Correctly calculating impedance of a biconical antenna and impedance matching

[polemon]

Hello, I'm planning to build a biconical antenna, for a center frequency of around 162MHz, and a flare angle of around 30° (both upper and lower cones are identical.

I've read in John D. Kraus' "ANTENNAS" (2nd edition), that the impedance of an infinite biconical antenna is Z_r = 120 * ln( cot(theta/2) ), where theta is the half-flare angle, so in my case around 15°.

What I found confusing, however, is how to calculate the impedance for a finite (i.e. an actual, practical antenna). Since the center frequency shall be around 162MHz, I imagine a quarter wavelength cone length is in order, but the book states this might not be the case. The rest of the book kinda goes over the top of my head when I really just require a formula to calculate the impedance depending on the flare angle and length of the cone. Is there a book or somewhere where I might find that?

Furthermore, the book doesn't really go into detail how the flare angle influences bandwidth. In its extreme form, (flare angle 0°) the antenna is basically just a regular half-wave dipole, but the larger the flare angle, the wider the band of the antenna. How exactly the angle relates to the band widening, is not explained.

And last but not least, How do I connect my Antenna to a 50 Ohm RG8 coax cable, when the impedances don't match. According to my (rather mediocre) calculations, the impedance of the antenna is much higher than 50 Ohm, roughly about 100 Ohms, How do I match them up properly? I imagine I need some sort of balun if I want to attach the lower cone to the shield of the coax and the upper cone to the core?

[CopperCone]

I made some bicones before. The formulas for understanding them are difficult and involved alot of integrals and calculus.

What I remember is that if you make it as tall as wide, it should be about 50 ohms. Also, some people said if you want it to be more broad band, is to avoid the balun and feed it from one of the cone bottoms (this is what I did). I made mine twice as tall as wide however, by accident. It is like 3 feet tall by 1.5 foot wide.

Based on what you say, it should be for like 900MHz ?

Also, I made a smaller bicone thats approximately 2.5 inches by 8  inches, and I found that when they are plugged into a SA, the gain of the antennas is very similar past like 300MHz.

Both are fed through the bottom. The large one I cut the top off the one of the cones, soldered a BNC connector in there (good for 4 GHz), mounted the two cones on spacers seperated by fiberglass rod, and soldered the tip of the BNC connector to the tip of one of the cones.

The smaller one I used rg141 hardline to do the same thing.

[polemon]

Well, the calculus and the maths for calculating the characteristics isn't a big deal to me, it's just that I can't find these formulas that I need.

I cannot find one single source explaining the characteristics depending on flare angle, cone length, etc.

Btw, the center frequency should be at 162MHz, as I've stated in my first post, I don't need them to be exceptionally wide band, around 100MHz - 300MHz would be more than sufficient.

Same thing for impedance depending on flare angle, cone length, etc.
Also, once I have these numbers in place: how should I construct the feeder? How should the coax be connected to the cones? Should it be crimped, soldered, etc? How large and what sort of spacer should I put between the two tips of the cones?

[T3sl4co1l]

There oughta be formulas out there, somewhere.  I don't know offhand, though.

If nothing else, minimum is 1/4 wave as you guess, but the impedance is going wonky down there, because of reflection from the edges.  That might be a reason why impedance and bandwidth are harder to find.  I'd guess 50% more length than needed would get you pretty reasonable performance, but I don't have measurements to put behind that.

HF limit is determined by symmetry (how much does the radiation pattern break up?) and how ideal the apex is.  Probably you could use a pretty hokey structure, wireframe if it's easier, or foil wrapped on cardboard say, to get a modest (few octave) bandwidth.

Tim

[polemon]

Well yeah, like I said, the textbook I've referenced kinda deals with it to some extent, but it also leaves out the details.

I've checked the current version of the ARRL handbook, and there's really no talk about biconical or discone antennas, unfortunately.

Now that I'm revisiting the material as I'm writing this, it seems the resistance is minimal and reactance is almost 0 when the length of the cone is 1/4 lambda. However the book is confusing when it comes to the formulas, as it claims they're only usable for small angles of around 3°, where the rest of the data for its diagrams is coming from, is not stated. The book assumes "thin cones" in almost all its mathematical parts, which isn't really helping.

There are diagrams in that book (the ANTENNAS book), but they're of such coarse resolution, that they're not really usable for deducing values.

[CopperCone]

https://www.slideshare.net/yariz16/design-and-application-of-biconical-antenna

this is useful and concise

[polemon]

https://www.slideshare.net/yariz16/design-and-application-of-biconical-antenna

this is useful and concise

I found this too, but without much explanation, I find myself poking in the blind a lot. The input impedance is "explained" in just one slide, there are no hints to what a Legendre polynomial or a Hankel function is. Also, I'd kinda like to see perhaps one example or so.

Also, when the input impedance is complex, how do I deal with the imaginary part?

cdev: I'd love to see the papers you referred to in your post (that you've since deleted).

EDIT: There also seems to be an error on slide 4: In the slide it's Z_0 = 60 ln x cot(alpha / 4)
The variable 'x' is used only in this instant and is not explained anywhere else. The entire formula is entirely different to my other literature, where the characteristic impedance is Z_k = 120 ln ( cot(alpha / 4) ) (theta = alpha/2 so that part checks out)

EDIT 2: How the gap 'g' affects the characteristics and how to calculate that, isn't explained anywhere. Not even as a footnote formula.

[CopperCone]

I thought it was a multiplication symbol lol

I think I traced their references on their formula, and one was behind a pay wall, and it sounded too complicated to pay for, or maybe you had to contact a university to make a photocopy for you or something, and you needed to be in a university (feels familiar)

And I could never find anything on the gap other then some emperical studies from some universities. No formula I found includes it.

If you google around it seems that some where less then 2mm is good. Having too wide a gap seems to mess it up. But its just VSWR and  Gain plots with different gap sizes.

if someone is in a university, feel free to send me a special PM lol
http://ieeexplore.ieee.org/document/1701411/

i am not paying for papa and kings old ass publication, their probably in the ground by now, and im probobly never gonna attempt solving somethign that has a legrende polynomial, henkel function and a complex auxiliary function in it

[cdev]

If you want 50 ohms without it being quite a bit wider than it is tall, you should consider using conductive spheres instead of cones.

Both will be 50 ohms, however the wide short antenna is going to have advantage as far as gain out to the horizon. It will also be as much as five times wider than the bispherical for an equivalent lower cutoff frequency.  So, kind of difficult to work with if made out of metal sheeting.

You can make it substantially smaller by enclosing it in a sphere of dielectric material. You could also make it out of wires instead of a continuous sheet.

The great thing about frequency independent antennas is you don't have to do the math.

If you follow the geometry, they just work.

This appears to be a source for the formula..
C. H. Papas,  and  RWP King,  "Radiation  from
wide-angle  conical antennas fed  by a coaxial  line,"

Proceedings. IRE , vol. 39, pp.49?51, Jan. 1951.

[polemon]

I thought it was a multiplication symbol lol

Well, ln takes an argument, just multiplying ln doesn't make much sense, so I believe 'x' is supposed to be a variable.

If you want 50 ohms without it being quite a bit wider than it is tall, you should consider using copper balls instead of cones. For example, two antique copper toilet floats.

Both will be 50 ohms, however the wide short antenna is going to have advantage as far as gain out to the horizon. It will also be as much as five times wider than the two copper ball antenna for an equivalent lower cutoff frequency. 

You can make it smaller by enclosing it in a dielectric material.

having a flattened bicone is fine with me, as it'll give me wider range (and the application is ground based) so having a flare angle of 90° or more is fine with me, when it gives me a "flattened donut" pattern.

But the thing is also understanding. I rather understand what I'm doing so I can build those antennas to my own spec, etc. I'm gonna try to get a version of the ARRL Antenna handbook and see what it says about it, if at all.

[cdev]

What is the intended use? General purpose radio communications between ground based stations?
For AIS and NOAA weather radio reception, you would likely always want your gain at the horizon.

For a single frequency band you might as well make a co-linear antenna, which will give you much more gain.

A biconical antenna is for broadband use and is similar to a discone but has better performance at the horizon than a discone.  The angle enclosed by the radiating elements roughly describes the half power points in the pattern.

[polemon]

What is the intended use? General purpose radio communications between ground based stations?

Receiving transponders of ground vehicles. I need an omnidirectional antenna, and using a vertical biconical seemed to be the best bet. I could use just a verdical dipole, but I wanted something slightly more sophisticated. Also, I've never built a bicone before, so I wanted to have a go at it.

[cdev]

Its actually got to be quite a bit wider than it is tall to be 50 ohms exactly. A few companies manufacture them (and they are very expensive)

The proportions are similar to those of a hatbox.

[polemon]

Yeah, I know, Schwarzenbeck makes very good measurement antennas, but they're several hundred Euros each.

I was thinking of making one like this: http://www.schwarzbeck.de/images/ANT/BICON/1790/resizedimages/Schwarzbeck%20RE%201790%20.jpg only more squat with the wires. The problem is: I still don't know the actual angle. Trial and error is one thing, bu I kinda want to be exact, too.

[CopperCone]

it looks like a profesional photo, you can probably measure it with a protractor with less then 5% error.

That one looks quite a bit taller then it is wide. Unless you mean the individual cones.

[Neganur]

PS, I think you can usually access IEEE papers from a library.
(At least here in Finland, you don't need to be a student to be a customer at university libraries)

[polemon]

it looks like a profesional photo, you can probably measure it with a protractor with less then 5% error.

That one looks quite a bit taller then it is wide. Unless you mean the individual cones.

This was just an example of how my antenna should look with the rods, etc. The flare angle on mine can be whatever, if it's like you say that a flatter cone arrangement gives me better width lateral range, I'd go for that.

Finding accurate information on calculating impedance for it turns into an enterprise similar to looking for a great white whale...

EDIT: One other thing: judging from the pictures and the descriptions of the Schwarzenbeck antennas, they contain some sort of balun and/or impedance matching element.

[cdev]

A balun at the feed point is quite desirable for a biconical antenna.

Then you can dispense with the ferrite beads, they aren't necessary.

You can use a 1:4 or a 1:1 RF transformer.

Any mismatch will not be corrected by a 1:1 transformer. a 4:1 transformer may be a better pick. They both help.   If you use a balun, you get a much quieter signal, without junk added by the feed line imbalance. 

I use a biconical to receive NOAA VHF hi and low UHF and a balun makes a big difference.

Use a broadband part.  If you make your own transformer use an appropriate iron powder core.

#61 material is I think what they use in CATV baluns. You could use a CATV balun. They are very cheap and widely available.

You really will notice that a balun vastly improves the quality of the signal. This is really noticeable for example with FM stereo reception. (in the US now many FM broadcast stations split their signals between vertical and horizontal polarization)

[polemon]

A balun at the feed point is quite desirable for a biconical antenna.

Then you can dispense with the ferrite beads, they aren't necessary.

You can use a 1:4 or a 1:1 RF transformer.

Any mismatch will not be corrected by a 1:1 transformer. a 4:1 transformer may be a better pick. They both help.   If you use a balun, you get a much quieter signal, without junk added by the feed line imbalance. 

I use a biconical to receive NOAA VHF hi and low UHF and a balun makes a big difference.

Use a broadband part.  If you make your own transformer use an appropriate iron powder core.

#61 material is I think what they use in CATV baluns. You could use a CATV balun. They are very cheap and widely available.

You really will notice that a balun vastly improves the quality of the signal. This is really noticeable for example with FM stereo reception. (in the US now many FM broadcast stations split their signals between vertical and horizontal polarization)

The frequency range you use it at pretty much the exact range I need it to: 162MHz. Could you give me the dimensions of your biconical? And what sort of balun did you use?

Also, when using a CATV balun: the F-connector part goes to the antenna, and the 8p8c part goes to the N-connector and the coax, right? (or is it the other way round?)

[T3sl4co1l]

I'm fond of this type balun:



Note that there are two twisted pairs (Zo ~ 100 ohms), in parallel at the BNC (50 ohm), and in series at the antenna (Zo ~ 200 ohm?), with the center tap to ground.  (Note that one pair technically doesn't need ferrite beads, but the other does.  Doing both does reduce CM currents.  Or grounding the tap minimizes CM voltage.)

I don't have much for equipment to test this against (like a proper TEM horn, or conical, or..), but it seems to cover a pretty good range, despite its simple design (the wires fan out about half a meter each side, at the angle seen here, and there are some cross wires to keep them in place).

Tim

[cdev]

Here are some baluns and an unun showing the details of how they are wired. These both show how to make em.

 You can use a switchable balun/unun to give you better power transfer and clean up junk.. They may also help smooth out the response and they may even give you some clues in figuring out the impedance of an antenna.

For VHF/UHF use an appropriate material and of course fewer turns.

The first two are of a nice switchable HF balun that is made by Elecraft and it has very low loss.

I copied it and I often use that for SWL. But you will notice that the design that both of us use is the second of the two switchable choices in the Elecraft balun.

The elecraft uses #43 material..

For VHF you should use #61 material.

I would just pick up a CATV balun. Maybe you already have one.


Its "figure 2".

[polemon]

I would just pick up a CATV balun. Maybe you already have one.

I'll probably go for the CATV solution, but just to clarify: I've attached a picture of a CATV balun. Now, the RJ45 / 8p8c side is the unbalanced, and the side where the F-connector is, is the balanced one, right?

Also, you mentioned in your earlier post, that you use a bicone antenna to receive NOAA weather information at around 162MHz, which is in the same vicinity where I need them, could you please explain the dimensions of your antenna? I.e. height, width, length of the rods, etc. Length of the rods and flare angle of the cones would suffice. I'd greatly appreciate that.

EDIT: I've since gotten a hold of the 22nd edition of the ARRL Antenna Handbook, unfortunately, no mention of bicone. It goes slightly into discone antennas at one point, but not into biconical. That aside, all measurements are in imperial, which slightly grinds my gears...

[cdev]

I meant the other kind of balun, also I have a splitting headache, so I hope you don't mind my pointing you to https://www.researchgate.net/publication/254050053

[polemon]

I meant the other kind of balun, also I have a splitting headache, so I hope you don't mind my pointing you to https://www.researchgate.net/publication/254050053

Hmm, OK, those were the only baluns I can find when searching for "CATV balun". The paper is a bit much, but I'll try to figure out  stuff that I need. It's where that one presentation a couple posts up took their information from, apparently. However in this paper, the formulas actually make sense.

The one thing I'm most confused about is if "kl" is supposed to be "k * l" where k = 2?/? and l is the length of the cone. Other than that, I think I'll use a 120° flare angle. How exactly I should manufacture it, especially how the rods should attach to the feed I'm not quite sure about, but I think I'm in the process of wrapping my head around it.

[cdev]

Basically, assume that the frequency where the elements of the cones would be a dipole is your effective lower frequency limit. (although actually the "wideness" of the conductor extends the frequency a bit lower) 

120 degrees is around what I am currently using, and it works. (I use that because it would be a major PITA for me now to make it any wider and keep it where I can easily grab it and turn it sideways when i need to do that for FM DX, which I do fairly often.)

Taking the same (wire) elements and changing the angle to 60 degrees would require a much larger structure - larger in terms of width, to hold it. (Think, maybe a meter wide, huge)

Re transformers, I would look at non-consumer level (professional offerings) RF transformers if you want to receive the highest frequencies. (which CAN be done with this kind of antenna)

Do a parametric search for whatever would work for you package wise.

A good (SMT or commercial/consumer) iron powder based 4:1 balun properly implemented often can and does work at 1575/1602 MHz - - this varies from one balun to the next- but if you go much higher the loss becomes much larger with all the inline baluns including the ones Ive made myself with #61 cores. This probably has to do with the size of the transformer winding and wavelength/self resonance. the higher you go the smaller the transformer you need. (If anybody here reading this can explain why in a concise way that would be great.)

Therefore, you should use the smallest RF transformer you can get away with, the best ones for broadband are really tiny. Do a parametric search, identify some candidates and get them to try out.

You should make a small testing jig with each of your transformers and an SMA connector. Keep your leads short. Take care not to use lossy wire. Use low loss insulated very thin wire.

As far as shape..  Copy commercial antennas proportions. Visuals of the pictures of successful commercial antennas will show the parameters they use.

You can easily take a design and scale it.

No need to be too precise, that's the great thing about these antennas.

And most importantly, have fun and learn stuff.