Regulation of coefficients used in magnetic field sensor virtual signal generation

1. A magnetic field sensor, comprising:

a plurality of magnetic field sensing elements configured to generate at least two measured magnetic field signals indicative of a magnetic field affected by an object and having a first phase difference ϕ p with respect to each other; and

a controller responsive to the at least two measured magnetic field signals and configured to generate at least one virtual magnetic field signal having a second predetermined phase difference ϕ i with respect to at least one of the measured magnetic field signals;

wherein the at least one virtual magnetic field signal is generated according to a mathematical function based on a first coefficient corresponding to a first channel, the first coefficient based on the first phase difference and the second predetermined phase difference, and a second coefficient corresponding to a second channel, the second coefficient based on the first phase difference and the second predetermined phase difference.

2. The magnetic field sensor of claim 1 , wherein the controller is further configured to:

calculate a virtual tangent comprising a tangent of the virtual magnetic field signal and at least one of the measured magnetic field signals;

calculate an arctangent extraction comprising an arctangent of the virtual tangent; and

calculate a second derivative of the arctangent extraction.

3. The magnetic field sensor of claim 2 , wherein the controller is further configured to:

select initial values for the first and second coefficients used to calculate the virtual tangent; and

determine if a slope of the second derivative of the arctangent extraction is equal to approximately zero.

4. The magnetic field sensor of claim 3 , wherein the controller is configured to adjust one or both of the initial values for the first and second coefficients until the second derivative of the arctangent extraction is equal to approximately zero.

5. The magnetic field sensor of claim 2 , wherein the controller is further configured to:

assume an initial predetermined value for the first phase difference;

calculate the first and second coefficients; and

determine if a slope of the second derivative of the arctangent extraction is equal to approximately zero.

6. The magnetic field sensor of claim 5 , wherein when the slope of the second derivative is not equal to zero, the controller is configured to:

adjust the initial predetermined value for the first phase difference to provide an adjusted first phase difference;

calculate the second derivative of the arctangent extraction using the adjusted first phase difference; and

determine if the slope of the second derivative of the arctangent extraction is equal to approximately zero.

7. The magnetic field sensor of claim 6 , wherein the adjusted first phase difference is indicative of the second predetermined phase difference when the slope of the second derivative of the arctangent extraction is equal to approximately zero.

8. The magnetic field sensor of claim 1 , wherein the second predetermined phase difference is 90-degrees.

9. A method comprising:

generating at least two measured magnetic field signals indicative of a magnetic field affected by an object, wherein the at least two measured magnetic field signals have a first phase difference ϕ p with respect to each other; and

processing the at least two measured magnetic field signals to generate at least one first virtual magnetic field signal having a second predetermined phase difference (Pi with respect to at least one of the at least two measured magnetic field signals;

wherein the at least one virtual magnetic field signal is generated according to a mathematical function based on a first coefficient corresponding to a first channel, the first coefficient based on the first phase difference and the second phase difference, and a second coefficient corresponding to a second channel, the second coefficient based on the first phase difference and the second predetermined phase difference.

10. The method of claim 9 , further comprising:

calculating a second derivative of an arctangent extraction of a virtual tangent of the virtual magnetic field signal and at least one of the magnetic field signals.

11. The method of claim 10 , wherein computing the second derivative comprises:

selecting initial coefficients used to calculate the virtual tangent;

calculating the second derivative using the initial coefficients; and

determining if a slope of the second derivative is equal to zero.

12. The method of claim 11 , wherein when the slope of the second derivative is not zero, further comprising:

adjusting at least one of the initial coefficients to generate adjusted coefficients;

calculating the second derivative of the arctangent extraction using the adjusted coefficients; and

determining if the slope of the second derivative is equal to zero, wherein the adjusted coefficients are correct when the slope of the second derivative is equal to zero.

13. The method of claim 10 , wherein computing the second derivative comprises:

assuming an initial predetermined value for the first phase difference between the at least two measured magnetic field signals;

calculating the coefficients using the initial predetermined value; and

calculating the second derivative of an arctangent extraction of the virtual tangent using the initial predetermined value for the phase difference.

14. The method of claim 13 , further comprising:

determining if a slope of the second derivative is equal to zero; and

when the slope of the second derivative is not equal to zero:

adjusting the value for the first phase difference to an adjusted phase value;

calculating the coefficients; and

computing the second derivative using the adjusted phase value.

15. The method of claim 14 further comprising:

determining if the slope of the second derivative is equal to zero, wherein the adjusted phase value is correct when the slope of the second derivative is equal to zero.

16. An apparatus comprising:

means for generating at least two measured magnetic field signals indicative of a magnetic field affected by an object, wherein the at least two measured magnetic field signals have a first phase difference with respect to each other; and

means for processing the at least two measured magnetic field signals to generate at least one first virtual magnetic field signal having a second predetermined phase difference with respect to at least one of the at least two measured magnetic field signals;

wherein the at least one virtual magnetic field signal is generated according to a mathematical function based on a first coefficient corresponding to a first channel, the first coefficient based on the first phase difference and the second phase difference, and a second coefficient corresponding to a second channel, the second coefficient based on the first phase difference and the second predetermined phase difference.

17. The apparatus of claim 16 , further comprising:

means for computing a second derivative of an arctangent extraction of a virtual tangent of the virtual magnetic field signal and at least one of the magnetic field signals.

18. The apparatus of claim 17 , wherein the means for computing the second derivative comprises:

means for selecting initial coefficients used to calculate the virtual tangent;

means for calculating the second derivative using the initial coefficients; and

means for determining if a slope of the second derivative is equal to zero.

19. The apparatus of claim 17 , wherein the means for computing the second derivative comprises:

means for assuming an initial predetermined value for the first phase difference between the at least two measured magnetic field signals;

means for calculating the coefficients using the initial predetermined value; and

means for computing the second derivative of an arctangent extraction of the virtual tangent using the initial predetermined value for the phase difference.

20. The apparatus of claim 19 , further comprising, when the slope of the second derivative is not equal to zero:

means for adjusting the value for the first phase difference to an adjusted phase value;

means for calculating the coefficients; and

means for calculating the second derivative using the adjusted phase value.