The electronic transadmittances, transmodulation functions, and other characteristics of a planar, multigrid high frequency tube are expressed in terms of four fundamental admittance and modulation functions which are sufficient for the description of the low level r‐f properties of the electron beam. A matrix representation is introduced based on the successive velocity moments of the beam which leads to the formulation of the characteristics as products involving excitation, grid transmission, modulation, and modulation admittance matrices. The electronic equations obtained are a formulation in which the Llewellyn approximation that the second and all higher velocity moments are zero is not made. Thus the theory allows for higher order velocity effects but is dependent on the knowledge of the fundamental admittance and modulation functions.