[time-nuts] Are cable delays frequency dependent?

Poul-Henning Kamp phk at phk.freebsd.dk
Sat Sep 12 18:44:50 UTC 2009

In message <20090912163352.8A958BCF7 at ip-64-139-1-69.sjc.megapath.net>, Hal Murr
ay writes:

>If so, what's the mechanism?

There are several mechanisms.

For microwave cables, I think the short and precise explanation is that
materials act weird once you get into the details.

>Context is a memory from 20 years ago.  I think it was a data sheet or app 
>note for clock recovery on a T1 line.

This is a lot simpler case:

The cables simply didn't have flat frequency responses.

To overcome this, various compensation circuits/methods where used.

These compensations incurred frequency dependent delays.

The concept you are looking for is "Group Delay", which is simply
"transmission delay dependent on frequency".

The reason it is called Group Delay, is that before digital transmission,
telephone circuits were modulated, like radio, to higher frequencies,
so that the same cable could carry multiple calls.

A bundle of 12 circuits, modulated on carriers 4kHz apart was called
a group, and was the maximum you could realistically transmit over a
4-wire twisted pair circuit.

Group delay was originally simply the difference between the slowest
and the fastest circuit, most often the highest and lowest carrier
frequency in such a group.

On Coax lines, multiple groups would again be modulated over each other
in frequency into "supergroups".  For instance a 12 MHz coax cable
could carry for instance 10 supergroups of 20 groups of 12 circuits
= 2400 circuits total.

You will notice that 2400*4kHz = 9.6MHz, and if you calculate backwards
that each group of 12 circuits must have occupied 60kHz, the extra
spectrum was used for pilot tones and filter-shapes.

This is why 56kBit became a modem standard speed: It was simply
occupying a group's worth of spectrum.

Anyway, supergroups is where group delay became important:
with two layers of modulation, even using pilot-tones, circuits
carried in frequency ranges where the group-delay changed a lot,
got badly distorted.


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.

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