This is my first attempt, mistakes can happen. This is a work in progress.
To get an orthogonal polarisation (near circular), two identical yagi share the same boom with a 90° polarisation angle (H/V), each of the two yagis are physical 90° apart on the bom (this will enable the use of a symmetrical phasing harness). Each of the yagi must have a 50 ohm feed point.
Then a power divider is needed to connect both antennas to the transmitter.
To my knowledge there is no easy formula to get a yagi with a direct 50ohm feed point. The only way is simulation.
A parametric model in CST will be very convenient :
The goals for this design :
Parameters to adjust to get this result :
Obviously to lower the reflector spacing is the key to success. Unfortunately to get a decent front to back radio we need to adjust the reflector length.
Here is a result that match the criterias :