16 BELL SYSTEM TECHNICAL JOURNAL 



3. Characteristic Equations of TEoi and TMn Modes 



The mode which one desires to propagate through the wave guide is the 

 TEui mode. In a straight wave guide with perfectly conducting walls 

 it is characterized by the following equations: 



w = 3-1 



Erx = £.1 = ^^1 = 3-2 



£^1 = £i6^"'-''Vi(y) = e,J,(y) 3-3 



^.1 = - '^' A(y) 3-4 



H.r= -^ My) 3-5 



JPOV 

 In these equations 



7] = A/ — = 377 ohm (intrinsic free space resistance) 3-6 



27r 



Ao 



3-7 



y = xr 3-8 



In a perfectly conducting wave guide 



Xo = ^— 3-10 



(cutoff factor) 3-11 



l\ = jdoVl - v' = jdx 3-12 



If the wave guide has the conductivity of g mho m, its intrinsic high 

 frequency impedance is 



Z,- = (1 + j)R^ - (1 + i)3-i.4 ^^ * 3-13 



This changes \ to 



(1 - j)RiV 



\X = Xn 



and 3-14 







* Ref. 4 pg. 83. 



t Compare Ref. 4, pg. 390. 



