I need to build a transformer that transforms the output of a signal
generator (0.5-2 Mhz 0-20Vpp into 50 ohms) into two opposite phases
at 0-250V.

Load is a few picofarads and a short length of shielded cable.

Where can I find formulas for winding such a transformer ?

Is it preferable to build it as an air or on a ferrite core ?

What ferrite material would I use ?

BTW the signal is used for driving multipole ion traps.

I am an electrical engineer but have not much experience with RF.

George