THE FIELD DISPLACEMENT ISOLATOR 891 



thus obtainable is limited by the scattering into this mode. The charac- 

 ter of these singular modes will be discussed in a subsequent paper. 



Results 



The performance of the isolator as a function of frequency is shown 

 in Fig. 13. Fig. 14 shows a completed model of the isolator. 



IV. FURTHER ANALYSIS 



While an exact characteristic equation is obtainable for the overall 

 geometry of the full height isolator, including the lossy film, the ex- 

 pressions which result are sufficiently complex to be all but impossible to 

 handle. However, if the resistance film is chosen to have small conduc- 

 tivity we may utilize a simple perturbation approach in which the field 

 at the ferrite face is assumed to be unaffected by the presence of the 

 loss film. A quantity rj may then be defuied* so that 



. = LM (IV- 1) 



For small conductance values ri is proportional to attenuation to first 

 order in either direction of propagation, Er , in equation (IV ^ — ■ 1), is 

 the electric field adjacent to the film and P is the power flowing across 

 the guide cross section. The loss in the ferrite material is not taken into 

 account in this approximation, but it would naturally have a deteriorat- 

 ing effect on the isolator characteristics. 



The ratio of the values of 77 corresponding to backward and forward 

 direction of propagation defines the isolation ratio, given in db/db, for 

 the limit of very small conductivity. 



Fig. 15 shows a calculated curve of the forward value of 17 and Fig. 

 16 shows the backward case. The isolation ratio shown in Fig. 17 dem- 

 onstrates surprisingly large bandwidth for values of the order of 200 

 db/db. Fig. 18 portrays propagation characteritics for both forward 

 and backward power flows and provides the interesting observation, in 

 conjunction with Fig. 16, that peak reverse loss occurs in the neighbor- 

 hood of X = \g . 



Fig. 19 is a plot of ai , the transverse wave number, over the fre- 

 quency range. The flatness of the forward wave number means that the 

 position of null moves very little with frequency across the band. Hence 

 the lossless transmission in the forward direction is broadband. Since 

 the forward and backward wave numbers have such radically different 



See Appendix 



