VACUUM TUBE ELECTRONICS 99 



the grid from carrying away any of the alternating current. Benham ^ 

 has suggested an alternative which seems to work fairly well when the 

 grid-cathode path of a negative grid tube is considered, but which offers 

 grave difficulties when the grid-plate path is included. A still different 

 alternative was employed in the present paper in connection with 

 negative grid triodes, and successfully indicates phase angles for the 

 mutual conductance of the tube which are qualitatively logical. The 

 grid-plate path is still without adequate treatment, however. 



As to the third general assumption : that of relatively small alternat- 

 ing-current amplitudes, there can be no objection from a strictly math- 

 ematical point of view, and for a very large proportion of the physical 

 applications the assumption is thoroughly justified. Indeed, it is the 

 only one which is successful in giving starting conditions for oscillators. 

 However, when questions as to the power efficiency of oscillators or 

 amplifiers arise, then the "small signal" theory is inadequate, and 

 should be supplanted by an approximate theory. The form which this 

 approximate theory should take is indicated by the standard methods 

 of dealing with the efficiencies of low-frequency power amplifiers and 

 oscillators where the wave shape of the plate current is assumed to 

 be given. The application of the same kind of approximation to ultra- 

 high-frequency circuits may eventually prove to be a simpler matter 

 than the "small signal" theory set forth in these pages. 



Besides the three main assumptions discussed above, there was a 

 fourth assumption which, although of lesser importance, deserves some 

 comment. This fourth assumption involves the neglect of initial veloc- 

 ities at a hot cathode. If all electrons were emitted with the same 

 velocity, the theory is adequate, and may be applied as indicated by 

 Langmuir and Compton.' When the distribution of velocities accord- 

 ing to Maxwellian, or Fermi-Dirac, laws is considered, some modifica- 

 tions may be necessary. In general, a kind of blurring of the clear-cut 

 results of the univelocity theory may be expected, which will be 

 expected to result in an increase in the resistive components of the 

 various impedances at the expense of the reactive components. Again, 

 lack of symmetry in the geometry of the tube structure may be ex- 

 pected to do the same thing, since the transit angles are then different 

 in the different directions. 



Finally, however, and with all its encumbering assumptions, it is 

 hoped that the excursion back to fundamentals which was made in 

 this paper, has resulted in a method of visualizing the motions of the 

 condensations and rarefactions of the electron densities inside of 

 vacuum tubes operating at high frequencies and has shown their rela- 

 tion to the conduction and displacement components of the total 

 current. 



