Antenna/Balun transmission line query

mjhilger · Feb 24, 2014

Hi, I'm building a Yagi antenna for the 440Mhz ham band. The outline I'm following uses a driven element of a folded dipole; Z = around 288 ohms. I am feeding this with 50 ohm source. Many internet sources describe a balun made from a 1/2 wave length coax (velocity factor adjusted). I will reference here http://www.ece.mcmaster.ca/faculty/nikolova/antenna_dload/labs/Exercise1-5.pdf page 1-77 where the balun is described. Now I follow that the voltage is doubled as we extend the transmission line 180 degrees down the line. But I'm really confused about the current paths of this. It seems that the I of the center conductor is all that is used to supply the antenna (load); and further as the coax shields are all tied together and not connected to the antenna at all - where is the coupling for the current that travels back to the transmitter on the shield of the coax? I had fields 30+ years ago, and antennas still mystify me, but I'm not seeing this. Can someone explain this?

Baluncore · Feb 25, 2014

Think of the half wavelength transmission line section as a centre tapped (auto)transformer providing a balanced signal. It is driven on one side by the unbalanced feed line.

The differential voltage is symmetrical about the shield. The balanced secondary circuit is loaded by the folded dipole which has equal and opposite terminal currents, so there is no shield current in the folded element.

The differential voltage will be twice the centre conductor voltage to shield. If there is no reflected energy on the line, the current must be half, so the impedance will be 4 times.

Note; your reference, page 1-76, fig 1-48 is missing a shield link on the input line. It is shown correctly on the next page.

mjhilger · Feb 25, 2014

Baluncore, Thank you for your reply. I had originally thought of an autotransformer; but that works through the energy transferred via the magnetic coupling. There is no magnetic coupling going on here. The main reason the shields are tied together is so the center conductor does not radiate and allow the signal to extend to its 180 degrees to the -V providing the 2V signal (which then implies a 4:1 Z coupling) - this part I understand. And likewise I understand that the voltage is symmetric about the shield at the initial feed point. (BTW: the paper I referenced is not mine, it is one I found on the internet that provided a good math presentation for the center conductor and impedance. Which I had already understood) But, at the initial feed point where is the current coming from which travels back to the transmitter on the shield?

Edit: I'm confident there is no magnetic interaction on the balun as the position and physical length do not matter. (Physical length is determined by velocity factor and wavelength; so different coax sections will be different lengths.)

Baluncore · Feb 25, 2014

A transmission line propagates an EM wave in the dielectric between the opposed internal metal surfaces. I do not believe you can say there is no magnetic coupling.

You can also think of the Half Wave transmission line as a non-radiating HW dipole. There will be a standing wave on the HW dipole. The HW dipole is driven by the feed line at one end, referenced to the braid attached at the mid-point. The ends of the HW dipole provide the symmetrical feed to the radiating element.

nsaspook · Feb 25, 2014

One thing to remember is that the shield is effectively two conductors that are only joined at the ends of the coax due to skin effect. The inner and outer surfaces are mainly electrically isolated at RF so the shields outer surface current distribution can be different than the shields inner surface.

mjhilger · Feb 25, 2014

Baluncore,
That is the best explanation I have read to visualize what is occurring on the HW loop. I can buy that. I still maintain there is no magnetic coupling (as energy transferred via the magnetic field in the transformer winding); however Mr Maxwell dictates that there is certainly magnetic fields if only because there is a varying electric field.

Still, your description does help me begin (and only begin) to try and understand the physics behind the current paths - Thank You.

Baluncore · Feb 25, 2014

The analogy between the HW dipole and the centre tapped transformer can be seen by considering a tuned centre tapped transformer with a capacitor across each winding to resonate at the operating frequency. That provides a flywheel effect, with energy storage in the tuned LC circuit.

The HW dipole with the standing wave has current without voltage at the centre, and voltage without current at the tips. The centre of the HW line therefore appears to have line inductance while the tips have line capacitance to shield. It is analogous to the tuned transformer.

Analysis of the balun requires understanding the reflection coefficient due to the mismatch where the HW dipole line meets the radiating elements and the feed line.

Averagesupernova · Feb 25, 2014

I'll throw in my 2 cents here. I think of it as a delay line. I find that for some reason it is easier to visualize it laid out in a straight line instead of the coax looped back as it is usually drawn and always positioned in the real world, but that cannot happen in reality since the shields need to be tied together closely. So we send a CW signal down the line and at the end of the line and 1/2 wave back from the end we have the same signal except 180 degrees out of phase. If we draw power from these 2 points ohms law tells us that it HAS to be operating as a 4:1 transformer since we have doubled the voltage compared to just a normally terminated transmission line.
-
Now with that out of the way, am I to understand that you assume the current is not the same in the center conductor as it is in the shield of the 1/2 wave section? I would believe this to be the case also. I had never thought of this before but I would assume that it does not radiate since it is folded back on itself. You will see stubs used to phase up antenna elements stacked on top of each other. They are 1/4 wave long with their conductors spaced closely connecting the upper element with the lower element. The same thing is happening here. Those stubs do not radiate either.

Baluncore · Feb 25, 2014

Yes, it is a delay line, but it is also a resonant element due to the impedance mismatches at it's ends.

A coaxial cable is really two transmission lines in one. Firstly, there is the internal dielectric and it's coaxial conductive walls. Secondly, there is an external transmission line, being the outside of the braid working against the Earth and environment. Those two lines can be treated quite independently.

Since all the coaxial braids are connected at one point in the balun there cannot be unbalanced internal currents. The centre conductor induces an equal and opposite current inside the braid. The unbalanced external line is unimportant in the analysis.

If the external braid on the HW loop is bare copper then it can contact “ground” anywhere without changing the balun function.

nsaspook · Feb 26, 2014

mjhilger said:

Baluncore,
That is the best explanation I have read to visualize what is occurring on the HW loop. I can buy that. I still maintain there is no magnetic coupling (as energy transferred via the magnetic field in the transformer winding); however Mr Maxwell dictates that there is certainly magnetic fields if only because there is a varying electric field.

The antenna/balun are both operating in the near-field area of their free space boundary regions where the primary energy coupling method in a loop is magnetic induction to and from conductors in a spherical wavefront similar to a transformer.

mjhilger · Feb 26, 2014

nsa,
The Antenna is a stand alone resonant element in free space as you state. However since we will operate it at its designed frequency it can be thought of as an independent resistor of 288 ohms (no reactance) for analysis of the balun. My original conception chasm is from the physics of current flow in the balun. At RF doesn't loop analysis still hold (taking into consideration propagation effects)? I didn't see where the current flow balanced. Since our desire is for the antenna to consume the power and max power transfer occurs at impedance match, and since we have a tuned element (I & V in phase) such that the resistor element holds true, then the bulk of I from the center conductor of the random length coax from the transmitter should go to the load. However, by tying the center conductor of the (transmitter) coax to the antenna and the balun center, the I is split. If we follow loop analysis then the balun adds an additional 150 ohms to the 50 of the coax to mate 200 to our 288. A mismatch, with minimal loss. But the current flow between the idealized model and the physical balun was where I have the problem grasping. I believe Baluncore put me on the right track by explaining that the E field and induced current of the balun create the balanced current(s). So I still state that magnetic coupling does nothing to connect the antenna, free space, or the original transmitter coax to the balun. The balun stands on its own as a matching device (still mysterious, but less so to me).

In any case if you or anyone has a firm grip on the physics to the extent that you can use those concepts to design other useful items - then you are way ahead of me. I try to understand things to a point where I can extend their usefulness to me or others. At frequencies -> 30Mhz, I can wind matching transformers and the magnetics in the toroid core are easily followed and so match number of turns needed and bingo no problem. But the physics of that breaks down at the higher frequencies as the efficiencies of magnetic coupling fall off. Which is why I am trying to better understand the physics (math included) of the balun. The common delay line visualization and the 180 degree phase shift explain the voltage propagation correctly to see the impedance matching, it was just the current flow I don't see clearly (to be able to model also).

I really do appreciate everyone's efforts to help explain the operation. As most things, it just has not clicked yet.

nsaspook · Feb 26, 2014

mjhilger said:

nsa,
My original conception chasm is from the physics of current flow in the balun.

Ok, I see what you mean on the original post, the 'return' current path is through the EM field coupling inside the coax transformer and the antenna.
http://www.interferencetechnology.com/how-to-configure-the-return-path-of-a-dipole-antenna/

coax transformer: