I saw a paper on dual band antennas where they used two dipoles under one feed where the other is about half the size as the other so that one works at f0 and the other at 2f0.
yes. but modified. if you look at the paper, it exactly covers the frequencies you need. you just need to make two of them, as shown. dipole antenna is scalable, lambda/2 for 75 ohm input impedance, where lambda is the wavelength for any frequency you want. you just plug in the frequency to the equation.
they printed it on pc board and they used a balun to balance the unbalanced line.
I don't know how to. I have no knowledge of numerical em calculations. But Balanis's book, I think, comes with software for simpler dipole antennas and his book has equations as well for radiation patterns. I thought of implementing it as an array but since these 2 dipoles don't work at the same frequency, I don't think pattern multiplication would apply. I apologize. However, I highly recommend that you may go to zeland.com to try a limited time period evaluation of their software. I highly recommend this software for planar structures as it takes the software shorter amount of time simulate. Their website has video tutorials to help you get started. If you're a student, I don't know if it's the same situation as mine, but the university I go to allows students to use the software for free as they purchased the license for it. Hope that helps