Vivaldi antenna feeding: Microstrip to slot line transiton /w marchand balun

Hi all,

I'm trying to understand the design process of a microstrip to slotline transition for a vivaldi antenna.

The microstrip width at the antenna port can be calculated to meet the desired \[Z_0\] value of e.g. 50 Ohms using one of the online microstrip calculators. In my case this is way lower than 1mm due to a thin substrate.
Furthermore I read that the high frequecy cutoff is determined by the width of the slotline at the transition. For 10.6 GHz this should be not more than \[\lambda_H / 2 = 14.14mm\].

My question now regards the area where the microstrip line and the slot line cross orthogonally:
I think the impedance of the microstrip line and the slot line should be equal for a good transition. Is this correct and where can i find a proper reference?

If I choose the slot line width to be 14.14mm, the impedance of this slot line would be higher than 300 Ohms.
For smaller slot lines the impeadnce seems to be asymptotic ~60 Ohms, so I'll need to taper the microstrip anyway to increase its impeadance at the transition.
What is the best way to determine the optimal impedance at the transition resp. the proper slot line width or microstrip width?

In Chapter III A. Schüppert [1] explains an example. Here he designs the microstrip to have 50 Ohms, while the slotline slightly exceeds 50 Ohms... But why exactly 50 Ohms?

For the design of the circular stub at the slot line and the radial stub at the microstrip line I found a lot of literature. This does not seem to be a problem for me. ;-)

Thank you in advance!
Daniel


Reference:
[1] Schüppert (1988): Microstrip/Slotline Transitions - **broken link removed**