which is correct for turstile or cross dipole antennas do you use a 1/4lamda balun or do you put it together directly to get LHCP polarization? does anyone understand how to make a 1/4lamda balun in CST STUDIO? please help me Thank you.
I expect both will be correct. The one with the balun feeds the two halves 90 degrees out of phase, the other one has slot stubs in one pair of the antennas so that those are 90 degrees out of phase, I expect.
You also have to make sure they are the right way round, whether you get 90 degrees or -90. This determines whether you get right hand circular of left hand circular, but you can change that by swapping the connections on one pair, or turning the antenna upside down. You can make all those parts, including the balun, just by modelling the actual bits, such as a coaxial cable a quarter wavelength long.