**From:** Clewell, Craig W (*[email protected]*)

**Date:** Tue May 30 2000 - 13:46:16 PDT

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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.
*

.

************************************************************

Doug Brooks' book "Electrical Engineering for the Non-Degreed

Engineer" is now available. See our web site for details.

.

Doug Brooks, President [email protected]

UltraCAD Design, Inc. http://www.ultracad.com

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**Next message:**Doug Brooks: "Re: [SI-LIST] : RE: Split Plane"**Previous message:**Dennis Tomlinson: "Re: [SI-LIST] : RE: Split Plane"**Maybe in reply to:**Barry Ma: "[SI-LIST] : RE: Split Plane"**Next in thread:**Mike Saunders: "RE: [SI-LIST] : RE: Split Plane"

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