LAMINATED TRANSMISSION LINES. II 1171 



plane Clogston 2 A\ith high-impcdaiiee walls, if tiie attemiation constant 

 of the pth mode is not to exceed its "flat" value ao by more than a speci- 

 fied small fraction Aa/cco at a top frequency jm , is easily shown from 

 (468) to be 



ZlifJiigjJm V OCo 



Measurino- /m in Mcsec" and thicknesses in mils, and j)utting in nu- 

 merical values for copper, we obtain 



. X 36.84p /a^ , , 



(/l),ni.s= (^rr N (f N 4/—' (470) 



We see from (461) tiiat for fixed 6, ao is inversely proportional to (a/p) , 

 where a is the total thickness of the stack and p is the mode number, 

 while from (469) the permissible value of U for a certain fractional 

 change in attenuation is inversely proportional to (a/p), and also in- 

 versely proportional to the top frequency fm ■ 



It is interesting to compare equation (470) for the principal mode 

 (p = 1) with equation (199) of Section V for the principal mode in an 

 extreme Clogston 1 line with copper conducting layers. Since in a plane 

 line AR/Ro = Aa/ao , equation (199) may be written 



where 27"! represents the total thickness of copper in both stacks. We 

 expect that for partially filled plane Clogston lines with different pro- 

 portions of the a\"ailable space occupied by stacks, the maximum per- 

 missible layer thickness will be given by equations similar to (470) and 

 (471), with values of the numerical coefficient intermediate between 

 36.84 and 40.62. 



We turn next to a discussion of coaxial Clogston cables with finite 

 laminae. A coaxial Clogston 2 is shown schematically in Fig. 11, and 

 an enlarged view of part of the laminated stack in Fig. 4. The bound- 

 ary conditions which apply to circular transverse magnetic waves on 

 this structure are satisfied if at every point the sum of the radial im- 

 pedances looking in opposite directions is zero. If we knew the explicit 

 relation between the impedances at the two surfaces of the stack in 

 terms of the stack parameters and the propagation constant y, the im- 

 pedance-matching conditions at the inner core and the outersheath 

 would yield a transcendental equation for the propagation constants of 



