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In this paper, high frequency behavior for a Rogowski coil is analyzed. Considering the coil frequency response model, a design method for this transducer is presented that the damping ratio based on termination resistor divides the coil frequency band into three bands: derivation band, proportion band and resonance band. Corresponding outside integrator circuits are built according with every band characteristic. A novel compound integration circuit is described in this paper which is consisted of self-integration, passive RC integration and active RC integration. This compound integrator improvements the measurement upper bandwidth limit of transducer above coil natural frequency. A coil of 100 wound number is constructed using compound integrator which is designed under 50 Hz~2.8 MHz and sensitivity of 1 mV/A. Simulation and experiment waveforms verify the transducer operates with both 50 Hz grid current and 750 A/us di/dt pulse current measurement.