The implants for family planning can not give false -ve result, The patch is meant to avoid pregnancy
,by avoiding ovulation.
Actually pregnancy test can not be false _ve any time. The -ve test means no human chorionic gonadotrophins( which indicate pregnancy) in the sample.-
Some patches are known To produce scanty /no periods, still they do have good effect as family planning device.
Please don't worry. be in touch/get regular check ups by a Gynecologist.
Well, a permanent sterelisation by Tubectomy would be ideal way of family planning for you.