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I want to build a DIY RFID reading system that can read a wide surface area. My idea is to connect one single PN532 chip with multiple RFID antenna using multiplexing. The antenna must be as thin as possible and flexible.

After after having removed the IC from a RFID sticker, can the sticker coil be used as a RFID reader antenna? Is there another cheap way to build 10 to 20 RFID reader antenna?

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It might be simpler just to build one antenna with the requisite operating area than trying to multiplex several smaller ones. The PN532 uses a magnetic field to talk to RFID devices and the antenna it uses is a coil of wire basically resonant tuned to emit more magnetic field than could be got for the same power supply current as an untuned antenna: -

enter image description here

Circled in red are the resonant tuning components. An inductance of 560nH and 220pF on their own tune the output to be a little above 14 MHz and the loop, C and C2 bring this down to 13.65 MHz.

I don't have details on the antenna inductance but I suspect that a single turn of wire probably about 0.5m diameter might be tunable and save you all the headaches of trying to multiplex multiple coils - because they are resonant they won't appreciate too much added series resistance and the voltage may be several tens of volts p-p.

Here is AN1445 from NXP that desribes how to design the antenna.

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