# RE: [SI-LIST] : RE: Split Plane

From: Clewell, Craig W ([email protected])
Date: Tue May 30 2000 - 13:46:16 PDT

Ok...I believe this to be correct...

The concept of bandwidth itself comes from low-pass RC filter theory. We
know that the classical low-pass RC filter passes low frequencies readily,
but attenuates high frequencies. For this RC filter, the bandwidth is given
by f2= 1/2(piRC) and is the frequency at which the gain of the filter falls
to 3dB (70%) of the low-frequency value. It is like a cutoff frequency and
is a "qualitative" measure of the transfer of energy through the filter. If
you put a step input into the filter the output will look sort of like a
charging cap. From theory you can show in the output graph that f2=0.35/tr.

craig

-----Original Message-----
From: Doug Brooks [mailto:[email protected]]
Sent: Tuesday, May 30, 2000 1:46 PM
To: [email protected]
Subject: RE: [SI-LIST] : RE: Split Plane

My 2 cents worth:

I'm not sure there IS a derivation of the .35/Tr=BW equation.

Here is a different, simplistic, but intuitive way to look at it. Look at
the rise time of the fastest signal you have. It (closely) resembles the
rise time of a sine wave. Superimpose a sine wave over that rise time so
that the rising edges are congruent. The frequency of a sine wave that has
the same rise time as the rise time of your signal is approximately
.3/Tr. (That is because the rise time of a sine wave is approximately 30%
of its period!) That is the maximum frequency you need to be able to pass
in order to pass the rise time of your signal.

Hence, BW is (approx) .3/Tr,
sometimes expressed as .35/Tr
other times expresser as 1/Pi*Tr (Pi = 3.14159...)
and then sometimes approximated by other ratios close to these, perhaps
allowing for a fudge factor.

Doug Brooks

At 09:55 AM 5/30/00 -0700, you wrote:
>The equation for bandwidth .35/Tr = BW assumes a critically damped Guassian
>response and 10% to 90% Tr times. Different filters (responses) will have
>different constants. For example, if the response of the filter is a
simple
>RC filter the bandwidth will be .4545/Tr.

.
************************************************************
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.
Doug Brooks, President [email protected]
UltraCAD Design, Inc. http://www.ultracad.com

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