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