Measuring system - with a magnetic field sensor arrangement, which comprises a first magnetic field sensor integrated in a semiconductor chip and for measuring a first component (B x) of a magnetic field vector in a first dimensional direction (x), a second magnetic field sensor integrated in the semiconductor chip and for measuring a second component (B z) of the magnetic field vector in a second dimensional direction (z) and a third magnetic field sensor integrated in the semiconductor chip and for measuring a third component (B y) of the magnetic field vector in a third dimensional direction (y), - with a transmitter, which is constructed to change, in dependence on its rotational and/or translational movement, the magnetic field vector in the first dimensional direction (x), the second dimensional direction (z) and the third dimensional direction (y), and - with an evaluating circuit with which the first magnetic field sensor, the second magnetic field sensor and the third magnetic field sensor are connected, - wherein the evaluating circuit is arranged to determine the position of the transmitter based on a first measurement signal (S x) of the first magnetic field sensor, a second measurement signal (S z) of the second magnetic field sensor and a third measurement signal (S y) of the third magnetic field sensor, characterised in that - together with the z-modulation the amount of the x-component (B x) and the y-component (B y) of the magnetic field vector is also modulated and in the case of projection of the vector on the X-Y plane the length of the projection of the magnetic field vector does not remain constant, and - the magnetic field vector for a complete cycle runs through several spirals in different planes adjacent to one another and as soon as the vector has arrived in an x-y plane at the outside or inside the magnetic field vector changes to the adjacent x-y plane and runs spirally inwardly or outwardly in the same direction in the adjacent x-y plane and as soon as it arrives in the last x-y plane the vector runs helically on a cylinder back to the start without crossing the previous vector paths - so that in both cases the change, which is produced by the movement of the transmitter, of the magnetic field vector describes a closed and intersection-free line in all three dimensional directions (x, y, z). - with a magnetic field sensor arrangement, which comprises a first magnetic field sensor integrated in a semiconductor chip and for measuring a first component (B x) of a magnetic field vector in a first dimensional direction (x), a second magnetic field sensor integrated in the semiconductor chip and for measuring a second component (B z) of the magnetic field vector in a second dimensional direction (z) and a third magnetic field sensor integrated in the semiconductor chip and for measuring a third component (B y) of the magnetic field vector in a third dimensional direction (y), - with a transmitter, which is constructed to change, in dependence on its rotational and/or translational movement, the magnetic field vector in the first dimensional direction (x), the second dimensional direction (z) and the third dimensional direction (y), and - with an evaluating circuit with which the first magnetic field sensor, the second magnetic field sensor and the third magnetic field sensor are connected, - wherein the evaluating circuit is arranged to determine the position of the transmitter based on a first measurement signal (S x) of the first magnetic field sensor, a second measurement signal (S z) of the second magnetic field sensor and a third measurement signal (S y) of the third magnetic field sensor, - together with the z-modulation the amount of the x-component (B x) and the y-component (B y) of the magnetic field vector is also modulated and in the case of projection of the vector on the X-Y plane the length of the projection of the magnetic field vector does not remain constant, and - the magnetic field vector for a complete cycle runs through several spirals in different planes adjacent to one another and as soon as the vector has arrived in an x-y plane at the outside or inside the magnetic field vector changes to the adjacent x-y plane and runs spirally inwardly or outwardly in the same direction in the adjacent x-y plane and as soon as it arrives in the last x-y plane the vector runs helically on a cylinder back to the start without crossing the previous vector paths - so that in both cases the change, which is produced by the movement of the transmitter, of the magnetic field vector describes a closed and intersection-free line in all three dimensional directions (x, y, z).