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The details in this article are very empirical, under-referenced, and lack all of the meaningful theory.
Some random details, in case someone has the time and interest to clean this article up before I come back.
A discone is merely a special case of a bicone (or biconic) antenna. The only reason I can find to use a discone (other than "It's the cool antenna all the big boys use!") rather than a biconic is that it requires half the vertical height (but necessarily is a little wider). As such, perhaps the discone and bicone antenna articles could be merged, with shared theory and math, examples of both, and perhaps later "further detail" articles about the parts unique to each.
A biconic antenna is one way to create an "electrically large antenna". It generally behaves like a dipole with the following special considerations: rather than having a bandwidth of a few percent of the resonant frequency, it has an equivalently measured usable bandwidth of several octaves (practical numbers are implementation-specific, and depend on differing acceptable swr/reactance parameters). It will provide a pattern that doesn't vary much over the entire conservative usable bandwidth, and is "similar" to that of a dipole near resonance. The function is to behave sort of like a capacitatively terminated dipole, with the surface of the cone (or the wire approximation) transitioning from signal aperture to capacitative loading as a function of the wavelength of the signal-of-interest. The physics works out in a way that is convenient for usage as a wide-band antenna. A "fat" or "cage" dipole broadens the bandwidth somewhat but doesn't have the convenient frequency-dependent capacity-hat effect, thus is MUCH narrower bandwidth than a biconic dipole even if it is broader than a traditional wire dipole.
The approximate impedance is controlled by the angle of the cone. I don't have a source for the formula, but ~ 60 degrees is ~ 50 ohms, and ~ 30 degrees is ~ 120 ohms. Changing angles also serves to change the effective aperture and efficiency at a given frequency unless the cone length is adapted. Note that these impedances are approximate, and there will be excursions. The number and severity are implementation dependent.
A biconic antenna can be compressed to two dimensions, where it begins to resemble a two-leg untrapped fan dipole. A bowtie antenna is a folded dipole that uses some of the same frequency-dependent electrical length properties to also see a substantial widening in bandwidth. The two antennas are mathematically related in the same way that traditional dipoles and traditional folded dipoles are related.
Some nice theory and background are in the midst of this task-specific article: http://www.armymars.net/ArmyMARS/Gen-Mil-Info/Resources/Dave-Fiedler/dave3.html
Hopefully this will end up being a note to myself so that nobody else has to try to understand it.
I have removed the over-complicated and largely meaningless passage from the first paragraph and re-worded the information in plain English. G7mzh (talk) 23:40, 13 March 2013 (UTC) Also, the phrase "unity gain" is pretty meaningless in this context; comparing it to a dipole (which most aerial gain is) is, I feel, more useful to the reader. G7mzh (talk) 21:46, 5 April 2013 (UTC)