# [time-nuts] A couple of answers to recent questions

Poul-Henning Kamp phk at phk.freebsd.dk
Tue Aug 9 16:43:56 EDT 2005

```In message <42F91308.6000801 at toad.net>, Tom Clark writes:

>Hi All,
>sults of his experience with it, I was curious what he meant when he spoke of t
>he "clock zero-beat times (TvB calls them "hanging bridges")" .Brooke, can you
>or Tom direct me to somewhere where I might get a better understanding of this?
>Thanks; Rich

The mathematical explanation for the hanging bridge is that the
PPS signal is superimposed with a function which is the modulus
of the error between the receiver local clock and the 'real' GPS
time.

The modulus period is the frequency used to generate the PPS signal,
it is the period of some frequency derived from the local receiver
clock and typically in the 20...150 nsec range.

As long as the receiver local clock is not close to perfect frequency,
the resulting superimposed function more or less has a box-shaped
histogram and it will cancel out by averaging over a few tens of
samples.

However, when the local receiver clock approaches perfect frequency,
or even worse: holds the perfect frequency for long periods of time
(if you're really lucky with the temperature), the function will
take a random value inside the modulus range and stay there until
the receiver clock drifts off frequency again.  In this case there
is no guarantee that any averaging period will be long enough to
cancel out this error.

The hanging bridge is the most common figure we see, but there
are others that are even worse.

The long and the short is, that unless you apply the "sawtooth
correction", which is the receivers prediction of this noise
function, your average, no matter the time period, can be
up to the modulus interval wrong.

--
Poul-Henning Kamp       | UNIX since Zilog Zeus 3.20
phk at FreeBSD.ORG         | TCP/IP since RFC 956
FreeBSD committer       | BSD since 4.3-tahoe
Never attribute to malice what can adequately be explained by incompetence.

```