Re: gEDA-user: Any DIY USB Scope project on schedule? Or some recommmendation?

[Dan McMahill <dan@mcmahill.net>]

On Tue, Nov 23, 2004 at 04:51:58PM -0800, Samuel A. Falvo II wrote:
> 
> It's a handy formula to have -- however, I'm curious though: where does 
> the factor of 0.35 come from?
> 

from a 1st order system.  BW (Hz) = 1/(2*pi*tau), step response =
1 - exp(-t/tau).  Time to 10% is

t10 = -tau*log(0.9),

time to 90% is

t90 = -tau*log(0.1),

10-90% risetime is 

tr = t90 - t10 = tau*(log(0.9) - log(0.1)) = tau*log(9)
   = 1/(2*pi*BW)  * log(9)

finally, BW * tr = log(9) / (2*pi) = 0.3497 = 0.35

And for other order systems, its an approximation, but a useful
one at that.

-Dan

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