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In this paper, the design, calibration, and performance improvement of four self-integrating Rogowski coils are presented. These coils are wound in single and double layers by a coaxial cable without its polyvinyl chloride (PVC) jacket and with air and ferrite cores. Nonuniformities due to the variation of turn density and/or core deformation are compensated by using a one-turn return loop placed inside the helical winding in the opposite direction to the pitch advancement. Oscillatory and overdamped unidirectional current waveforms up to a 7-kA peak value are generated by using different linear and nonlinear loads and impulse-current generator configurations. These large-magnitude short-duration current pulses are measured by different methods, namely, a commercial impulse-current transformer, a commercial Rogowski coil, and the four newly designed self-integrating Rogowski coils. The 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 is also investigated. Results reveal that the magnitudes of measurement errors for the current peak and front and tail times are very low when using ferrite cores with a low termination resistance. The trend of the results is also explained in terms of coil termination resistance, transit time, and sensitivity bandwidth.