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The compact, small-sized device based on a pulsed transformer combined with a semiconductor switch is a feasible solution that generates the high-frequency and high-voltage pulse. Compared with other types of transformers, spiral Tesla transformer is much easier to achieve a high output-voltage ratio. By an in-depth analysis of the resonance circuit of Tesla transformer, the expressions of secondary voltage, transformation ratio, peak, and steepness of the primary current are deduced and analyzed in this paper. The development test of a small-size Tesla transformer prototype has been performed. The key electrical characteristics are further measured, estimated, and discussed. The specification parameter selection of the primary semiconductor switch must rely on the characteristics of primary current. Applied to a 6.0 kΩ resistor, the high-voltage repetitive pulse generator based on the Tesla transformer prototype can generate a series of pulses with a peak voltage of 100 kV and a rise time of 40 ns at the repetition rate of 200 Hz. Atmospheric air nonequilibrium plasma can be formed using the developed pulse generator and some typical images are presented.