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

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From: Larry Miller (ldmiller@nortelnetworks.com)
Date: Mon Jun 12 2000 - 11:08:29 PDT


An excellent treatment.

Taking all of this into account, what would you say is a rough limit
frequency for PCBs and coupling caps as a circuit packaging methodology? It
seems like it would be size dependent. For a 6 inch square effective board,
maybe 1 GHz? Do you think you can extend this up by putting in stitched
moats to subdivide a board into smaller effective sheets? Hoo-ha?

Larry Miller

> -----Original Message-----
> From: Larry Smith [SMTP:Larry.Smith@Eng.Sun.COM]
> Sent: Monday, June 12, 2000 10:45 AM
> To: dmckean@corp.auspex.com; doug@dsmith.org
> Cc: si-list@silab.eng.sun.com
> Subject: Re: [SI-LIST] : Upper limit of interplane capacitance
>
> We have experimental data on power plane resonances and good model to
> hardware correlation. There has been a lot of discussion of these
> topics on si-list recently and I feel that it is time to comment.
> Everyone in the industry is using power planes for power distribution,
> but there does not seem to be good agreement for the behavior of these
> planes or how to model and measure them.
>
> Take for example a pair of 1 oz copper planes separated by 4 mils of
> FR4 with dimensions of 6 inches on a side. The planes behave like a
> parallel plate capacitance at low frequency. The capacitance is
> epsilon*area/thickness and works out to be 225 pF/square_inch or 8.1 nF
> for the plane pair.
>
> The time of flight down the length of the planes is 1 nSec for e0=4
> (FR4). A full wave will stand in the cavity at 1 GHz and a half wave
> at 500 MHz and create high impedance resonances. From a point source,
> the planes behave like a radial transmission line, but in my view, this
> not very important. If a point anywhere on the board (except dead
> center) begins to stimulate the planes at a multiple of 500 MHz (half
> wavelength), energy builds up in the resonant cavity. After several
> cycles, there are plane waves bouncing back and forth between the open
> circuit ends of the planes. High voltage is always found at the edges
> and high current nodes are found in the center of the planes. It doesn't
> matter where the source is because the resonance is a function of the
> cavity dimensions. All that is important is that the cavity got
> stimulated.
>
> These effects can be measured nicely with a network analyzer. Connect
> port 1 and port 2 just about anywhere on the board. It is best to
> leave at least an inch between them so that the vertical connections do
> not couple with each other. Fifty Ohm transmission line soldered to
> empty decoupling capacitor pads work nicely for this. At low
> frequency, the network analyzer will show you an impedance that
> decreases with frequency at 20 dB per decade. If you do the math on
> the impedance you calculate the plane capacitance, Z=1/(j*omega*C). At
> frequencies below cavity resonance, all points on the power planes are
> at the same potential at any given point in time and it does not matter
> where the probes are located. For the 6x6 square inch example, this is
> true up to about 100 MHz (1/4 wavelength stands in the board at 250
> MHz).
>
> There are many ways to model this, but my favorite is a matrix of
> transmission lines. We divide the board into an 8x8 array of 64
> sections. Transmission lines are used to connect the nodes in an x-y
> fashion. The transmission line parameters are easily calculated from
> plane capacitance, inductance and resistance. Ray Anderson mentioned
> some of these calculations last week. The calculations have been
> documented by the HP guys at EPEP conferences and Journal articles over
> the past couple of years. HSpice will allow .ac analysis on frequency
> dependent resistors which are used for skin and dielectric loss.
> HSpice also enables parameter calculations and it is possible to
> calculate dB = 20*Log(V/I) to simulate the impedance that matches the
> output of the Network analyzer.
>
> We have very good model to hardware correlation on bare fabs (unstuffed
> PCB's) that correctly shows the capacitance at low frequencies and all
> important cavity resonances up to several GHz. For cavity resonances,
> the position of the probes on the power planes is very important to get
> the low impedance dips associated with 1/4 lambda to a board edge. The
> high impedance peaks occur at the same frequency everywhere on the
> board but the magnitude of the peak varies with position. The height
> of the peaks and depth of the valleys are determined by the Q of the
> circuit which is a strong function of skin and dielectric loss at
> cavity resonant frequencies.
>
> But all that changes as soon as decoupling capacitors and components
> are mounted on the power planes. With well chosen decoupling
> components, it is possible to make the impedance vs frequency flat up
> to 100 MHz. The capacitors force he impedance of the planes to -60 or
> -70dB from 30 kHz to 100 MHz where the bare fab was much higher than
> that, perhaps -30 dB with a slope associated with 8.1 nF. Decoupling
> capacitors still dominate the cavity resonances between 100 and 400
> MHz, but the position on the power planes now becomes important.
> Decoupling capacitor placement is important at these frequencies.
>
> One very important impedance peak occurs between the decoupling
> capacitors (that have gone inductive) and the relatively pure
> capacitance of the power planes. These two elements form a parallel LC
> tank circuit with a high impedance resonance, usually at several
> hundred MHz. If the discrete capacitors are well distributed on the
> power planes (as they usually are on our products), we have an
> inductance and capacitance per square area and position on the PCB is
> not important. This impedance peak must be carefully managed,
> particularly if we have taken advantage of low ESR capacitors to
> minimize the number of mounted components. It is usually more of
> an EMI problem than an SI problem.
>
> We notice several dB of change above 100 MHz when a large uP is
> inserted or removed from it's socket. It takes a lot of careful
> modeling of the active devices and the decoupling capacitors mounted on
> pads and vias to get the simulated models to match the hardware
> measurements. (but that is beyond the scope of this already long
> email..).
>
> regards,
> Larry Smith
> Sun Microsystems
>
> > Date: Fri, 09 Jun 2000 14:44:30 -0700
> > From: "Douglas C. Smith" <doug@dsmith.org>
> >
> > I am not a guru on this topic either, however I have thought
> > that there is more than a radial transmission line here, in
> > that the two dimensional transmission line has lots of funny
> > mid-plane loads in the form of bypass capacitors that give
> > reflectons (I am talking of power to ground plane here).
> > That combined with the open sides would make for a driving
> > point impedance that would should be quite lumpy with
> > frequency. I am ignoring the lossy loads of the devices
> > themselves which are another set of complicating factors.
> >
> > Does anyone have experimental data they have taken on this
> > handy?
> >
> > Doug (Smith)
> >
> > Doug McKean wrote:
> > >
> > > "Chan, Michael" wrote:
> > > >
> > > > I would like to point out that what would be the impedance look like
> when
> > > > you looks at it from the center of the two plates viewing from the
> top? Can
> > > > you still qualify it as a rectangular wave guide as the wave is
> spread out
> > > > in
> > > > 360 degree other than in one particular direction. Instead of
> calling it the
> > > >
> > > > traditional "characteristic impedance" I would prefer to see it as "
> driving
> > > >
> > > > point impedance". Any comment from any guru ????
> > >
> > > The "equations" come out the same. Just as if you
> > > were asking if there would be any difference with
> > > the characteristic impedance of a one dimensional
> > > transmission line at the end or in the center.
> > > Reality would dictate something different with the
> > > geometries and cutouts in the planes.
> > >
> > > But there's a couple of different issues going on
> > > with parallel plates structures and quite different
> > > in many ways. One structure is that the parallel
> > > plates make a transmission line, the other is that
> > > they make a waveguide. The transmission line supports
> > > electric and magnetic fields in the dielectric as
> > > currents move in the plates. The waveguide simply
> > > *guides* fields between them. either along the axis
> > > of the plates or by reflecting them off the walls.
> > >
> > > In the case of the plates constituting a transmission
> > > line, circulating currents say in the power plane would
> > > terminate at the edges. Since there's no termination
> > > at the edge, this would cause theoretically a complete
> > > positive reflection.
> > >
> > > Like ripples on a pond, these would create nodes at
> > > various points about the planes depending upon many
> > > factors geometry being one. Which is in fact the case.
> > > Termination of such could not be accomplished with
> > > a single point connection such as a resistor.
> > >
> > > This phenomena cannot be explained when considering
> > > the planes as a *waveguide*.
> > >
> > > - Doug McKean
> > >
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> >
> > --
> > -----------------------------------------------------------
> > ___ _ Doug Smith
> > \ / ) P.O. Box 1457
> > ========= Los Gatos, CA 95031-1457
> > _ / \ / \ _ TEL/FAX: 408-356-4186/358-3799
> > / /\ \ ] / /\ \ Mobile: 408-858-4528
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