THERMIONIC VACUUM TUBES 41 



negative potential immediately around the cathode which persists for 

 all values of E p less than that required to produce voltage saturation. 

 It is the minimum potential V' (see Fig. 5) that limits I p , and any 

 increase in V' will result in an increase in I p . Because the grid is 

 close to the filament, small changes in the grid potential, E g , are as 

 effective in changing V' and therefore I p , as large changes in E p . 

 This leads to the so-called amplification constant n of the tube which 

 may be taken as 



in which ±e p and ^e g are changes in E p and E g , the changes being 

 opposite in sign as indicated, and such that they leave I p unchanged. 



It has also been shown' 20 that if AE P and AE g are increments of 

 E p and E g which cause equal increments in the electric field at the 

 surface of the cathode (considered simply as an equipotential surface 

 and not as a source of electrons) the amplification constant, n, of the 

 tube will be the ratio AE p /AE g . 



8. Characteristic Equation. The electrical characteristics of the 

 three-electrode vacuum tube may be represented 21 by the equation 



l,=«(^+j^ + «)! r (2) 



The constant k is related in a simple way to the internal resistance of 

 the tube. A consideration of e which expresses the contact difference 

 of potential between grid and filament is usually essential only in 

 tubes which operate at a low E p and particularly in detectors and 

 amplifiers. In tubes with coated filament, e may not only vary 

 within a range of two or three volts between different tubes, but may 

 also change during the life of any one tube. The exponent 77 varies 

 in a given tube with applied voltage, being usually equal to about 2 



when the effective voltage ( — - -\-E g + e ) is comparable with the poten- 

 tial drop in the filament (see Fig. 9), and tending to approach the 

 theoretical value 3/2 with increasing effective voltage. It has been 

 found possible to deduce relations between the constants /z and k of 

 Equation 2 and the structure and dimensions of any tube which are 

 in very fair agreement with experimental values. 22 



Typical curves corresponding to the characteristic Equation 2 are 

 shown in Figs. 10 and 11. These curves are referred to as static char- 



20 R. W. King, Phys. Rev., Vol. 15, p. 256, 1920. 

 11 Van der Bijl, Phys. Rev., 12, 180, 1918. 

 M King, 1. c. 



