What is the proper antenna measurement equation?

[chihhao]

Antenna measurement

Measured by Horizontal receiver antenna = P_H
Measured by Vertical receiver antenna = P_V

The total power is P_Total

Which one is right

(1) P_total = P_H + P_V (W)
(2) P_total = [(P_H)^2+(P_V)^2]^(1/2) (W)

Where can I find the document explaining this?
Thanks.

 

[dowjones]

Antenna measurement

you should write in amplitudes, better than in voltage. They are coherent vector signals and the correct way is amplitude.

Then, E_total = (E_h, E_v) and

P_total = E_total*conjg(Etotal) = E_h^2 + E_v^2 , since the two components are orthogonal. Then it follows
=> P_total = P_h + P_v