Traveling-Wave Tubes 



By J. R. PIERCE 



Cop.vright, 1950, D. Van Nostrand Company, Inc. 



[SECOND INSTALLMENT] 



CHAPTER IV 



FILTER-TYPE CIRCUITS 



Synopsis of Chapter 



SIDE FROM HELICES, the circuits most commonly used in traveling- 



A^ 



wave tubes are iterated or filter-type circuits, composed of linear 

 arrays of coupled resonant slots or cavities. 



Sometimes the geometry of such structures is simple enough so that an 

 approximate field solution can be obtained. In other cases, the behavior of 

 the circuits can be inferred by considering the behavior of lumped-circuit 

 analogues, and the behavior of the circuits with frequency can be expressed 

 with varying degrees of approximation in terms of parameters which can be 

 computed or experimentally evaluated. 



In this chapter the field approach will be illustrated for some very simple 

 circuits, and examples of lumped-circuit analogues of other circuits will be 

 given. The intent is to present methods of analyzing circuits rather than 

 particular numerical results, for there are so many possible configurations 

 that a comprehensive treatment would constitute a book in itself. 



Readers interested in a wider and more exact treatment of field solutions 

 are referred to the literature.^- 



The circuit of Fig. 4.1 is one which can be treated by field methods. This 

 "corrugated waveguide" type of circuit was first brought to the writer's 

 attention by C. C. Cutler. It is composed of a series of parallel equally spaced 

 thin fins of height h projecting normal to a conducting plane. The case treated 

 is that of propagation of a transverse magnetic wave, the magnetic field 

 being parallel to the length of the fins. It is assumed that the spacing ( is 

 small compared with a wavelength. In Fig. 4.2, ^h is plotted vs. /3n//. Here /3 

 is the phase constant and /Jo = w/c is a phase constant corresponding to the 

 velocity of light. 



1 E. L. Chu and W. W. Hansen, "The Theory of Disk-Loaded Wave Guides," Journal 

 of Applied Physics, Vol. 18, pp. 999-1008, Nov. 1947. 



2L. Brillouin, "Wave Guides for Slow Waves," Journal of Applied Physics, Vol. 19, 

 l>p. 1023-1041, Nov. 1948. 



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