716 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1953 



3.1.3 Variation of Input Phase Angle with Frequency 737 



3.2 Mode Shapes Resulting from Interaction Between Elec- 

 tronic Admittance and Input Admittance of Two Coupled 

 Resonators of Equal Q's 739 



3.3 Driving Point Properties of Two Coupled Resonators Hav- 

 ing Unequal Q's 742 



l^ 3.4 Mode Shapes Obtainable With Two Coupled Resonators 



of Unequal Q's 746 



4.0 An Experimental Coupled-Resonator Reflex Klystron 746 



4.1 Constructional Features of Experimental Tube and Circuit . 748 



4.2 Qualitative Verification of Theory 750 



4.3 Quantitative Verification of Theory 750 



4.3.1 Determination of Primary Q 752 



4.3.2 Calibration of Secondary Resonator 754 



4.3.3 Comparison of Experimental and Theoretical Mode 

 Shapes 757 



4.4 Performance Data 760 



5.0 Applications of the Coupled Resonator Reflex Klystron 762 



6.0 Conclusions 764 



References 765 



1.0 INTRODUCTION 



The conventional reflex klystron derives its performance characteris- 

 tics from the interaction between the electronic admittance due to a 

 bunched electron stream and the input admittance of a resonant cavity. 

 As is well known, this interaction results in mode shapes which are 

 closely related to certain input properties of the passive resonant circuit. 

 Thus, the dependence of power output upon frquency, which results 

 from variations in repeller voltage about its mid-mode value, bears 

 close resemblance to the input-impedance-versus-frequency plot of a 

 parallel resonant circuit. Similarly, the curve relating frequency to 

 repeller voltage has the same general shape as that relating frequency 

 to the input phase angle of the resonator. Recognition of these relation- 

 ships has resulted in the consideration of different and, perhaps, more 

 useful mode shapes which might be obtained if the electronic admittance 

 were made to interact with impedance or admittance functions of passive 

 circuits other than that due to a single resonator. 



What do we mean by "more useful** mode shapes? The answer, of 

 course, depends on the application, although an "ideal" mode shape could 

 probably be defined as one having a flat top, i.e., power output inde- 



