High Frequency Rogowski Coil Response Characteristics

The high frequency response characteristics of differentiating and self-integrating Rogowski coils have been calculated for arbitrary values of the coil terminating resistance assuming Ampere's law to be valid. Effects due to a reactive terminating impedance are also discussed. When the displacement current is taken into account in the measurement of the current of a charged particle beam, it is found that an effective rise time is introduced into the self-integrating coil response on the order of a/ϒυ, where a is the major radius of the coil, υ is the velocity of the beam, and ϒ = (1 -υ2/c2)-1/2.