[time-nuts] Help w/integration problem
John Miles
jmiles at pop.net
Mon Jan 2 04:44:33 EST 2006
Thanks; yes, I've got the sqrt() part already, from both my original source
who requested the feature, and the Zarlink app note.
Naturally, the two sources don't agree. Equation 13 (and others) in the
Maxim app note at http://pdfserv.maxim-ic.com/en/an/AN3359.pdf says, in
effect:
RMS = sqrt(sum * 2)
On page 7 of the Zarlink app note, the x2 factor is left outside the radical
sign:
RMS = sqrt(sum) * 2
Unlike the question of whether to interpolate the column midpoints in dBc
space or linear spectral-density space, the position of that x2 term makes a
big difference in the final result. Any insights into who's got THAT one
right?
-- john, KE5FX
> -----Original Message-----
> From: Magnus Danielson [mailto:cfmd at bredband.net]
> Sent: Monday, January 02, 2006 1:28 AM
> To: time-nuts at febo.com; jmiles at pop.net
> Subject: Re: [time-nuts] Help w/integration problem
>
>
> From: "John Miles" <jmiles at pop.net>
> Subject: Re: [time-nuts] Help w/integration problem
> Date: Mon, 2 Jan 2006 00:49:19 -0800
> Message-ID: <PKEGJHPHLLBACEOICCBJGEOCGBAA.jmiles at pop.net>
>
> > Never mind, I think I see what's wrong... you can't integrate the dBc/Hz
> > values directly. You have to turn them back into linear ratios, do the
> > interval sum, and then, if you want dBc coming out, take 10*log10(sum).
>
> You are almost there... you need to square the linears sum, which
> is quickly
> done...
>
> sum = 0
> sum = sum + pow(10,value[1]/10)
> sum = sum + pow(10,value[2]/10)
> ...
> sum = sum + pow(10,value[n]/10)
> rms = sqrt(sum)
> dBc = 10 * log10(sum)
>
> Normally you would use pow(10,value[1]/20) etc. to get the
> amplitudes back, but
> RMS is about summing the power and that is the amplitude square
> as you recall.
>
> Hmm... I'm less a math-freak this morning than usual. A good morning it is
> anyway.
>
>
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