There is no relation between antenna size and radiated power. An infinitesimal antenna can radiate a lot of power, it just needs a way of feeding it with extremely high currents or voltages, or both. If an antenna is a lot smaller than a wavelength across it will usually be extremely inefficient, but some of the most powerful antennas in the world fall in this category (long wave antennas).
A small microstrip antenna might melt or burn out at high powers, but this is not fundamental, but due to the resistivity of its tracks and the loss tangent of the board, or lack of cooling. I think that perhaps a superconducting microstrip with air insulation could handle a lot of power. If you want to make it much shorter than a half wavelength you would need tuning components that would also need to be superconducting.
Article Antenna Applications of Superconductors
This article might be helpful.
Malcolm White is right, if the antenna size is much small than the wavelength then it is highly inefficient. There is a relation between Directive Gain, wavelength and the effective aperture of an antenna, but you cannot prove that small size patch is a low power device. That depends upon the power handling capability of the antenna and also its environment.
If too small and power is too high, you could get arcing due to atmospheric breakdown. That is to say You could get sparks, generate heat, and start a fire. Don’t know the electrIc field that is required for breakdown. It is higher at higher pressure and probably varies with humidity and ambient temperature. However, you could probably look it up. I think it is around 3 kilovolts per meter In standard atmosphere.
- Badges
- Science topic