Radiation resistance is pretty much what the writer wants it to be.
Consequently, it has to be explicitly each time it's used whenever an
ambiguity might arise. It's simply a resistance whose "dissipation"
(absorbed power) is the amount radiated. Most writers would probably
argue that power lost from the near field to nearby lossy objects such
as ground never got radiated, and therefore the corresponding resistance
should be considered loss rather than radiation resistance. The presence
of nearby ground, however, can also change the value of the remaining
resistance due to mutual coupling and alteration of the current
distribution, so a particular antenna doesn't have a single inherent
value of radiation resistance independent of environment.

As for the location where radiation resistance is defined, I believe
it's common in AM broadcasting, for example, to refer the radiation
resistance of a monopole to a current loop (maximum). If this is a
different location than the feed point, the resistance (neglecting loss)
at the base will be different from the loop radiation resistance. The
ratio of base radiation resistance to loop radiation resistance will in
fact equal the square of the ratio of loop current to base current. So
radiation resistance measured at the base can be "referred" to the loop
by scaling by this ratio. (The power "dissipated" by radiation
resistance referred to a loop or any other point has to equal the
"dissipation" of the radiation resistance seen at the base or any other
point. So Rr has to differ to keep I^2 * Rr constant as Rr is referred
to points having different values of I.) The radiation resistance can be
referred to any point on the antenna, so the writer has to specify what
point is used. But one point is as acceptable as another. It's vital,
though, when using radiation resistance, that the current at the defined
point is used for calculations. And loss resistance must also be
referred to the same point if efficiency calculations are to be made.

Some authors, for example Kraus, consistently refer the radiation
resistance to the feed point. But Kraus doesn't explicitly apply the
term "radiation resistance" to a folded dipole. There's nothing at all
wrong, however, with declaring the radiation resistance of a folded
dipole to be ~300 ohms. The power radiated is the current measured at
the feed point, squared, times that resistance. It's equally legitimate
to declare the radiation resistance of a folded dipole to be that of an
unfolded equivalent, or ~75 ohms. If you do, though, you also have to
work with the current of the unfolded dipole to make the power come out
correct.

A common mistake when dealing with folded unipoles, made by at least
several prominent people who should have known better (and marketing
people who probably do know better but find it advantageous to be
incorrect), is to refer the radiation resistance to the feed point but
the loss resistance to the unfolded equivalent. This results in an
erroneous efficiency calculation that incorrectly attributes an
improvement due to folding. As I said, you can refer the radiation
resistance to either, but if you want to calculate efficiency, you have
to refer the loss resistance to the same point and having undergone the
same transformation. And when you do, you find that folding fails to
produce the often-claimed efficiency improvement.

Roy Lewallen, W7EL

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.

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.

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.

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.

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???).

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

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

Owen Duffy wrote in
:

Rr/(Rr+2Rg)

That should have an exponent in the

Rr/(Rr+2^2Rg)