[SI-LIST] Re: Interconnect Simulations-V2
- From: Ray Anderson <Raymond.Anderson@xxxxxxx>
- To: KaiKeskinen@xxxxxxxxxxxxx
- Date: Tue, 20 May 2003 09:55:01 -0700 (PDT)
>
>
>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,
>
I've seen a number of different derivations for the ~.35 in .35/Tr
expression. Each comes up with a slightly different #.
I won't go into all the numerical details here, but one derivation
is based on the fact that the impulse response of a Gausssian filter is
Gaussian. Also the unit step response is the integral of the impulse
response. It can be shown that the for the case of 10% to 90% risetime
the number arrived at in the derivation is .34/Tr
Another way to come around to the number (as Kai described) is to take a fft
of a repetitive trapezoidal waveform. It will be seen that the spectra falls
off at about 20dB/decade up to a certain freq. (when pi*f*Tr <1) and then at
40 dB/decade starting at pi*f*Tr~1. Solving for f you get f~=.32/Tr.
Both of these derivations are approximations based on some assumed
conditions (gaussian response in the first case, and trapezoidal
waveform in the second). As such they are 'rules-of-thumb' which are
useful, but not analytically rigourous and correct.
See Ron Poon's text "Computer Circuits electrical Design" (Prentice Hall
1995) pages 144-145 for the mathematical details.
-Ray
Sun Microsystems Inc.
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