micro-strip balun
Hi again
Thanks for the paper, I'll have a look at it on Google Translate.
In my opinion, the total transition (i.e., both tapered microstrip and parallel-plate line) should be λ/4. However, the Klopfenstein taper has a relationship between length and minimum reflection ripple in the pass-band, so you should determine the total length from your requirement for return loss over the band (or, if you only have a fixed amount of space to work with, you use that length and the Klopfenstein taper will give you the minimum reflection ripple possible for that length). Either way, you'll have a choice to make about how long the two parts are - are they equal in length (i.e., λ/8 each if the total length is λ/4) or unequal (e.g., 3λ/16 and λ/16)? There may be an optimum point, but I'm not aware of any research either way.
As far as the simulation time goes, that's not really avoidable. The only way to reduce it (assuming you have no supercomputer or cluster!) is to reduce the step size, which will affect the accuracy of the eventual taper and, therefore, the return loss. That can only be determined by you, according to your requirements.
Hope that helps.