I am at a loss to see the basis of the disagreement. We both agree that
there is increased shunt capacitance and inductance in the region of the
meander between incremental segments of the trace, and that each effect
leads to the decreased impedance.
Perhaps I misunderstood your intent when you stated:
"What's interesting with the case originally asked
is that characteristic impedence is theoretically
immune to length. Thus, even if the meandering
does add more capacitance from it's relationship
with the ground plane, it also adds more inductance
because of the increased length. Since characteristic
impedence is dependent on the per length values of
capacitance and inductance, it would require IMHO,
the addition of another parameter in order to
change the CI. "
I interpreted that to mean that you contended that the meander did not
change the ratio of parallel capacitance to series inductance per unit
length. From your subsequent postings it does not appear that was your intent.
At 10:08 AM 8/30/1999 -0700, you wrote:
>At 10:04 PM 8/28/99 -0700, S. Weir wrote:
>>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 /
>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.
>> 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
> +---| |---+
> | |
> | L |
> +---+---mmmm--+--- ...
> --- C
> +-------------+--- ...
> | <-- dx --> |
>And some shunting of the trace inductance is achieved.
>And thus, the reason for reduced CI.
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