Calltrex wrote:

How can one couple this ?
A coaxcable with a dummyload: runningwaves everywhere and U and I are in
phase.
Now the resonant dipole: the U peaks at the ends end I tops in the
midle. So very reactive for the driver.

Nope, you are confused, at least about resonant standing
wave antennas like the 1/2WL dipole. Those peaks and nodes
of the voltage and current are *AMPLITUDES*. Amplitudes have
nothing to do with reactance. To detect the reactance, one
must look at the *PHASE*. You are not looking at the phase.

Instead of looking at the amplitudes of the voltage and
current, take a look at the phase of the voltage and current.
The phase angle which determines the reactance is the difference
between the voltage phase angle and the current phase angle.

Hint: The phase angles of the standing waves on a standing wave
antenna (like a 1/2WL dipole) don't change over the entire
length of the 1/2WL dipole. The standing wave is approximately
90% of the total wave on a 1/2WL dipole so the phase angle
of the total wave on the antenna changes very little from
end to end.

Should be. Now the dipole is coupled at the coax instead
of the 'inphase' load
and, oh wonder, the coax cable doesn't notice the difference ?? The
mind boggles.

At the antenna feedpoint, for a resonant antenna, the total
current and total voltage are in phase so the resulting
impedance is *purely resistive, not reactive*.

There is a forward wave at the feedpoint which, in a 1/2WL
dipole, travels to the end of the antenna and is reflected.
At the reflection point, the forward voltage and reflected
voltage do not undergo a phase shift but the forward current
and reflected current are 180 degrees out of phase at the
reflection point.

Bottom line is that the reflection phasor adds to the forward
phasor after a 180 degree round trip. In a 1/2WL dipole, Vfor
is 180 degrees out of phase with Vref and Ifor is in phase with
Iref. Assuming a zero degree reference, Vfor is at zero degrees
and Vref is at 180 degrees. Ifor and Iref are both at zero
degrees. Since everything is in phase or 180 degrees out of
phase, we don't need any trig. The feedpoint impedance of a
resonant 1/2WL dipole becomes a *magnitude only* calculation:

1/2WL Zfp = (Vfor-Vref)/(Ifor+Iref)

The negative sign on Vref takes care of the 180 degree phase
shift. The feedpoint impedance of a resonant one wavelength
dipole is also a *magnitude only* calculation but the signs
of the magnitudes change because of the extra 180 degree delay:

1WL Zfp = (Vfor+Vref)/(Ifor-Iref)

It's easy to see why the feedpoint impedance of a 1WL dipole
is so much higher than it is for a 1/2WL dipole. The reflected
voltage and current are delayed by an additional 180 degrees.
--
73, Cecil, IEEE, OOTC, http://www.w5dxp.com