1168 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBEK 1954 



results which show that the rotation in a thin disc is independent of the 

 dielectric constant of the disc. 



2. THE PARALLEL PLANE CABLE 



^Measurements on ferrites are sometimes made by a coaxial cable tech- 

 nique. The ferrite fills a section of the cable, and is magnetized axially. 

 In this section we consider a simplified problem of the same kind: that of 

 wave motion between parallel conducting planes bounding a ferrite slab 

 magnetized in the propagation dii-ection. The characteristic ec^uation for 

 the propagation constant has been established by a number of authors, 

 particularly Van Trier, but as in the case of the cjdindrical waveguide, 

 no analj^sis of the equation in terms of the laboratory variables appears 

 to have been made. We shall make such an analysis by means of the 

 methods already used in Part I for the cylindrical waveguide. The dis- 

 cussion ^^•ill be limited to the dominant (TE^I-limit) mode; and to the 

 prmcipal features of the incipient modes (shape resonances). 



The distance between the two conducting boundaries vn\\ be denoted 

 by 2a. The system of axes is as in Fig. 7; the y-axis is perpendicular 

 to the walls (located at 7/ = ±a), the 2-axis is the magnetization and 

 propagation direction. The microwaA'e fields are assumed not to ^ary 

 along the a;-axis. 



The solution of Maxwell's equation proceeds just as in the case of the 

 cylmdrical waveguide (Part I, Section 3), with the simplifjang feature 

 that one of the coordinates (x) drops out of the problem. We shall use 

 the reduced notation of Part I. /3, the propagation constant will be meas- 

 ured in units of coVTtjJI, the propagation constant of the uimiagnetized, 

 unbounded medium, a will denote aco\/^, the half-spacing measured 



in terms of the reduced wavelength — of the unmagnetized, extended 



medium. 



CONDUCTING 

 BOUNDARIES 



Fig. 7 — Parallel plane cable filled with ferrite magnetized along propagation 

 direction. 



