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By utilizing power semiconductor switches, especially high-voltage insulated gate bipolar transistors (IGBTs), as main switches, Marx modulators have demonstrated many advantages such as variable pulse length and pulse-repetition frequency, snubberless operation, and inherent redundancy. However, the relatively slow turn-on speed of the IGBT influences the pulse rise time of the Marx modulator. In this paper, a newly developed all-solid-state pulsed-power generator is proposed. This generator consists of a Marx modulator based on discrete IGBTs and a magnetic pulse-sharpening circuit, which is employed to compress the rising edge of the Marx output pulse. The experimental results are presented with a maximum voltage of 20 kV, a rise time of 200 ns, a pulse duration of 500 ns (full-width at half-maximum), and a repetition rate of 5 kHz on a 285- resistive load. The output power of the generator is 2.5 kW, and the average power in one pulse is 1 MW. The design methods of the IGBT drive circuits and the parameter calculation of the magnetic pulse-sharpening circuit are introduced in detail in this paper. The factors influencing the performance of the generator are also discussed.