Analytical Method for Determining Errors in Current Measurements with a Rogowski Coil

Algebraic expressions are derived for the open-circuit voltage induced on a toroidal coil with unevenly spaced turns, by a sinusoidal current through its aperture. The derivation requires that the winding layer is thin, the number of turns is large, and the cross-section of the winding is rectangular. These expressions are used to determine the effects of the gap between the ends of the coil and other irregularities in the spacing of the turns on the position sensitivity, defined as the dependence of the induced voltage on the location of the current. This technique may be used to define the criteria to meet a specified upper limit for the positional sensitivity.