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Can someone tell me what dB gain over an isotropic radiator means?

Let's say I have a 3 element vertically polarized 10 m Yagi (which I do) which is meant to have 7.5 dBi gain.

Which of the following is correct?

  1. If I measure the signal strength 1 km away in line with the boom in the direction in which the Yagi is pointing, and in exactly the same plane as the elements, and then compare that to the signal from an isotropic radiator, the yagi will have a signal which is 7.5 dB stronger.

  2. If I do a 3 dB azimuth plot of both antennas and then compute the surface area of both plots and relatively compare them in dB, then I get 7.5 dB difference.

  3. If I do a 3 dB 3 dimensional plot of both antennas a then compute the Volume of both and compare them in a relative way then I get 7.5 dB.

  4. Some other method I don't know about yet.

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If I measure the signal strength 1 km away in line with the boom in the direction in which the Yagi is pointing, and in exactly the same plane as the elements, and then compare that to the signal from an isotropic radiator, the yagi will have a signal which is 7.5 dB stronger.

This is correct. The others are incorrect; antenna gain is always considered in some specific direction, and if you sum it up all around then you have thrown out the information about directivity and the number you have left is only the antenna efficiency (how much power it transmits vs. turning into heat).

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  • $\begingroup$ thank you. So gain is meaningless without a reference to a direction ... $\endgroup$ – Andrew Feb 25 at 2:34
  • $\begingroup$ And by direction i mean a three-dimensional direction ... $\endgroup$ – Andrew Feb 25 at 2:49
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    $\begingroup$ @Andrew If you see talk about an antenna's gain without further specification, it will be referring to gain in the direction(s) the antenna is intended to be used — for example, along the boom of a Yagi, or in an arbitrary horizontal direction for a vertical antenna. $\endgroup$ – Kevin Reid AG6YO Feb 25 at 4:41
  • $\begingroup$ one reason i ask is that vertical omni directional antennas are often specified with gain but the gain is in the elevation plane not the azimuth plane, so it's confusing if you compare the 4 odd dbi a .64 wave ground plane antenna has in the elevation plane to the 7.5 dbi that a yagi has in the azimuth plane, but it's still all gain that makes a difference. $\endgroup$ – Andrew Feb 25 at 5:34
  • $\begingroup$ "and if you sum it up all around then you have thrown out the information about gain and all antennas are the same.". This would be true if all antennas had the same efficiency - but they do not. Gain = Directivity * Efficiency $\endgroup$ – Glenn W9IQ Feb 25 at 11:59
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If I measure the signal strength 1 km away in line with the boom in the direction in which the Yagi is pointing, and in exactly the same plane as the elements, and then compare that to the signal from an isotropic radiator, the yagi will have a signal which is 7.5 dB higher.

Theoretically correct. In practice you'll have some trouble actually performing this measurement. Firstly, isotropic radiators don't exist. Secondly, if the specified gain of 7.5 dBi is in free space, the antenna installed over ground will have different characteristics. The location of the mast or tower on which the antenna is mounted, feedline, and other nearby antennas can also perturb the pattern, sometimes very significantly.

Your other two examples seem to involve in some way integrating the power radiated by the antenna over all possible directions. You'll find most antennas likely to be used for amateur radio transmitting will give about the same total power as an isotropic radiator.

The reason should be fairly intuitive considering the law of conservation of energy: if a directional antenna radiates more strongly in a particular direction, it must radiate less strongly in some other direction. To do otherwise would require creating additional energy from somewhere.

The relevant metric comparing total power radiated in all directions is called antenna efficiency. It's not difficult to achieve efficiencies above 99%. Consider a simple wire dipole: the wire has very low resistance, so there isn't anywhere for a significant amount of energy to be lost: it has nowhere to go but into electromagnetic radiation. A mobile HF antenna has lower efficiency: the electrical shortening increases the current in the antenna, making the resistive losses in the antenna and the loading coil much more significant. A vertical installed without radials has lower efficiency due to the high resistance of the soil. But antennas that aren't shortened, and are properly installed, can have efficiencies that are very nearly 100%.

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  • $\begingroup$ thanks the dbi was really a typo and i get that part. What you say all makes sense to me. $\endgroup$ – Andrew Feb 25 at 5:35
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    $\begingroup$ "You'll find most antennas likely to be used for amateur radio transmitting will give about the same total power as an isotropic radiator." This seems to be a contradiction to your otherwise excellent dissertation regarding efficiency. Consider two popular antennas: the small loop and the 1/2 CF dipole. Nearly equal directivity but far from radiating the same total power. $\endgroup$ – Glenn W9IQ Feb 25 at 12:07
  • $\begingroup$ @GlennW9IQ San Francisco has homeless people everywhere, but that does not mean most of the population is not homeless. "Most" denotes significant exceptions exist. That you've found one does not negate the point. $\endgroup$ – Phil Frost - W8II Feb 26 at 16:55
  • $\begingroup$ Rather than the absolute percent of the population of antennas, I was thinking of more of these commonly encountered antennas: small loop, end fed wire, HF verticals/flag poles, HF mobile, inverted L, Carolina Windom, linearly loaded, and antennas < 0.1λ. $\endgroup$ – Glenn W9IQ Feb 26 at 20:48

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