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From: "Peter Martinez" <peter.martinez@btinternet.com>
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Date: Fri, 3 Mar 2006 09:54:08 -0000
MIME-Version: 1.0
Subject: Re: LF: LORAN spurious emission levels
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>From G3PLX:

I calculated the radiated power of a LORAN line now, but I would like other 
people to check if I did it right, because the result is surprisingly small.

The spectrum measurement made at Rugby gives a chart of dB levels for 2kHz 
steps over 70-130kHz, going from -8dB in the centre to -53dB at 130kHz, and 
I extrapolated by eye to estimate the levels at three more steps up to 
136kHz. Here are the numbers themselves...

-52.00,-49.95,-47.49,-45.03,-43.10,-41.42,-40.24,-38.42,-35.72,-31.13,-28.75,-22.49,-17.82,-13.84,-8.01,-8.46,-13.29,-16.76,-18.44,-21.41,-27.43,-29.16,-33.89,-40.21,-40.09,-43.32,-45.47,-44.45,-48.63,-51.86,-52.94,-55.24,-57.44,-59.54

Notice that there are two 'largest' figures, so although the chart shows 
these two as being at frequencies of 98 and 100kHz, I am guessing that they 
are really figures for the centre of bands 98-100 and 100-102kHz. The last 
three are my guesses for the values for the bands 132-134, 134-136, and 
136-138 kHz.  From the other information in the spreadsheet I was sent, I am 
quite certain that this spectrum was measured at an antenna current sampling 
point.

For each of these figures I calculated the relative "current-squared" values 
from 10^(dB/10) then multiply each one by (F/100)^2, where F is the 
frequency in kHz. This gives a figure for the relative radiated power in 
each 2kHz slot. The square-frequency factor arises because the radiation 
resistance will be proportional to F-squared, and I am seeking to calculate 
the I-squared-R for each 2kHz slot. The figure I get for the 136-138kHz slot 
is 0.0021.

Next I add all these figures to give me a total of 454.6338 units of power. 
I don't  know what the units are because I don't have enough information 
about the transmitter or the antenna, but I can divide 0.0021 by it to give 
me the fraction of the total mean power that is radiated in the 136-138kHz 
slot. This is 4.62e-6.

For the Lessay chain I know the group repetition interval is 67.31mS which 
means there are 14.85 pulse groups per sec. Because half the pulses are 
constant polarity and half are alternating, I know that half the energy goes 
into spectral lines at this spacing and half goes into lines at odd 
multiples of half this figure. Effectively there are twice as many spurious 
lines as the GRI says, spaced at 7.43Hz. There are about 270 of these 
(2000/7.43) in a band of 2kHz wide.

Therefore the proportion of the total mean power which is radiated in a 
single spectral line at 136kHz is 4.62e-6 / 270 = 1.71e-8.

If we estimate (from the info given by Marco) that each LORAN transmitter 
radiates 7.5kW mean power, then the radiated power in each LORAN line is 
1.71e-8 * 7500 = 0.128 mW.

I don't know if I should believe this!  Can anybody find a mistake or at 
least check my calculations?  All the figures needed for the calculations 
are in this email. Does anyone have any evidence that any of these figures 
are wrong?

73
Peter G3PLX