Baron wrote:

Please could you elaborate on how and why a common mode current has a
different VF on a balanced line.

Sure.

First, a balanced line, whether it's twinlead or coax, doesn't have any
common mode current, by definition -- the lack of common mode is what
makes it balanced. We're talking about a physically symmetrical line.

Whenever you have a two conductor line, you effectively have two
transmission lines, differential mode and common mode. Although you
actually have only one current on each conductor, by taking advantage of
the principle of superposition you can mathematically separate the two
currents into two *sets* or components of currents, analyze their
effects separately to gain a better understanding, and simply add the
results if you want to know the overall solution. The sum of the common
mode and differential currents are the actual conductor currents, and
the sum of the common mode and differential responses is the actual
response.

The differential or transmission line mode waves (voltage and current)
are the components which are equal and opposite on the two conductors,
so the field is strongest between the two conductors, fringing outward
in the case of ladder line. The presence of the dielectric material in a
major portion of the field slows down the waves, lowering the velocity
factor. In the case of coax, the field is entirely within the dielectric
so we can easily calculate the velocity factor if we know the dielectric
constant of the material. In the case of ladder line, we don't know what
fraction of the field is in the air and what's in the dielectric without
a very advanced computer program, so we have to measure the velocity
factor. The fraction and therefore velocity factor changes, by the way,
with frequency, a phenomenon known as dispersion.

The common or antenna mode waves are the components that are equal and
in the same direction or polarity on the two conductors. The field is
the same as it would be if the two conductors were connected together to
make a single conductor. One conductor of the common mode transmission
line is the two conductors of the ladder line, and the other is the
Earth and/or surrounding conductors. These two common mode transmission
line conductors are usually much farther apart than the ladder line
conductors, so the common mode characteristic impedance is higher than
the differential mode impedance. The velocity factor is usually higher,
too, because the field is between the two common mode conductors -- the
ladder line and the Earth --, and almost none of it is in the line
dielectric. So its velocity factor is nearly 1. In my TDR demonstration,
the common mode open end reflection occurred before the larger
differential mode reflection because of the higher velocity factor, so
it looked like a differential mode reflection from a point short of the
end. (And I helped reinforce this mistake in order to get the audience's
attention.)

Any two conductor line supports both modes and behave the same, but coax
is a little easier to understand because the differential and common
mode currents are actually physically separate -- so no mathematical
hocus-pocus is necessary. The differential currents and waves are
entirely inside the cable, and the common mode currents and waves are
outside. The velocity factor inside (differential mode) is determined by
the dielectric material, and the velocity factor of the outside (common
mode) is nearly 1.

Roy Lewallen, W7EL