From: "John Miles" <[EMAIL PROTECTED]> Subject: Re: [time-nuts] Help w/integration problem Date: Mon, 2 Jan 2006 01:44:33 -0800 Message-ID: <[EMAIL PROTECTED]>
> 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:[EMAIL PROTECTED] > > Sent: Monday, January 02, 2006 1:28 AM > > To: time-nuts@febo.com; [EMAIL PROTECTED] > > Subject: Re: [time-nuts] Help w/integration problem > > > > > > From: "John Miles" <[EMAIL PROTECTED]> > > Subject: Re: [time-nuts] Help w/integration problem > > Date: Mon, 2 Jan 2006 00:49:19 -0800 > > Message-ID: <[EMAIL PROTECTED]> > > > > > 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. > > > > > > > _______________________________________________ > time-nuts mailing list > time-nuts@febo.com > https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts _______________________________________________ time-nuts mailing list time-nuts@febo.com https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts
