TRAVELING-WAVE TUBES 7 



Here fSg is a phase constant corresponding to the electron velocity (2.16) 

 and C is a gain parameter depending on circuit and beam impedance (2.43). 

 A solution of the equation for the case of an electron speed equal to the 

 speed of the undisturbed wave yields 3 values of 8 which are shown in Fig. 

 2.4. These represent an increasing, a decreasing and an unattenuated 

 wave. The increasing wave is of course responsible for the gain of the tube. 

 A different approximation yields the missing backward unattenuated wave 

 (2.32). 



The characteristic impedance of the forward waves is expressed in terms 

 of 0c, C, and 8 (2.36) and is found to differ little from the impedance in the 

 absence of electrons. 



The gain of the increasing wave is expressed in terms of C and the length 

 of the tube in wavelengths, N' 



G = 47.3 CN db (2.37) 



It will be shown later that the gain of the tube can be expressed approxi- 

 mately as the sum of the gain of the increasing wave plus a constant to take 

 into account the setting up of the increasing wave, or the boundary condi- 

 tions (2.39). 



Finally, the important gain parameter C is discussed. The circuit part of 

 this parameter is measured by the cube root of an impedance, (E^/^^P)'^, 

 which relates the peak field E acting on the electrons, the phase constant 

 /3 = (jo/v, and the power flow. {E-f^-P)^ is a measure of circuit goodness 

 as far as gain is concerned. 



We should note also that a desirable circuit property is constancy of 

 phase velocity with frequency, for the electron velocity must be near to the 

 circuit phase velocity to produce gain. 



Evaluation of the effects of attenuation, of varying the electron velocity 

 and many other matters are treated in later chapters. 



2.1 Description of a Traveling-Wave Tube 



Figure 2.1 shows a typical traveling- wave tube such as may be used at 

 frequencies around 4,000 megacycles. Such a tube may operate with a 

 ( athode current of around 10 ma and a beam voltage of around 1500 volts. 

 There are two essential parts of a traveling- wave amplifier; one is the helix, 

 which merely serves as a means for producing a slow electromagnetic wave 

 with a longitudinal electric field; and the other is the electron flow. At the 

 input the wave is transferred from a wave guide to the helix by means of a 

 short antenna and similarly at the output the wave is transferred from the 

 liclix to a short antenna from which it is radiated into the output wave 

 ii;uide. The wave travels along the wire of the helix with approximately the 

 speed of light. For operation at 1500 volts, corresponding to about x? the 



