LAMINATED TRANSMISSION LINKS. 1 891 



Ky ;^ —r)Jhc~''% 

 ^ 2 Zo{yo)Hoy 



III, r^ r— 



(22) 



where //,, is an aihilraiy amplilude factor. 



As an example of the use of (20) and (21), suppose that the impedance 

 sheets in Fig. 1 are electrically thick metal walls of permeability jui and 

 (iiip;h) conductivity gi . Then to a N'ery good approximation at all en- 

 gineering fi-ecpuMicies and foi' all oi'dinary dielectrics between the walls, 

 the surface impedance is 



^(to) = (1 + i)/gA , (23) 



where 



8i = \/2/ co/xif/i (24) 



is the skin depth in the metal. We thus obtain from (20) and (21) the 

 familiar formulas 



a = l/rjohgiSi , (25) 



i3 = coVmoco + l/vokli^i . (26) 



It should be noted that in practical cases the inequality (17) on which 

 we based the approximations (20) and (21) does not hold down to the 

 mathematical limit of zero frequency. In the present paper, however, 

 when we speak of "low" frequencies" we shall mean frequencies still high 

 enough so that the approximations (20) and (21) for a and j8 are valid. 

 Generally this will be equivalent to the assumption that the attenuation 

 per radian is small. In our applications this assumption will usually be 

 justified down to frequencies of the order of a few kc-sec~ . 



Xow let us consider transmission lines bounded by coaxial circular 

 cylinders and confine our attention to circular transverse magnetic waves 

 propagating in the z-direction. For these waves the fields are inde- 

 pendent of the angle <f), and the only non-vanishing field components are 

 H0(p, z), Ep(p, z), and E^ip, z). The field components are shown in Fig. 2. 



For circular transverse magnetic fields Maxwell's curl equations in a 

 homogeneous, isoptropic medium leduce to 



dHJdz =-((/ + tcot)7?p , 



(27) 

 d{pH^)/dp = (f7 + iwt)pEz , 



