Use Sony A7S for live video feed

[GusanOrate]

Hi!
I'm setting up a (guess what) low budget proyect and need to buy the correct hardware for it. I have a Sony A7S and was wondering if anyone around here has used one for live video using the HDMI output, either in Resolume Arena or other software like OBS. I've read people say they did this with an A7s II or III, is it possible with the plain A7S version? If so, what kind of setup can be used? Those people almost always use a BlackMagic capture card, is there any alternative that is both Windows and Mac compatible?
I can't afford to buy a wrong capture card! Thanks in advance for your help.

[Scratchpole]

Do you want to use the full UHD 4k output from the camera or will 1080 be sufficient?

I have used the A7s with the Blackmagic UltraStudio 4K for UHD capture.
https://www.blackmagicdesign.com/products/ultrastudio

I think the Magewell USB3 HDMI capture would happily work for 1080p
http://www.magewell.com/products/usb-capture-hdmi-gen-2
or
Blackmagic UltraStudio Mini Recorder
https://www.blackmagicdesign.com/products/ultrastudio

[GusanOrate]

Thank you for your response!
1080 would be just enough, those are great options. Would you happen to know about any cheaper ones? I would prefer to spend some of that money on the length of my cables