Ab initio model for triode tube

The 3/2-power scaling symmetry is explicitly demonstrated to govern triode vacuum tube operation at negative grid bias. A simple model based on this 3 /2 scaling is derived from ab initio physical considerations. This model is suggested as a triode replacement for the Child diode law. Its accuracy is checked for 12AU7, 12AX7, and 6SN7 triode tubes.