Equivalent diode and inter-electrode capacitance modeling of cathode current in coaxial cylindrical tetrodes with mesh cathodes and rectangular-mesh grids

Cathode current determines the output power and transconductance of high-power tetrodes, yet its direct estimation remains challenging due to the coupled modulation of electrode voltages and complex geometries. This paper proposes a semi-analytical method combining space-charge-limited current (SCLC) theory with electrostatic equivalent analysis. First, by analyzing the diode composed of a mesh cathode and a rectangular-mesh anode with varying transparencies, a modified SCLC formula incorporating a geometric correction factor is established. Second, based on the inter-electrode capacitance theory, the coupled effect of multi-electrode voltages is equated to an effective voltage at the control grid surface. Substituting this effective voltage into the modified SCLC formula enables rapid prediction of the cathode current in the space-charge-limited region. The results show that the relative deviations between the theoretical and simulated diode and tetrode currents are both less than 5%, and the deviation between the measured and simulated control grid currents of the tetrode is within 6%. The proposed “equivalent diode and inter-electrode capacitance” framework exhibits strong universality: it not only resolves the current calculation for rectangular-mesh grid structures but also provides a valuable reference for tetrodes with other grid configurations (e.g., helical and squirrel-cage grids).