From: Pat Zabinski ([email protected])
Date: Mon Nov 01 1999 - 05:05:05 PST
Chris,
The overall system was far too complex for a full-wave, 3D analysis,
so I looked for gross simplifications. In addition, the "nominal"
case where the average voltage could statistically be considered
zero was not of particular interest. I wanted to cut to the case,
so I tried to simulate what I felt would be the worst-case extremes.
If the simulation results looked reasonable within the extremes,
then I'd be happy.
So, I talked it over with several folks, and we agreed the two
worst-case extremes would be "odd-mode" and "even-mode". Please
excuse my loose use of these terms, but it is analogous with
differential pair terminology. I defined odd-mode where the
victim line on layer-A was rising (or falling) at the same
time as *all* signals on *all other* layers (B, C, & D). In
addition, all signals on the other layers did not toggle
simultaneously, but they toggled in a rippled fashion such
that as the signal on Layer-A propogated down the trace, the
corresponding signals on Layers B, C, & D were time-aligned
with the rising edge of the signal on Layer-A. In essense,
the signals on Layer-B would need to be delayed with respect
to one another by the same amount of time the signal on Layer-A
propogated between the two crossover points. Sorry if this
is clear as mud, but I'm having a difficult time trying to
come up with a verbal explanation for it (I'm a bit under
the weather this morning). Anyway, I tried to set up
a case which was the most-extreme, even to the point
where was likely to never occur. In fact, the chances
that all crossing traces on all other layers were time
aligned with the trace propogating on Layer-A was very
remote (roughly 1 out of 32^2250 in my case!!!), that
I said it would never happen.
For even-mode, I wanted the same effect but the adjacent layers
would toggle in the same direction as the signal on Layer-A.
To set this up, I used a four-line W-element model, where
each of the four lines represented a trace on one of the
layers. For the diagonal elements, I used L, C, & Ro
from our 2D EM tools (i.e., self parasitics). For the
off diagonal elements (i.e., mutual coupling), I assumed:
1) G & R were null; 2) simple parallel plate capacitance;
and 3) relative-angle dependent, parallel plate inductance.
Assumption 1) simply assumed good dielectrics, which I
felt comfortable with. Assumption 2) and 3) are crude,
but after some thought and much discussion, I believe they
are accurate within a first-order approximation. I
admit there is room for improvement in these two assumptions,
but my gut feeling says they're accurate enough for this
experiment.
So, once I have determined mutual inductance and capactance matrices
for single crossover effects, I then scaled the matrix values
up by the number of crossovers expected per-meter. I then
manually inserted these matrices into the W-element RLC
file off-diagonals.
I then put four independent sources (actual transistor-based
driver models) on the w-element, and ran
an eye diagram sim where each of the sources had a
500-bit, non-correlated, random bit stream. I looked at
the resulting far-end (received) signal on all four layers.
In the most extreme case, a logic-zero did bump up to within
0.25 volts of threshold, and a logic-one drooped down to
within a similar distance from threshold. In the next-to-worst
case, the voltage separation from threshold was nearly 0.5V.
If I was simulating a "typical" or "nominal" case, I would have
considered these results to be cause of great concern. However,
given the unlikelihood of all the signals to line up exactly
to obtain these extreme results, I felt comfortable stating
that it was never going to happen.
In terms of the details, it would take several pages of explanation
(e.g., what I meant by "relative angle dependent, parallel plate
inductance" and how I calculated it), which is far too much
for me to explain in this forum. However, assuming my approach
isn't bashed too badly, I do plan on writing a paper
on it, where I'll present the details. I am also hoping
to get some time (or a co-op) to run a small passive experiment
to add some level of validity to my approach.
This is a rather new approach to us, so if you have any suggestions
or criticism, I'd love to hear it.
Pat
> interesting, how do u simulate the non TEM mode interaction
> between layer S-Y or T-X with W element ?
> chris
>
> > > >
> > > > ---------------------- plane
> > > > ---- signal-T
> > > > ---- signal-S
> > > > ---- signal-Y
> > > > ---- signal-X
> > > > ---------------------- plane
> > > >
> > > > X is horizontal, Y is vertical, S is 45, and T is 135. We have
> > > > buried vias between S & T and between X & Y. For a particular
> > > > signal, we only route on orthogonal layer-pairs.
> > > >
> > > >
> > > > * using the minimum-pitch per layer, mutual capacitance
> > > > and inductance of the crossovers (taking into account
> > > > the relative angle of the traces), and a W-element
> > > > representation of lines on each of the four
> > > > layers, we ran an SSN eye diagram simulation of random
> > > > signals on all four layers to determine the effects
> > > > of the mutual parasitics from the other layers.
> > > >
>
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