COUPLED HELICES 157 



have to be supplied to each helix at the input end. A natural way of doing 

 this might be by means of a two-conductor balanced transmission line 

 (Lecher-line), one conductor being connected to the inner helix, the other 

 to the outer helix. Such an arrangement would cause something like the 

 transverse (-| — ) mode to be set up on the helices. If the two con- 

 ductors and the balanced line can be shielded from each other starting 

 some distance from the helices then it is, in principle, possible to intro- 

 duce arbitrary amounts of extra delay into one of the conductors. A delay 

 of one half period would then cause the longitudinal ( + + ) mode to be 

 set up in the helices. Clearly such a coupling scheme would not be 

 broad-band since a frequency-independent delay of one half period is not 

 realizable. 



Other objections to both of these schemes are: Balanced lines are not 

 generally used at microwave frequencies; it is difficult to bring leads 

 through the envelope of a TWT without causing reflection of RF energy 

 and without unduly encumbering the mechanical design of the tube plus 

 circuits; both schemes are necessarily inexact because helices having 

 different radii will, in general, require different voltages at either input 

 in order to be excited in a pure mode. 



Thus the practicability, and success, of any general scheme based on 

 the existence of a pure transverse or a pure longitudinal mode on coupled 

 helices will depend to a large extent on whether elegant coupling means 

 are available. Such means are indeed in existence as will be shown in the 

 next sections. 



3.1.2 Tapered Coupler 



A less direct but more elegant means of coupling an external circuit 

 to either normal mode of a double helix arrangement is by the use of the 

 so-called "tapered" coupler.^' ^' ^^ By appropriately tapering the relative 

 propagation velocities of the inner and outer helices, outside the inter- 

 action region, one can excite either normal mode by coupling to one 

 helix only. 



The principle of this coupler is based on the fact that any two coupled 

 transmission lines support two, and only two, normal modes, regardless 

 of their relative phase velocities. These normal modes are characterized 

 by unequal wave amplitudes on the two lines if the phase velocities are 

 not equal. Indeed the greater the phase velocity difference and /or 

 the smaller the coupling coefficient between the lines, the more their 

 wave amplitudes diverge. Furthermore, the wave amplitude on the line 

 with the slower phase velocity is greater for the out-of-phase or trans- 

 verse normal mode, and the wave amplitude on the faster line is greater 



