I use Semirigid for my antenna but you can use coax 50 ohm cable also but you will need to support the shape for the balun and the antenna.
I use two pieces of semirigid.
One the picture below I have used the silver one for the balun (4 turns not touching, size not too important).
The copper one is the j-pole.
Solder outer and inner at about 1 cm from start. Outer shield connects to the short length, the inner conductor to the longer part.
I start with lengths of about 22cm and 6.5 cm, this puts the antenna below 1 GHz.
Cut back two nibbles for one nibble on either side to raise frequency to 1090 MHz.
Adjust gap to minimize SWR. Less than 1.2 should be possible. Squashing lowers frequency, this means more nibbleing of the ends ...
With preamp and angle F ready to go:
Balun:
SWR Plot:
