660 BELL SYSTEM TECHNICAL JOURNAL 



General Relations in Negative Grid Triodes 



The high-frequency values of the amplification factor and the plate 

 impedance could be computed in detail from (87) and (88) together 

 with the various expressions given for the impedances involved. To 

 do this would require an enormous amount of computation, so that 

 the details are deferred until such time as it becomes evident that (87) 

 and (88) express the high-frequency properties of tubes in the most 

 useful way. The fact that they are analogous to the ordinary low- 

 frequency conventions does not at all assure their general utility in 

 the high-frequency field, and the fundamental equations (76) to (79) 

 may be arranged in a wide variety of forms. For example, a com- 

 panion equation to (85) may be obtained from the fundamental 

 equations by eliminating Va, Ip and /c and thus obtaining: 



(95) 



^^--^-)--( z.+z;+zj ^^--^-^- 



-'■[ 



(Z2 + Z3 + Zc)Z„ + (Zi 4- Z2)Z. 



Z2 + Z3 + Zc 



Just as (85) gives an equivalent circuit between cathode and plate 

 involving the whole current reaching the plate, so does (95) give an 

 equivalent circuit between cathode and grid involving the whole 

 current reaching the grid. The two equations completely describe 

 the tube performance when the external connections are known. 

 Because of the way in which Ig and Ip are defined they include the 

 so-called grid-plate path, which is treated as a separate circuit at low 

 frequencies. 



The impedance presented by a tube to an e.m.f. applied between 

 cathode and grid may now be calculated. To carry out the com- 

 putation in general, it would be necessary to know the impedance 

 attached between plate and cathode in the external circuit so that 

 {Vc — Vp)i could be obtained from (85). However, the high-fre- 

 quency properties of negative grid tubes may be illustrated more 

 directly by choosing for consideration a special case that avoids 

 having to take this additional step involving (85). This special case 

 is the one where such a large capacitance is connected between the 

 plate and cathode that {Vc — Vp)i is zero for any of the frequencies 

 to be considered. The result will therefore be particularly applicable 

 to finding the input impedance of screen tubes where the requirement 

 for the special case is fulfilled. 



For this special case where ( Vc — Vp) \ is zero, (95) may be solved 



