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BELL SYSTEM TECHNICAL JOURNAL 



"space charge" associated with it causes the voltage gradient at the cathode 

 surface to be zero. A greater current would mean a negative gradient at 

 the cathode and hence no emission; a smaller current would mean a positive 

 gradient at the cathode and unlimited emission. On this basis Child's law 

 is derived, which gives the current per unit area h in amperes in terms of 

 the voltage Vq and the spacing in centimeters x as 



/o = (2.33) 10-«Fo'''A' . (35) 



Fig. 5 — Part of the electrons leaving the cathode of a diode are turned back before 

 reaching the potential minimum; others proceed to the anode. Ordinarily the greater 

 amount of noise is associated with the space between the potential minimum and the anode. 



From (35) we can obtain a useful relation for the conductance G 



G = dh/dV, = (3/2)(/o/Fo). (36) 



The resistance R is 



i? = 1/G = (2/3)(Fo//o). (37) 



In actual diodes, the electrons are emitted from the cathode with a 

 thermal velocity distribution; a potential minimum of some negative voltage 

 Vm. is formed at some distance Xm from the cathode surface. If the magni- 

 tude of the emitted electron current is /, and the actual current passing the 

 potential minimum is h , then because of the Maxwellian velocity distribu- 

 tion we have 



/o = /.,-^«/*- 



_ r ii,eooF«/r ^ ^ 



— i«€ 



