# [time-nuts] 3 corner hat for phase noise

John Miles john at miles.io
Tue Aug 25 17:18:03 EDT 2015

```One nice thing about phase noise is that it's computable with complex FFTs, rather than the one-dimensional phase or frequency differences that ADEV uses.  Another nice thing is that it's stationary -- meaning its probability distribution can (usually) be treated as unchanging from one measurement to the next.  These two properties allow PN measurements to be performed with vector averaging over time, resulting in a single "correct" value at each bin.  Unlike a stability measurement, the expectation with PN is that repeated measurements will always yield the same plot.

So you don't need to use statistical hacks like N-corner hats to measure phase noise with a TimePod or other multichannel instrument.  Pull the SMA jumpers off of the Ch0 and Ch2 jacks and feed two independent references to them.  Over time, the measurement will converge to the phase noise of the source at the REF IN jack, even if it is quieter than either of the two sources at the input jacks.

The TimePod/3120A firmware can't compensate for frequency offsets between Ch0 and Ch2, so the two independent sources need to be very close in frequency and they need to stay that way over the course of the measurement.  A pair of good-quality rubidium or GPS clocks can be a good way to go.

-- john, KE5FX
Miles Design LLC

> -----Original Message-----
> From: time-nuts [mailto:time-nuts-bounces at febo.com] On Behalf Of Tom Van
> Baak
> Sent: Tuesday, August 25, 2015 11:11 AM
> To: Discussion of precise time and frequency measurement
> Subject: Re: [time-nuts] 3 corner hat for phase noise
>
> This is from 3hat.c -- C code, but you get the idea:
>
>         A[i] = sqrt( (0 + SQUARE(AB[i]) - SQUARE(BC[i]) + SQUARE(AC[i])) / 2.0 );
>         B[i] = sqrt( (0 + SQUARE(AB[i]) + SQUARE(BC[i]) - SQUARE(AC[i])) / 2.0 );
>         C[i] = sqrt( (0 - SQUARE(AB[i]) + SQUARE(BC[i]) + SQUARE(AC[i])) / 2.0 );
>
> And watch out for negative square roots.
>
> /tvb
>
> ----- Original Message -----
> From: "Martyn Smith" <martyn at ptsyst.com>
> To: <time-nuts at febo.com>
> Sent: Tuesday, August 25, 2015 9:36 AM
> Subject: [time-nuts] 3 corner hat for phase noise
>
>
> >
> > Hello,
> >
> > Does anyone have an EXCEL spreadsheet that calculates the individual phase
> > noise of  3 oscillators when they are compared against each other, e.g  A vs
> > B, A vs C, B vs C.
> >
> > I.e the 3 corner hat technique.
> >
> > I do have a Timepod and I thought Timelab could do that, have haven't found
> > how to do that.
> >
> > Regards
> >
> > Martyn

```