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Correctly calculating impedance of a biconical antenna and impedance matching

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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.

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