LAMINATED TRANSMISSION LINES. I \1\\ 



1 , , 



a = Re -77: , . /ry f M , (!()()) 



TjoOlgrs + l/Z„(7o)J 



In general the sheath impedance Zn{yu) will b(» large compared to the 

 impedance \/gs of the stack, since even if the sheath is an electrically 

 I hick metal plate of the same material as the conducting layers, its 

 impedance is 



Z„(7„) = (1 + i'l'gA, (LOS) 



whereas ds will usually be several times the skin thickness 8y in the fre- 

 quency range of interest. If the sheath is free space, its impedance is a 

 fortiori much greater than 1/gs, since then it may be shown that 



Z„(7o) = -iVvinoreor - l)^ (109) 



where ??„ = 376.7 ohms is the intrinsic impedance of free space, and 

 /ior and €or are the relative permeability and relative dielectric constant 

 of the main dielectric. Under most circumstances, therefore, we may 

 neglect l/Z„(7o) in comparison with gs, and obtain the very simple 

 results, 



a = l/r],bgs, (110) 



13 = coVmI^o . (Ill) 



To this approximation the line exhibits neither amplitude nor phase 

 distortion. 



For a coaxial stack of infinitesimally thin layers with Clogston's con- 

 dition satisfied, the stack matrix given in (98) reduces to 



1 



(112) 



9' / 2 2>, 



-— (.p„ - pdj 



where po and p„ denote the inner and outer radii of the stack. It follows 

 from (112) that 



Zrjyo) ^ 1 ^ 1 



pi Igipl - «^) + a/Za{yo) gsiia + |si) + a/Za{yo) ' 



( 1 10) 

 Z,(yo) 1 1 



P2 



\g(b' - pi) + 6/25(70) gS2{b - W + b/Z,{yo) ' 



