Antenna apparatus for transmitting data of a fill-level measuring device, comprising at least two coil arrangements (i=1, 2 . . . n). The coil arrangements i=1, 2 . . . n have a coil length (li) and a coil diameter (di), wherein the coil diameter (di) is less than the associated coil length (li). The coil arrangements (i=1, 2 . . . n) each intersect a straight line (e) in such a way that the straight line (e) and the longitudinal axis of the coil arrangements (i=1, 2 . . . n) form at the intersection an acute or 90° angle of intersection (g) of at least 85°, wherein the intersection of each coil arrangement (i=1, 2 . . . n) is arranged at a position between 3 7 ⁢ l i ⁢ ⁢ and ⁢ ⁢ 4 7 ⁢ l i , wherein the at least two coil arrangements (i=1, 2 . . . n) are arranged along this line (e) in a sequence, in the case of which the coil lengths li of the coil arrangements (i=1, 2 . . . n) monotonically decrease l1>l2> . . . ln. The at least two coil arrangements (i=1, 2 . . . n), in each case, have a separation (si) along the line (e) between the coil arrangement (i) and (i+1), which is, at most, a fourth as large as the coil length (li).