:34:26 -0700
> >
> > I advocate thin dielectric layers, using ordinary FR-4
> > dielectric materials. I don't like using high-dielectric
> > materials for power-and-ground plane separation.
> >
> > As we go to higher frequencies, in order to attain ever-lower values
> > of spreading inductance, we will need thinner and thinner
> power-ground
> > spacing. If we cannot make our power-ground
> > dielectric layers sufficiently thin, we may have to switch to
> > a layer-cake approach with several pairs of power-ground layers.
> >
> > To deal with our resonance problems, I'm hoping that someone
> > will develop some materials with somewhat higher loss
> > properties that FR-4 and copper. Either a more lossy dielectric,
> > or perhaps a copper layer with a surface treatment that
> > increases its skin-effect loss (like plating with tin or
> > something less conductive that copper) could begin to help
> > in this area.
> .
> .
> .
> >
> > Best regards,
> > Dr. Howard Johnson
> >
>
>

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