A transponder with an antenna module having a chip module and an antenna; a booster antenna having a first antenna structure in the form of a flat coil having a number of turns, an outer end and an inner end, and a second antenna structure in the form of a flat coil having a number of turns, an outer end and an inner end; the inner end of the second antenna structure connected with the outer end of the first antenna structure. The antenna module may be positioned so that its antenna overlaps one of the first antenna structure or the second antenna structure. An antenna module having two additional antenna structures is disclosed. Methods of enhancing coupling are disclosed.