It is very true that antenna analyzers are affected adversely, without 
filtering, in the near field of transmitters such as AM stations.

Here at the research lab, we are about a mile from a directional AM station. 
One of the popular antenna analyzers gave swinging SWR meter readings 
following the AM station modulation.  It was necessary to "eye ball average" 
the swings to a value for what we were measuring at 400 MHz!

Now there are filters sold for that AM interference.
The other way of dealing with the directional station is to wait and do 
measurements after sundown when they reduce power in our direction.  Many 
stations drop power in all directions at sundown to avoid skip interference 
to others.

Near field can be distinguished from far field by knowing that the energy is 
leaving the antenna in all directions in the near field, and has not reached 
a planar directional wave front appearance.  In the far field, you can find 
the wave has its plane wave orientation, and the distinguishing character of 
the field by horizontal or vertical polarization of the electric component.

Near field can be out to a couple of wavelengths, and far field beyond that, 
as a rough generalization. 



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