[TowerTalk] RFI Radius vs Ant Height

[Jim Lux]

At 09:05 AM 8/3/2006, Dave Fuller wrote:
>For a given distance D to the antenna the field strength is proportional
>to 1/D(squared).   In other words double the distance  and you reduce
>field strength by 4.    Will be different for "near field" areas....not
>sure how far that is for a typical HF system.

The near field for a HF antenna is surprisingly large, and doesn't have a 
lot to do with the physical size of the antenna.  The classic (and somewhat 
arbitrary) definition of "near field"  is the volume within which the 
energy stored in the fields around the antenna is greater than or equal to 
the energy radiated away.

Another definition is  where the ratio of the E and H fields is equal to 
free space impedance (377 ohms). For a small antenna (where size of antenna 
is much less than a wavelength), this is roughly at wavelength/(2 pi).  A 
small magnetic loop would follow this sort of rule. However, something as 
simple as a dipole violates the assumption inherent in this.

This definition is handy in the RF safety and EMI/EMC complianceworld, 
because it sets the boundary where you can just measure E or H, and not 
have to worry abou the other (because the ratio is fixed).  In the EMI/EMC 
area, you're usually not worried about power density, per se, but E field 
or H field, depending on the vulnerability of the victim circuit. In the RF 
safety world, power density is the important thing, either as a whole body 
absorbed energy or a peak absorption in a small volume.

Generally, one divides the volume around the antenna into three categories: 
Reactive near field (where the dominant process is one of energy storage), 
radiative near field (where radiation is starting to be the dominant 
process) and the far field (where it's all radiation).  The reactive near 
field is where if you put something, it screws up the pattern, because 
you're changing the energy flow in and around the antenna.  The radiating 
near field is less sensitive, but really, it's where you can't make a plane 
wave assumption for propagation (that is, power doesn't fall off as 1/r^2)

Where you can get tangled up is in a gain antenna which has significant 
energy stored in the field (which applies to just about all Yagis).  If you 
consider an antenna with an "antenna Q" of, say, 10 (which isn't all that 
high), that means that 10 times as much energy is stored in the field as is 
radiated away.  Fortunately, that energy is spread out within the antenna 
volume, so it's not like you'd have to multiply the far field numbers 
(which is the "radiated away" part) by 10.

A good example of a system with a LOT of energy stored in the near field, 
but radiating fairly little in the far field, is a Tesla coil (which is 
really just a LC tank where the C is the capacitance of the coil to 
ground).  You'd have to be pretty far away from the tesla coil to get to a 
distance where the radiated field (which is pretty small) is equal to the 
stored field (which is pretty big).

Here are some (conservative) rules of thumb for the boundaries, all based 
on D being the largest dimension of the antenna (diagonally across a Yagi!):
The reactive near field is out to r = 0.62 Sqrt(D^3/lambda).
The radiating near field out to 2*D^2/lambda.
The far-field exists beyond 2 D^2/lambda.

Looking at a typical yagi with elements roughly a half wavelength long, and 
on a half wavelength boom, we'd take D as 0.707 lambda 
(diagonal!)..  Plugging in the numbers:

Reactive near field to 0.62*sqrt( (.707^3) * Lambda^2) = 0.62*lambda * 
.707^3/2, or, about 0.36 lambda
radiating near field out to 2 * .707^2*lambda^2/lambda or 1 wavelength
far field beyond a wavelength.

The takehome message here is that if you're calculating field strengths, 
you can only use the far field approximation (i.e. doubling the distance is 
1/4 the power density) if you're a least a wavelength away.  A 20m 3 
element yagi  on a 70 foot tower just meets this.  If you're any closer, 
then you need to really look at the near fields using something like NEC.



http://home.iae.nl/users/bergervo/gouy/dipole.html has some fascinating 
movies of the fields around a dipole


Jim
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