Antenna efficiency from S11

Hi,

how to i calculate the antenna efficiency from the antenna s11 return loss i measured from VNA.

thanks.

You can't do that.

From S11 data, you can't tell anything about radiated power vs. power loss in the antenna.
If you have s11=0, this can be a perfect antenna or a 50 Ohm resistor, you can't tell.

This is very true.
Meantime, thousands of antenna papers or antenna books, most of the time when shows performances of the antennas, they provide ONLY S11 (or VSWR) plots...in English there is an expression: Go tell it to birds.

okie. understood. maybe i should re-phase my question.
How do i know the efficiency of the terminal efficiency. as in how much power is forwarded to antenna and how much power is reflected? does this make sense?

Actually, that antenna efficiency (percentage of power that is actually radiated) is a useful number and we use it in many projects. It's easy to obtain from simulation, not so easy from measurement because you need to measure the pattern over all directions.
So I don't agree with vfone: it's nothing theoretical, it's a practical and useful figure of merit for antenna performance.

What you call "terminal efficiency" is trivial: S-parameters are voltage ratio, so normalized reflected power is |S11|² and your requested efficiency is 1-|S11|²
But as mentioned, that has nothing to do with antenna efficiency, which is defined differently.

so what does this antenna s11 mean? what can we conclude from the S11 ?

Reasonable matching of the antenna to your source is a requirement, so that you get your transmitter power into the antenna, at your frequency of interest.

This doesn't tell anything about radiation efficiency. There are some nicely matched wideband antennas which radiate poorly, and most of the input power is lost (heat the antenna). Antenna efficiency depends on antenna structure and sometimes on materials. For example, the popular cheap FR4 PCB material is very lossy at RF, so you can build antennas with FR4 that look fine in S11 but have poor radiation efficiency -> poor performance. You can get an idea about radiation efficiency if you look at antenna gain and pattern, and compare to similar antennas.

S11 tells you how to perform optimal antenna impedance matching. This also assures maximal efficiency with a given antenna. You still don't know which part of the input power is radiated respectively dissipated.