ULTRA-HIGH-FREQUENCY VACUUM TUBES 657 



ponent, only. Then we have: 



^- z, + z, - zT+X ' ^ ^ 



_ (Ze + Z2 + Z^)Z, + (Zi + Z2)Z, ,.^- 



^^ " ZTX ■ ^ ^ 



The relations involved in these two equations may be made some- 

 what clearer by finding what they resolve into at low frequencies. 

 This may be done by going to (80)-(84). The first thing to notice is 

 that Zi and Zg become very large because the frequency term p = io) 

 appears in their denominators. The other terms are relatively small 

 at low frequencies and we have: 



Ho -^ Zi/Zg, (87a) 



rj, = Zp^ Z,(l + mo) + Zo + Z3. (88a) 



It will be shown below that this formulation for the amplification 

 factor is in accord with that derived by Maxwell in his " Treatise on 

 Electricity and Magnetism " for the shielding effect of a grid mesh. 



Low- Frequency Relations in Negative Grid Triodes 

 In (87a) and (88a) the general form of the low-frequency triode 

 relations is given. It is instructive to compute these in some detail 

 so that the role played by the capacitance Cg between the planes A 

 or B and the grid wires is demonstrated. 



To do this, (82) which gives the impedance Zi may first be trans- 

 formed by aid of (57) and (67) to give 



Zi = ^(l -¥ly). (89) 



The impedance Zg may be written as in (80) so that the low-frequency 

 amplification factor is 



MO = ^ Cg{\ - h'/y). (90) 



It is of interest to note that e/xp is the capacitance per unit area 

 between the plate and a solid plane at the grid. As expressed by 

 Compton and Langmuir ^ from Maxwell's analysis the low-frequency 

 amplification factor is 



Mo = 



a , a 



ZTT ZtTC 



(91) 



