LAMINATED TRANSMISSION LINES. I 903 



Henceforth we shall take the layers of thickness ti to be such good 

 conductors that the ratio co€i/(/i of displacement current to conduction 

 current is negligible in comparison with unity. For metals like copper 

 this is an excellent appro.ximation at even the highest engineering fre- 

 quencies. Then on introducing the characteristic skin thickness 5i , we 

 have for the conducting layers, 



(Ti = y/ioJuiQi = (1 + i)/5i , 



(74) 



Vi = Vioip-i/gi = (1 + ^OM^i J 

 where 



5i = WoifiiQi . (75) 



For pure copper the permeability and conductivity are 

 Ml = 1.257 X 10~^ henrys-meter~\ 

 gi = 5.800 X 10 mhos -meter \ 

 from which we obtain the numerical values 



cri = 1.513 X 10* (1 + i)v5^ meters"', 



(77) 

 7,1 = 2.609 X 10 * (1 + ^0 V/mc ohms, 



and 



6.609 X 10-5 2.602 ., 



5i = 7^= meters = ~~Jj= mils, (78) 



V jMo VjMc 



where /mc is the frequency in Mc-sec~\ Referring to equations (56) 

 and (69) and bearing in mind the above numerical values, we see that 

 for the conducting layers we have 



Ki ;^ ai = (1 + i)/8i , 



(79) 

 Viy = Vip ^ Tji = (1 4- r)/giSi , 



to a very good approximation, since in our applications the quantity y 

 will always be of the order of 2iri/Xv , where the vacuum wavelength 

 X„ is at least a few meters, while the skin thickness 5i will be at most a 

 small fraction of a centimeter. 



For the insulating layers of thickness ^2 we shall set the conductivity 

 fif2 equal to zero, so that 



0-2 = i(^\/niti , V2 = y/ml^ ' (80) 



We denote the relative dielectric constant and permeability by eor and 

 jU2r respectively; dissipation in the insulating layers may be included 



