I first got interested in active antennas in the UCLA plasma physics lab; we often used such devices for probing quiescent plasmas and such.

The active antenna is a beautiful, elegant intellectual exercise...and it really puts "meat" on the concept of limits...not a mathematical abstraction at all.

A very short antenna (in terms of wavelength) has insufficient size to develop standing waves on it....which makes it a very curious analytical situation...is it an antenna or not?

The radiation resistance of a very short wire is essentially zero...but the capacitive reactance approaches infinity. This tells us that the POWER FACTOR of an active antenna is essentially ZERO. Hence any power "extractable" from the antenna is, for all practical purposes...also ZERO.

How does this antenna work at all? From experience, we know that the active antenna not only limps along, but can perform quite admirably! What laws of physics are we breaking when we build a vanishingly small antenna?

Next stage. We always use a VOLTAGE FOLLOWER of some sort after the active antenna. What is an ideal voltage follower like? What is its input impedance?

Essentially infinite, right? What is the power gain of a voltage follower? Well, if the output impedance is anything LESS than infinity, we have INFINITE POWER GAIN! That's right! We don't need to supply any signal power to the device....only signal VOLTAGE....the POWER FACTOR of a pure voltage is irrelevant (not to mention undefined!)

So, we have a zero power antenna (our voltage source) followed by an infinite power gain voltage follower! End result....finite power!

The elegance of this, both physically and mathematically, is staggering. This is the sort of thing that fascinates the tar out of me...and I've been doing electronics for 45 years.

eric