A current sensing circuit for use with a Rogowski coil arranged around a conductor having a primary current includes input terminals structured to receive an output voltage of the Rogowski coil, an analog to digital converter structured to convert a differential voltage to a digital differential voltage signal, a digital integrator structured to receive the digital differential voltage signal, to implement a discrete-time transfer function that is a transform of a transfer function of an analog integrator, and to output a digital integrator output signal, and a direct current blocker filter structured to remove a direct current bias from the digital integrator output signal and to output a digital current output signal that is proportional to the primary current in the conductor.