166 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956 



required over a bandwidth of maybe 2 octaves, or even more. Further- 

 more, such attenuation should present a very good match to a wave on 

 the heHx, particularly to a wave traveling backwards from the output 

 of the tube since such a wave will be amplified by the output section of 

 the tube. 



Another requirement is that the attenuator should be physically as 

 short as possible so as not to increase the length of the tube unneces- 

 sarily. 



Finally, such attenuation might, with advantage, be made movable 

 during the operation of the tube in order to obtain optimum performance, 

 perhaps in respect of power output, or linearity, or some other aspect. 



Coupled-helix attenuators promise to perform these functions satis- 

 factorily. 



A length of outer helix (synchronous with the inner helix) one half of a 

 beat wavelength long, terminated at either end non-reflectively, forms a 

 very simple, short, and elegant solution of the coupled-helix attenuator 

 problem. A notable weakness of this form of attenuator is its relatively 

 narrow bandwidth. Proceeding, as before, on the assumption that the 

 attenuator is a fraction 8 larger or smaller than half a beat wavelength 

 at frequencies coi and W2 on either side of the center frequency co, we find 

 that the fraction of power transferred from the inner helix to the attenu- 

 ator is then given by (1 — sin" (ir8/2)). The attenuation is thus simply 



A = sin^ (I) 



For helices of the same proportions as used before in Section 3.4.1, we 

 find that this will give an attenuation of at least 20 db over a frequency 

 band of two to one. At the center frequency, coo , the attenuation is in- 

 finite; — in theory. 



Thus to get higher attenuation, it would be necessary to arrange for a 

 sufficient number of such attenuators in tandem along the TWT. More- 

 over, by properly staggering their lengths within certain ranges a wdder 

 attenuation band may be achieved. The success of such a scheme largely 

 depends on the ability to terminate the helix ends non-reflectively. Con- 

 siderable work has been done in this direction, but complete success is 

 not yet in sight. 



Another basically different scheme for a coupled-helix attenuator rests 

 on the use of distributed attenuation along the coupling helix. The diffi- 

 culty with any such scheme lies in the fact that unequal attenuation in 

 the two coupled helices reduces the coupling between them and the moi'c 

 they differ in respect to attenuation, the less the coupling. Naturally, one 



