Quadrature error correction

A method of encoding the position of an element comprising generating electrical quadrature signals (SIN and COS) the frequency of which is indicative of the rate of change of position of the element and the lead-lag relationship of which is indicative of the direction of change of position and correcting quadrature signal errors dks, So, dkc, Co and .phi. in said signals where SIN=(1+dks)sin(.theta.)+So and COS=(1+dkc)cos(.theta.+.phi.)+Co and wherein dks and dkc represent amplitude errors and So and Co represent bias errors comprising the steps for:

• a) generating an error function signal E by summing the squares of the signals SIN and COS and subtracting a constant K therefrom,
• b) saving the value of the error function E at .theta. equals approximately 0, .pi./4, .pi./2, 3.pi./4, .pi., and 3.pi./2,
• c) generating signals indicative of the quadrature errors as follows:
• ##EQU2## d) generating corrected quadrature signals S and C by processing the signals SIN and COS as follows:
• S=[1/(1+dkse)] SIN-Soe, and
• C=[1/(1+dkse)] COS-.phi.es-Coe, and
• e) encoding the quadrature signals into position signals.

A system of encoding the position of an element comprising generating electrical quadrature signals (SIN and COS) the frequency of which is indicative of the rate of change of position of the element and the lead-lag relationship of which is indicative of the direction of change of position and correcting quadrature signal errors dks, So, dkc, and Co in said signals where SIN=(1+dks)sin(.theta.)+So and COS=(1+dkc)cos(.theta.)+Co and wherein dks and dkc represent amplitude errors and So and Co represent bias errors comprising:

• a) circuit means for generating an error function signal E by summing the squares of the signals SIN and COS and subtracting a constant C therefrom,
• b) circuit means for saving the value of the error function E at .theta. equals approximately 0, .pi./2, .pi., and 3.pi./2,
• c) circuit means for generating signals indicative of the quadrature errors as follows:
• ##EQU3## d) circuit means for generating corrected quadrature signals S and C by processing the signals SIN and COS as follows:
• S=[1/(1+dkse)] SIN-Soe, and
• C=[1/(1+dkse)] COS-Coe, and
• e) circuit means for encoding the quadrature signals into position signals.

A system of encoding the position of an element comprising generating electrical quadrature signals (SIN and COS) the frequency of which is indicative of the rate of change of position of the element and the lead-lag relationship of which is indicative of the direction of change of position and correcting quadrature signal errors dks, So, dkc, Co and in said signals where SIN+(1+dks)sin(.theta.)+So and COS=(1+dkc)cos(.theta.+.phi.)+Co and wherein dks and dkc represent amplitude errors and So and Co represent bias errors comprising:

• a) circuit means for generating an error function signal E by summing the squares of the signals SIN and COS and subtracting a constant C therefrom,
• b) circuit means for generating an error function signal E by summing the squares of the signals SIN and COS and subtracting a constant C therefrom,
• b) circuit means for saving the value of the error function E at .theta. equals approximately 0, .pi./4, .pi./2, 3.pi./4, .pi.and 3.pi./2,
• c) circuit means for generating signals indicative of the quadrature errors as follows:
• ##EQU4## d) circuit means for generating corrected quadrature signals S and C by processing the signals SIN and COS as follows:
• S=[1/(1+dkse)] SIN-Soe, and
• C=[1/(1+dkse)] COS-.phi.es-Coe, and
• e) circuit means for encoding the quadrature signals into position signals.