[time-nuts] Help w/integration problem
Magnus Danielson
cfmd at bredband.net
Mon Jan 2 05:42:53 EST 2006
From: "John Miles" <jmiles at pop.net>
Subject: Re: [time-nuts] Help w/integration problem
Date: Mon, 2 Jan 2006 01:44:33 -0800
Message-ID: <PKEGJHPHLLBACEOICCBJEEOEGBAA.jmiles at pop.net>
> Thanks; yes, I've got the sqrt() part already, from both my original source
> who requested the feature, and the Zarlink app note.
I didn't bother to look at the Zarlink app note. Until now.
> 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)
Yes, the magic happends between (11) and (12). The integration is 0 to infinity
and not -infinity to infinity, since we already know it mirrors arround 0.
Mind you that these are twice the power, not twice the amplitude. The energy at
fc-f will have the same energy and be coherent to the energy at fc+f, so these
energies add up perfectly. There is a special-case when you can't argue like
this, but we can look the other way here and pick out the real reference
literature when we need to.
> On page 7 of the Zarlink app note, the x2 factor is left outside the radical
> sign:
>
> RMS = sqrt(sum) * 2
Looks like sloppy work to me compared to the Maxim paper, which gives
motivation to the formulas.
> 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?
I hope you've got some insight on that. I could dig deeper into the issue if
you are not quite satisfied. I have better references than the two PDFs you
mentioned. The whole single-sides/double-side spectra issue is a bit confusing
and painstaking at first, I know.
Cheers,
Magnus
> -- 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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