Here's the basic problem: Somewhere along the line you've got to match
the impedance seen at the input of the feedline to the 50 ohm resistive
(50 + j0 ohm) load your transmitter needs to see. (You don't actually
have to get it exact, but reasonably close.) The impedance of a half
wave dipole is in this ballpark all by itself, but other antennas (and
even the dipole if not resonant) usually need some kind of matching. The
farther the impedance at the feedline input is from 50 + j0, the harder
the job for the matching network -- voltages across and/or currents
through the matching network components increase and can become
downright awesome, if the impedance to be matched is far from 50 + j0.

If you start shrinking a dipole to a shorter length than a half
wavelength, or a monopole to shorter than a quarter wavelength, the
resistance drops and the amount of reactance increases. See Fig. 7 on p.
2-5 of the Antenna Book, which shows that a quarter wave dipole has a
feedpoint impedance of around 15 - j1000 ohms. Shorter dipoles have even
lower resistance and larger reactance.

Matching an extreme impedance involves, as I mentioned, high voltages
and/or currents, which is why the MFJ caution. These high voltages and
currents also result in increased loss, sometimes to the point where
most of your power is going to heating the matching system components.

It's entirely possible to use electrically small antennas, but there are
tradeoffs involved. Here are some ways you can do it:

1. Split the matching chore between the tuner and other external
components, such as a loading inductor to reduce the amount of reactance
the tuner has to deal with.
2. Use transmission lines to accomplish some or all of the matching.
This isn't usually the most efficient possible way (contrary to
folklore) but it distributes the heat and voltage gradient. Often you
can use the transmission line to transform an extreme impedance to
another impedance that might also be extreme but within the range a
tuner can more comfortably handle.
3. Use relatively lossy components, even possibly an intentional
resistor, as part of the matching network. This reduces voltages and
currents and increases bandwidth at the expense of some reduction in
radiated power.
4. Reduce power if necessary to keep your tuner from self destructing.

If you make an efficient matching network for an extreme impedance
transformation, it will be very narrow banded, so will require frequent
retuning as you QSY. Lossier systems have broader bandwidth (in
general). Trading loss for bandwidth might be worthwhile depending on
your circumstances. B & W has sold an antenna for decades which
incorporates a resistor, and it's widely used. Browse through the QRP
sites and you'll see that large numbers of QSOs are routinely had by
people running a watt or less. Countless others are undoubtedly made by
people with 100 watt transmitters who are radiating 10 watts without
realizing it. So don't stay off the air just because you can't make an
efficient antenna system. Any radiated power is better than none.

If you have a decent ground system, connecting the two transmission line
conductors of a short dipole together and feeding it against ground
(that is, connect the shorted dipole to the "hot" side of the tuner
output and the ground to the "cold" side) is a good suggestion. What you
have then is a top-loaded vertical, with the radiating vertical being
the feedline and the dipole being the largely nonradiating top hat. But
I wouldn't consider this unless you can bury at least a few radial wires
or lay them on the surface of the ground.

Roy Lewallen, W7EL