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This paper presents the operating principles, design, and performance improvement and limitations of three slow-wave air-core Rogowski coils that enable plateau bandwidths up to 11 MHz and sensitivities of less than 0.25 V/kA to be achieved. The frequency response for these coils is examined to optimize the coil termination resistance in order to achieve the suitable transit time, minimize the droop effect, and achieve desired bandwidth. In the present design, the coil inductance is increased to compensate for the resulting reduction in the sensitivity due to the coil termination resistance. Oscillatory and overdamped unidirectional current waveforms up to 10 kA peak value are generated by using different linear and nonlinear loads, and impulse current generator configurations. These high impulse currents are measured by different methods, namely, a commercial impulse current transformer (ICT), a commercial Rogowski coil (CRC), and the three newly designed self-integrating Rogowski coils. Distortion of the measured current pulses is studied by using the lumped-element model of Rogowski coil and its termination resistance, and the signal cable and its matching resistance. The optimal coil termination resistance is obtained under these impulses, and the linearity of all newly designed self-integrating Rogowski coils' output voltages are also investigated. Calibration results and a comparison between ICT, CRC, and the developed three coils for measurements of different high impulse currents demonstrate that the developed coils can accurately reproduce the actual waveform with a constant sensitivity over the desired bandwidth.