# [time-nuts] New topics (was Re: He is a Time-Nut Troublemaker....)

Didier didier at cox.net
Wed Dec 24 14:04:10 UTC 2008

```> -----Original Message-----
> On Behalf Of Magnus Danielson
>
> Didier skrev:
> > John,
> >
> > When you add two (statistically independent) 5 MHz signals
> > and get a 10MHz signal, the 10 MHz signal's *relative* noise
> > and drift will be the average of the *relative* noise and
> > drift of the two 5 MHz signals.
>
> Not to ruin your analogy here, but what I was discussing on
> interlocking was intended as means to phase-lock the two
> oscillators (say 5 MHz but I was thinking 10 MHz) and you
> could then just add their sines, not mix them up. Thus, you
> do not get the sum frequency, you get the average frequency.
> Of course you could go for the frequency multiplication
> variant if you want.
>

locking them, that's why I added "statistically independent".

> > So as when you average n signals, the noise and drift are
> > reduced by sq.rt of n, in this case, 1.4, or about 2dB
> > (if I am correct), a modest improvement.
>
> Square root of 2 is about 1,414 or about 3,01 dB.

I am always confused when considering noise, is it 10*log(p1/p0) or
20*log(p1/p0)?

>
> > Combining more than 2 signals that way (to get more than 2dB
> > improvement) gets complicated in a hurry.
>
> Actually no. Not really. You can build pairs and then
> interconnect them together the same way to form a quad, and
> so you go on. The neat thing is that the combined oscillators
> behave as a new oscillator. This is a very traditional way of
> combining sources to reduce noise. It is certainly not new.
>

First of all, that only works for a number of oscillators that is a power of
two. Then I suppose that as you increase the number of pairs, it will become
harder for individual oscillators to lock themselves to the output (unless
you add circuitry), so you move away from an interlocked system and closer
to a purely added system. Adding the outputs from a bunch of independent
oscillators does not give you one clean output, it gives you a narrow band
of noise. I must be missing something?

> > I guess the idea behind differential locking was to simplify the
> > circuit so that a large n could be used to get meaningful
> > improvement without too much additional circuitry.
>
> Indeed.
>
> Cheers,
> Magnus
>

Didier

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