Paul wrote:
"Roy Lewallen" wrote in message
...
[...]
Coaxial lines do, however, have an interesting characteristic not shared
by other kinds -- the differential and common mode components aren't
simply a mathematical convenience, but are actually physically separate.
If we do the analysis described above, we find that the common mode
current equals the current on the outside of the shield and the
differential current equals the current on the inside. As Owen pointed
out, the differential current is solely on the inside of the shield and
the common mode current solely on the outside. While this makes the
effects of each mode current easier to visualize and sometimes to measure,
the net effects of common mode and differential currents are exactly the
same for coaxial and non-coaxial lines.

Owen Duffy wrote:
In the case of coax, so-called common mode current flows only on the
outside of the outer conductor, and differential mode current flows only
on the inside of the outer conductor and outside of the inner conductor.

I assume that you are talking about a length of coax that is attached to a
free-space antenna. What about the case where the coax shield is grounded
at both ends? (make it a non-ideal ground if you like.) Wouldn't this
create a ground-loop that will cause some of the signal current to flow
through the ground-connection, thus unbalancing the center-conductor/shield
current? In this case, the common-mode current isn't necessarily flowing on
the outside of the shield. (I am asking a question here).

A tricky part in answering this is determining what you mean by "shield
current". There are separate and distinct currents on the inside and
outside of the shield. I'll assume that by "shield current" you mean the
vector sum of these two currents.

The first part of the answer is that the current on the outside of the
inner conductor is always equal to the current on the inside of the
shield, and in the opposite direction (that is to say, they comprise a
pure differential current), provided that the shield is at least several
skin depths thick. This is a consequence of the confinement of the field
by the shield, and has nothing to do with what we connect the cable to.
Connections only impact the current on the outside.

Now consider what happens when the coax is connected to a free-space
dipole, for example. All the current from the center conductor flows
into one half the dipole. But the current on the inside of the shield
has two possible paths: to the other half of the dipole or around the
end of the shield to the outside of the shield. I won't go into more
detail about this, since I've already done so -- you can see what I've
written at http://eznec.com/Amateur/Articles/Baluns.pdf.

If you "ground" both ends of the coax, that is, connect them to
conductors which provide another path between the two ends, you have a
third path the inner shield can follow -- along the "ground" path. So it
splits three ways instead of two. If you use a "pigtail" wire for
grounding or connecting to the load, it adds inductance to the desired
path to the load, which makes the path back along the outside of the
coax more desirable, so you end up with more common mode current than
you would with a low impedance connection.

Also, consider the case at frequencies low enough that skin-effect doesn't
apply. Here there is no inside or outside of the coax shield. Still, the
magnetic fields caused by imbalance between center-conductor and shield
currents are the same, with or without skin effect.

I'm not sure I follow this. When the frequency gets low enough that the
field can penetrate the shield, the line behaves more like a twinlead
line behaves at HF. As I mentioned in my earlier posting, the line can
still have common and differential mode currents -- they're just no
longer physically separated.

At least these are the thoughts I had while I was discussing the
installation of antennas and tuners on boats. There is no end to the
controversy surrounding the grounding of radio equipment on a boat. There
the antennas are typically end-fed wires (usually part of the rigging), and
some combination of radials and seawater connection for the RF counterpoise.

Grounding would be much easier to understand if people would realize
that calling a conductor or connection "ground" doesn't impart magical
qualities. And that currents flow wherever the impedance dictates.

Roy Lewallen, W7EL