A cylindrical antenna arrangement in a magnetic resonance apparatus has two feed points to feed in two partial signals, the two feed points being arranged on a cross-section of the antenna arrangement. The cross-section has a center point. A first angle is formed by the connection of a first feed point with the center point relative to a horizontal axis of the cross-section while a second angle is formed by the connection of a second feed point with the center point relative to the horizontal axis of the cross-section. An apparatus for controlling such an antenna arrangement has a device for signal splitting with two outputs and an input. A radio-frequency magnetic resonance signal is connected at the input. This signal is divided by the device for signal splitting into two partial signals of equal amplitude that are respectively supplied to an associated output. Each output of the device for signal splitting is connected with precisely one associated feed point of the antenna arrangement. An ellipse position in space is set for an elliptical polarization via the selection of the two angles. A device for phase adjustment is interposed between precisely one output of the device for signal splitting and the associated feed point in order to set an elliptical semi-axis ratio via variation of the phase difference of the two partial signals.