Calculation of High-Frequency Breakdown Voltages of Point-to-Plane Air Gaps

The performance of point-to-plane air gaps under a high- frequency voltage is studied theoretically. The electric field distribution along the gap axis is represented as a function of gap dimensions and applied voltage. This derived function yields accurate field values throughout the ionization zone which correspond to the peak value of the applied voltage. The condition for positive-ion space charge accumulation in the ionization zone is considered to be criterion for breakdown. An equation describing the temporal motion of positive ions under the alternating voltage wave is derived. For any given wave frequency and gap dimensions, the peak value of the breakdown voltage is obtained by equating the distance traveled by the positive ions during the positive half voltage cycle to the corresponding length of the ionization zone. An expression for the peak value of breakdown voltage corresponding to a particular frequency is analytically obtained as a function of the point-to- plane air gap dimensions. Comparison of calculated results with corresponding measurements reported in the literature indicated a reasonable agreement.