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THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1953 



admittance vector with the load line moves down along the latter as 

 indicated by the arrows in Fig. 10(a), power changes smoothly until 

 the F«- vector becomes tangent with the loop at 4. At this point there 

 occurs a discontinuous jump in both power and frequency caused by 

 the sudden shortening of the Fe- vector from 4 to 7. From here on, power 

 and frequency again become single valued functions of Vr . The mode 

 shape corresponding to this uni-directional sweep is shown in Fig. 10(b). 

 If the mode is traversed in the opposite sense we again encounter this 

 discontinuity although it will now occur on the opposite side of the 

 loop and, therefore, at a different repeller voltage and frequency. Fig. 



2^*^3^^ 



_A\ 



(0 



Fig. 10 — Production of load hysteresis by overcoupled cavities, (a) Load line 

 for overcoupled cavities, (b) Oscillographic mode representation for unidirectional 

 (sawtooth) repeller sweep, (c) Oscillographic mode representation for sinusoidal 

 repeller sweep. 



10(c) shows the load hysteresis effect as one might expect to observe it 

 on the oscilloscope screen with a sinusoidal sweep applied to the repeller. 



3.3 Driving Point Properties of Two Coupled Resonators Having Un- 

 equal Q^8 



The presentation of the theory of the coupled resonator reflex klystron 

 will now be concluded by a discussion of the more general and, as we 

 shall see, more useful case of two coupled cavities of unequal Q's. Specifi- 

 cally, we are considering the equivalent circuit shown in Fig. 11. By 

 making approximations similar to those which led to equation 3.2, the 

 input admittance for the case of unequal Q's may be derived as,^' ** ^ 



J-[ 



1 + 



k'QQ. 



1 -h (2Q.5)2 



]'-'H'-rvmJr\' ''■''' 



