896 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1952 



€o = 60 — ?eo = eo(l — i tan </»o), 

 Mo = Mo — •^'mo = Mo(l — i tan fo), 



(50) 



where tan </)o is the dielectric loss tangent and tan fo is the magnetic 

 loss tangent (if any). Inserting (50) into (18) or (43), we find for the at- 

 tenuation due to dielectric and magnetic losses, 



ttd = Re 0- = Re zaj\/)Uo€o(l ~ * tan 0o)(l — i tan fo) 



(51) 

 = I"Vmo«o (tan <^o + tan fo), 



provided that tan <^o and tan f o are both small compared to unity, as they 

 will always be in practice. We shall neglect second-order effects and so 

 regard the dielectric losses, the magnetic losses, and the wall losses as 

 additive. 



III. SURFACE IMPEDANCE OP A LAMINATED BOUNDARY 



The main problem in the theory of Clogston 1 transmission lines is the 

 computation of the surface impedance of a laminated plane or cylindrical 

 boundary having alternate thin layers of conductor and dielectric. Por- 

 tions of such laminated structures are shown schematically in Figs. 3 

 and 4. We shall begin with an analysis, similar to Clogston's, of the plane 

 stack. This will lead to a convenient point of view for the treatment of 

 the mathematically more complicated coaxial stack. 



Let us consider a wave with field components H^ , Ey , E^ , propagating 





Fig. 3 — Portion of laminated plane stack. 



t, 



Reference 1, Section III. 



