The Analysis of Magnetic Flux Density Inside Rogowski Coil Based on Full Current Theory

The Rogowski coil is the most common sensor for measuring alternating and impulse currents. At present, the coil is used to measure the current with frequencies ranging from hertz to gigahertz. Ampere's law has been the basis for Rogowski coil measurement principle. However, Ampere's law is just an approximate theory of full current theory when the frequency is low. Therefore, full current theory should be adopted instead of Ampere's law to support the measurement of the Rogowski coil under high frequency. In this letter, the exact expression of the magnetic field through the coil based on full current is presented. Furthermore, the error between the result based on Ampere's law and full current law is discussed. The results show that the error is related to the frequency and coil radius. It increases with the increasing frequency and radius of the coil. The error will be 10% when the frequency is 50 MHz and about 200% when the frequency is 1 GHz at 0.3 m radius.