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On the transfer function of multi-cavity klystrons Taylor, Michael Gordon

Abstract

The objective of this thesis is to consolidate previously reported results on numerical methods for attaining flat amplitude response in multi-cavity klystrons. The work done by Isaacs, Schrack, and Yuan at the University of British Columbia is extended so as to apply to a representation of the power-gain function based on Bers' theory of the interaction between an electric field and an electron beam. It is shown that an iterative numerical method can be used in designing for flat response, contrary to the conclusion drawn by McCullough on the basis of Bers' theory. That conclusion results from the failure to consider the frequency dependence of the transadmittances appearing in the power-gain function. It is shown that one of the two terms in the transadmittance is an odd function of frequency which can be approximated by a linear function. The other term is an even function of frequency which can be approximated by a constant. If these approximations are made for each transadmittance, the resulting power-gain function is even, a requirement which must be fulfilled for physical realizability as well as for the applicability of the iterative method. Yuan has previously shown that the optimum tuning pattern for a multi-cavity klystron can be determined by considering the numerator polynomial of the power-gain function. It is shown here that the variations, in the loaded Q's of the input and output cavities must also be considered. A modified method for selecting the optimum tuning pattern is presented. A numerical example is given which illustrates the application of the modified method, using the iterative procedure to determine the pole positions and power gain for each tuning pattern. The numerical data for this example was the same as that used by Blötekjaer at the Norwegian Defense Research Establishment in a similar study in which an analog device was used to determine the relative merit of the different tuning patterns for a klystron. It is shown that the predicted optimum tuning pattern does actually give the highest gain and that the results from the numerical and analog methods are essentially identical.

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