But if the vertical dimension from the mesh grid to the transmission line
is approximately the same as the aperture size (as it is in most
technologies), the E and B fields throughout most of the dielectric
will be influenced by more than one of the grid elements. Superposition
will occur and the net fields will be more in the directions that are
parallel or orthogonal to the transmission line. Similar arguments can
be made for power transmission in a diagonal direction on gridded power
You reported a 20% decrease in velocity for an diagonal line over
a mesh plane, even at low frequency. This makes sense. There should
be a 41% decrease (1/sqrt2) if all the fields went in the diagonal
direction. Apparently it is an averaging of the fields in the transmission
line direction and the diagonal grid line direction that leaves us with
about half of the 41% reduction in velocity. Now it is more obvious
why dispersion takes place at high frequencies where the wavelength
is comparable to physical dimensions. Low frequencies simply average
and travel fast. High frequencies travel close to the conductor and
must travel further, leading to reduced velocity.
Thanks for pointing this out. This is an important discussion that
should be on SIlist. If you want to post your comments, I will respond.
Or else, you could just copy this note to SIlist. I do not want to
post your comments back to me without your permission.
> Date: Wed, 6 May 1998 10:35:35 -0700 (PDT)
> From: Xiaojun Zhu <firstname.lastname@example.org>
> To: Larry.Smith@Eng
> Subject: Re: [SI-LIST] : Propagation velocity / discontinuous reference plane
> The propagation delay really depends on the relative location of the
> signal line to the apertures. If the signal line is parallel to the
> aperture edge, then the delay caused by the aperture is small when
> the signal line is above the conductor area, and large when the signal
> line above the apertures. The variation of the propagation constant as
> a function of the location is significant. The same is true for the
> characteristic impedance of the signal line, which is larger above
> the aperture, and smaller above the conductor area.
> For the diagonal case, the variation of the propagation velocity
> and characteristic impedance is small compared to the parallel case.
> For the same aperture size, the signal travels faster than the
> parallel, above aperture case, but slower than the parallel, above
> conductor case.
> The above is true even at very low frequencies. For the fixed
> aperture size ratio, the propagation velocity does not change
> with frequency if the aperture size is very small compared to the
> wavelength (with the surrounding dielectric considered). The
> propagation velocity slows down when the aperture size is comparable
> to the wavelength, and dispersion kicks in.
> Although the propagation velocity is associated with fields, considering
> J=nxH on the conductor surface, I think one can use the longer current
> path to explain the propagation delay, espacially at very low frequency
> where circuit theory is valid.
> The propagation velocity equals c/sqrt(er) is true only if the plane
> is solid. For meshed planes, the number can be 20% smaller, even at
> very low frequencies.
> Xiaojun Zhu
> Cadence Design Systems
> > From owner-si-list@silab.Eng.Sun.COM Wed May 6 09:09 PDT 1998
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> > Errors-To: si-list-approval@silab.Eng.Sun.COM
> > Date: Wed, 6 May 1998 08:49:01 -0700 (PDT)
> > From: larry smith <Larry.Smith@Eng.Sun.COM>
> > Reply-To: larry smith <Larry.Smith@Eng.Sun.COM>
> > Subject: Re: [SI-LIST] : Propagation velocity / discontinuous reference
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> > Status: RO
> > Andrew - This is more opinion than hard theory, but I believe Mike's
> > comments about propagation velocity on 45 degree lines apply at
> > very high frequencies where the wavelength is on the same scale as
> > the mesh (or other structure).
> > For most of the work that we do, structures are much smaller than
> > a wavelength. For example, one wavelength in FR4 at 1GHz is 3 inches,
> > much larger than the size of typical mesh grids or vias.
> > The velocity of propagation is determined not at all by the conducting
> > material, but is a fundamental property of the medium outside of the
> > conductor. The propagation velocity in FR4 is just c/sqrt(eR). At
> > frequencies where the wavelength is much bigger than the structure,
> > all fields in the dielectric (E and B) will be superposition's of the
> > fields associated with the current tracks. I am sure somebody will
> > tell me if I am wrong, but I think those fields will propagate through
> > the structure at c/sqrt(eR) as expected. The fact that there is
> > electric current flowing at 45 degrees to the average electric and
> > magnetic fields is just an interesting phenomenon, but should not
> > influence the propagation velocity of the fields. Remember that
> > the drift velocity of electrons (or holes in a semiconductor) is
> > much less than the speed of light, and is unrelated to the speed
> > of light.
> > Now, when the structure size is similar to a wavelength, the
> > field propagation will more closely match the direction of current
> > flow. But with the dimensions and frequencies that we deal with
> > in signal integrity, I do not believe this is a concern.
> > regards,
> > Larry
> > > From: Preston Andrew MMUk <email@example.com>
> > > To: "'Signal Integrity Mailing List'" <firstname.lastname@example.org>
> > > Subject: [SI-LIST] : Propagation velocity / discontinuous reference plane
> > > Date: Wed, 6 May 1998 15:29:25 +0100
> > > X-Priority: 3
> > >
> > > Whilst trawling through the si-list archive, I came across the following
> > > throw-away comment (Mike Jenkins, "+3.3,5-board stackup problem", 7 July
> > > 1997):
> > >
> > > > Regarding mesh power planes, one caveat: If the plane uses a diagonal
> > > > mesh (i.e., lines at 45 degrees to signal lines), then the ground
> > > > current can't follow the signal path directly. This can substantially
> > > > reduce the velocity of propagation.
> > >
> > > The reasoning seems to suggest that whenever a return current is unable
> > > to follow the signal path closely, then the propagation delay will
> > > increase. This will occur in many circumstances, such as a power-plane
> > > split, a poorly placed bypass cap, or even when there is no appropriate
> > > return plane available.
> > >
> > > Can anyone provide any more theory on this phenomenon?
> > >
> > > Andrew Preston,
> > > Micromass Ltd.
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