[SI-LIST] Re: Transmission line behaviour of on-chip interconnects

You can always consider transmission line behavior, no matter how short the
interconnect is.

It's just that the calculations can be easier if you don't treat them as
transmission lines.  For example, if a length is VERY short compared to a
wavelength, you can ignore it because its effect is negligible.  If it is
not very short but is still shorter than (say) one tenth of a wavelength,
then you may be able to approximate the interconnect by using a lumped (LC,
LRC, or RC) circuit, and the difference between this and the full
transmission line treatment, may be acceptably small.

If an interconnect length approaches or exceeds a quarter wavelength of the
highest frequency of interest to you, then I believe you need to consider
transmission line behavior.  A quarter wavelength of interconnect might
behave radically differently than its LRC equivalent circuit, which is only
an approximation.

The "longest dimension of the chip" is a convenient rule-of-thumb because
most interconnects on a chip are (hopefully) much shorter than the size of
the chip.  Also, it might be that the very lossy on-chip environment (R
dominates over Xl) alters the rules-of-thumb somewhat.

Also be aware that our mathematical representations of lossy transmission
lines do not always work well.  Some are reasonably accurate, others are
much less so, especially with very lossy lines.

At the highest level of accuracy, is real-world physics.  Maxwell's
equations are believed to correctly represent what actually happens in the
real world.  Below that, is transmission line analysis, which (if done well)
comes very close to showing what actually happens, but only in a subset of
cases; fortunately it works well for most cases that we think of as
"transmission lines".  Below that, are simpler electrical models such as
lumped L-R-C circuits, which do not accurately represent anything in the
real world larger than a point, but which can come close when the dimensions
are much smaller than a wavelength.

Regards,
Andy


> Some papers which I referred explains that if the
> longest dimesion of the chip is greater or equal to
> the wavelength of the signal then we consider.
>
> So what happens when longest dimesion of the chip is
> greater or equal to the wavelength of the signal? Why
> are we considering then only transmission line
> behaviour? I would like to understand the complete
> theory behind it.





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