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BELL SYSTEM TECHNICAL JOURNAL 



etc. then the electron stream exhibits a negative resistance. From 

 this it may be inferred that oscillations are possible not only for values 

 of n equal to unity but also for larger values, thus yielding the possi- 

 bility of higher order oscillations when the circuit coupled to the 

 electron stream is properly proportioned. If we start with a given 

 cathode temperature with space charge and attempt to obtain the 

 longer transit times by a decrease in applied potential, the smaller 

 currents obtained will decrease the negative resistance. Hence, with 

 space charge it is advisable to employ the smallest value of n possible 

 in actual circuit design. 



For computation work the general formula (2) may be greatly 

 simplified because we need to know only the maximum values which 



0.03 

 0.02 

 0.01 



-0.03 



2 4 6 6 10 12 14 16 18 20 22 



e 



Fig. 2 — Relation between transit angle d and diode resistance. 



the negative resistance attains. These occur in the neighborhood of 

 transit angles given by 



^ = 27rw+-, « = 1, 2, 3, ••. 

 and under these conditions the effective negative resistance is 



Rn = 



1.4X4/o/4w + 1 



area 10^ irr-^ 



ohms. 



(7) 



(8) 



The detailed steps in circuit design are these: First the allowable 

 value of current density /o must be determined. This depends upon 

 the ability of the cathode to emit electrons and as a practical limit 

 something in the neighborhood of 300 mils per square centimeter 

 cannot be exceeded. When this current has been decided upon then 

 the value x of the separation between cathode and anode may be 

 found from (3) and (7) with the lowest value of n which will give 

 practical figures. The space charge condition (4) also gives the lowest 

 allowable potential for which the required current can flow and hence 



