Electrically short antenna
am trying to understand fully the problem with using electrically short antenna to transmit RF signals (i.e length significantly shorter than the intended wavelength).


Currently my understanding is that such an antenna does not radiate

It radiates, but with a slightly different radiation pattern, and an efficiency problem related to its impedance.

since the length of the antenna is much shorter than the wavelength the voltage distribution on the antenna at any given moment is roughly uniform. In particular there is no voltage fluctuation on the antenna and hence no magnetic field and hence no radiation.

A short antenna has predominantly capacitative reactance. Current does flow, just not alot.

But let's suppose I match the input impedance with the antenna impedance

You would do that by adding a loading coil, to add inductive reactance to compensate for the capacitative reactance.

I am wondering if the high impedance is really the only issue that prevents an electrically short antenna from radiating?

Again, a short antenna does radiate. But there is a problem you have missed. You are correct, the impedance for a short antenna is high. As I mentioned, there is a very high capacitative component to that impedance. What I didn't mention is that the resistive component, or more precisely the radiation resistance can very small (1 or 2 Ohms). When matching the impedance, the ohmic resistance of the loading coil might be comparable to, or larger than the radiation resistance. That means more power lost to heat, and less power radiated.