I Antenna made from a pair of metal cones, radiation gain verses frequency.

[Spinnor]

Take one of a pair of metal cones and put a coax cable sized hole in the center of that cone. Let the "tops" of the cones face each other separated a distance a fraction of the diameter of the metal cones. Take a coax cable and connect it to the hole of the one cone (from the "inside" of the cone) and let the center conductor of the coax pass through the hole and connect to the metal point of the other cone. Looks like this from the side and cut in half,

Let a variable frequency signal generator be connected to one end of the coax cable and let the other end be connected to our cone pair. Should one be able to argue that for low frequencies our cone antenna will act like a dipole antenna and that as the frequency is increased the antenna will have an increased gain in the horizontal direction, and if we really know what we were doing we could approximate the gain as a function of the radiation frequency (and maybe also as a function of the antenna geometry)?

I am thinking that in some respects our cone antenna should start to act like a microwave horn antenna at high enough frequencies (in the sense that a microwave antenna has significant gain in the vertical direction so also with our cone antenna but not in the sense that the microwave horn antenna will also have gain in the horizontal direction whereas our cone antenna will have constant gain about the horizontal direction)?

Thanks for any help.

 

[Baluncore]

The correct term for the antenna you describe is a "biconical antenna".
See chapter 8 of: "Antennas", by John D. Kraus.

Biconical antennas are well understood and come in many forms.
https://en.wikipedia.org/wiki/Biconical_antenna

I am thinking that in some respects our cone antenna should start to act like a microwave horn antenna at high enough frequencies (in the sense that a microwave antenna has significant gain in the vertical direction so also with our cone antenna but not in the sense that the microwave horn antenna will also have gain in the horizontal direction whereas our cone antenna will have constant gain about the horizontal direction)?

The "discone" antenna is broadband, VHF to UHF, and so is often used with scanners. It is omnidirectional, but the disc gives it more gain towards the horizon.
https://en.wikipedia.org/wiki/Discone_antenna

Start by analysing the "bow tie" antenna. That leads to an understanding of the biconical antenna.
https://www.antenna-theory.com/antennas/wideband/bowtie.php

The cone angle determines the impedance of the biconical antenna.
A dipole can be made from two λ/4 long cones, that will also work at higher frequencies. The first biconical antenna was built in about 1897 by Oliver Lodge, in London, while he was inventing tuning.

An HF "reference cone" is a standard antenna, mounted above a ground plane, so it has one physical element above ground, with an image below.

Maybe the best approach is to specify the requirements for your antenna, then call for suggestions of optimum designs.