# [time-nuts] (Residual) Allan Deviation Calculations

John Miles jmiles at pop.net
Thu Sep 22 13:53:09 UTC 2011

```> >> So the 1 sec Allan dev with my amp included, has gone up by 9.9E-14
> >> for the
> >> 1 sec measurement.
> >>
> >> How to I calculate the actual Allan Dev of my amp for the 1 sec period?

Unless your amp has some serious phase-stability problems you won't be able
to measure its residual ADEV with a counter.  The residual floor of a decent
isolation/distribution amp is close to the limits of the best off-the-shelf
phase noise analyzers, in the high 1E-15/low 1E-14 range at one second.

As an example, here's a couple of measurements on 2N2222A-based multistage
isolation amps designed by Bruce G. and John A. (attached), which I didn't
take any special care in constructing, and didn't bother to warm up for more
than a few minutes.  Two different instruments give similar results for two
different amplifiers, both orders of magnitude below the floors of the best
counters.

The sine-to-CMOS shaper circuit from Charles Wenzel's app note can also be
seen on this plot, again not too far from the instrument's own floor.

> > I have always thought of a noise floor as the lower limit to which you
> > can trust your measurement. Measurements below the floor can be
> > statistically derived IIRC, but calculating the Allan deviation of it
> > makes no sense to me.  As your measurements are all above it , you can
> > trust them.

It's reasonable to use ADEV to measure the residual floor of a counter or
other instrument -- and it's important to do so, in fact, to establish a
working floor for a given measurement configuration.  You should end up with
roughly the same value as the counter's own standard deviation function at
the measurement interval, with (ideally) a 1:1 downward slope due to white
noise until the flicker floor is reached and the trace flattens out.  You
cannot make measurements below this floor, and you don't want to make
measurements close to it, if you can help it.

In the case of the SR620, its residual performance is not going to come
anywhere near 9E-13 at t=1s, unless you are triggering at a faster rate and

Residual measurements are harder than absolute measurements because they
tend to require very low instrument floors... but they're also easier than
absolute measurements because they don't depend on a clean reference
oscillator*.   Lacking a cross-correlating analyzer with a big green button
to push, you might be able to make the measurement by running one arm of
your 2-port residual setup through 90 degrees' worth of coax.  Then drive a
mixer with the two arms and use a sensitive voltmeter to log the phase
differences at the IF port.

With this setup, one radian per second of phase shift at 10 MHz would be
then a cheap DMM with 1-millivolt resolution would already be competitive
with the SR620, with no further tinkering required.  Adding a low-pass
filter and a quiet opamp should get you an equivalent "ADEV floor" near
1E-14.

Basically, you want to crib some techniques from the tight-PLL school of
thought.  TICs and frequency counters are a total dead end for this type of
measurement, but that doesn't mean it has to be difficult or expensive.

-- john, KE5FX

*: You still need to use a source with well-filtered broadband noise to