DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws;
  s=s1024; d=btopenworld.com;
  h=DKIM-Signature:Received:X-Yahoo-SMTP:X-YMail-OSG:X-Yahoo-Newman-Property:Message-ID:From:To:References:In-Reply-To:Subject:Date:MIME-Version:Content-Type:Content-Transfer-Encoding:X-Priority:X-MSMail-Priority:X-Mailer:X-MimeOLE;
  b=5sT9r66Hezoz0TCGGkGKaazQbjOZF2cloMcp4npiaFw5APC87hzf8oe7ndaSODlO8tIhZJVMgZFWnnUiDJ8XZYIqSKsY8pWZiLSwOtCDRiez8J/fPPJRv46IMMnH2r+5bUQZeqfJgu4qdsmHFCWQqlfCEkbZThMU+oOVow0D2cs=  ;
Message-ID: <53AF10453AF44765B62710310385A7A2@JimPC>
From: "James Moritz" <james.moritz@btopenworld.com>
To: <rsgb_lf_group@blacksheep.org>
References: <F5C1A6105D684AE1828B5F61AA44007F@AGB> <FAAC8E9CA7F14815A420B17329E858F5@DennisPC> <C1D2152788594A25978C3F9F2100C06B@EA3WXPC>
In-Reply-To: <C1D2152788594A25978C3F9F2100C06B@EA3WXPC>
Date: Sun, 1 May 2011 11:31:05 +0100
MIME-Version: 1.0
DomainKey-Status: good (testing) 
Subject: LF: Re: ERP 
Content-Type: text/plain;
	format=flowed;
	charset="iso-8859-1";
	reply-type=original
Content-Transfer-Encoding: 7bit
Sender: owner-rsgb_lf_group@blacksheep.org
Precedence: bulk
Reply-To: rsgb_lf_group@blacksheep.org


Dear Luis, LF Group,

To calculate ERP, one needs to determine the radiation resistance of the 
antenna, Rrad, and the antenna current, Iant. Rrad depends on the geometry 
of the antenna and the wavelength:

Rrad = 160*pi^2*(Heff/lambda)^2

Where Heff is the "effective height" of the antenna, which depends on its 
shape and size. For simple wire antennas, Heff is nearly equal to the 
average height of the conductors, so for a plain vertical wire it is about 
1/2 the overall height, and for a T or inverted L with very long horizontal 
wires, it is nearly equal to the overall height. You can find some formulae 
to work out Rrad for different antenna geometries at 
http://wireless.org.uk/on7yd/ . For your antenna, Heff works out to about 
13m, so Rrad is about 0.74ohms at 500k.

The ERP is then:

Perp = D*Iant^2*Rrad

D is the directivity of the antenna compared to a free-space half-wave 
dipole, for a short vertical over an infinite ground plane D is 1.8 
(2.62dB). The information we do not have is Iant. The best way to find Iant 
is to measure it with a RF ammeter. Or you can calculate Iant if you know 
the TX power and the RF resistance at the feed point of the antenna. 
Typically antenna resistance at 500k might be between several ohms and 
several 10s of ohms - let us assume it is 20ohms for your antenna. In that 
case, with 35W TX power, Iant = 1.3A. Using the formula above, Perp = 2.3W. 
The actual ERP is likely to be reduced by a few dB if there are many 
buildings and trees, etc, around the antenna.

A more definitive ERP measurement can be obtained by measuring the field 
strength, E, of the signal at distance d some km from  the antenna, in which 
case:

Perp = (Ed)^2 /49

Measuring E requires a calibrated antenna and receiver - but that is another 
story...


Cheers, Jim Moritz
73 de M0BMU