We present a technique for contactless angular position sensing that allows low power consumption while keeping dynamic properties comparable to existing sensors. The technique essentially consists in combining a recently developed sensing element, the so-called Circular Vertical Hall Device, with a simple and robust signal treatment based on phase detection. Because of its low startup time, this circuit is specially suited for pulsed mode operation, which enables to further decrease the power consumption. More generally, the absence of complex digital signal treatment makes this technique a natural method for measuring the magnetic field direction and therefore for designing an angular position sensor using Hall probes.