THE FIELD DISPLACEMENT ISOLATOR 



883 



2 7^2 



a2 = K 



tr / 2 

 — iMr 



kr') 



+ ai" 



(II -2) 



where nr and /iv are the relative diagonal and off-diagonal terms of the 

 Polder tensor, respectively, K is the free space wave number and £r is 

 the relative dielectric constant. 



Mr = 1 + 



4:7rMsyo}o 



kr = ± 



4:irMsyo} 



7 = 2.8 X 10^ cycles/sec/oersted 

 4iTrMs = saturation magnetization in gauss 

 Ho = static magnetization in oersteds 

 COo = yHo 

 27r 

 X 



K = 



The following transcendental equation results from satisfying the 

 boundary conditions on E and H:^ 



(II -3) 



tan aia\jjLT(X2 + kr^ tan a28] + (/Mr — kr) ai tan a2B tan ai6 



+ 



= 



Oil 



(|3^ — K'HrSr) tan aia tan q:25 + ai(ju,Q;2 — Av/3 tan aaS) 



where /3 is the propagation constant. 



The minimum nontrivial value of an causing a null to appear at the 

 ferrite face is ai = t/g. Placing this value in (II • — • 3) produces the fol- 

 lowing transcendental equation for the null: 



TT / 2 



a 



(jur — kr) tan a28 



UrOCi — kr^ tan a28 



-j- tan aih =0 



(II -4) 



y///////////////^//////////////////////" "// 



••• •; ' 



>v2v; 



^////y/////yy/////y//////////w/vy//'/////,v/>'>///>/^////y/'^ 



=. a 



.4..4.-b-J 



Fig. 6 — Full height geometry. 



