Traveling-Wave Tubes (Fourth Installment)

POWER OUTPUT THEORETICAL EVALUATION of the power output of a travelingwave tube requires a theory of the non-linear behavior of the tube. In this book we have dealt with a linearized theory only. No attempt will be made to develop a non-linear theory. Some results of non-linear theory will be quoted, and some conclusions drawn from experimental work will be presented. One thing appears clear both from theory and from experiment: the gain parameter C is very important in determining efficiency. This is perhaps demonstrated most clearly in some unpublished work of A. T. Nordsieck. Nordsieck assumed: (1) The same a-c field acts on all electrons. (2) The only fields present are those associated with the circuit ("neglect of space charge"). (3) Field components of harmonic frequency are neglected. (4) Backward-traveling energy in the circuit is neglected. (5) A lossless circuit is assumed. (6) C is small (it always is). Nordsieck obtained numerical solutions for such cases for several electron velocities. He found the maximum efficiency to be proportonal to C by a factor we may call k. Thus, the power output P is P = kCI0Vo (12.1) In Fig. 12.1, the factor k is plotted vs. the velocity parameter b. For an eiectron velocity equal to that of the unperturbed wave the fractional efficiency obtained is 3C; for a faster electron velocity the efficiency rises to 7C. For instance, if C = .025, 3C is 7.5% and 7C is 15%. For 1,600 volts 15 ma this means 1.8 or 3.6 watts. If, however, C = 0.1, which is attainable, the indicated efficiency is 30% to 70%.