COUPLED HELICES 



151 



2.11 The Conditions for Maximum Power Transfer 



The transmission line theory has led us to expect that the most efficient 

 power transfer will take place if the phase velocities on the two helices, 

 prior to coupling, are the same. Again, this would be true were it not for 

 the dispersion of the helices. To evaluate this effect we have used the 

 field equation to determine the parameter of the coupled helices which 

 gives maximum power transfer. To do this we searched for combinations 

 of parameters which give an equal current flow in the helix sheath for 

 either the longitudinal mode or the transverse mode. This was suggested 

 by L. Stark, who reasoned that if the currents were equal for the indi- 

 vidual modes the beat phenomenon would give points of zero RF current 

 on the helix. 



The values of cot T/'2/cot 4/i which are required to produce this condi- 

 tion are plotted in Fig. 2.8 for various values of b/a. Also there are shown 

 values of cot ^2/cot \{/i required to give equal axial velocities for the helices 

 before they are coupled. It can be seen that the uncoupled velocity of the 

 inner helix must be slightly slower than that of the outer. 



A word of caution is* necessary for these curves have been plotted 

 without considering the effects of dielectric loading, and this can have a 

 rather marked effect on the parameters which we have been discussing. 

 The significant point brought out by this calculation is that the optimum 



04 0.8 1.2 1.6 2.0 2.4 



/3oaCOT J^, 



2.8 



3.2 



3.6 



4.0 



Fig. 2.6 — The coupling phase-constant which results from the two possible 

 modes of propagation on a bifilar helix shown as a function of jSoo cot i/-! . 



