Aperture antenna directivity calculation

[baby_1]

Hello
Here is an uniform E filed distribution aperture antenna E and H far filed euations

and here is directivity calculation approach

my problem is why don't we calculate D with both E(theta) and E(phi)? My mean is:
instead of using

we should use

because both of them are not zero in far-filed zone and not zero at theta=pi/2

 

[marcusl]

E_0 is the magnitude of the electric field vector E. If you were to compute the sum of the magnitude squared of the components as you suggest, it should come out as E_0^2 as written in the text.

BTW, you have written something different. I assume that you mean E_\theta^2 + E_\phi^2 rather than E^2(\theta)+E^2(\phi)? The latter is valid but means something else.

 

[baby_1]

Dear marcusl
you are right I wanted to write

As the writer wrote we have

and we assume phi=pi/2 that maximizes U.
and with my approach:

and I didn't know why we assume only

to calculate power intensity ( U) ( as in the book mentioned)?

 

[marcusl]

The book didn't say to use E_\theta, it said that the field is maximum at \theta=0. Putting that angle into the equations and finding the sum of the squares of the components, as you did, gives the answer.