Radiation Resistance
 

I am not trolling.

What I want to know is the radiation resistance, referred to the base,
of a short vertical wire above a perfect ground, the current in the
wire being assumed uniformly distributed.

The radiation resistance at the base is in the form of -

C * Square( Length / Lambda )

where Length is the physical length or height of the wire and Lambda
is the free-space wavelength.

What is the value of the constant C ?

Thank you.
----
Reg.

Radiation Resistance
 

C = 160 * pi^2 ~ 1579.

This is exactly 4 times the radiation resistance of a short dipole with
linear current distribution (i.e., one without a top hat), since the
average current is twice the amount for the same radiated power.

Of course, this assumes an infinitely thin wire. Any real wire will have
a higher radiation resistance than this.

Roy Lewallen, W7EL

Reg Edwards wrote:
I am not trolling.

What I want to know is the radiation resistance, referred to the base,
of a short vertical wire above a perfect ground, the current in the
wire being assumed uniformly distributed.

The radiation resistance at the base is in the form of -

C * Square( Length / Lambda )

where Length is the physical length or height of the wire and Lambda
is the free-space wavelength.

What is the value of the constant C ?

Thank you.
----
Reg.

Radiation Resistance
 

Reg Edwards wrote:
I am not trolling.

What I want to know is the radiation resistance, referred to the base,
of a short vertical wire above a perfect ground, the current in the
wire being assumed uniformly distributed.

The radiation resistance at the base is in the form of -

C * Square( Length / Lambda )

where Length is the physical length or height of the wire and Lambda
is the free-space wavelength.

What is the value of the constant C ?

Reg, I believe it would be 10*pi^2 = 98.7, half of the
value of a small dipole. Balanis gives a dipole a very
thorough treatment and then says the monopole is half
of those values. His constant in the value of radiation
resistance for a short dipole is 20*pi^2. Kraus rounds
that constant off to 200. That value assumes the short
dipole is not infinitessimal and has a linear standing
wave current distribution. That constant doesn't seem
to need to be a very exact value.
--
73, Cecil http://www.qsl.net/w5dxp

Radiation Resistance
 

Roy Lewallen wrote:

C = 160 * pi^2 ~ 1579.

This is exactly 4 times the radiation resistance of a short dipole with
linear current distribution (i.e., one without a top hat), since the
average current is twice the amount for the same radiated power.

Since the resistance is inversely proportional to the current,
shouldn't you have divided by 4 instead of multiplying by 4?
--
73, Cecil http://www.qsl.net/w5dxp

Radiation Resistance
 

Roy Lewallen wrote:
C = 160 * pi^2 ~ 1579.

This is exactly 4 times the radiation resistance of a short dipole with
linear current distribution (i.e., one without a top hat), since the
average current is twice the amount for the same radiated power.

Roy's formula above is correct. It is approximatey 1580 times the
square of effective height over the wavelength.

http://www.w8ji.com/radiat1.gif

http://www.w8ji.com/radiation_resistance.htm


Cecil's answer is not correct, but I'm sure you figured that out on
your own.

73 Tom

Radiation Resistance
 

wrote:
Cecil's answer is not correct, but I'm sure you figured that out on
your own.

Silly me, I was assuming the length of the monopole was
assumed to be 1/2 the length of the dipole.
--
73, Cecil http://www.qsl.net/w5dxp

Radiation Resistance
 

Reg wrote:
"What is the value of the constant C?"

395

It is found on page 137 of Kraus` 1950 edition of "Antennas".

Best regards, Richard Harrison, KB5WZI

Radiation Resistance
 

Richard Harrison wrote:
Reg wrote:
"What is the value of the constant C?"
395
It is found on page 137 of Kraus` 1950 edition of "Antennas".
Best regards, Richard Harrison, KB5WZI

Richard,

You didn't read something correctly.

Reg asked for "C" for a small vertical with uniform current over a
perfect groundplane.

You are off by nearly a factor of 4 times.

For a monopole with uniform current, C=1580
For a monopole with triangular current C= 395

Radiation resistance is four times greater when the antenna has uniform
current.

73 Tom

Radiation Resistance
 

Cecil Moore wrote:
Reg, I believe it would be 10*pi^2 = 98.7, half of the
value of a small dipole.

My bad. I falsely assumed that the length in the
monopole equation was 1/2 the length in the dipole
equation. Another senior moment.
--
73, Cecil http://www.qsl.net/w5dxp

Radiation Resistance
 

wrote:
For a monopole with uniform current, C=1580
For a monopole with triangular current C= 395

Radiation resistance is four times greater when the antenna has uniform
current.

Reg didn't say "uniform current". He said "uniformly distributed
current". A triangular current wave is uniformly distributed,
i.e. it has a linear taper. Seem to me we need to find out
what Reg meant by "uniformly distributed current". I thought
he meant uniformly triangularly distributed. I think Richard
thought the same thing.
--
73, Cecil http://www.qsl.net/w5dxp

Radiation Resistance
 

On Sun, 12 Mar 2006 12:14:43 -0600, (Richard
Harrison) wrote:

Reg wrote:
"What is the value of the constant C?"

395

It is found on page 137 of Kraus` 1950 edition of "Antennas".


Is that for uniform current as Reg asked?

Owen
--

Radiation Resistance
 

Tom, W8JI wrote:
"You didn`t read something correctly."

OK, here is the arithmetic.

Radiation Resistance of a Short Electric Dipole:

RR = 80 pi squared (L/lambda)squared

Constant = 80 (8.97) = 790

But a short monopole has 1/2 the resistance of a short dipole.

790 / 2 = 395

All Reg asked for was the constant.

Best regards, Richard Harrison, KB5WZI

Radiation Resistance
 

Owen Duffy wrote:
Is that for uniform current as Reg asked?

Reg asked for "uniformly distributed current". I took
that to mean having a constant slope. Wonder what Reg
really meant?
--
73, Cecil http://www.qsl.net/w5dxp

Radiation Resistance
 

On Sun, 12 Mar 2006 20:46:21 GMT, Cecil Moore wrote:

Owen Duffy wrote:
Is that for uniform current as Reg asked?

Reg asked for "uniformly distributed current". I took
that to mean having a constant slope. Wonder what Reg
really meant?

In the context of his use, I think the most probably reasonable
interpretation of Reg's words is that the current is uniform at all
points on the radiator.

Yes, it does also have a constant slope (of zero), so you will ba able
to argue a correct interpetation either way, even if the results are
different.

It was interesting how many different interpretations were made, and
then how many different answers to such a simple questions, even a
text book incorrectly quoted (yes, subject to your interpretation of
Richard's interpretation of what was in Reg's mind. Reg will no doubt
chuckle when he wakes in the morning.

Owen
--

Radiation Resistance
 

Richard,

Your calculation is OK as far as it goes. However, you overlooked the
fact that "L" is different for the dipole and the monopole. The monopole
has 1/2 the length of the dipole or 1/4 the length squared.

The coefficient Reg asked for is therefore 4 times the number you quoted.

73,
Gene
W4SZ

Richard Harrison wrote:
Tom, W8JI wrote:
"You didn`t read something correctly."

OK, here is the arithmetic.

Radiation Resistance of a Short Electric Dipole:

RR = 80 pi squared (L/lambda)squared

Constant = 80 (8.97) = 790

But a short monopole has 1/2 the resistance of a short dipole.

790 / 2 = 395

All Reg asked for was the constant.

Best regards, Richard Harrison, KB5WZI

Radiation Resistance
 

On Sun, 12 Mar 2006 15:06:15 -0600, (Richard
Harrison) wrote:

Owen Duffy wrote:
"Is that for uniform current as Reg asked?"

Reg described a short vertical wire above a perfect ground.

Without a capacitive hat or some such device, you have an open circuit
at the tip of the antenna (zero current) and a finite current at the
driven end of the wire. How would the current be uniform end to end?

That is *your* logic, and on the basis of it, you have chosen to
ignore part of the original question, the explicit statement "the
current in the wire being assumed uniformly distributed", without
qualifying your one word answer.

Owen
--

Radiation Resistance
 

Owen Duffy wrote:
Yes, it does also have a constant slope (of zero), so you will ba able
to argue a correct interpetation either way, even if the results are
different.

OK, I will change my statement to a "constant non-zero
slope". I really think that what's Reg meant but obviously
only Reg's opinion is important on that matter. :-)

Reg will no doubt
chuckle when he wakes in the morning.

:-) When I chuckle with a hangover, it hurts. :-)
--
73, Cecil http://www.qsl.net/w5dxp

Radiation Resistance
 

Richard Harrison wrote:
Owen Duffy wrote:
"Is that for uniform current as Reg asked?"

Reg described a short vertical wire above a perfect ground.

Without a capacitive hat or some such device, you have an open circuit
at the tip of the antenna (zero current) and a finite current at the
driven end of the wire. How would the current be uniform end to end?

For the answer to that, open your Kraus again, and go to the beginning
of the chapter (5) you quoted from. It's explained in the first
paragraph. There's even a picture, Fig. 5-1.

Roy Lewallen, W7EL

Radiation Resistance
 

Richard Harrison wrote:
Tom, W8JI wrote:
"You didn`t read something correctly."

OK, here is the arithmetic.

Radiation Resistance of a Short Electric Dipole:

RR = 80 pi squared (L/lambda)squared

Constant = 80 (8.97) = 790

But a short monopole has 1/2 the resistance of a short dipole.

790 / 2 = 395

All Reg asked for was the constant.


If you'll read more in the chapter of Kraus you're quoting, you'll
notice that L is the length of the dipole, not the length of a monopole.
Do the proper substitution and you'll get the correct answer.

Roy Lewallen, W7EL

Radiation Resistance
 

Roy, W7EL wrote:
"There`s even a picture Fig 5-1"

Yes, exactly as I speculated.

Reg`s question that I tried to answer was:
"What is the value of the constant C?"

My answer is 395 and I`nm sticking with it until someone shows me the
error in my ways.

Best regards, Richard Harrison, KB5WZI

Radiation Resistance
 

Richard Harrison wrote:
Roy, W7EL wrote:
"There`s even a picture Fig 5-1"

Yes, exactly as I speculated.

Reg`s question that I tried to answer was:
"What is the value of the constant C?"

My answer is 395 and I`nm sticking with it until someone shows me the
error in my ways.

Best regards, Richard Harrison, KB5WZI

Is everyone from Texas like this?

Radiation Resistance
 

Roy, W7EL wrote:
"Do the proper substitutionn and you`ll get the correct answer."

Yes. The warning also appears on page 137:
"In developing the field expressions for the short dipole, which were
used in obtaining (5-56), (5-56) is the value of radiation resistance,
the restriction was made that lambda is much larger than the length of
the dipole L." No problem there, Reg specified a short monopole.

Kraus does a sample calculation for a short dipole. I used Kraus` data
and got the same answer when duplicating his calculation.

But Reg was not asking for an answer to a specific problem. Reg was
asking for the value of the constant in a formula of the same form.
Kraus gives it as 80 pi squared for a dipole.. This is 790.

We know that a monopole has half the resistance of a dipole. Example: 73
ohms and 36.5 ohms. 790 / 2 = 395. That`s not a resistance, it is only
the value of a constant which must be multiplied by (L/lambda) squared
to give the radiation resistance of a very short monopole.

Best regards, Richard Harrison, KB5WZI

Radiation Resistance
 

Gene Fuller wrote:
Richard,

Your calculation is OK as far as it goes. However, you overlooked the
fact that "L" is different for the dipole and the monopole. The monopole
has 1/2 the length of the dipole or 1/4 the length squared.

The coefficient Reg asked for is therefore 4 times the number you quoted.

1.) He could have gotten length correct and assumed current was
triangular. That would reduce radiation resistance by a factor of four.

2.) He could have assumed uniform current and gotten length wrong by a
factor of two, and that would reduce radiation resistance by a factor
of four.

Radiation Resistance
 

wrote:
Is everyone from Texas like this?

Before you jump the gun, we should probably wake Reg
up and ask him what he really meant. I don't think
he was asking about an infinitessimal vertical.
--
73, Cecil http://www.qsl.net/w5dxp

Radiation Resistance
 

Gene Fuller wrote:
"However, you overlooked the fact that "L" is gifferent for the dipole
and monopole."

L is not a constant. L is a variable in another part of the formula. The
difference in radiation resistance between a dipole and a monopole is a
constant. It equals 2, not 4, not 8, or not 16.

Best regards, Richard Harrison, KB5WZI

Radiation Resistance
 

Richard Harrison wrote:
We know that a monopole has half the resistance of a dipole. Example: 73
ohms and 36.5 ohms. 790 / 2 = 395. That`s not a resistance, it is only
the value of a constant which must be multiplied by (L/lambda) squared
to give the radiation resistance of a very short monopole.

Does it matter that for a vertical that is 1/2 of the length
of the dipole, (L/lamda)^2 is different by a factor of 4?
--
73, Cecil http://www.qsl.net/w5dxp

Radiation Resistance
 

Cecil, W5DXP wrote:
"Does it matter that for a vertical that the length of a dipole
(L/lambda)squared is different by a factor of 4?"

It doesn`t make a ratio different than two to one in the ratio of
resistances of the 1/2-wave dipole to the 1/4-wave monopole. We are not
comparing a monopole that is the the length of a dipole with the dipole.
We are comparing a monopole that is 1//2 the length of a dipole to the
dipole when we make the resistance ratio.

The small dipole is working against a perfect ground in Reg`s
specification. It would see its reflection in that perfect ground, so
its equivalent length is doubled. Kraus` dipole is presumed to be in
free space.

Best regards, Richard Harrison, KB5WZI

Radiation Resistance
 

On Sun, 12 Mar 2006 20:56:05 -0600, (Richard
Harrison) wrote:

Roy, W7EL wrote:
"Do the proper substitutionn and you`ll get the correct answer."

Yes. The warning also appears on page 137:
"In developing the field expressions for the short dipole, which were
used in obtaining (5-56), (5-56) is the value of radiation resistance,
the restriction was made that lambda is much larger than the length of
the dipole L." No problem there, Reg specified a short monopole.

Kraus does a sample calculation for a short dipole. I used Kraus` data
and got the same answer when duplicating his calculation.

But Reg was not asking for an answer to a specific problem. Reg was
asking for the value of the constant in a formula of the same form.
Kraus gives it as 80 pi squared for a dipole.. This is 790.

We know that a monopole has half the resistance of a dipole. Example: 73
ohms and 36.5 ohms. 790 / 2 = 395. That`s not a resistance, it is only
the value of a constant which must be multiplied by (L/lambda) squared
to give the radiation resistance of a very short monopole.


Is all that to mean that you used the formula given by Kraus for a
short thin dipole and applied your own rule to halve the coefficient.

In your original response you said "395 It is found on page 137 of
Kraus` 1950 edition of "Antennas"."

Is that correct, or did you make the number 395 up according to your
own rules and then attribute it to Kraus?

Owen
--

Radiation Resistance
 

Richard Harrison wrote:

Cecil, W5DXP wrote:
"Does it matter that for a vertical that the length of a dipole
(L/lambda)squared is different by a factor of 4?"

It doesn`t make a ratio different than two to one in the ratio of
resistances of the 1/2-wave dipole to the 1/4-wave monopole. We are not
comparing a monopole that is the the length of a dipole with the dipole.
We are comparing a monopole that is 1//2 the length of a dipole to the
dipole when we make the resistance ratio.

Richard, Balanis doesn't say that the 'L' in the monopole
formula is 1/2 the 'L' in the dipole formula. Does Kraus?
--
73, Cecil http://www.qsl.net/w5dxp

Radiation Resistance
 

Richard Harrison wrote:
Gene Fuller wrote:
"However, you overlooked the fact that "L" is gifferent for the dipole
and monopole."

L is not a constant. L is a variable in another part of the formula. The
difference in radiation resistance between a dipole and a monopole is a
constant. It equals 2, not 4, not 8, or not 16.

Best regards, Richard Harrison, KB5WZI

Richard,

I guess this must be the week for basic math explanations.

Let's try it with numbers.

The equation shown in Kraus "Antennas", 2nd edition, page 216, for the
radiation resistance of a short dipole with constant current is:

Rr = 80 pi^2 (L/lambda)^2

80 pi^2 is about 790, so the equation is rewritten as:

Rr = 790 (L/lambda)^2

In the convention used by Kraus, "L" is the total length of the dipole.

I presume the equivalent discussion is contained in the 1950 edition of
"Antennas".

As a test case, let's suppose that L is 8 meters, and lambda is 80
meters. We immediately see that Rr is 7.9 ohms.

OK, now take the monopole over perfect ground that Reg mentioned. The
monopole length that corresponds to one half of the test case dipole is
4 meters. The radiation resistance of the monopole is 3.95 ohms.

So, the question becomes determining the correct coefficient for the Rr
equation. (L/lambda) is now 0.05, not 0.10.

Therefore,

Rr = 3.95 ohms = X (0.05)^2

I believe you will discover that "X" must be 1580.

This is set up using the definitions for L as stated in Kraus (dipole)
and as stated by Reg in his monopole query. Of course you can set up
your own rules, but that would be addressing a different problem.

73,
Gene
W4SZ

Radiation Resistance
 

"Roy Lewallen" wrote

C = 160 * pi^2 ~ 1579.

====================================

Thank you Roy.
----
Reg

Radiation Resistance
 

Owen Duffy wrote:
"Is that correct---?"

No, I don`t think so.

Kraus` formula is:
Radiation resistance = 80 pi squared L squared

L is the fraction of a WL made by a tiny dipole.

For the same wavelength, a monopole is only 0.5 the length of a dipole
and it has 0.5 the radiation resistance.

If we use its length in the formula abbove, the radiation resistance
would calculate as only 1/4 that of a dipole because the constant is the
same and L squared is 0.5 squared.

I speculrte from the resistance ratio of a normal dipole to a normal
monopole that the answer should be 0.5. So I erred by halving the
constant. I should have doubled it to offset the quartered answer an
unchanged constant would produces when L = 0.5.

My new and improved answer to what the value of C is:

1580

Best regards, Richard Harrison, KB5WZI

Radiation Resistance
 

wrote:
This newsgroup, like any public forum, allows anyone to say almost
anything without censorship. Because of that two things none of us like
to see will happen:

1.) Incorrect information is posted

By gurus as well as everyone else. I asked some technical
question in another posting, Tom. In the past, you simply
ignored my technical questions by trimming them from my
posting and then you objected to my style which is all
that was left.

Let's see if you are still unwilling to answer my technical
questions one of which is:

Why isn't a century old method of determining the phase
shift (delay) through a coil by measuring the self-
resonant frequency good enough for you? How do you
explain an 81% difference between this old accepted
method and your recently measured results?
--
73, Cecil http://www.qsl.net/w5dxp