. The Bell System technical journal . we plot time Aj . The solid lines connect corresponding times inthe absence of signal for increments of time dl^ and df-: . \\ hen sufficiently REFLEX OSCILLA TORS 643 arge signals are applied some of the electrons in the original interval dtiwill gain or lose sufficient energy to be thrown outside the original cor-responding interval dt^ as for example as indicated by AB. If we considera whole cycle of the gap voltage in time /o it is apparent that, under steadystate conditions, for every electron which is thrown outside the correspond-ing cycle in (2 ano
. The Bell System technical journal . we plot time Aj . The solid lines connect corresponding times inthe absence of signal for increments of time dl^ and df-: . \\ hen sufficiently REFLEX OSCILLA TORS 643 arge signals are applied some of the electrons in the original interval dtiwill gain or lose sufficient energy to be thrown outside the original cor-responding interval dt^ as for example as indicated by AB. If we considera whole cycle of the gap voltage in time /o it is apparent that, under steadystate 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 phasediffers by a multiple of Itt as for example CD. In summing the effects ofthese charge increments the difference of 2ir in starting phase produces nophysical efifect. This is of course also true mathematically in the Fourieranalysis of a periodic function since in integrating over an interval 2-k it isimmaterial 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 thegap 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 to27r;/o -f- (-, etc. where the subintervals sum up to 2ir. Hence we concludethat the preceding analysis is also valid up to (c7) for signals sufficientlylarge so that k and /i are related by a multiple valued function and is validbeyond that point provided that we do not violate (c8). APPENDIX I\ Drift Angle .as .a. Function of Frequency and \oltageLet 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. 644 BELL SYSTEM TECHNICAL JOURNAL Thus Ae/e = Aco/w + At/t (d2) = Aw/W + ((dT/dV)/T)AV As shown in Appendix VT, the derivative of t with respect to repellervoltage, dr/dVK , is always negative, while the deri
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