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Re: LF: LORAN spurious emission levels

To: <[email protected]>
Subject: Re: LF: LORAN spurious emission levels
From: "Peter Martinez" <[email protected]>
Date: Fri, 3 Mar 2006 09:54:08 -0000
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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



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