[SI-LIST] Re: Interconnect Simulations-V2

Hello,

I donot know if this answers your question...but just
a piece of information...the fourier coefficients of a
trapezoidal wave comprises of product of three terms.

1. (tau+tr)/T
2. sinc(n*pi*tr/T)
3. sinc{n*pi*(tr+tau)/T}

where tau is the high time, tr is the rise time ( or
fall time) and T is the period. For tau>>t1, till
Frequency 1/tr, the 2nd sinc pulse decays slowly,
hence 20dB / decade attenuation due to 3rd sinc
pulse.....beyound this knee frequency both the sinc
terms act and hence 40dB/decade attenuation.....

Hope this helps.

Sincerely

Himanshu Arora
PhD student,
Duke University,
Durham, NC.


--- Tom Dagostino <tom@xxxxxxxxxxxxx> wrote:
> 
> If I remember correctly, and its been over 20 years
> since I've seen this,
> but a 2 pole Gaussian low pass filter that is
> critically damped is the basis
> for this number.  That is the response that scope
> designers were trying to
> design to.
> 
> Tom Dagostino
> Teraspeed Consulting Group LLC     Teraspeed
> Consulting Group LLC
> 2926 SE Yamhill St.                Device Modeling
> Division
> Portland, OR 97214                 13610 SW Harness
> Lane
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> tom@xxxxxxxxxxxxx
> 
> 
> -----Original Message-----
> From: si-list-bounce@xxxxxxxxxxxxx
> [mailto:si-list-bounce@xxxxxxxxxxxxx]On
> Behalf Of Keskinen, Kai
> Sent: Tuesday, May 20, 2003 9:24 AM
> To: si-list@xxxxxxxxxxxxx
> Subject: [SI-LIST] Re: Interconnect Simulations-V2
> 
> 
> 
> If you work out the amplitude of the harmonics of an
> infinitely repeating
> trapesoidal waveform with equal rising and falling
> edges, you find that the
> harmonics on a log-log plot fall at 20dB per decade
> until you reach
> 1/(pi*Tr) ~ 0.318/Tr . After that knee frequency,
> they fall at 40dB per
> decade. Most of the significant harmonics are
> present to the knee frequency.
> Clayton Paul's book on EMC has both measurements and
> the derivation for
> those who last did a fourier analysis in undergrad.
> Does anyone know where
> the 0.35 number can be derived from?
> 
> Cheers,
> 
> Kai Keskinen
> Signal Integrity Advisor
> Solectron Technical Center
> 21 Richardson Side Road,
> Kanata, ON K2K 2C1
> <mailto:kaikeskinen@xxxxxxxxxxxxx>
> <http://www.solectron.com/>
> "This message may contain information proprietary to
> Solectron so any
> unauthorized disclosure, copying or distribution of
> its contents is strictly
> prohibited."
>
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