COUPLED HELICES 1G3 



power transfer of proportions other than 100 per cent two possibilities 

 are open: either one can reduce the length of the synchronous coupling 

 helix appropriately, or one can deliberately make the helices non-syn- 

 chronous. In the latter case, a considerable measure of broad-banding 

 can be obtained by making the length of overlap again equal to one half 

 of a beat-wavelength, while the fraction of power transferred is deter- 

 mined by the difference of the helix velocities according to 2.4.7. An 

 application of the principle of the coupled-helix transducer to a variable 

 delay line has been described by L. Stark in an unpublished memo- 

 randum. 



Turning again to the complete power transfer case, we may ask: 

 How broad is such a coupler? 



In Section 2.7 we have discussed how the radial falling-off of the RF 

 energy near a helix can be used to broad-band coupled-helix devices 

 which depend on relative constancy of beat-wavelength as frequency 

 is varied. On the assumption that there exists a perfect broad-band match 

 between a coaxial line and a helix, one can calculate the performance of 

 a coupled-helix transducer of the type shown in Fig. 3.2. 



Let us define a center frequency co, at which the outer helix is exactly 

 one half beat-wavelength, \b , long. If oj is the frequency of minimum 

 beat wavelength then at frequencies coi and co2 , larger and smaller, 

 respectively, than co, the outer helix will be a fraction 5 shorter than 

 }i\b , (Section 2.7). Let a voltage amplitude, Vo , exist at the point where 

 the outer helix is joined to the coaxial line. Then the magnitude of the 

 voltage at the other end of the outer helix will be | F2 • sin (x5/2) | which 

 means that the power has not been completely transferred to the inner 

 helix. Let us assume complete reflection at this end of the outer helix. 

 Then all but a fraction of the reflected power will be transferred to the 

 inner helix in a reverse direction. Thus, we have a first estimate for the 

 "directivity" defined as the ratio of forward to backward power (in db) 

 introduced into the inner helix: 



D = 



10 log sin" 



(3.4.1.1) 



We have assumed a perfect match between coaxial line and outer helix; 

 thus the power reflected back into the coaxial line is proportional to 

 sin^(x5/2). Thus the reflectivity defined as the ratio of reflected to 

 incident power is given in db by 



i^ = 10 log sin' ^ (3.4.1.2) 



