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### E(I)RP

In most countries there is an E(I)RP limit rather than a TX output power limit. This limit is between 1 and 5 Watt EIRP (except New Zealand with a 25 W EIRP limit).
The effective radiated power (ERP, in W) depends on TX power (P, in W), antenna gain (G, in dBd) and antenna efficiency (η):

ERP = η · P · 10G/10

The ratio between ERP and EIRP (effective isotropic radiated power) is:

ERP = EIRP/1.64   or   ERPdB = EIRPdB - 2.15dB

A small (toploaded) vertical monopole antenna has a theoretical gain of 3 (4.77 dBi or 2.62 dBd). For an unobstructed antenna and a good ground (low loss) the real gain will be close to the theoretical value. But as the ground conductivity drops (and the ground loss rises) the radiation pattern of a vertical monopole will  be affected, resulting in a lower gain.

Obstructions near or even under the antenna will reduce the effective antenna height. The radiation resistance will be less than the theoretical value (based on the physical dimensions of the antenna) and thus the efficiency will drop. Small antennas seem to suffer more from this effect than big antennas. Measurements on 136 kHz have shown that his additional loss can vary from 1 dB (large unobstructed antenna) to 5 dB (small antenna with lot of objects around). On 472 kHz this effect is probably less profound, but with small or heavily obstructed antennas up to 3 dB extra RF power might be needed.

The theoretical gain of a small loop antenna is 1.5 (1.76dBi or -0.39dBd) and is much less affected by obstructions or poor ground.

A result of the rather low E(I)RP limit is that with most antennas (except for very small ones) it is not so hard to reach this limit, it is just a matter of RF power:

• Case 1: a small toploaded vertical antenna (6 m high and 20 m topload wire) with a radiation resistance RA = 0.1 Ω and a loss resistance RG = 100 Ω.
The efficiency η = RA/(RA+RG) = 0.1/100.1 = 0.000999 (-30.0 dB) and the antenna gain G = 1.5 (due to very poor ground).
This means that 667 W RF power is needed to reach 1 W EIRP (1094 W RF for 1 W ERP and 3337 W RF for 5 W EIRP).
• Case 2: an average toploaded vertical antenna (10 m high with 30 m topload wire) with RA = 0.3 Ω and RG = 50 Ω.
The efficiency η = RA/(RA+RG) = 0.3/50.3 = 0.00596 (-22.2 dB) and the antenna gain G = 2 (due to poor ground).
This means that 84 W RF power is needed to reach 1 W EIRP (138 W RF for 1 W ERP and 419 W RF for 5 W EIRP).
• Case 3: a large toploaded vertical antenna (18 m high with 50 m topload wire) with RA = 1 Ω and RG = 30 Ω.
The efficiency η = RA/(RA+RG) = 1/31 = 0.0323 (-14.9 dB) and the antenna gain G = 2.5 (due to average ground).
This means that 12 W RF power is needed to reach 1 W EIRP (20 W RF for 1 W ERP and 62 W RF for 5 W EIRP).
• Case 4: a "giant" toploaded vertical antenna (50 m high with 100 m topload wire) with RA = 8 Ω and RG = 15 Ω.
The efficiency η = RA/(RA+RG) = 8/23 = 0.348 (-4.6 dB) and the antenna gain G = 3.
This means that 0.96 W RF power is needed to reach 1 W EIRP (1.6 W RF for 1 W ERP and 4.8 W RF for 5 W EIRP).

With large antennas it is easy to generate several 10 or even 100 Watts EIRP. Running 500 W RF power into the "giant" antenna (case 4) will result in a theoretical EIRP of 522 W. Even taking into account an additional loss of 2 dB due to a lower effective height the EIRP is still about 320 W!