Numerical determination of the spacing of N loops for minimum inductance in a B sensor

In this paper, the possibility of minimizing the total inductance of an N loop B sensor is considered by numerically determining the optimum spacing between the loops. This technique involves formulating a set of simultaneous nonlinear equations for the loop separations using the maxima-minima theory with constraints, and then solving these equations using a multidimensional Newton-Raphson algorithm. It is found, however, that the mutual inductance is not a strong function of the loop positions, which implies that the total loop inductance is relatively insensitive to these values.