How does co-ax cable actually work?!?
- From: Jim Lesurf <jcgl@xxxxxxxxxxxxxxxxxx>
- Date: Thu, 21 Jul 2005 10:00:19 +0100
In article <_NzDe.4119$Hd4.1331@xxxxxxxxxxxxxxxxxxxx>, harrogate2
<harrogate2@xxxxxxxxxxxx> wrote:
> [snip]
> > >On top of all that, coax presents a steady 50 or 75 ohm impedance
> all the
> > >way along its length provided it is terminated each end with a
> circuit of
> > >the same impedance.
> [snip]
> Excuse me if I have missed something earlier in this link but cable does
> NOT have an impedence itself. It has characteristic impedence which is
> defined as the impedence of the cable when maximum power transfer takes
> place through the cable from a source into a resistive load both of the
> same impedence, i.e. if maximum power transfer takes place over a cable
> when the source is 75R and the resistive load is 75R then the
> characteristic impedence of the cable is 75R.
I would have put the above somewhat differently. Consider the following
thought-experiment:
1) Take an ideal *very long* run of transmission line of characteristic
impedance Z.
2) Inject a signal at one end, but ensure that the duration of the signal
is 'brief'. Here 'brief' means 'much shorter than the time taked for
signals to propagate the full length of the cable'.
3) Observe the voltage and current at the input end during the period when
the signal was injected.
The result will be that when the signal voltage applied was V(t) that the
current was I(t)=V(t)/Z.
i.e. the transmission line behaves like a load impedance Z.
This is regardless of any load on the 'far end' since the signals haven;t
had time to reach that end yet, and 'report back' on what they found there.
Thus the characteristic impedance does behave just like a 'genuine'
impedance in determining the relationship between V and I. In detail the
actual energy transmission is in terms of the guided E and H field
patterns, which are associated with the V and I values observed at some
specific places.
Over a longer duration the impedance exhibited at the input end will be a
result of the combination of the cable and the load. But given the above I
think it is quite reasonable to regard the cable as having an impedance of
its own.
> One thing that many people overlook is that cables with the same
> characteristic impedence can still cause a mismatch when connected in
> series. This will happen when a thin cable such as UR76 is used as a
> tail on the end of a big cable such as LDF4. The characteristic
> impedence is a consequence of lumped capacitance and lumped inductance
> and to a lesser extent the d.c. resistance. These lumped capacitances
> and inductances will be different for physically different cable
> structures, mainly in terms of size, and a mismatch will occur at their
> joining point.
Again I would put this slightly differently. :-)
The characteristic impedance may be better thought of as a measure of the
relative amounts of energy in the E field and H field per length. The
values of the capacitance per unit length (C') and inductance per unit
length (L') then become ways to describe the consequences in circuit
terms.
The usual condition people mention for a join between two transmission
lines to show no reflection loss is that the characteristic impedance
should be the same for both lines joined. However it is also necessary that
the join should not have a physical discontinuity that affects the fields
local to the join.
This means that, for example, if we join two lines of different size or
shape, then we may get a reflection even if the lines share the same
impedance value. This arises due to the field shapes which arise at the
join being different to those propagating in each individual guide/line.
However this isn't always the same as having different L' and C' values.
A little-known example is described by Kraus in his books. (I think it is
in 'Electromagnetics', but I'm not sure. ) In his case he deals with media
that have epsilon or my values (and hence velocities of light) that differ
from free space, but which have the same impedance as free space, so
signals enter or leave without reflection. (This is useful for things like
radar absorbing materials.)
If you put a suitable material/materials into a line like a co-ax you can
change both the L' and C' prime values, and preserve the Z value, but
change the velocity of propagation. But the result may couple to unloaded
line of the same size and shape with no reflection loss.
Hence the problem with dissimilar lines of the same characteristic
impedance that you quote isn't due to the change in L' and C' values. It is
due to the required change in EH field shapes/sizes at the join. This local
effect may tend to set up a reflected wave as well as a transmitted one.
> That is one good reason wherever possible to use a single cable run of
> cable, or to use the same type of cable if a joint cannot be avoided. If
> a cable size transition has to take place then it should be at an
> amplifier or splitter which will or will tend to mask the mismatch.
Agreed. :-)
Slainte,
Jim
--
Electronics http://www.st-and.ac.uk/~www_pa/Scots_Guide/intro/electron.htm
Audio Misc http://www.st-and.demon.co.uk/AudioMisc/index.html
Armstrong Audio http://www.st-and.demon.co.uk/Audio/armstrong.html
Barbirolli Soc. http://www.st-and.demon.co.uk/JBSoc/JBSoc.html
.
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