I am loking for a badge about 2"x3", free if possible in hus format.

perhaps these?

My Embroidery Haven has a Yahoo group. In that groups files are tons of free applique shapes that can be used as badges. Join her group and check it out. It's free and you'll get very little mail from the group. Good luck in your search.

I uploaded a larger one in Designs by Cuties some time ago. The image is of a 2 x 3 " one, if you want that let me know by PM. Both are done as an applique: you stitch an outline on hooped stabiliser, attach a piece of material with colour #2, cut it back and stitch colour #3, a satin stitch outline.

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I don't know if I understood. But you can make your own design of badge Here: http://bighugelabs.com/
and after this (I don't know if it's free), save as jpg or bmp and let me know. So I or other people here can digitize for you and you choose one you like more!

Please, be more specific, I'll try to help you. What purpose, color.