Date sent: Wed, 07 Jun 2000 10:25:14 +0100
To: [email protected]
From: Walter Blanchard <[email protected]>
Subject: LF: Formula
Send reply to: [email protected]
I found the following in an article recently.
Quote:
"The intensity E (known as the field strength) of a transmission
at a distance D from a source transmitting P watts of RF power via
a half-wave dipole in a free, unobstructed space, can be estimated
using the formula:
E=(7*sqrt (P))/D.
Dear Walter & Group,
If the propagating wave is a transverse electromagnetic wave
(which it will be a reasonable distance from the antenna, in 'free
space'), the electric (E volts/m) and magnetic (H amps/m) fields are
proportional; E/H = 120pi ohms. This 'free space wave impedance'
is about 377ohms and is a constant provided the permeability and
permittivity of the medium is the same as a vacuum, or air is near
enough. This comes about ultimately from the definitions of volts
and amps. E times H has the dimensions of watts/sq. metre and so
is called the power density, S. A bit of algebra gives you power
density S = (Esquared)/120pi (compare with P = (Vsquared)/R), so
measuring E is effectively also a measure of power density, and
also a measure of H. Rearranging this gives E = sqrt(120piS)
If the antenna in free space radiated equally in all directions, (ie.
an 'isotropic radiator'), at a distance d the radiated power P would
be evenly distributed over the surface of a sphere of radius d. the
surface of the sphere would have an area 4pi(d squared), so
power density would be S = P / 4pi(d squared). Putting this value of
power density into the equation for E gives
E= sqrt (30P/(d squared), or E= 5.477 sqrt(P)/d.
This applies to an isotropic radiator, but all real antennas have a
directional pattern, and so in the direction of their maximum
radiation, the power density is increased by a factor D (note not d,
the distance), the directivity or directional gain. This makes E =
5.477 sqrt (PD)/d.
The value of D depends on the geometry and voltage and current
distribution of the antenna. It's quite complex to work out, but can
be done for simple antennas - refer to an antenna text book for
details! - it can be calculated by programs such as EZNEC for
more complicated antennas. For a half wave dipole it is 1.64, for a
short monopole it is 3. Putting D = 1.64 into the formula gives
E = 7.01 sqrt (P) / d for a half wave dipole,
E = 9.49 sqrt (P) / d for a short monopole.
Hope that is some help,
Cheers, Jim Moritz
73 de M0BMU
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