158 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 195G 



for the longitudinal normal mode. As the ratio of phase constant to 

 coupling constant approaches infinity, the ratio of the wave amplitudes 

 on the two lines does also. Finally, if the phase velocities of, or coupling 

 between, two coupled helices are changed gradually along their length 

 the normal modes existing on the pair roughly maintain their identity 

 evan though they change their character. Thus, by properly tapering the 

 phase velocities and coupling strength of any two coupled helices one 

 can cause the two normal modes to become two separate waves, one 

 existing on each helix. 



For instance, if one desires to extract a signal propagating in the in- 

 phase, or longitudinal, normal mode from two concentric helices of equal 

 phase velocity, one might gradually increase the pitch of the outer helix 

 and decrease that of the inner, and at the same time increase the diameter 

 of the outer helix to decrease the coupling, until the longitudinal mode 

 exists as a wave on the outer helix only. At such a point the outer helix 

 may be connected to a coaxial line and the signal brought out. 



This kind of coupler has the advantage of being frequency insensitive ; 

 and, perhaps, operable over bandwidths upwards of two octaves. It 

 has the disadvantage of being electrically, and sometimes physically, 

 quite long. 



3.1.3 Stepped Coupler 



There is yet a third way to excite only one normal mode on a double 

 helix. This scheme consists of a short length at each end of the outer helix, 

 for instance, which has a pitch slightly different from the rest. This 

 has been called a "stepped" coupler. 



The principle of the stepped coupler is this: If two coupled transmis- 

 sion lines have unlike phase velocities then a wave initiated in one line 

 can never be completely transferred to the other, as has been shown in 

 Section 2.4. The greater the velocity difference the less will be the maxi- 

 mum transfer. One can choose a velocity difference such that the maxi- 

 mum power transfer is just one half the initial power. It is a characteristic 

 of incomplete power transfer that at the point where the maximum trans- 

 fer occurs the waves on the two lines are exactly either in-phase or out-of- 

 phase, depending on which helix was initially excited. Thus, the condi- 

 tions for a normal mode on two equal-velocity helices can be produced 

 at the maximum transfer point of two unlike velocity helices by initiating 

 a wave on only one of them. If at that point the helix pitches are changed 

 to give equal phase velocities in both helices, with equal current or volt- 

 age amplitude on both helices, either one or the other of the two normal 

 modes will be propagated on the two helices from there on. Although the 



