Study of Ultra-High-Frequency Tubes by Dimensional Analysis

The complete theory of the operation of ultra-high-frequency tubes being extremely difficult, it is shown that dimensional analysis in conjunction with experimental work is a powerful tool in this field. If certain general assumptions are fulfilled, the properties of ultra-high-frequency oscillators can be expressed in terms of a dimensionless parameter ϕ = (f×d)/√V. The dependence of efficiency on frequency in an ultra-high-frequency oscillator is considered in the first part of this paper. In the second part, combining the previous results with the Child-Langmuir equation, the relationship between the voltage, the dimensions of the tube, and the frequency are discussed when the efficiency is maintained constant.