COUPLED HELICES 



147 



1.80 



1.60 



(0 



n 1.40 

 <5. 



I 

 to 



t.OO 



0.80 



0.60 



0.5 



1.0 



1.5 



2.0 2.5 



/3oaCOTi^, 



3.0 



3.5 



4.0 



4.5 



Fig. 2.4.2 — 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 

 hia = 1.5. 



line of Curve B in Fig. 2.5. Again the coupling phase constant j3c is given 

 by the difference of the individual phase constants: 



^cO- — /3oa cot \f/ — ya 



(2.9.1) 



which is plotted in Fig. 2.6. Now note that when /So <3C 7 this equation is 

 accurate, for it represents a solution of the field equations for the helix. 



From the simple unsophisticated transmission line point of view no 

 coupling between the two helices would, of course, have been expected, 

 since the two helices are identical in every way and their mutual capacity 

 and inductance should then be equal and opposite. 



Experiments confirm the essential correctness of (2.9.1). In one experi- 

 ment, which was performed to measure the coupling wavelength for the 

 l)ifilar helices, we used helices with a cot 1/' = 3.49 and a radius of 0.036 

 cm which gave a value, at 3,000 mc, of ^oa cot i^ = 0.51 . In these experi- 

 ments the coupling length, L, defined by 



(/3oa cot xp — 7a) — = TT 

 a 



was measured to be 15.7o as compared to a value of 13.5a from Fig. 2.6. 

 At 4,000 mc the measured coupling length was 14.6a as compared to 



