Sounds like an aircraft type transponder antenna.  Two manufacturers from my old general aviation days that come to mind are "Comant" and "Dorne & Margolin", and I am sure there are others.  These antennas are often referred to as L-Band or ATC transponder antennas.  One of these might meet your needs without having to create a new design.

They are specifically designed to TX@1090Mhz and RX@1030Mhz and are omni-directional.  You can check websites for the above for other specifications.

Thanks debodine, you got that in one !.  I do like to push my limits tho, so I would prefer to see the calculations, and methods used.  This project is partly to extend my knowlege, and part commercial development.  For OEM use, a "home-grown" solution would probably work out more economical.  Besides...aircraft stuff is slow to use recent developments and techniques.  I was thinking ..a foam dielectric, with microstrip emitters

Tsk, Tsk,

These Computer Guys, always trying to reinvent the wheel.



You might check out any white papers published by the aircraft antenna manufacturers.  Over the years, I have received many an insight from other manufacturers technical papers.

Good luck with your forray into Radio Frequency (intentional) radiators.  Perhaps we can seduce you away from the "Dark Side" to the true "Force", Radio Frequency.

I remain,
The Old Soldering Gunslinger

The true "Force" !!.  I do anything from welding (that is a power transmitter !), machining, Mechanical CAD, Digital, building aircraft , boats, (classic)mo'bikes etc, but this is my first serious foray into RF.  My college days were 25 years ago, and almost all that I now know has come from experience, not college.

Skenn:

I admire you for wanting to push your limits, and I wish you success in your latest endeavor.  Since aviation is my background, I would like to suggest that you may have a challenge ahead of you to create a new design that would be more cost effective than existing antennas.

You mention that you have built aircraft previously, and to my knowledge the 1090Mhz/1030Mhz frequency pairing exists only for aviation transponders, so I am leaping to the conclusion that your intended application is aviation.

I have tested designs, including antennae, in the DO-160C/D environment in the past, and the investment in designing to pass DO-160 testing is huge, as is the investment to accomplish the testing.  Unless you have easy (and cheap) access to a qualified testing laboratory, what you save on creating a new design may be lost (and then some) in proving to the FAA the acceptability of your design.

Sorry if this is TMI as you may already know all this.  In any case, if you believe you have a new idea and you have the drive to go for it, go for it!  You may invent the next major innovation in aircraft antenna design, and more power to you if you do!

Initially, at least, this will be for experimental (non-certified)a/c.  When we're up n running, we may look at certification

For a low profile anenna, you might look into an annular slot antenna.  These arevery low profile and are often used on high speed (read military) aircraft where drag becomes a major factor.

I remain,

The Old Soldering Gunslinger

skenn
I recently completed a patch antenna design for the "433 Mhz flat antenna design" which you can find the reference on this website. It's essentially the same antenna as what you described. This quarter wave 433 Mhz patch antenna was approx. 4"x2"x0.060" in size and had about 20 Mhz bandwidth using FR4 dielectric. Temperature from zero to 120F drifted the frequency +/- 5 Mhz due to dielectric constant variations.
That size translates to a smaller size for yours by the frequency ratio, although I'd suggest making the antenna as thick as possible to handle temperature and manufacturing variations. Antenna bandwidth is proportional to thickness (more gives more) and inversely proportional to sqrt of dielectric constant (high dielectric constant, lower bandwidth). Hence Foam is better than FR4 for bandwidth, though FR4 is much cheaper than a foam sandwich if you consider assembly time. You'd just need to consider mounting technique for the antenna.
If you have more details khiggins  at  Toyon dot com is my email.
Thanks,