Cecil Moore wrote:
Owen Duffy wrote:
Cecil, do you have some quantitative explanation / support for this?

Nope, but there were no disagreeing postings.

I am not asking whether or not field conditions (and V/I on the
conductors) immediate to the discontinuity are not Zo of either of the
lines, just where has the 2% of a wavelength come from?

As I remember it came from the spacing between conductors Vs wavelength.
The spacing between conductors is about 0.1 inches for RG-58. How many
times that value would you think it would take for a transmission line
to force its Z0 upon the signals? At 10 MHz, 2% of a wavelength (24 inches)
is about 250 times the spacing between conductors.

Maybe the electromagnetics people have a useful way to visualize it...

Deep inside the coax, the electric field lines between the inner and
outer of the coax are exactly at right-angles to the main axis. Where
that is exactly true, you have a pure TE10 mode so it's also valid to
assume that V/I is exactly equal to Zo.

Very close to the end of the coax, the electric field lines from the
center conductor start to reach out and connect with whatever is out
there beyond the end of the shield. Then you no longer have pure TE10
and can no longer assume that V/I=Zo.

Coming at it from the other direction, the question would be: how far
into the coax must you go before the field lines become accurately at
right-angles?

We can be sure that the field lines won't suddenly snap from being
divergent to being accurately at right-angles, so what we're really
asking is: how far before the field lines are near-enough at right
angles to make V/I=Zo a good engineering approximation?

Intuitively, the diverging field lines only seem likely to occur within
a few diameters of the end of the shield. Field lines always connect
with highly conducting surfaces at right-angles, and they won't like to
be sharply bent to run along the axis of the coax.

In other words, the effect would seem to be mainly a function of shield
diameter D. Again intuitively, I can't see where wavelength would come
into it, unless D itself is a significant fraction of the wavelength
(which is normally never true, and even microwave engineers try to avoid
it).

Following this picture of diverging field lines, there should also be a
secondary effect depending on how the inner and shield of the coax are
connected to the circuit outside.

All of this suggests that it's impossible to give a single answer that
would be valid for all cases (unless you choose a number that's so big,
it can't fail to be correct... like "120 radials" :-)

However, none of this speculation is of any practical consequence. All
practical experience indicates that if a line is so short that V/I is
not quite equal to Zo, the impedance transformation along that line will
be so small that the effect of any Zo error is lost in the noise.



--
73 from Ian G/GM3SEK 'In Practice' columnist for RadCom (RSGB)
http://www.ifwtech.co.uk/g3sek