Here's Garmin reaching into your wallet yet again for another accessory to get full functionality from their devices that you've already paid a premium for. Your GDL52R requires a TNC connection for the SXM antenna. Go try to find a TNC SXM antenna except Garmin's  GA24TNC for about $77 and let me know how that works out for you.

For under about $25 it is possible to bypass the $77 profit fattening antenna accessory from Garmin and create a functionally equivalent antenna to receive your SXM subscription.

The two items pictured below are all that's required - a conventional SXM antenna at approximately $15 from eBay and a short length of SMB Male to TNC Male adapter cable at about $8, also from eBay.

Enjoy your low cost alternative to the GA24TNC antenna and enjoy the 12 or so gallons of Avgas or a couple of filet mignons or that favorite adult beverage that you can spring for without feeling guilty!

PS: If you are mounting the SXM antenna near any compass or magnetometer, the usually fitted magnets in the bottom of the SXM antenna can easily be removed from behind the label on the bottom of the antenna. A hook & loop (aka Velcro) strip can then be applied to the back of the antenna for removable mounting.