LF: 472kHz ERP calculations based on WSPR results

[Roger Lapthorn <rogerlapthorn@gmail.com>]

With several repeatable ground wave reports on 472kHz WSPR using my 20m baseline earth-electrode antenna today, I decided it was time for a recalculation of my ERP based on a formula (for 500kHz) supplied some years ago by Jim M0BMU.  The assumption (from M0BMU, that I am now unsure is right) is that the noise floor is around 3uV/m in a 2500Hz (WSPR) bandwidth. So, based on the WSPR S/N ratio the field strength when using the earth-electrodes can be calculated.

G3ZJO at 79km gets me at around -19dB giving my field strength around 355nV/m. 
G3XDV at 61km he gets me around -12dB S/N giving my field strength around 810nV/m.  
M0BMU at 69km he gets me around -30dB S/N giving a field strength around 100nV/m

ERP Calculations  (NB the earth-electrode antenna behaves like a loop so has directionality that has not been considered)

ERP using G3ZJO's results = (E*d)^2/49; with E = 355nV, d = 79km   ERP = 16uW
ERP using G3XDV's results = (E*d)^2/49; with E = 810nV, d = 61km  ERP  = 49uW
ERP using M0BMU's results =  (E*d)^2/49; with E =100nV, d = 69km  ERP = 1uW

Now, to me these figures seem far too low, so perhaps the noise level is much higher than 3uV/m or my maths are wrong?

Certainly the noise floor here is S4- S8 due to SMPSUs and other noise sources, so higher than 3uV/m. 

I think these ERP numbers can be doubled based on ground wave losses but, even so, the figures appear to be extremely low.  My Marconi antenna is some 8dB (average) better than the earth-electrode antenna and I am sure the ERP is well above 1mW using this antenna. My RF into the earth electrodes is 10W.

Conclusions
I am totally puzzled: measuring antenna current on the Marconi I get ERPs that are an order of magnitude higher yet measured results with the earth-electrode antenna average just 8dB down on the Marconi. This suggests ERPs for the earth-electrode antenna in the low mW region, which I find much more believable. My maths has never been good, so it is possible I have made mistakes, so I would welcome any corrections.

For now, I am of the view that the ERP is around 5mW for the earth-electrode antenna and around 30mW with the Marconi, yet measured results suggest much less.

Any thoughts please?

73s

Roger G3XBM

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