CHAPTER IX 

 DISCONTINUITIES 



Synopsis of Chapter 



WE WANT TO KNOW the overall gain of traveling-wave tubes. So 

 far, we have evaluated only the gain of the increasing wave, and we 

 must find out how strong an increasing wave is set up when a voltage is 

 applied to the circuit. 



Beyond this, we may wish for some reason to break the circuit up into 

 several sections having different parameters. For instance, it is desirable 

 that a traveling-wave tube have more loss in the backward direction than it 

 has gain in the forward direction. If this is not so, small mismatches will 

 result either in oscillation or at least in the gain fluctuating violently with 

 frequency. We have already seen in Chapter VHI the effect of a uniform 

 loss in reducing the gain of the increasing wave. We need to know also the 

 overall effect of short sections of loss in order to know how loss may best 

 be introduced. 



Such problems are treated in this chapter by matching boundary con- 

 ditions at the points of discontinuity. It is assumed that there is no re- 

 flected wave at the discontinuity. This will be very nearly so, because the 

 characteristic impedances of the waves differ little over the range of loss 

 and velocity considered. Thus, the total voltages, a-c convection currents 

 and the a-c velocities on the two sides of the point of discontinuity are set 

 equal. 



For instance, at the beginning of the circuit, where the unmodulated elec- 

 tron stream enters, the total a-c velocity and the total a-c convection cur- 

 rent — that is, the sums of the convection currents and the velocities for the 

 three waves — are set equal to zero, and the sum of the voltages for the three 

 waves is set equal to the applied voltage. 



For the case of no loss (d = 0) and an electron velocity equal to circuit 

 phase velocity (b = 0) we And that the three waves are set up with equal 

 voltages, each ^ of the applied voltage. The voltage along the circuit will 

 then be the sum of the voltages of the three waves, and the way in which 

 the magnitude of this sum varies with distance along the circuit is shown in 

 Fig. 9.1. Here C.V measures distance from the beginning of the circuit and 

 the amplitude relative to the applied voltage is measured in db. 



The dashed curve represents the voltage of the increasing wave alone. 



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