396 BELL S 1 STEM TECH NIC A L JOURNA L 



the input conductance of a tetrode or pentode can be re-written, neglecting 

 the higher order terms, to give the approximate expression 



b 



„ _ 5.0 X \Qr\^fGr. 

 ^'" Fi 



1 + ?>.?> 



(13) 



where Gm is the triode-connected transconductance, a is grid-cathode spacing 

 in cms, h is grid-screen spacing in cms, Vi and V-i are the eflfective grid-plane 

 and screen-plane potentials in volts, and / is the frequency in mc. It is 

 assumed that there are no lead inductances and that there is no potential 

 minimum in the grid-cathode region. For a given transconductance, (13) 

 shows that close spacings are necessary for minimum grid conductance. 



If the lead inductances between the external circuit and the tube elements 

 are appreciable, the input loading may be excessive even though the transit 

 time through the tube structure is negligibly small. The general case taking 

 account of the mutual and self inductances of all the leads of a pentode has 

 been treated by Strutt and van der ZieP. The equations are cumbersome 

 even though only the first order terms in frequency are retained. If all of 

 the lead inductances except that in series with the cathode are neglected, 

 and transit time is assumed to be negligible, the input conductance of a 

 pentode becomes approximately^ 



Gin = CjO-G,„LlcCk (14) 



where Lk is the cathode lead inductance and C/.- is the grid-cathode capaci- 

 tance. It is further assumed that the plate-grid capacitance is negligible. 

 Work done at the Naval Research Laboratory includes data on the input 

 conductance of 6AK5 tubes in the frequency range from 100 mc to 300 mc. 

 Through the courtesy of the Naval Research Laboratory some of the data 

 are reproduced in Fig. 9. It is of interest to check a point on this curve 

 against equation (14). For the 6AK5, 0.02 micro-henry is the estimated* 

 cathode lead inductance, G„, = 5000 X 10-« mhos, and Q- = 4 X 10-^2 f^rad. 

 At a frequency of 250 mc we hav^e a calculated conductance of 990 

 micromhos, which checks roughly with the value of 1110 micromhos from 

 the curve in Fig. 9. Equation (13) can be used to obtain an approximate 

 value for the loading due to transit time. Taking a = 0.0089 cm., b = 

 0.032 cm., G„ = 6.7 X lO"' mhos,/ = 250 mc, Vi = +2.3 volts, and Fa 

 = -|-120 volts, a calculation giv^es G,„ = 177 micromhos. These results 



■• "The Causes for the Increase of the Admittance of Modem High-Frequency Amplifier 

 Tubes," M. J. O. Strutt and A. van der Ziel, /. R. E. Proceedings, Vol. 26, No. 8, August 

 1938. 



^ "Hyper and Ultra-High Frequency Engineering," Sarbacher and Edson, p. 435. 



* This has been checked roughly by Q-meter measurements. 



