A sensor apparatus for detecting a target object is provided, together with a corresponding method for operating the sensor apparatus. The sensor apparatus comprises a transmitter device which is operated by periodic excitation signals at a basic frequency, a receiver device which couples to the transmitter device, wherein the coupling is dependent on a relative position of the target object with respect to the receiver device, and the receiver device delivers signals at the basic frequency which are dependent on the relative position of the target object with respect to the receiver device. A threshold value checking device checks whether signals lie within or outside a threshold value range. A linking device acts on signals from the receiver device or signals derived therefrom in such a way that signals or signal combinations are shifted into the threshold value range insofar as they previously lay outside this range.