Owen Duffy wrote:

George,

Fundamental relationships depend on dBi, it is dBd that is the fudge.

dBd seems to have its popularity from the mistaken view by some that
because it is not possible to construct a real isotropic radiator, that dBi
doesn't have a real meaning.

Owen

At least one manufacturer has taken advantage of the fact that, unlike
dBi, dBd has no universal definition. Some think it's dB relative to a
dipole in free space; others think it's relative to a dipole mounted
over ground. And few seem to realize that the difference between the two
is typically 4 - 6 dB. Creative marketeers are able to capitalize on
this confusion, and have.

Roy Lewallen, W7EL