The antenna is electrically a half wave on 10M to 40M, the electrical
length of an element is not directly related to it's physical length.
That is how they make a "halfwave" in a stick shorter than a physical
quarter wave.

Ok... could you please explain me how i can build an, e.g., electrical half
wave for the 20 meters in a 3 meters stick ??

I repeat, i'm a great newbie on antenna theory and related arguments, so the
question i pose to you now is not ironic but really posted to increase my
knowledge, if is possible.

The short explanation is "reactive loading".

The simplest way to achieve what you're looking for, is to take a
three-meter stick, and wind it with a spiral of wire. The wire should
be insulated, to prevent adjacent turns from shorting together. You
would feed the antenna in the center, just as if it were a full-sized
half-wave dipole.

The exact number of turns required (and thus the total length of the
wire you'd need) can probably be calculated, but I lack the detailed
information to know just what the calcs are. I'm sure that there are
examples shown on the Web, and/or in the ARRL Antenna Compendium
books. You can see one example of this approach at

http://www.w0ch.net/travel_antenna/travant.htm

There are a bunch of design alternatives, divided roughly into

(1) Wind the wire evenly along the whole length of each half of the
shortened dipole.

(2) Run the wire straight along the pole for part of the way from the
center to the end, and wind turns over the rest.

The "travel antenna" is of the latter sort - it puts most of the added
inductance (the coiled turns) down near the feedpoint. He designed it
as a shortened quarter-wave, but you could take two of these and
stick them back-to-back and have a shortened half-wave.

If you measure the resonant frequency of this shortened half-wave and
find that it resonates at too low a frequency, then you've got too
many turns... remove some and run the wire straight along a portion of
the pole (or space all of the turns further apart). If it resonates
at too high a frequency, you need more turns (more inductance).

The behavior of this sort of shortened dipole will be similar to that
of a full-length dipole, with several differences:

- Slightly less directional gain

- Higher electrical losses in the dipole

- Lower radiation resistance

The latter two factors result in a loss of electrical efficiency...
more of your transmitter power turns into heat in the antenna itself,
and less is radiated.

The feedpoint impedance is likely to be different than a full-sized
half-wave, too... it may be lower (due to the lower radiation
resistance) or higher (due to the additional loss resistance) or
nearly the same (if these two factors cancel out).

The approach I've described uses inductive loading - you add
inductance in series with the antenna in order to resonate it.
Another approach is capacitive loading - you add additional capacitive
coupling at the ends of the antenna. This can be done by adding a
circular metal "hat" at each end, or a set of radial wires sticking
out at a 90-degree angle.

The MFJ antenna under discussion actually uses both techniques - it
has an inductive loading coil, and a "capacity hat" of wire spokes, at
each end of the antenna (actually, one per band that it's supposed to
tune). The combination of added inductance, and added capacitive
loading, creates the necessary resonance on each band.

--
Dave Platt AE6EO
Friends of Jade Warrior home page: http://www.radagast.org/jade-warrior
I do _not_ wish to receive unsolicited commercial email, and I will
boycott any company which has the gall to send me such ads!