REFLEX OSCILLA TORS 



643 



arge signals are applied some of the electrons in the original interval dti 

 will gain or lose sufficient energy to be thrown outside the original cor- 

 responding interval dt^ as for example as indicated by AB. If we consider 

 a whole cycle of the gap voltage in time /o it is apparent that, under steady 

 state conditions, for every electron which is thrown outside the correspond- 

 ing cycle in (2 another from a different cycle in /i is thrown in whose phase 

 differs by a multiple of Itt as for example CD. In summing the effects of 

 these charge increments the difference of 2ir in starting phase produces no 

 physical efifect. This is of course also true mathematically in the Fourier 

 analysis of a periodic function since in integrating over an interval 2-k it is 

 immaterial whether we integrate over a single interval or break it up into a 



Fig. 127. — Diagram showing the relation between /i , the time an electron crosses the 

 gap for the first time, and t-i , the time the electron returns across the gap. 



sum of integrals over intervals — tt to a, 2x;zi + a to lirih + b, Itth-' + 6 to 

 27r;/o -f- (-, etc. where the subintervals sum up to 2ir. Hence we conclude 

 that the preceding analysis is also valid up to (c7) for signals sufficiently 

 large so that k and /i are related by a multiple valued function and is valid 

 beyond that point provided that we do not violate (c8). 



APPENDIX I\' 



Drift Angle .as .a. Function of Frequency and \'oltage 

 Let r be the transit time in the drift space. Then the drift angle is 



^ = COT (dl) 



For changes in voltage (resonator or repeller), both r and co will change. 



