DIELECTRIC-COATED WAVEGUIDE 1277 



ill which 5i is a first order approximation as given by (10) for a particular 

 mode. Equation (47) then yields a value 62 which is usually accurate 

 enough. To improve the accuracy the same calculation is repeated using 

 62 . Since for small values of 5 a change in 8 affects the right hand side 

 only slightly this method converges rapidly. 



APPENDIX II 



The TEoi Attenuation in the Dielectric-Coated Waveguide 

 The attenuation constant of a transmission line can be expressed as 



IPm 



a = 



2 P 



in which Pm is the power dissipated per unit length in the line and P is 

 the total transmitted power. For the dielectric-coated guide the power 

 Pm is dissipated in the metal walls with finite conductivity a. 



For TKom waves the wall currents are i = Hz{a) {H^ axial component 

 of the magnetic field) and therefore 



1 r'^ a* 



Pm = ^ -—a dip 



Z Jo t- a 



t(T 



where t = skin depth and a- = conductivity. 

 The total transmitted power is 



P = - ^ [ [ E^H*rdr d<p. 

 Z Jo Jo 



We introduce expressions for the field components, which are listed 

 elsewhere ' and carry out the integration. Finally we express the wall 

 current attenuation in terms of the functions (2) and (35); 



Pom Y -12 e^i I -^ , , 



(18) 

 •(^ - 1) (c/i(.i-2 , P.r2) + ^ R^{X2 , pxd^ R,{x, , px,) I -• 



To get an approximation for a thin dielectric coat we use the expressions 

 1(37) and (38) and obtain 



AaM OCm — OCcm I i\Pom -2 /,^n 



1 = = {€ — 1) -V— . (49) 



