872 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956 



field 



which integrates to give a normalized ac circuit voltage 



V 



2V2V0C'' 



i/i 



(20) 



(21) 



RELATIVE PHASE BETWEEN WAVE, VELOCITY AND CURRENT 



The velocity analyzer provides no convenient measure of relative 

 phase between the helix w^ave and the beam modulation. Therefore we 

 compute the relation of helix field and beam modulation for a small ]| 

 signal, and for large amplitudes measure the phase of each relative to 

 that at small amplitudes. 



-VTV 



Pierce gives the relationship' 



V = 



Uo(j^ - r) 



which using (9) and the fact that j3eC8 — jjSe — T 

 gives for the small signal beam modulation 



(22) 

 (23) 



AV 



V2 



4/l=^v1 IHi:)-i (-) 



2VoC ' b 



Similarly we have for the small signal current modulation 



h 



\/-'l 



■8- 



2 tan- 



Vi 



(25) 



The value of 8(= xi + jiji) is given in Fig. 18, drawn from data sup- 

 plied by P. K. Tien, from Pierce' and from Birdsall and Brewer. ^^ This 

 figure was also used as a basis for determining the values of yi and h used 

 in several of the curves. 



MEASUREMENT OF POWER 



The output power, and relative output phase was measured using a 

 tnicro-oscilloscope." The subharmonic of the signal was used for a sweep 

 voltage, and phase was measured from the shape of the observed lissajou 

 figures. The oscilloscope deflection was compared with the dc deflection 

 from a battery standard, and checked on occasion with a bolometer 

 power meter at the operating frequency. 



THE VELOCITY ANALYZER 



There are many ways in which one may separate velocities in an elec- 

 tron stream. Crossed electric and magnetic fields were used in this ex- 



