Method to calculate the positional sensitivity of a Rogowski coil

Rogowski coils can measure time-dependent electrical currents noninvasively, but deviations from a perfectly uniform winding cause the measurements to depend on the position of the current within the aperture. An analytical solution is presented for the output of a toroidal coil when the number of turns per unit length is proportional to the sine or cosine of the product of the azimuthal angle and an integer. Then it is shown how a Fourier series can be used to represent a given deviation in the winding of a Rogowski coil to obtain an algebraic expression for the positional sensitivity. Calculations are made for several examples including a gap between the ends of the winding and a specified random error. This method may be used to estimate the positional sensitivity for a Rogowski coil and to determine the precision which is required in order for the positional sensitivity to have a specified upper bound.