Several basic questions about Antenna

Hi, I work on RFdesign in circuit and device level now, I'm not familiarized with
Antenna. I have several questions of antenna as following.

1)If we don't match the PA output impedance to antenna, does the antenna gain decrease?

Is the antenna terminated by a matched load when we define the "Antenna gain"?

2)Is the radiating resistance changed with different loading?

3)Is the power on radiation resistance is equal to the power transmitted to free space?


Thanks,

If between the output of the PA and the Antenna Connector you have a mismatch, you will get a mismatch loss:
Missmatch Loss (dB) = ? 10*LOG (1 ? Γ^2)
Where Γ is the reflection coefficient:
Γ = (VSWR ? 1) / (VSWR + 1)
For example at VSWR=6:1 you lose 3.1dB from the radiated power (half of the power)

The gain of the antenna will remain the same but you get less radiated power (subtract Mismatch Loss from Antenna Gain).
Gain of the antenna is defined for a specific load.

Radiated resistance does not have anything with load. Is related to conductor resistance, eddy current loss, dielectric loss, corona loss, ground resistance loss, and any other power loss.

Radiated resistance is equal to the power radiated by an antenna divided by the square of the rms (effective) antenna current at antenna feeding point.