NEGATIVE-GRID VACUUM TUBES 577 



long as frequencies were low enough to allow this last approximation 

 to remain valid. With the advent of higher frequencies it became 

 evident that the internal tube capacitances played an important role 

 in the operation of the device. The lengths to which early workers 

 went to include the capacitance effects are illustrated by the compli- 

 cated formulas on page 207 of Van der Bijl's well-known book on 

 Thermionic Vacuum Tubes. F'urther study, however, showed that 

 the complication could be overcome largely by a modification of the 

 simple network of Fig. 1 so that capacitances are introduced between 

 all three elements of the vacuum tube. The result is Fig. 2 which 

 has been adequate in the past for all purposes. In comparatively 

 recent years, however, increasing frequencies demand that a further 

 revision be made. 



The necessity for revision first became evident with the discovery 

 that the impedance measured between grid and cathode when a very 

 large condenser was placed between plate and cathode, showed an 

 important resistive component at very high frequencies so that the 

 simple combination of Fig. 2 involving only capacitances for the grid- 

 cathode and grid-plate impedance was no longer valid. The tools for 

 effecting the modification of Fig. 2 are available ^ and already have 

 been employed to a certain extent. These tools are the result of a 

 theoretical analysis of the motions of electrons within vacuum tubes 

 and started from fundamentals. With the reservation that they 

 apply strictly to planar rather than cylindrical tube structures, the 

 results should therefore require little further modification for some 

 time to come. 



The first result of theoretical analysis was to produce an equivalent 

 network which, on the face of it, resembles Fig. 2 only remotely, but 

 which can be shown ^ to be exactly equivalent at low frequencies. 

 This generalized theoretical network is shown in Fig. 3. It may be 

 seen to consist of two branches only, which exist respectively between 

 cathode and grid and between cathode and plate. Both branches 

 contain internal generators and, in general, the impedance in neither 

 branch is a pure resistance but depends upon a number of factors 

 including the time required by electrons in traversing the vacuum 

 tube. The immediate query which results from inspection of Fig. 3 

 is "What has become of the grid-plate path?" The answer to this 

 lies in the definition of current in Fig. 3 so that the cathode-plate 

 path is included in the network as shown. This definition of current 

 is merely the generalized one adopted years ago by Maxwell when he 



^ F. B. Llewellyn, "Operation of Ultra-High-Frequency Vacuum Tubes," Bell 

 Sys. Tech. Jour., Vol. XIV, pp. 632-665, October 1935. 



