Well, actually, no. The radiation resistance generally decreases as an
antenna gets smaller, assuming it's small compared to a wavelength.

Roy Lewallen, W7EL

John Larkin wrote:

An antenna has radiation resistance. If you deliver power into Rr, it,
well, radiates it. As an antenna gets smaller, its radiation
resistance increases, so to dump X watts into space using a smaller
antenna, you need to drive it from a higher voltage. P = E^2/Rr. One
gadget used to increase the voltage is an "antenna tuner", just a
resonant matching network. There are practical limits on how much
power you can force into a small antenna: skin effect heating,
ionization, matching network Q, stuff like that. Nothing mysterious
here.

John