COUPLED HELICES 139 



words, complete power transfer occurs when ,81 = /So regardless of the 

 relative impedances of the helices. 



The reader will remember that (3io and (820 , not jSi and ^o , were defined 

 as the phase constants of the helices in the absence of each other. If the 

 assumption that h ^ x is maintained, it will be found that all of the de- 

 rived relationships hold true when (Sno is substituted for /3„ . In other 

 words, throughout the paper, /3i and /So may be treated as the phase con- 

 stants of the inner and outer helices, respectively. In particular it should 

 be noted that if these ciuantities are to be measured experimentally each 

 helix must be kept in the same environment as if the helices were coupled ; 

 onl}^ the other helix may be removed. That is, if there is dielectric in the 

 annular region between the coupled helices, /Si and ^2 must each be 

 measured in the presence of that dielectric. 



Miller also has treated the case of lossy coupled transmission systems. 

 The expressions are lengthy and complicated and we believe that no 

 substantial error is made in simply applying his conclusions to our case. 



If the attenuation constants ai and ao of the two transmission systems 

 (helices) are equal, no change is required in our expressions; when they 

 are unequal the total available power (in both helices) is most effectively 

 reduced when 



^4^'^l (2.4.11) 



Pc 



This fact may be made use of in designing coupled helix attenuators. 



2.5 A Look at the Fields 



It may be advantageous to consider sketches of typical field distribu- 

 tions in coupled helices, as in Fig. 2.1, before we go on to derive a quanti- 

 tative estimate of the coupling factors actually obtainable in practice. 



Fig. 2.1(a) shows, diagrammatically, electric field lines when the 

 coupled helices are excited in the fast or "longitudinal" mode. To set up 

 this mode only, one has to supply voltages of like sign and equal ampli- 

 tudes to both helices. For this reason, this mode is also sometimes called 

 the "(+-f) mode." 



Fig. 2.1(b) shows the electric field lines when the helices are excited in 

 the slow or "transverse" mode. This is the kind of field required in the 

 transverse interaction type of traveling wave tube. In order to excite 

 this mode it is necessary to supply voltages of equal amplitude and 

 opposite signs to the helices and for this reason it is sometimes called the 

 "(-| — ) mode." One way of exciting this mode consists in connecting one 



