A product such as a tire includes a radio frequency identification device (RFID) assembly located along an outer sidewalk The RFID assembly has a thin, flexible, substantially planar, elongated non-conductive rubber, elastomer, or polymer substrate. First and second thin, flexible, elongated, substantially planar first antenna portions formed at least in part of the same conductive rubber, elastomer, or polymer are provided on the substrate. Opposite first and second ends of the first antenna portion have different first and second widths. A chip has opposite first and second ends in operative electrical connection with the first and second antenna portions, respectively, and is located between the outer sidewall and the substrate.