The behavior of a group of triodes of an electron gun having all the same cutoff voltage is discussed with respect to its physical dimensions. Especially the relation between gun characteristics and a design number (

) is investigated where

is the distance between cathode surface and modulator and B between modulator and anode. For a fixed-grid drive pulse the total emitted cathode current and the portion of it passing through a beam-limiting aperture increases with increasing

(decreasing

) whereas the resolution decreases. If the electrical parameters like anode voltage and cut off voltage are already determined it can be concluded that there is a certain design number (

) for optimized beam density on a phosphor screen.