DIELECTRIC-COATED WAVEGUIDE 1275 



TEo^ waves: ^x = -^ {x{ - VoJ)h\ (44) 



If we write for the perturbed propagation constant 



we get with (3) and (4) : 



\ 2 §71711 A 



Ax = a Ay 



Pnm 



Vnm 



and 



in which 



X2 = (e — 1 + Pnm^) 



2 



_ X _ Pnm X 

 Acnm ^TT 0, 



i Using these expressions in (43) and (44) we finally get approximate 

 I formulae for the perturbation of the propagation constant as caused 

 ! by the dielectric coat: 



TMnm waves : — = 5 



TE„„ waves: — = ■ 5 (4o) 



n^O Tnm Pnn, — Tl^ C 1 — Vnm 



n^Tjy A7 Pom e — 1 .3 



1 Eom waves : — = '-— 8 . 



Tom 'J 1 Vom' 



The series expansions used so far hold only when (1 — p)x « 1. Approxi- 

 mate expressions which require only (1 — p) <K 1 are:^ 



. 1 - p , 



sni — 7^ V p.r- - n^ 



Vni^x, 8x) = ^ ^' 



^ W py? — r? 



Sn{x, 8x) = - 



TT (I - p)x _ 



Vp COS (— 7^ Vpx'- -in- 1)2 j 



