So--is this a homework assignment?

David wrote:
What sort of mode should be used on a Network Analyser for phase matching?
Should it be some sort of Time Domain Reflectometer mode?

Since the VNA operates "native" in the S-domain, I would recommend just
doing S-parameter measurements. I believe you will find that all other
measurements are derived from the measured S parameters. As I wrote
before, if you believe that the cables are adequately represented by a
linear two-port model, then the S-parametes tell you everything you
need to know. (But a two-port model may not be adequate.) Caveat: be
sure to measure them over a wide enough frequency range that you are
sure that there is no phase ambiguity. VNAs typically do not
distinguish among 0 degrees, -360 degrees, +360 degrees, +720 degrees.
But the slope of phase versus frequency is pretty much a give-away
clue.

Input impedance of network analyser is 50 ohms. Many cables are 75 ohms
impedance. For tests on these, a 75 ohm to 50 ohm converter or adaptor is
used. Adaptor name is something like 'min loss pad'.

OK, noted. If you are doing a lot of 75 ohm testing, you may perhaps
want to get a 75 ohm VNA.

My application is a system that checks the RF performance of a Unit Under
Test (UUT). The test cables that mate with the UUT are longer than the UUT,
so the aim is to get the cables to be exactly the same. This is reason for
phase and batch matching - to avoid differential error.

I'm not clear on what you're saying here. If you think that simply
matching the pair of cables that go from your HP8753 VNA's Port 1 and
Port 2 to the UUT will yield accurate test results on the UUT, you are
sadly mistaken. To begin with, there is no need that the cables be
matched in impedance, physical or electrical length, or loss. They may
even have impedance irregularities, and things will still work. What
will work _best_ is if they are low loss and stable. There definitly
IS an Agilent/HP ap note about this sort of thing. What is important,
if you want accurate absolute measurements on your UUT, is that you
CALIBRATE the test system, including the VNA, the cables, and whatever
else you have to connect up to the UUT. Modern VNAs, and in particular
the HP/Agilent 8753, are designed to be calibrated at some plane in
general remote from the VNA's ports, to automatically remove the
effects of whatever cables you use to connect to your UUT.

Because a lot of cables are analysed, the analysis is performed by computer
which connects to Network Analyser. What data sets e.g. S12 should be
compared by the Network Analyser to batch match the cables?

OK, back to matching cables: what you match is up to you. YOU decide
what's important. YOU may wish to put together a "cost function" that
accounts for how badly you want each parameter matched. What is
important in your particular application? You have four
two-dimensional parameters to deal with: S11, S12, S21, S22.
Presumably on a passive line, S11=S22 and S21=S12...

Cables have different connectors on end, but still have to be batch matched.
Have you any suggestions about this? Cables all have SMA connector at one
end. At other end, the connector can be 1) SMA 2) 50 ohm N type 3) coax
contact in circular connector.

And you are trying to match cables with different connectors? That is,
you're trying to match one cable with an SMA and an N, to another with
two SMAs? Good luck! How do you then define where each cable ends?
There are ways to do it, but it's going to depend on just what you are
trying to accomplish in the end.

If you're only trying to match cables of one type with others of the
same type, what's the problem? You can put in whatever adapters you
need, and measure the cables. For matching, what's important is that
they are the SAME, not that they are some absolute value.

Normally, phase matched cables are all made from same coax drum. Ensure coax
comes in on one big drum, not lots of small drums that may have been made at
different times using different processes (e.g. different operator or
machine setting).

And you have control over this? And you'll maintain control over
this when they cables end up being manufactured by a CM overseas? You
may well end up spending all your time just making sure they put the
connectors on the cable properly. Anyway, if it ends up not affecting
your final yield, does it really matter? Maybe you should just buy the
raw cable from a vendor that has taken to heart the idea that process
control is key. That vendor's cable may well be more consistent from
reel to reel than another's is within a single reel.

Cables are batch matched and assembled. If several years later, a cable
breaks, how do I get a replacement batch matched cable to repair system?
Although, I would have kept spare cables from original build, the cables on
the system will have been subject to a different environment e.g. different
stresses and humidity.

You want them matched? Buy a new set. If one broke, and they are all
subject to roughly the same conditions, the others are most likely near
(or beyond) the end of their service life. If there are stresses on
them that can change them, and if matching is important, why have you
not set up a calibration cycle on them? If you kept a spare or spares
of the set, why did you not cycle those through the active set on a
regular basis, if you think that they will be affected by whatever
environment the active set is subject to? If, for example, they are
bundled, why not just include the spare(s) in the bundle, terminated in
dummy connectors, so they are always ready to go? There are solutions
for what you suggest. There are undoubtedly engineering (technical,
cost, ...) tradeoffs among the different solutions. Evaluate them
against the application and pick one. If you discover you picked the
wrong one, learn from the mistake and do it differently the next time.

Another scenario. RF cable is built in slightly more humid environment,
resulting in more moisture in dielectric. Vector gen run and passes. Cable
dries out becoming much better. Vector gen then fails. It appears that a
cable can become too good.

If you're worried about that, why have you not set up a calibration in
the "vector gen" that takes care of it? (The dielectrics and jackets
on cables properly chosen for the application should not have a problem
with humidity. Also, consider where most of the loss in coaxial cable
is...)

Your questions sound a lot like they are spurred by a homework
assignment; they are too broad it seems to be targetting a particular
application. That's all OK, but at some point, you have to get down to
the tradeoffs for a specific application, and make your choices based
on that--on what you have control over, on what the specific needs are,
on the costs ($, time, other resources, ...) associated with various
solutions.

Cheers,
Tom