Message-ID: <2539.200006071127@gemini>
From: "James Moritz" <j.r.moritz@herts.ac.uk>
Organization: University of Hertfordshire
To: rsgb_lf_group@blacksheep.org
Date: Wed, 7 Jun 2000 12:34:49 +0000
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Subject: Re: LF: Formula
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Date sent:      	Wed, 07 Jun 2000 10:25:14 +0100
To:             	rsgb_lf_group@blacksheep.org
From:           	Walter Blanchard <blanch@pncl.co.uk>
Subject:        	LF: Formula
Send reply to:  	rsgb_lf_group@blacksheep.org

> 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