# [time-nuts]Application note

Jeroen Bastemeijer J.Bastemeijer at EWI.TUDelft.nl
Tue Jul 26 03:02:30 EDT 2005

```Hello Everybody, dear Joseph,

I'm new to the list, however I have been reading the list for some time
with great interest. My name is Jeroen, living  in the Netherlands. I
have always been interested in accurate frequency sources, but the
interest really came to live after buying a HP Z3801A on Ebay last
december.

O.K., I'm writing this mail on the coaxial cable measurement "issue". (I
spend quite some time on doing these measurements in the laboratory I'm
working in).

Cable measurements can be done in different ways. But one thing should
always be held in mind; a coaxial cable is a transmission line. This
means that the end (which end depends on how you use the cable) should
always be terminated with the characteristic impedance (Z0) of the
cable. The velocity of, e.g. a pulse, travelling on the cable is given by:

v * c = 1 / (SQRT (Lm * Cm))

v = velocity factor
c = speed of light
Lm = Inductance of the cable per meter
Cm = Capacitance of the cable per meter (sorry European standards....)

The speed is linked to the cable impedance by means of the following
formula:

Z0 = SQRT (Lm / Cm) = SQRT (Lc / Cc)

Lc = Inductance of the total length of the cable
Cc = Capacitance of the total length of the cable

The impedance, and thereby the velocity factor, of your cable can be
verified by doing two simple measurments and some math.
* Measure the open cable capacitance. Connect one BNC(?) connnector to
the capacitance bridge, do not connect the other side.
* Measure the cable inductance, connect the BNC to the inductance meter
and short the other end.
The math should give you the impedance Z0. This approach works for any
given length of cable.

In this way you could check the quality (= impedance) of your cable.

As mentioned before, a coaxial line is a transmission line. So, if it is
not terminated correctly reflections will occur! These reflections could
really cause big errors in your measurments. I always did measurments by
means of a digital HP oscilloscope, so I could "see" what was happening
on the cable. By measuring the time with the cursors on the oscilloscope
I was able to measure the length of a cable (including the connectors)
within 1 cm (two/fifth of an inch approx).

I never did these measurments by means of a counter, though I would like
to try the experiment ;-). But beware of reflections on your cable, did
you switch the channel B to 50 Ohms? The nice thing of an oscilloscope
is that you "see" when things are going "wrong"....

The fun thing is: in order to get rid of reflections only the
terminating impedance is important! Not the impedance of the feeding
generator. However, the generator output impedance is important when:

* You really want to transfer energy (e.g. with transmitters). Allthough
this is not important for the cable, only the terminating impedance counts.
* If the end of your cable is not correctly terminated. The reason: A
pulse will be reflected at the end, bounce back to the generator. If the
generator impedance is not equal to Z0, not all energy will be absorped,
so it will be reflected.... The pulse will bounce a number of times.
(You can try it with e.g. a 5 ns pulse (short rise time) and watch the
proces with the oscilloscope).

Other sources of error I'm thinking of:

* temperature (v changes with temperature, as Cc is changing strongly
with temperature)
* rise time of the 1pps is too low
* damage to the cable

Could luck with your measurements! Best regards,

Jeroen Bastemeijer PE1RGE

--
Ing. Jeroen Bastemeijer

Delft University of Technology
Department of Electrical Engineering
Electronic Instrumentation Laboratory
Mekelweg 4, Room 13.090
2628 CD Delft
The Netherlands

Phone: +31.15.27.86542
Fax: +31.15.27.85755
E-mail: J.Bastemeijer at EWI.TUDelft.nl

```