# Re: [SI-LIST] : PCB impedance variation v.s. layout pattern

Douglas McKean ([email protected])
Mon, 30 Aug 1999 10:08:17 -0700

At 10:04 PM 8/28/99 -0700, S. Weir wrote:
>Doug,
>
>I believe there is an error in your conclusion on the inductance. I
>believe the "pure" view of a transmission line is an infinite, unvarying
>geometry which is uniform to all wavelengths of interest. It is with that
>assumption that if we cut the transmission line, we get infinity less a
>finite, which ultimately leads to the differential view of C / X, and L /
>X.

I'm not convinced of that. In a truly lossless line,
characteristic impedence Z0 = [ L0/C0 ]^0.5 where L0
and C0 are per length parameters of inductance and
capacitance respectively. So that theoretically, a
2 inch trace should have the same CI of a 20 inch trace.

> When a meander is added, it alters the geometry.

Agreed.

> If the curvature is tight enough, then the AC field
> distribution will be noticeably different in the region
> of the meander than for some distant segment.

I'm in absolute agreement up to here.

> We observe
>this as an increase in the apparent capacitance per unit length in the
>region of the meander.

Here's where I diverge. The lumped parameter model
from which CI is derived (I'm sure you're aware, but
for sake of the discussion) takes on the form

R L
+---/\/\/\---mmmm---+--- ...
|
--- C
---
|
+-------------------+--- ...
| <----- dx -----> |

For a lossless line, R=0.

What I was suggesting with my drawing in a previous
post is that meandering causes parasitic capacitance
in parallel with the trace is the following model

Cp
+---| |---+
| |
| L |
+---+---mmmm--+--- ...
|
--- C
---
|
+-------------+--- ...
| <-- dx --> |

And some shunting of the trace inductance is achieved.
And thus, the reason for reduced CI.

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