146 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956 



0.5 



1.0 



2.0 2.5 



/io a COT ^, 



3.0 



3.5 



4.0 



4.5 



Fig. 2.4.1 — Beat phase-constant plotted as a function of /3oa cot i^i • These 

 curves result from the solution of the field equations given in the appendix. For 

 hi a = 1.25. 



normalize in terms of the inner helix radius, a: 



jSbO 



7<a — 7/a 



This has been plotted as a function of /5o a cot i/'i in Fig. 2.4, which 

 should be compared with Fig. 2.2. It will be seen that there is considerable 

 agreement between the results of the two methods, 



2.9 Bifilar Helix 



The failure of the transmission line theory to take into account dis- 

 persion is well illustrated in the case of the bifilar helix. Here we have 

 two identical helices wound in the same sense, and at the same radius. 

 If the two wires are fed in phase we have the normal mode characterized 

 by the sheath helix model whose propagation constant is the familiar 

 Curve A of Fig. 2.5. If the two wires of the helix are fed out of phase we 

 have the bifilar mode; and, since that is a two wure transmission system, 

 we shall have a TEM mode which, in the absence of dielectric, propa- 

 gates along the wire with the velocity of light. Hence, the propagation 

 constant for this mode is simplj' /3oa cot \p and gives rise to the horizontal 



