There are many ways in which serial numbers are assigned to tags. For read-only tags, a chip manufacturer burns serial numbers into the tags that it produces. For proprietary read-write tags, a user can assign random serial numbers.
Most RFID standards created by the International Organization for Standardization (ISO) govern how tags and readers communicate (the air-interface protocol), but some deal with the structure of tag data. The ISO 11784 standard, for example, specifies the structure of the identification code for animal tags, while ISO 28560 creates a standard for tagged items at libraries.
GS1 has created a suite of standards regarding the Electronic Product Code (EPC). There is an air-interface protocol standard (generally referred to as EPC Gen 2), there are standards for how EPC readers interface with software and so forth. But there is also a tag-data standard that defines the structure of EPCs. You can use an EPC tag and write a proprietary number to it, but then it would not be compliant with the standard, or be meaningful to any company other than your own.
The EPC provides a unique identifier that signifies a firm as being a GS1 member company, as well as a unique identifier for a specific product. A company is responsible for ensuring that the serial-number portion of the EPC is unique to one specific product. In that way way, no two EPCs are ever duplicated.
As for how tags modulate radio waves coming from a reader, although I am not an engineer, my understanding is that the chip changes the electrical load on the antenna, and is thus able to modulate the wave. There are a number of different modulation schemes, including phase shift keying, frequency shift keying and amplitude shift keying.
—Mark Roberti, Founder and Editor, RFID Journal
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