From: Dennis Tomlinson ([email protected])
Date: Thu Jun 01 2000 - 06:53:48 PDT
[email protected] wrote:
> Doug et al-
> Has anyone extended the '0.35' rule beyond single-order systems?
> Radio Engineers Handbook talks about '0.45' for multi-order waveforms
> with overshoots in the 10% range - but doesn't reference any derivation.
> I'd be curious about high Q networks up to 50% for ex.
I'll take a shot at a second order low pass with two infinite zeros. It
may necessarily contain terms like Q or z[eta], and w0 in addition to
BW (a function of z and w0). I expect the result to be mucked up a
bit more that the first order case.
One caveat, It'll have to wait for the weekend. Anyone else wishing to
take a crack at it is welcome.
> Greg Kimball
> Apps Engr
> TI Storage Products GP
> Doug Brooks wrote:
> > 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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