From your description I can't imagine what you have exactly, but:
Gain = directivity - mismatch loss - 10*log(efficiency). All in dB.
@drkirbly: To avoid confusion about nomenclature:
To avoid confusion about nomenclature:
If I have a directivity 15 dBi (for example from a 4 element stacked structure), |s11| = 0.5 and efficiency of 40% (40% of real input is radiated, 60% is converted to heat), the net gain is:
Gain = 15 dBi - -10*log(1-|s11|^2) - -10*log(0.5)
Gain = 15 - 1.25 - 3 = 10.8 dBi
10.8 dBi is what the user will experience.
@drkirkby: If follow your reasoning regarding nomenclature (accepted versus incident issue). It was the reason for me to mention efficiency and mismatch loss (and the example after your comment).
Regarding "the" gain definition, it is not just "right" or "wrong". Google the web, and you will see that many people don't follow the IEEE definition (especially in the EMC community where mismatch loss is included in the gain as stated by manufacturers).
@drkirkby: You are correct with respect to the source or load impedance, it should be specified.
Especially wide band EMC antennas have varying VSWR across the band and you can't make a matching network that covers the whole band. It is therefore convenient to specify gain based on incident power (or maximum available generator power).
This document: www.conformity.com/PDFs/0712/0712_F05.pdf deals with EMC antennas. On page 43 (under Directivity and Gain), it mentions why they deviate from the Gain definition as used in IEEE.
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