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BELL SYSTEM TECHNICAL JOURNAL 



figure, the natural logarithm of the ratio of saturation current to the 

 plate current is plotted as a function of the plate voltage for several 

 constant values of the coef^cient X. These curves show for a fixed 

 positive value of plate voltage that as the space charge is decreased 

 toward zero, by a reduction in the ratio of the saturation current to the 

 plate current, the value of X for moderately large values of space charge 

 increases but little from 0.644, and then for a very low space charge, 

 increases very rapidly to its limiting value given by the shot noise 



-4 -2 



20 22 24 26 28 





Fig. 3- — Modification of effective plate resistance temperature produced by 



space charge. 



£/2 = ^krp{\T)dJ. 



which is represented by the axis of abscissae. Thus, the value of X 

 digresses markedly from 0.644 only for the narrow region of operating 

 conditions for which the saturation current is less than 1.25 times the 

 plate current and the plate voltage is less than 2Se/kT volts. For an 

 oxide coated cathode for which T is 900° K., the effective plate re- 

 sistance temperature is 0.6447" for any operating condition for which 

 plate current is less than eight-tenths of the saturation current and the 

 plate voltage is greater than two volts. 



For a cylindrical diode, the general method of analysis used in the 

 parallel plane case results in equations which are practically impossible 



