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We have designed and realized a new integrated Hall structure that converts the magnetic field vector in the chip plane, into an ac signal, whose amplitude and phase correspond to the magnitude and direction of the field, respectively. It is the first Hall sensor that provides the field angle without the need of computing an arctan function. The Hall element is formed by a n-well ring with a large number of contacts equally distributed along the ring, like a circular railroad track. Each contact is connected to the control electronics through switches. The measurement consists in activating a small portion of the ring at the time, forming a vertical Hall probe and acting on the switches to make this portion circulate. The measurement sequence suppresses the zero-field offset and the 1/f noise. Without calibration, in a 100 mT field, we obtain an angle resolution better than 1°. We propose a measurement scheme that further reduces the offset, in order to remove the need for calibration.