958 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1954 



(T + I + p , 



The l3+ mo(l(> ni-opjiaates for all a, , , , t: decliiiiiiQ; steadily trom 



0- + 1 + p/2 



I + p 



; — , — to unity. The /3_ mode on the other hand is cut ol'f, with B' = 



1 + p/2 



at a = I — p and then reappears with (S" = x at a ^ 1 — p/2. The 



behavior of the two modes is shown in Fig. 5. Self-consistency requires 



that /S" » oj'e/io or oo'e \ Heft \, whichever is the greater. The condition 



/3^ y> co'e I Meff I fails to be met near 



when 



(7 = (To = 



(To 



9 



r + 1 ^ 2 



f + i-f- 



< 



P JV , 1 ^ /? _ i\ + ^Ao) cotiA 



- 1 



The condition fi' » w'e/jo will fail for j8_ near <j = I — p. The range for 

 this to occur is given by 



1 - p - (T < :| . 



- (1 + e/eo) cot lA - 1 



The extension of the Polder formulae to the case of a lossy ferrite 

 was given in Part I, (Section 2.1). From the results given there one 

 may write 



, -, ^ , o-(l + «") — sgn B + ja 

 M + K sgn /5 = 1 + p \ 7, \ , ^Z 



where a is a damping parameter. Substitution of these expressions in 

 the slow wave formula for /3" will give the effect of loss on the propagation 

 constant. In Fig. 6 the complex value of |8_ is shown for a = 0.1 and 

 several values of p. The imaginary part of (8+ is small and varies only 

 slightly with o-. Fig. 7 shows the initial loss (o- = 0) for three values of a 

 and a range of p values. From a knowledge of /3 as a function of o- = co/^/co 

 and p = wm/co it is possible to calculate the loss, Im /3-/(/3o -x/l + e/eo 

 cot yp), as a function of frequency when the magnetic field and satura- 

 tion magnetization of the ferrite are held constant. Fig. 8 shows the re- 

 sults of such calculations. It should be noted that the horizontal scale is 

 linear in a or 1 co and that the \'ertical scale implicitly contains the fre- 

 (luency m the form of l/|So • Both of these distortions of scale tend to 



