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

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From: Larry Smith ([email protected])
Date: Wed Jun 14 2000 - 14:37:06 PDT

Erik Daniel sent me the attached note, but I am not sure that it went
to the rest of the si-list. With his permission, I am passing it

He correctly points out that I missed a sqrt(L) in a calculation, and
so dielectric loss is independent of dielectric thickness.

So, of the two terms in the alpha equation, only the skin effect term
increases as we reduce the dielectric thickness. The dielectric loss
still contributes to the total loss of alpha, but it is independent of

In the simulation shown earlier today, the reduction of cavity
resonance as we reduce the dielectric thickness is due entirely to the
skin effect term.

Larry Smith,
Sun Microsystems

------------- Begin Forwarded Message -------------

From: "Daniel, Erik S." <[email protected]>
To: [email protected]
Cc: "Daniel, Erik S." <[email protected]>
Subject: RE: [SI-LIST] : Upper limit of interplane capacitance
Date: Wed, 14 Jun 2000 13:34:54 -0500
MIME-Version: 1.0


I agree with most of your comments on power plane capacitance, but I have to
disagree with one point -- dielectric loss does NOT increase 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: [email protected] Rochester, MN 55905

> -----Original Message-----
> From: Larry Smith [mailto:[email protected]]
> Sent: Wednesday, June 14, 2000 12:39 PM
> To: [email protected]
> 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: [email protected]
> > 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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