REDUCTION OF SKIN EFFECT LOSSES 515 



where A is some constant. Matching fields dX y = dy we obtain the char- 

 acteristic equation 



m tanh m = - %(i (V-6) 



We might also have obtained this equation by placing h = and s = dm 

 equation (IV-10). 



We can verify that an approximate solution of equation (V-6) is 



(f^) = T[i-M-J -1.3.V- (V-7) 



Proceeding as before, we find for the propagation constant 



*„ = Vc;;w[i + ^,(^y]. (v-8) 



and for the attenuation 



If we place w = 1 in equation (V-9) and compare the result with equation 

 (IV-21), we see that the attenuation of the transmission line has been indeed 

 decreased by completely filling it with laminations, and without sacrifice of 

 the frequency independent characteristic. Furthermore, it is no longer nec- 

 essary to supply a dielectric with dielectric constant equal to e. This case 

 clearly represents something unfamiliar in the way of transmission Unes. 

 We might in fact consider the laminated material as a new kind of trans- 

 mission medium. 



In order to visualize this situation more completely, let us study the 

 distribution of fields and currents inside the transmission line. We will be 

 interested in H^, Ey which can be obtained from equations (11-10) and (V-8), 

 the current J = d Ex, the Poynting vector P = 1/2 Real part {EyH*), 



I r'^ /"^ 



the total current / = / Jdy and the total power W = l Pdy. From 

 equation (V-7), we can take f equal approximately to -— and obtain 



ff, = cos^ (V-10) 



E, = V;Vi cos ^ (V-11) 



