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The development of a three-electrode trigatron gap with the trigger electrode inside the main electrode is discussed in this paper. Two models of the operation mechanism are proposed to explain the breakdown in the trigatron gap. In addition, a mathematical model was proposed to calculate the breakdown time based on the theoretical analysis. The influence of different parameters on the breakdown time is discussed. Some characteristics in dry air have been experimentally determined such as the influence of the air pressure and the influence of the undervoltage ratio on the spark gap operation. The experimental results show that the operating voltage range between 0.5 and 0.7 might be reasonable. Then, the experimental results and analysis demonstrate that there are three regions divided by two inflection points, and the corresponding values of the undervoltage ratio are threshold values presenting different breakdown processes.