# [time-nuts] ensemble oscillators for better stability

John Miles jmiles at pop.net
Mon Dec 31 00:00:11 UTC 2012

```> and not having a -175dBc/Hz reference, how you can tell that your dual
> -150dBc/Hz performs like a -170dBc/Hz?
> Moreover: what is the physical principle that can explain this? Injection
> locking? Average in the power summer? Taking hundreds or thousands
> oscillators it seems possible to reach astonishing levels...

Good questions!  Phase noise (and AM noise for that matter) is considered to
be a "stationary process," meaning that its statistical properties are
expected to remain the same from one measurement period to the next.  If the
quantity you're trying to measure is both random and stationary, then it's a
good candidate for measurement by averaging.

To take advantage of the stationary property of phase noise, you start by
measuring the spectral density of the DUT noise with two independent FFT
measurements based on the output of two independent phase comparators.  The
DUT is fed to both of the comparators' input channels with a splitter, while
their references come from two independent oscillators.    With repeated
measurements, the average of the two FFT output arrays will converge on the
spectral characteristics that are common to both channels.

The key idea is that because the two references have nothing in common,
their phase and amplitude contributions are as likely to be positive as
negative at any given instant, and will average to zero.  Since the FFT bins
contain complex 2D quantities (I and Q), what actually happens is that the
inner product between the two vectors approaches the correct value when
averaged over time.

So, given a stationary noise process, you are not limited to the usual
sqrt(N) improvement in statistical fidelity, where N is the number of
references that contribute to the measurement.  All you have to do is let
the measurement run longer with N=2.   The measurement floor will improve in
proportion to sqrt(M), where M is the number of averages taken with your
pair of independent references.

Cross correlation (the process I just described) sounds like a free lunch,
and it is -- but only for stationary processes.  When measuring a source's
frequency stability or phase drift, you can't rely on the statistics to
remain the same from one block of data to the next, since observing how the
underlying process changes over time is the whole idea.  So you can only
improve stability measurements by increasing N, not M.  (In a limited sense
ADEV can be 'backed out' of a cross-correlated phase noise measurement, but
only to the extent that the short term statistical properties are
stationary.)

For further reading and less hand waving, see the Agilent E5052A/B
literature, the TSC 5120A-01 manual and white paper by Sam Stein, and Enrico
Rubiola's book/website.

-- john
Miles Design LLC

> On Sun, Dec 30, 2012 at 10:44 AM, Bruce Griffiths <
> bruce.griffiths at xtra.co.nz> wrote:
>
> > Tom Knox wrote:
> >
> >> Dual oscillators in Cross Correlated
> >> measurements will also produce a 3dB theoretical reduction in a Phase
> >> Noise measurement system.
> >>
> >>
> > Since when?
> > Its way better than that.
> > I routinely achieve a PN floor below -170dBc/Hz (I don't have an OCXO
with
> > a phase noise floor below ~ -175dBc/Hz) using a pair of oscillators each
> > having a PN floor (~ -150dBc/Hz) well above that
> >
> > Bruce
> >
> >
> >
> > _______________________________________________
> > time-nuts mailing list -- time-nuts at febo.com
> > To unsubscribe, go to
> > https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts
> > and follow the instructions there.
> >
> _______________________________________________
> time-nuts mailing list -- time-nuts at febo.com
> To unsubscribe, go to https://www.febo.com/cgi-
> bin/mailman/listinfo/time-nuts
> and follow the instructions there.

```