

884 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956 



where h = L-a-8. Equation (II — 4) demonstrates that the null condi- 

 tion is nonreciprocal since, in general, the solutions differ for Av positive 

 and kr negative. The quantity Av has the same sign as the direction of 

 the dc magnetic field; reversing the sign of Av is equivalent to reversing \ 

 the direction of propagation. 



A numerical analysis of etiuation (II • — 4) has led to the conclusion 

 that the null condition is most broadband when | /x^ | < | Av |.* We use 

 the criterion \ Hr\ = [ A\ | to determine a critical magnetic field: 



Hc = --^tM8 (11 — 5) 



7 



Clearly we require co/7 > AttIMs for physically realizable solutions. The 

 saturation magnetization (47rM's) is subject to the following: 



1 . A choice of too large a 4^ttMs might create a mode problem and in 

 addition will not satisfy the limit on AtvMs implied in (II — 5). 



2. 4xil/s must be sufficiently large so that the field needed to make 

 I jUr I < I Av I not be excessive. 



3. y\/H(H + 4:tM) (this being the slab resonance frequency for 

 small slab thickness^) must be sufficiently far from the operating fre- 

 quency to avoid loss due to resonance absorption. In addition, this con- 

 dition improves the frequency insensitivity of the null. 



Further analytic considerations are presented in Section IV. 



III. EXPERIMENTAL DESIGN CONSIDERATIONS 



Aside from the partial height nature of the slab, there are two other 

 basic factors in the experimental situation which are not present in the 

 analysis of Section IIB (see also Section IV). First, the ferrite has both 

 finite dielectric and magnetic loss. Second, higher order modes may be 

 present. These deviations from the simplified analysis are by no means 

 trivial and it would not be surprising if one found a considerable modifi- 

 cation of the analytic results. As it turns out, there are broad areas of 

 general agreement between the theoretical and experimental results 

 and in no case examined here does one find a basic inconsistency. In 

 considering the various parameters which must be adjusted to optimize 

 the broadband performance of the isolator we will point out, where 

 possible, how the theoretical results are modified by the factors men- 

 tioned above. The parameters of interest are: 



* This is partially evident from eciuation II — 4. The quantity fj.r \ must be 

 less than | A;, | if the angle (aib) is to be small and in the first quadrant. Second 

 quadrant solutions cause the guide cross section to be excessively large, with 

 attendant higher mode complication. 



