Re: Modeling - Fast TR

J. Eric Bracken (
Wed, 04 Sep 1996 17:27:36 -0400

Here are a few thoughts:

> I have a generic question regarding creating interconnect models for
> simulation at extremely fast rise times. The scenario is this: signals with
> 150ps rise time are being transmitted through an interconnect, like a right
> angle connector, which is 200ps long. Since the connector is electrically
> long, what is the best alternative for creating an electromagnetic model that
> will yield accurate results at 150ps edge rates? My options are, using BEM
> or FEM analysis:

Keep in mind that a 150ps rise time corresponds to a "knee" frequency
in the signal spectrum of about 3.3 GHz, or a wavelength of perhaps 4.5cm
if your dielectric has epsilon = 4*e0.

> 1) Break connector into seven to ten 2D slices, and create lumped element
> model subcircuits

Probably no good: you won't capture capacitive/inductive coupling between
the elements on one side of the bend and the other. You can't capture the
"3D" nature of the problem with 2D solvers.

> 2) Break connector into seven to ten 2D slices, and create distributed model
> subcircuits

Same problem as 1.

> 3) Draw a one section 3D model of the connector, and create a lumped element
> subcircuit.

This is often surprisingly good, so long as the bend is a lot smaller than
one wavelength. (It probably is.) You can find a lumped "excess"
capacitance and inductance for the bend that will model it pretty well.
"Excess" here means the added capacitance and inductance relative to a
short piece of transmission line of the same length as the bend.

> 4) Draw a one section 3D model of the connector, and create a distributed
> model subcircuit.

This would be good, but I'm not sure how you'll do it. Also, the added
accuracy may be so small compared to a lumped model that you can't justify
the added compute expense of the distributed model.

Final comment:

The most rigorous way to solve the problem is to draw the 3-D structure
in a full wave field solver. Compute the S-parameters for the thing,
sweeping the frequency over a few points (say, from 500MHz to 5GHz).
>From the resulting data for S11 and S22 (the "reflections"), you can
compute the effective capacitance and electrical length of the transmission
lines associated with the bend.

If there's interest, I'll post an example.

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