ULTRA-HIGH-FREQUENCY VACUUM TUBES 655 



CO 00 



re=0 TO=0 



, 2^/2.(« + l)(w + 2) + (« + 2)(w + 2) - //(« 4- l)(w + 1) 



(w + 2) !(m + 3) ! 



The attainment of (68) and (75) does not completely solve the 

 problem because it is the potential of the grid wires that can be 

 measured rather than the poteatial at A and B. The transformation 

 may be readily accomplished, however, by writing 



{Va - F,)i = 7,Z„ (76) 



where Zg is the effective impedance between the plane A (or B) and 

 the grid wires. In the negative grid tube when A and B are close 

 together, Zg is a pure capacitance, Cg. 



Writing (68) and (75) respectively in terms of V and / instead of W 

 and / we now have in symbolic form 



where 



The four equations, (76), (77), (78) and (79) are the basis of nega- 

 tive grid triode analysis. The impedances involved refer to a square 

 centimeter of area and are as follows: 



Zg = —7T = impedance between plane A (or B) and the grid (80) 

 wires, 



Z. = 12r. E (- ^e)"(w + 2)/(w + 4) !, (81) 



n=0 



Zi = nrXgy^ + l)/2/3„ (82) 



Z^ - Mr^h' E (- }i^:)-{n + 2)/(« + 4) !, (83) 



re=0 



Z3 = 12a- [E(- m\ 2(^^^^\ )\ 



+ 12a Te e (- ^0)"+"/^" 



L n=0 m=0 



/2,?//.(w + l)(w + 2) + {n + 2)(m + 2) - //(« + l)(m + 1)\] 

 >^^ {n + 2) !(w + Z) ! /J' ^ ^ 



The value of re is expressed by (65). 



