Owen Duffy wrote:
Thanks Roy.

I note you observe similar variation in usage as I note.

Yes, consistency in an application is more important than a common meaning
of the term, but a common meaning of the term assists simpler
communication.

True. But we can't force consistency of a term that's already ubiquitous
in the literature with a variety of meanings. Saying it's so doesn't
make it so.

Regarding say, a base fed folded monopole and efficiency calculations, if
the connection to ground is though of as having some actual value Rg, since
the current flowing in Rg is twice the feedpoint current, consistent
development of the circuit model will reveal the correct efficiency as:

Rr/(Rr+2Rg)

where Rr is the sum of power in the far field divided by feed point current
squared. You don't need to fudge Rr to get the result, proper allowance of
the power due to the actual current in Rg provides the correct result.

Ok, here we go. Remember that efficiency is really a power ratio, not a
resistance ratio. It reduces to the familiar resistance formula only
when the currents in both radiation and loss resistances are the same.

Let's talk about Rg. An unfolded monopole has a single connection to
ground, and we can call this resistance Rg. If Rr is the base radiation
resistance, then the same current flows through Rr and Rg, so efficiency
= Pr/(Pr + Pg) = Rr/(Rr + Rg) and everything's fine. But when we fold
it, there are two connections to ground -- the "cold" side of the
feedline and the non-feed monopole conductor. Each has half the original
current. The "hot" side of the feedline carries the same current as the
"cold" side so its current is half the original value also. You have
your choice for Rg -- you can consider it to be the original ground
system resistance but with twice the current flowing through it as
through the feedpoint resistance; or you can split the original into two
equal parallel resistances of twice the value, each with the same
current as at the feedpoint. In the first case, you get the equation you
posted. In the second, you get Rr/(Rr + Rg). We've basically referred
the ground resistance to the transformed feedpoint.

The surest way to stay out of trouble is to always calculate efficiency
as a ratio of powers. If you use I^2 * R for radiation power and loss
power, you can't go wrong, regardless of where you choose either R to
be, as long as the I is at the same point.

Kraus (Annennas for All Applications) effectively defines Rr as part of his
development of the concept of a pair of conductors transitioning from a
non-radiating transmission line to an antenna to free space radiation.

He does say "... the radiation resistance Rr, may be thought of as a
"virtual" resistance that does not exist physically but is a quantity
coupling the antenna to distant regions of space via a "virtual"
transmission line."

It is his use of "distant regions of space" that suggests in the case of
ground reflection, it is the remaining total power in distant free space
after lossy reflection that is used to calculate Rr. The power lost in
reflection would be a component of feed point R, but not Rr.

Well, we can get carried away with this, too. Nearby ground sucks power
from the near field and that power is never radiated. The longer
distance ground reflection primarily responsible for elevation pattern
development uses power which has been radiated from the antenna
conductor(s). Is that reflection "distant"? When you calculate an
antenna's efficiency, do you include the power radiated from the
conductor before or after the ground reflection? What about power that's
lost by radiation to space? It's just as surely lost for terrestrial
communication as power warming the ground. Answer: It's entirely up to
you. You could even consider all energy which doesn't strike your
receiving antenna as "loss". All you have to do is clearly state what
you're including and what you're not.

He also states a little earlier "... the antenna appears to the
transmission line as a resistance, Rr, called the *radiation resistance*.
It is not related to any in the antenna itself, but a resistance coupled to
the from space to the antenna terminals." This seems fairly clear to me
that he defines radiation resistance to be at the transmission line /
antenna interface.

Kraus is consistent with this, but other respected authors use the term
radiation resistance differently. The few who use the term radiation
resistance when lossy ground is present, though, seem to regard
near-field coupling loss to ground as loss, and not consider far field
reflection in efficiency calculations at all.

Both of these statements by Kraus are simple, but would seem to be capable
of application to real antenna systems. I can't immediately think of
exceptions (game on???).

As I said above, how distant?

In Kraus's language, ground reflections might reasonable be considered part
of the 'antenna' since they influence its pattern and loss, and loss in the
ground reflections is due to resistance "in the 'antenna' itself" and so
excluded from Rr.

Is there anything in Kraus's statements that is wrong, or my
interpretatiohn of them.

Owen

Kraus isn't wrong. Neither are the other respected authors who use the
term differently. I'm sorry, but you're looking for something that
doesn't exist, and I don't see the point in trying to invent a strict
definition just for your own use.

Roy Lewallen, W7EL