[Lowfer] loop Rr

[lowfer@mailman.qth.net]

Paul C,

here's some info on single-turn, electrically short loops (<1/10 wavelength 
circumference). The radiation resistance for a loop in free space is found by 
this formula: Rr = (4 X 10E-6)(F^4)(A^2), F in MHz, area in square meters. 
For a loop over perfect GND the Rr doubles. Example: A square loop 1 meter on 
a side at 1 MHz has a radiation resistance of 4 micro-ohms. Place it over GND 
and it is 8 micro-ohms.

So, for your question about reducing the area of a loop by a factor of 4. The 
reduction in radiation resistance is A^2 = (1/4)^2 = 1/16. Given equal 
current when the loop area is reduced by a factor of 4 the power radiated 
drops by a factor of 16. This is 12 dB. Another way to look at it is that the 
Electric Field (in the far field) is proportional to the area of the loop. In 
your case the area was reduced by a factor of 4 so the E-field is reduced by 
a factor of 4. This is 20LOG4 = 12 dB.

A lowfer loop that is 50 feet on a side, and is placed over a ground plane, 
has a radiation resistance of 2.2 u ohms at 185 kHz.


   Dave WX7G


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