Why are you trying to make this so complicated?  It's a straightforward 
calculation.  A half-wave dipole is assumed to have 0 dBd gain (what a 
surprise) or a multiplier of 1. (There is no mention of ground, takeoff angle, 
blah, blah, it's zero dBd, period.)

You model the antenna you want to use and get its gain (usually in dBi) and 
convert to dBd if necessary. Convert this number to a ratio and divide it into 
50.  That equals the allowable power input to the antenna.

Using the example I offered earlier, I model a short whip over an assumed 20 
ohm of ground loss.  EZNEC reports -9.7 dBi or ~ -11.8 dBd. As a ratio this = 
0.065.  Dividing 50 by 0.065 we find that the allowable input power is ~765 W.

You write this stuff down in your station engineering notes justifying your 
assumptions and operate in good faith.

Wes Stewart,  N7WS


--- On Thu, 5/7/09, Guy, K2AV <[email protected]> wrote:

> From: Guy, K2AV <[email protected]>
> Subject: Re: [Elecraft] dBi dBd correction
> To: [email protected]
> Date: Thursday, May 7, 2009, 7:30 PM
> ARRL ain't the FCC.  And the ARRL's opinion is no
> mitigation whatsoever if I get an FCC pink slip. The reg is
> the reg, and it's a strange brew for the FCC, where ERP
> normally has nothing to do with dBd.
> 
> 73, Guy.
> 
> ----- Original Message ----- 
> From: Augie Hansen (via Nabble) 
> To: Guy, K2AV 
> Sent: Thursday, May 07, 2009 5:14 PM
> Subject: Re: [Elecraft] dBi dBd correction
> 
> 
> Guy, K2AV wrote: 
> 
> > The way the regulation reads, hams are being told they
> can put 50 watts PEP 
> > on an antenna, up to the gain of a dipole, and call
> that 50 watts ERP. 
> > Higher gain must be referenced to the dipole and the
> 50 watts reduced 
> > accordingly. 
> > 
> > For mobile stations there is no mention of the idea
> that a LESSER antenna 
> > may have the 50 watts increased. 100 watts appears to
> be in excess of 
> > regulation.  Stated another way, 50 watts max
> regardless, unless the antenna 
> > has more gain than a dipole in which case power must
> be reduced by a factor 
> > representing the gain of that antenna over a dipole. 
> >   
> 
> Where did you get that interpretation? The ARRL Q&A,
> based on the FCC 
> rules, says the following: 
> 
> <quote> 
> The "best" antenna configurations are those with
> a proven track record 
> on the lower bands, keeping in mind that using a loop or an
> array of 
> some kind will require you to "do the math" to
> ensure you are not 
> radiating more than 50 W ERP /in any direction/. The math
> is fairly 
> straightforward. You must reduce your power by the number
> of decibels 
> your antenna gain exceeds 0 dBd (0 dB relative to a
> half-wave dipole). 
> Conversely, you can increase your transmitter power if your
> antenna 
> exhibits loss compared to a dipole. Be prepared to document
> these 
> situations in your station records, however. 
> <endquote> 
> 
> Gus Hansen 
> KB0YH 
> 
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