Imagine that you put 100 watts into an isotropic radiator in free space
and measure its field strength at some distance. Then you create a
ground plane like the ones used by most modeling programs, perfectly
flat and infinite in extent, and make it perfectly conductive. Now
distribute that 100 watts evenly in all directions, above the ground
plane -- imagine a sort of hemi-isotropic radiator which does this.
Measure the field strength at the same distance from the radiator as
before. You'll find that the field strength is 3 dB higher, and the
power density twice as great, as for the isotropic source in free space.
It's simply because you're distributing the same amount of power in half
the amount of space.

That illustrates the first principle, that putting an antenna over
ground gives you an automatic 3 dB increase in average field strength
compared to free space. If you compare the field strength of an antenna
over ground with a free space isotropic source (i.e., give its gain in
dBi), you'll find it has a gain of 3 dBi when averaged in all
directions. (EZNEC's "Average Gain" calculation automatically takes this
into account and normalizes to 0 dB when a ground is present; NEC-2's
average gain calculation doesn't.)

You can also pick up about 3 dB additional gain because of the increased
directivity you get when putting an antenna over ground. You get the
same pattern you'd have if there were another antenna below the ground
(an "image" antenna) and with out of phase current relative to the
actual antenna -- it's like having a two antenna beam. (Pattern gain
won't usually be exactly 3 dB because of the impedance change of the
antenna caused by interaction with the ground -- when the ground is
perfect, it's exactly the same as mutual coupling to the "image"
antenna.) So typically a dipole over ground has a gain somewhere between
about 3 and 6 dBi -- around 4 or 5 is common for most typical grounds
and heights.

Comparing the gain of an antenna to that of a dipole over ground
requires calculating or measuring the gain of the dipole over ground --
you can't just assume some gain. The most universally used way is to get
both gains in dBi, since dBi is universally defined and understood, then
subtract to find the difference.

Roy Lewallen, W7EL

Cecil Moore wrote:

In *free space* the gain of a dipole over isotropic is about 2.14 dB.
Over ground, the reflections from the ground add another few dB.
dBi is *always* referenced to free space. An isotropic over perfect
ground would probably have a gain of about 3 dBi assuming no destructive
interference. A dipole over perfect ground has a gain of about 7.5 dBi.
Rule of thumb: A dipole over average ground has a gain of about 6 dBi.