Not an EE, but I (think) I know a cheap charging solution for us non-technical guys (not you). I couldn't find specs on the EWS charging ring, but did on the charger I am using.

I followed the advice of several sources, on YouTube and several BMW forums, and bought a Philips Sonicare (toothbrush) inductive charger for my only diamond key, that had gone dead shortly after I got it.

Though some people insist that it doesn't work on these keys, I tried charging the original dead battery on it and it worked again (for a day or so), but eventually died (a 20 years-old battery). After replacing the rechargeable battery myself, I've used the Sonicare charger everyday in the two years since then, as I sometimes don't use the key for two months at a time.

My reasoning to try the toothbrush charger, was that I found out that the Sonicare toothbrush battery is a Sanyo LI-ion 3.7v (but the charger puts out 3.7v-4.0v), and the VL2020 battery used in the X5 key is nominally 3v (but actually charges at 3.4v +/- 1.5v), so the Sonicare charger is in the ballpark (for a non-electrical guy like me).

I have several Samsung Qi charging pads at home, but they have an output of 5-9v (per Samsung), so I didn't try them on my key. Those pads have caused three of our Samsung phones' (a S7, S8, and S8+, all Galaxy models) batteries to overheat while charging, and swell up or lose functionality. So far, my S9+ hasn't (yet). My sole BMW diamond key is too valuable to risk.

If you build a better mousetrap, I'd be interested in the specs, but I'd not be able to make one myself, so I'm stuck using what I've got.

__________________
01 BMW X5 E53,3.0i-5L40E, 7/13/01
topas-blau,Leder-grau,"resto-project car"

Here:
14 Lexus ES350,3.5L-U660E
09 HHR Panel,2.2L-4T45E
04 Chevy 2500HD,6.0L-4L80E
98 GMC Sierra 1500,5.7L-4L60E

Gone:
66 Chevelle Malibu 2dr ht.,327>441c.i.-TH350>PGlide/transbrake
08 Cobalt Coupe,2.2L-4T45E
69 & 75 C10s,350c.i.-TH350
86 S10,2.8L-700R4
73 Volvo 142,2.0L-MT4
72 & 73 VW SuperBeetles,1.6l-MT4
64 VW,1.2l-MT4
67 Dodge Monaco 500 2dr ht.,383c.i.-A727
56 Chevy 210 4dr,265c.i.-PGlide