# 1/2 Wave center fed resonant dipole --- why is the impedance 72 Ohms

Discussion in 'Antennas, Feedlines, Towers & Rotors' started by K9AXN, May 25, 2019.

1. ### KX4OMHam MemberQRZ Page

Jim,
You said "During the rise and fall period DISPLACEMENT current flows causing radiation ---- Displacement current is varying Surge current."

In Maxwell's terminology displacement current is the rate of change of the electric field. In the May/June 2007 QEX, Doug Smith, KF6DX (the editor at that time) in a Tech Note "Electromagnetic Radiation: A Brief Tutorial" discussed Maxwell's concept of a displacement current. Smith wrote, "Displacement current is not the actual of the movement of charge but it is equivalent in every way for changing fields." That is a five page article.

In your continued development of your ideas, it is useful to draw correlation wherever possible to Maxwell, Lenz Lorentz and others. Again, from Smith's article, he draws from Feynman, who wrote "...we have inherited a prejudice that an accelerating charge should radiate..." and (quoting Smith) " he went on to show, as did H. Lorentz that the force Frad associated with the radiation resistance is not proportional to to acceleration, but to the rate of change of acceleration, or jerk, as it is commonly called" and "This explains why why a stationary charge in a gravitational field does not radiate."

The article contains a lot of mathematics, but Smith also makes the topic of Maxwell's theory readable, which I believe is one of your objectives. You might benefit from reading it.

Ted, KX4OM

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2. ### W5DXPHam MemberQRZ Page

In Antenna Theory by Balanis, section 4.6, he develops the math behind the 73 ohms radiation resistance in free space. He integrates to get the total radiated power and comes up with:

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Has anyone read anywhere, the sequential progression of events that results in the radiation resistance becoming 72 ohms in such a way that most on this list will be able to grasp???? I asked if anyone would be willing to explain it in a way that others would understand receiving no responses. There is an equation that represents the answer but apparently not one of the experts understood it or had the courage to write the explanation for fear of the criticism that comes with censorship. The explanation that I provided is correct and provable and if you think it is not, YOU EXPERTS give it a try or point to what you find invalid. Some of you say it's coincident. How can you say coincident when you cannot even understand the equations that you read.

Oh, you do understand? What I wrote is the sequence of events that renders the value of radiation resistance --- same as the equation. Please point to the failure of logic in the following paper!
http://k9axn.com/attachments/PART__FINAL_6.docx

The sequential breakdown that was written is complete, logical, understandable, and BTW the fully dissected logic of the equation below.

I asked WPA to write the logic of the 72 to 600 Ohm transmission line interface! He apparently can't do so. He can manipulate the equations but has no idea how the incident and reflected values occur. Give it a try partner and if you can't do it I'll help. You stated once that I don't understand transmission lines and further I don't understand filter design. Where the filter design issue came from I HAVE NO IDEA. A guess is that you have designed a filter i.e. the brick filter.

Nope, the CAD software designed the filter to your specifications then drew the charts ---- you carried the coffee for the computer. There is not a chance in hades that you could hand analyze the infinite relationships between the 20 poles of that filter ---- none. Same thing happens on this list, folks that don't understand antenna logic dump stuff into the antenna tools then interpret the output as some sort of gospel then argue until the cows come home.

So for the folks that claim that there is something wrong with the paper that I invested the time to write, please point to the invalid logic ---- or keep your caustic comments to your selves ---- there are 900 other people on this list that might be interested.

Regards Jim

Last edited: Jun 12, 2019
5. ### SM0AOMHam MemberQRZ Page

There is still no "proof" that your antenna model is consistent with the analytical or numerical models drawn from Maxwell's field equations.

I have previously referred to the brilliant Princeton physicist Kirk Macdonald, and I suggest that you first study the derivation of energy transport by radiation from a wire done in pages 455 - 457 of the 1898 Abraham paper, and then explain why his conclusion that the damping decrement decreases, and Q increases with diminishing wire diameter should be wrong:

Then I would suggest that these papers by Kirk Macdonald are studied, and their derivations of radiation resistance and antenna reactance behaviour understood:

and

http://physics.princeton.edu/~mcdonald/examples/transmitter.pdf

The derivations made here are consistent both with classical physics and with modern relativity taken into account.

Schelkunoff's mode theory, which is derived in his 1941 paper and further expanded in his 1952 textbook "Advanced Antenna Theory" which has previously been referred to, provides workable engineering approximations to solve even quite complex antenna design problems.

Then I, for one, am waiting for you to present your arguments why the previous authors are applying obsolete or simply wrong theories.

I sometimes wonder what Professor Erik Hallén,
Famous lecturer in electromagnetics at the Royal Institute of Technology in Stockholm

caught on photo with W8JK at the left in 1957
and author of a textbook which still is used

would have said about discussions like this and those about the CFA and "EH-antenna"...

73/
Karl-Arne
SM0AOM

Last edited: Jun 12, 2019
6. ### W5DXPHam MemberQRZ Page

Jim, it's easy to do in terms of s-parameter equations. Note that voltages are normalized to Z0 and if one squares those normalized voltages, the result is power.

b1 = s11*a1 + s12*a2
b2 = s21*a1 + s22*a2

a1 is the normalized forward voltage incident upon the 72 ohm to 600 ohm junction from the source side.
a2 is the normalized reverse (reflected) voltage incident upon the 600 ohm to 72 ohm junction from the load side.

s11 is the reflection coefficient looking forward into the 72 to 600 ohm junction from the source side.
s12 is the transmission coefficient associated with s11.
s22 is the reflection coefficient looking back into the 600 to 72 ohm junction from the load side.
s21 is the transmission coefficient associated with s22

b1 is the total normalized reflected voltage toward the source.
b2 is the total normalized forward voltage toward the load.

If s11(a1) equals -s12(a2) then total destructive interference occurs, zero reflected energy reaches the source because b1 equals zero, and the system is matched. The result of that match is total constructive interference on the other side of the impedance discontinuity and all of the available energy is contained in b2 traveling toward the load.

It's all explained in the following HP App Note:

http://www.sss-mag.com/pdf/an-95-1.pdf

Last edited: Jun 12, 2019

How very interesting!! Probably would make some sense to present your thesis paper to an audience composed of Physics doctorates but this venue is an absurd location. I don't know if you've noticed, but this list is not populated with graduate or doctoral level individuals. None the less they/we are entitled to explanations that are dissected and worded so as to convey the concepts appropriate to the audience. In that you apparently do not have the ability to present the internal concepts to this audience I would suggest you hang around the Physics blogs.

The concepts that I wrote are accurate and if you find something so bizarrely inaccurate I would encourage you to point to those things in the paper. You had an opportunity to write the explanation regarding the progression to 72 Ohms for a 1/2 wave resonant wire and you declined. So please tell me what part was incorrect and articulate it for all on this list to enjoy --- no equations just concept.

So that your not ignored, I will ask you to explain as I did for the center fed dipole, the progression to 5000 Ohms for the end fed 1/2 wl wire using the same level of complexity that I did. If you don't respond, I'll do it for you.

BTW, did you understand the surge impedance measurement experiment using the 54 foot wire?

Regards Jim

Cecil, thanks but I wanted WPA to do this. What I wanted him to do is explain the events at the junction, calculating the incident, reflected and the integration without using the equations.

Thanks again

Regards Jim

9. ### KX4OMHam MemberQRZ Page

Jim,

I went back and read the thread in its entirety, as well as your document. One of the things I am having difficulty is "600 ohms." Everything I've read on surge impedance relates to the presence of two parallel wires in a transmission line, whether they be high voltage AC in a transmission and distribution system, or parallel conductors in an RF transmission line. What I don't get is the idea that one can separate a twin lead 72 ohm characteristic impedance line into two 33.5' long at 90 degrees and get 6oo ohms surge impedance. I guess that implies that as one starts to separate the cut sections, moving each to 90 degrees gradually becomes 600 ohms.

We already know that the characteristic impedance of a free space dipole is 73.2 ohms in free space. Cut the transmission line from the array, and there is still a resonant dipole with an impedance of 72.2 ohms. Obviously, it is not resistive; 33.5' of AWG 12 is 0.053 ohms, which would not count since resistive impedance of the wire doesn't count for radiation resistance. A chart from one of the documents linked by another poster shows a family of curves of radiation resistance due to length and diameter held constant, with frequency changed, and 600 ohms antenna resistance prominent on the graph.

Please explain again how you developed that.

Thanks,

Ted, KX4OM

Last edited: Jun 12, 2019