Abstract: A compact air-core pulse transformer with an energy conversion efficiency of 50% was theoretically investigated. The transformer was employed to repetitively charge a small-sized solid state Marx modulator. A pulse forming network (PFN) was added to each stage of the Marx to lengthen the pulse width to several ten ns. By an in-depth analysis of the equivalent circuit of pulse transformer, the expressions for calculating the energy conversion efficiency, the peak of the secondary voltage, the peak and steepness of the primary current of the transformer were deduced in this paper. The calculation results were compared with the simulation ones by Pspice software. The analysis results indicate that the theoretical calculation of the primary voltage and current waveform were in accordance with the results of the simulative calculations. Therefore, the correctness of the theory in this paper was verified. Meanwhile, the structural parameters of the transformer with an energy conversion efficiency of 50% were obtained by theoretical calculation. The parameters will provide a theoretical guidance for the design and fabrication of the pulse transformer.