[time-nuts] Help w/integration problem

[Magnus Danielson]

From: "John Miles" <jmiles at pop.net>
Subject: Re: [time-nuts] Help w/integration problem
Date: Mon, 2 Jan 2006 11:42:33 -0800
Message-ID: <PKEGJHPHLLBACEOICCBJIEPKGBAA.jmiles at pop.net>

> > 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.
> 
> Thanks; you're right, given the integration limits in the Maxim note, their
> way makes more sense.

Indeed. It took some time to get sure, but once I was sure it was obvious.

> > > 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.
> 
> Agreed.  I'll leave the *2 operation inside the radicand.  Much appreciate
> the help!

Anytime! Also, if you look at the Maxim paper, it rather looks like a graphical
error not to extend the squareroot sign all the way. The logical place to put
the 2 if not included in the square-root is actually before as customary.

Cheers,
Magnus