A device for recognizing when an object or a person crosses a threshold that is marked by a magnetic field comprises a first magnetic field sensor that is designed to detect a first magnetic field component of the magnetic alternating field and to deliver an associated magnetic field sensor signal. The device comprises a second magnetic field sensor that is designed to detect a second magnetic field component of the alternating magnetic field. The device also comprises an evaluator that is designed to deliver information in response to a change in a phase relationship between the magnetic field sensor signal delivered by the first magnetic field sensor and a reference signal based on the detection of the second magnetic field component by the second magnetic field sensor, said information indicating that the object or person has crossed the marked threshold.