From: "Mike Dennison" <mike.dennison@rsgb.org.uk>
Organization: Radio Society of Great Britain
To: rsgb_lf_group@blacksheep.org
Date: Fri, 25 Jun 1999 10:17:07 +0100
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Subject: Re: LF: ERP Calculations
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ON7YD wrote:
> 
> Pure mathematical the radiation resistance of a short (in wavelength)
> vertical monopole above a perfect ground is :
> 
>    Ra = 40 . Pi^2 . l^2 / L^2
> 
> where Pi = 3.1415... , l = antenna-length , L = wavelength and ^2 means
> squared.
> 
> simplified for 136.75kHz this means that Ra (milli-Ohm) = 0.082 x l(meter)
> 
> The same vertical with a infinite top-capacitance has a radiation
> resistance of
> 
>    Ra  = 160 . Pi^2 . l^2 / L^2
> 
> so 4 times the radiation resistance of the same vertical without tophat and
> with the same antennacurrent it will have a 6dB higher ERP.
> 
> Any 'real-world' vertical with tophead wil have a radiation resistance
> somewhere inbetween.
> 

OK, so you agree with the Admiralty Handbook figure of 160 for a 
perfect top section (the figure 40 you quote at the start must 
assume that L is the =actual= height of a vertical antenna as the 
effective height is half that of a Marconi with a perfect top). Of 
course the figure of 160 must be corrected for effective height as 
you suggest.

So for any practical short Marconi, ERP is:

I^2 x 160 x pi^2 x effective height^2 divided by wavelength^2

which simplifies to:

I^2 x  0.325 x effective height^2

to give a figure in mW on 136kHz.

That makes my ERP 43mW.

And, incidentally, just over 10mW on 73kHz.

You mentioned the effect of an imperfect ground. Doesn't that just 
come into the losses that reduce the current?


Mike