# far field-antenna theory

Joined Dec 29, 2004
83
Hi ,
I cannot figure out how to find this problem:
An infinitesimal electric dipole of length l = λ/50 is placed horizontally at a
height of h = 2λ above a flat, smooth, perfect electric conducting plane which
extends to infinity. It is desired to measure its far-field radiation characteristics
(e.g. amplitude pattern, phase pattern, polarization pattern, etc.). The system
is operating at 300 MHz. What should the minimum radius (in meters) of the
circle be where the measurements should be carried out? The radius should
be measured from the origin of the coordinate system, which is taken at the
interface between the actual source and image.

I know in the far field, the Er=0 and other equations, but i cannot extract "r" from it because they are all in the product forms and lead me nowhere.
Also, i know the formula for the far field but the fact that we need to include the image element confuses me.

Please can I have some directions on how to solve it?
Thank you

#### t_n_k

Joined Mar 6, 2009
5,455
One equation that's often mentioned in the literature is

$$r>>\frac{2d^2}{\lambda}$$

where d is the largest antenna dimension.

The transition [Fraunhofer] region from near to far field is somewhat gradual so I'm not sure one can define a precise distance.

Given you have a dipole with a ground mirror I'm not sure what the value of d is for your case.