Jimmy wrote:
"Efficiency is based on how much of your signal your antenna turns into
heat compared to the amount radiated and nothing more."

With some reshuffle of terms, Terman seems to agree. On page 893 of his
1955 edition:

"The efficiency of the antenna as a radiator is the ratio: Rradiation
/ Rradiation + Rloss----."

Best regards, Richard Harrison, KB5WZI

On Sat, 21 Feb 2004 19:04:24 GMT, "Jimmy"
wrote:
Gain and efficecey have nothing to do with each other

Hi Jimmy,

In the classic sense, this is very true.

However, when we look at gain integrated over all dimensions, we
arrive at the concept of the isotropic reference. As a basis of
comparison (skip the sophistry of there being no such physical device)
this too reveals how gain and efficiency can be compared.

In other words, with gain you can play the numbers to claim efficiency
by sweeping the bad news under the carpet if you simply ignore the
integration factor. A prime example is the recent glowing reports of
the cfa. The "inventor" claims that his "FCC" tests reveal a gain of
his antenna over the standard monopole, through substitution with an
actual broadcast band, licensed transmitter.

Well, perhaps in the direction of the nearby tower it was supposed to
replace. When you look in every other direction, and step well away
from the source (say, like were the listeners actually live and
listen); then it is a different game altogether. Only 20 miles out
and you find the cfa 30dB down into the mud compared to FCC standard
charts (I won't go deeply into the fact that the comparison BC station
had a ****-poor antenna itself 10dB down from those same charts).

True, no one did a helicopter flyover to vindicate the cfa's
redemption of superb cloud warming capabilities, but that was not
where the listening audience lives. Further, given that the cfa's
poor performance conformed to modeling along the testing scenario, it
was hardly an indictment of the models that they did not reveal the
glow in the sky.

So, when you see claims based against gain tied to arguments of
efficiency (apply any special terminology you wish) ask the hard
questions and observe the answers. Do they respond with technical
specifications that answer the issue, or are they laden with conflict
and personality?

73's
Richard Clark, KB7QHC

Good evening Art, I have a few minutes to put some thoughts on email
regarding efficiency per unit length of an antenna, or antenna elements.
I hope I don't glaze your eyes :-)

Efficiency by definition is work delivered to a load divided by the
total work available.

The work [power] delivered to the load is the work available minus
losses all divided by work available. Your car engine may have 100
horsepower available but losses [heat] in the transmission, drive shaft,
differential, oils, fluids, bearings, tires and wheels may limit
horsepower delivered to the road to 30 horsepower. In this model then
the efficiency is 30%.

Note: bandwidth is not a factor. It is total work[power] delivered
divided by total work[power] available.

For an antenna the following definition is applicable by similarity:

Efficiency = Radiated Power/Total power. By definition an antenna is a
linear device and the Principle of Reciprocity is applicable. That is,
it has the same efficiency either transmitting or receiving.

Now, total power = I^2*Reffective

Reffective = Radiation Resistance [Rradiation] + Loss Resistance.

Radiated Power = I^2*Rradiation.

Where I = Io*cos[wt + b]. Where wt = frequency, b = phase shift along
antenna element.

By definition radiation resistance is that determined by integrating the
total radiated power over the surface of the sphere containing that
power. [1] For a half wave dipole that converges to the value at a
current maximum. So, radiation resistance for a 1/2 wave infinitely thin
dipole is 73 ohms at the current maximum.[1]

As one moves away from the current maximum the radiation resistance
increases as 1/cosine(angle from the maximum)^2 i.e. 1/cos^2[theta].[2]

Now, in a uniform cross section antenna the Loss Resistance per unit
length is constant.

So, the Radiation Resistance at the ends of the antenna is infinite.
[Cosine 90 degrees = 0] That means the efficiency at the ends of a 1/2
wavelength dipole is 100%. Isn't that a surprise?? [It's the same for a
dipole or a Yagi!!!!]

The Radiation Resistance at the 45 degree point from the current maximum
of a thin 1/2 wavelength dipole is 73 ohms/(cos^2(45 degrees)) = 146 Ohms.

The conclusion is that the efficiency of an antenna element varies along
it's length and can vary between maximum of infinity at the ends and
have a minimum value, that depends on the length of the antenna, at a
current maximum.

The total antenna efficiency is measured in the radiated pattern by
integrating the power density per square steradian [or square degrees]
over the full surface of a sphere divided by the power into the antenna.

So, a Yagi with 8.14 dBi (6 dBd + 2.14 dBi) gain has concentrated it's
radiated power into 15.38% of the three dimensional space defined by the
surface of a sphere. [See Note 1.] Now if the Yagi is 95 % efficient and
a dipole is 95% efficient the 6 dBd value remains constant.

_____________
Note 1 [I'm using degrees instead of steradians to simplify
understanding. The Science/math is the same]

The diameter of the earth is 360 degrees as measured from E-W and N-S.
The surface is then proportional to 360^2 = 129600 square degrees. [I
will be dividing the constant Pi in a subsequent step so it is deleted
here.]

A 6 dBd Yagi is also +2.14 dBi giving a net gain of 8.14 dBi. This
normalizes the value to a sphere.

So, 8.14 dBi = 10*Log(129600/X)
X = 19938.4 square degrees.

The Yagi has concentrated it's pattern into a piece of the surface of
the sphere that represents 15.38% of the total surface [19938.4/129600].
This is Gain NOT efficiency.

_____________
Reference [1]: Antennas, Kraus, McGraw-Hill 1950, Chapter 5, section
5-6, pages 143-146.

Reference [2]: Antennas, Kraus, McGraw-Hill 1950, Chapter 5, section
5-7, pages 147-148.

Reg, G4FGQ wrote:
"What allows a class-C amplifier to exceed 50% efficiency is a small
operating angle."

Exactly, and during the majority of the degrees it`s switched completely
off. It draws no current and suffers no "IsquaredR loss" during the
amplifier off-time. Impedance is approximately E/I, but I is the average
I, which is much less than the bursts of I during the conduction angle.

The switched-off time makes the I in the denominator of E/I very small
indeed and the solution to Ohm`s law is a high impedance without the
dissipation of a resistance that remains in place continuously while
agitating the atoms of a poor conductor to limit current.

Instead, we have a low-resistanc in high conducton for short spurts.
On-time is limited, instead of conduction, to produce a certain
effective resistance.

An automobile Kettering ignition system may use a dwell-meter to
indicate how much of the time the points are closed. An ohmmeter
indicates the resistance between its test prods. The two test circuits
are almost the same although limitation of the deflection of the
dwell-meter is different from limitation of the deflection of the
ohmmeter due to the difference between limited conduction angle ignition
points, and the continuous conduction through a current-limiting
resistor. There`s an analogy between Class C and Class A amplifiers in
there somewhere.

Best regards, Richard Harrison, KB5WZI

Dave Shrader wrote:
Lots of good stuff. Reciprocity is applicable to antennas. Antenna gain
and directivity are the same transmitting or receiving. Impedance is the
same as a source or load.

Dave wrote:
"That is, it has the same efficiency transmitting or receiving."

I hadn`t given that much thought but it seems to me there may be a
difference. When an antenna is receiving, it is excited by the received
signal, resulting in voltage and current on the antenna. The antenna
doesn`t care about the source of the signal. If the antenna is
conjugately matched to the receiver, radiation resistance is the source
resistance of the signal feeding the receiver. Half the signal power is
consumed in the source resistance (radiation resistance) and half is
consumed in the receiver. The half consumed in the radiation resistance
is re-radiated. The antenna doesn`t know that re-radiation is uncalled
for. If the antenna is mismatched to the receiver, more than 50% of all
power received is re-radiated, depending upon the severity of the
mismatch.

If we have a Class C amplifier feeding power to the same antenna and
enjoying a conjugate match, we can have a source that takes less than
50% of the available energy. So, the transmitting antenna system can be
more efficient than the receiving antenna system, it seems to me.

Best regards, Richard Harrison, KB5WZI

Dave wrote,

Where I = Io*cos[wt + b]. Where wt = frequency, b = phase shift along
antenna element.


wt is radians per second times seconds which is just radians, an angle. b is
time related
also. Are you thinking of perhaps kl?



By definition radiation resistance is that determined by integrating the
total radiated power over the surface of the sphere containing that
power.

Are you thinking of Rr=2Prad/|Io|^2?

[1] For a half wave dipole that converges to the value at a
current maximum. So, radiation resistance for a 1/2 wave infinitely thin
dipole is 73 ohms at the current maximum.[1]

Balanis gives (eta/4pi)Cin(2pi)=73.
Cin is .5772+ln(2pi)-Ci(2pi) which is approximately equal to 2.435.
Ci is a tabulated function.


So, the Radiation Resistance at the ends of the antenna is infinite.
[Cosine 90 degrees = 0] That means the efficiency at the ends of a 1/2
wavelength dipole is 100%. Isn't that a surprise?? [It's the same for a
dipole or a Yagi!!!!]

The Radiation Resistance at the 45 degree point from the current maximum
of a thin 1/2 wavelength dipole is 73 ohms/(cos^2(45 degrees)) = 146 Ohms.

The conclusion is that the efficiency of an antenna element varies along
it's length and can vary between maximum of infinity at the ends and
have a minimum value, that depends on the length of the antenna, at a
current maximum.

The total antenna efficiency is measured in the radiated pattern by
integrating the power density per square steradian [or square degrees]
over the full surface of a sphere divided by the power into the antenna.

So, a Yagi with 8.14 dBi (6 dBd + 2.14 dBi) gain has concentrated it's
radiated power into 15.38% of the three dimensional space defined by the
surface of a sphere. [See Note 1.] Now if the Yagi is 95 % efficient and
a dipole is 95% efficient the 6 dBd value remains constant.


Very entertaining.
73,
Tom Donaly, KA6RUH

Know what ya mean Ed. Used to mention Maxwell every now and then
myself but lets face facts, the coffee just isn't that good. Know whut
I mean!

Ed Price wrote:
"Butch" wrote in message
...

Time out!! You people are taking all this far to seriously. Just throw
an aerial out the window, feed it to your rig via a tuner, and enjoy
Amateur radio.

Butch Magee KF5DE



It just not that simple, Butch.

I'm sure you have heard that Ham radio is a hobby that has many facets;
construction, public service, contesting, field trips, QRP DX, etc. Some of
our members get their kicks merging theory with rag chewing. I don't think
there's any structure to this sub-category, other than to require at least
one mention of Maxwell in every discussion.


Ed
WB6WSN

Richard Harrison wrote:
SNIP
Dave wrote:
"That is, it has the same efficiency transmitting or receiving."

I hadn`t given that much thought but it seems to me there may be a
difference. When an antenna is receiving, it is excited by the received
signal, resulting in voltage and current on the antenna.

SNIP: Agree

The antenna
doesn`t care about the source of the signal. If the antenna is
conjugately matched to the receiver, radiation resistance is the source
resistance of the signal feeding the receiver.

SNIP: This resistance is the Radiation resistance of the antenna, i.e.
approximately 73 ohms in a thin 1/2 wavelength dipole.

Half the signal power is
consumed in the source resistance (radiation resistance) and half is
consumed in the receiver.

SNIP: Not quite. Half is RE-RADIATED. [It does not dissipate it
radiates!][See your next statement]. The other half is delivered to the
transmission line sub-system then to the receiver.

The half consumed in the radiation resistance
is re-radiated.

SNIP: Agree

The antenna doesn't know that re-radiation is uncalled
for.

SNIP: I wonder if this statement is the root of our misunderstanding? My
understanding is that the antenna does not have to know anything other
than passively allowing the Laws of Nature [Physics] to operate.

If the antenna is mismatched to the receiver, more than 50% of all
power received is re-radiated, depending upon the severity of the
mismatch.

SNIP: Have to think about what you are trying to say. If the antenna has
received a 10^-12 watt signal and 4*10^13 watts is delivered to the
transmission line and 5*10^-13 watts is reradiated then 1*10^13 watts
is energizing a standing wave in the antenna.


If we have a Class C amplifier feeding power to the same antenna and
enjoying a conjugate match, we can have a source that takes less than
50% of the available energy.

SNIP: Help me understand what you are trying to say.

So, the transmitting antenna system can be
more efficient than the receiving antenna system, it seems to me.

SNIP: I probably disagree. But, I do not fully understand what you are
trying to say in the previous paragraph.

Deacon Dave


Best regards, Richard Harrison, KB5WZI

Dave Shrader wrote:
"Help me understand what you are trying to say."

I`ll elaborate.

Efficiency is output / input.

1/2 or more of the power received by a receiving antenna is re-radiated.

Nearly all of the power received by a transmitting antenna is
transmitted.

Considering the energy available to the antenna, the job done by the
transmitting antenna system as compared with the job done by the
receiving antenna system, the transmitting system is better.

A receiving antenna must be resonant to enable full acceptance of
available energy, and it must be matched to avoid re-radiation of more
than 50% of the energy it is able to grab.
If off-resonance, the receiving antenna has too-high impedance for
significant induced current. Of course, we have such good receivers we
can do without good efficiency.

A transmitting antenna will radiate energy proportional to the current
in the antenna.

Ronold W.P. King says in "Transmission Lines, Antennas, and Wave
Guides":

"---the power (Io squared)(Ro) supplied to a highly conducting antenna
(of Copper), with Ro taken from the curves of Sec. 10, is for practical
purposes all radiated to the more or less closely coupled universe
outside the antenna, while that used in heating the antenna itself is
negligible." This information is on page 113.

Inefficiency is to be found elsewhere from the transmitting antenna
itself. We may use inefficient transmission lines and our wave
generator, the transmitter, may be inefficient. We usually try to keep
their losses low.

It is not uncommon to produce RF in a Class C amplifier with an
efficiency of 70%. With reasonable lines and antennas, nearly 100% of
this power output can be radiated, producing appropriate millivolts per
meter at one mile from the antenna.

This is not completely reversible due to re-radiation of 1/2 or more of
all the power a receiving antenna can grab.

The hope for point to point wireless power transmission is in using
antennas like large dishes, for example, which concentrate power within
such a small angle that the receiving antenna captures all the
transmitted beam. Similarly, all re-radiated power is beamed back to the
transmitting antenna for another trip to the receiver.

Best regards, Richard Harrison, KB5WZI

On Sun, 22 Feb 2004 13:07:46 -0600 (CST),
(Richard Harrison) wrote:
Efficiency is output / input.

1/2 or more of the power received by a receiving antenna is re-radiated.

Nearly all of the power received by a transmitting antenna is
transmitted.

Considering the energy available to the antenna, the job done by the
transmitting antenna system as compared with the job done by the
receiving antenna system, the transmitting system is better.

Hi All,

This is because of a shift in the perception of efficiency. To the
transmitter ALL of matched power is irrevocably lost and to the
perception of transmission wholly in-efficient (absolutely no transfer
of power has been engaged to any mechanical benefit). Radiation
Resistance is as lossy as any resistor, sans the caloric benefit of
work.

From the point of view of the wave impinging upon an antenna, only
half the power is irrevocably lost, half survives (in a Zeno's
paradoxical fashion). Again, absolutely no mechanical benefit is
derived except for a incredibly minute caloric gain (unless you test
your antennas inside a microwave oven) but this does invert the
expectation (some work has been accomplished).

Given efficiency is too often stated in terms of mechanical theory
(adiabatics and such) and then duct-taped to other disciplines
(notable through the egregiously wild claims of fantasy laws of
conservation) it is no surprise that other paradoxes emerge.

73's
Richard Clark, KB7QHC