150 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956 



2.4 



0.5 ).0 1.5 2.0 2. 



5 3.0 3.5 

 /3oaCOT^ 



4.0 4.5 



Fig. 2.5 — Propagation constants for a bifilar helix plotted as a function of 

 /3oa cot i/-! . The curves illustrate, (A) the dispersive character of the in-phase 

 mode and, (B) the non-dispersive character of the out-of -phase mode. 



where ^^ is the coupling phase-constant in the presence of dielectric, 

 /3j is the phase-constant of each helix alone in the presence of the same 

 dielectric, ^c is the coupling phase-constant with no dielectric, and (3 is 

 the phase constant of each helix in free space. In many cases of interest 

 /3o(d/2) cot lA is greater than 1.2. Then 





3£ + 1 " 

 _2£' + 2_ 



g—(v'2« '+2-2)^0 (dl2) cot \l/ 



(2.10.1) 



Appearing in the same figure is a similar plot for the case when there is a 

 conducting shield inside the inner helix and outside the outer, and 

 separated a distance, "s," from the helices. Note that 



c? = 6 — a. 



It appears from these calculations that the effect of the presence of 

 dielectric between the helices depends largely on the parameter /So (d/2) 

 cot \{/. For values of this parameter larger than 0.3 the coupling wave- 

 length tends to increase in terms of circuit wavelength. For values smaller 

 than 0.3 the opposite tends to happen. Note that the curve representing 

 (2.10.1) is a fair approximation down to /3o(c?/2) cot i/' = 0.6 to the curve 

 representing the exact solution of the field equations. J. W. Sullivan, in 

 unpublished work, has drawn similar conclusions. 



