Here is a description of how one guy extracted the electronics from a smart card and then embedded it into a ring wearable on a finger.
The card in question is more or less similar to the card in another question, the minor difference is that the card in the current question uses a thin (presumably copper) wire as antenna and the card in the linked to question uses wide thin flat traces. The wires run along the card perimeter. The card is credit card size, so the antenna is more or less an ellipsis.
So that guy uses solvent to soften the card plastic, strips the card and extracts the electronics. Then he rewinds the antenna wire so that the antenna coil can be embedded into the ring.
The resulting coil has several times smaller diameter yet the electronics work.
How does it happen that rewinding the antenna into a smaller loop does not break the card operation?
Best Answer
Without a link to the ring related page it's hard to be very specific BUT
There is much rubbish and many false claims published on the internet.This has a good chance of being less veracious than may appear.
The system may still function but with reduced range.
It is exceedingly unlikely that it will work anything like as well as it did in its original form.
Patch antennas are based on a good grasp of the technology involved, a certain degree of magic and variable amounts of luck and experimentation. An antenna that worked in a card will have different area, different inductance and capacitances, different relationships of portions to other portions in terms of fractions of a wavelength and relative phase, and more.
A look at Microchip's AN710 RFID Antenna design application note description page here and PDF here will demonstrate the differences that varying geometry makes - and will also show you what may work best in a ring.