Petrie indicated that the wadj is from Dynasty 26 onwards1. However, a few New Kingdom examples inscribed with documented names, have a much wider umbrella and a shorter and wider rod2

Glass H 6.5, W 2.5
© 2006 Musée du
Louvre/Georges
Poncet #E 22625

Amazonite
H 8.0, W 3.4, D 1.8
© 1994 Musée du Louvre/
Georges Poncet #AF 2557

Gold and amazonite
H 9.0, W 3.8, D 1.5
© 2012 Musée du Louvre/
Christian Décamps #E 75

References

1Petrie W M F. Amulets, 1914, pp. 12-13
2Unpublished observation