1348 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1953 



ability of its occurrence will be greatly reduced. In particular it has been 

 found that a flat-ended cylinder completely filling the waveguide can be 

 introduced into the full-sized waveguide without mode complications, 

 but Fox and Weiss^^ have shown that putting conical tapers on the ends 

 will favor the establishment of the modified TMn mode. In most ap- 

 plications of the Faraday effect the ferrite element is in the form of a 

 very thin pencil at the center of the waveguide so that the mode problem 

 is greatly simplified, but in order to obtain quantitative fundamental 

 information about ferrites themselves it is often necessary to work with 

 a completely filled waveguide. In such cases considerable care must be 

 taken to insure the validity of the measurements. 



One method of making impedance measurements which has been used 

 successfully by H. Suhl is to cut a shallow longitudinal slot in the cylinder 

 of ferrite and to make standing wave measurements directly in the 

 medium. Because the slotted section is filled with ferrite the size of the 

 waveguide can be reduced to insure the presence of a single mode. This 

 is restricted to unmagnetized materials as rotation of the plane of polari- 

 zation would result in radiation by the slot. 



Another suggested procedure is to make a transformer from full-size 

 rectangular waveguide to circular waveguide of diameter equal to c?/\/e 

 where d is the diameter of a dominant-mode air filled pipe and e is the 

 relative dielectric constant of the ferrite. This transformer can be treated 

 as a four terminal impedance transformer and its network impedances 

 can be determined by measurement. Impedances measured in the air 

 filled guide will have to be transformed through this network to obtain 

 the true impedances of the ferrite-filled guide, but this can be done if 

 the need for the measurements warrants such effort. 



An exact solution of the partially filled waveguide is considerably more 

 difficult to obtain than the solution for a completely filled waveguide. 

 Yet this geometry is the one usually used in most practical applications 

 of the Faraday effect. In the absence of an exact solution one must 

 develop simple physical explanations based upon plane wave theory 

 plus intuition for numerous observed phenomena. A theory for the 

 partially filled longitudinally magnetized waveguide can easily be de- 

 veloped from two simple observations. First, we consider the circular 

 components of the wave separately and observe that each sees an effec- 

 tive scalar permeability which is a weighted average of the permeability 

 of the pencil for that component and that of the surrounding medium, 

 and second we postulate that a small enough pencil will not act as a 

 dielectric rod waveguide and will merely create a small perturbation of 



»» A. O. Fox .irid M.T. Weiss, Revs. Mod. Fhys., 25, p. 262, Jan., 1958. 



