far field-antenna theory

Thread Starter


Joined Dec 29, 2004
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


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


where d is the largest antenna dimension.

Presumably you've seen that already.

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.

Thread Starter


Joined Dec 29, 2004
Thank you t_n_k,

Yes I have seen this formula already and as you point out the mirror image confuses me as far as D and r are concerned.
I will continue to work on it.