REDUCTION OP SKIN EFFECT LOSSES 495 



The flat range of the conventional Une might be alternatively increased 

 to equal that of the laminated line by decreasing D to a, new value Di. In 

 this case the attenuation would be increased by a factor 



l/^^(l)(w) 



just the square root of the factor achieved by changing <r, but still a large 

 number. 



In the frequency range in which the attenuation of the laminated line is 

 governed by the skin depth 8w, and is therefore increasing linearly with fre- 

 quency, this attenuation is less than the attenuation of the conventional 

 line by a factor 



c8^~V3\8) ^^'^^ 



It is interesting to note that the position of this region is governed by the 

 conductivity of the conducting laminations, but that the attenuation is 

 independent of the conductivity. 



Considerable theoretical and experimental work has been carried out 

 on laminated transmission lines by the author's colleagues. The following 

 report therefore will be limited to bringing out some of the fundamental 

 ideas in a simple way. We will for instance consider only planar systems so 

 that the results will be only approximately applicable to real transmission 

 lines. Other papers will more fully develop the formal theory, particularly 

 for cylindrical systems, and discuss the practical and experimental aspects 

 of the problem. 



II. Skin Effect 



We shall begin the discussion with this section by considering skin effect 

 in various kinds of conducting media. We will first derive the skin depth 

 equation (I-l) for an ordinary conductor like copper, and then discuss the 

 behavior of a composite conductor made up of many thin, insulated con- 

 ducting laminae. This second discussion will be first carried out for the case 

 of infinitesimally thin laminae, and then in Section III the effects of the 

 finite thickness of the conducting sheets will be considered. 



Let us first set down and integrate Maxwell's equations in a form that 

 will be useful in all our following discussions. Referring to the orthogonal 

 coordinate system in Fig. 3 we shall be concerned with fields that have no 

 variation along the z-axis and for which the z-component of electric field 

 is zero. The only component of magnetic field is then H-^ and the field equa- 

 tions become, in rationalized MKS units. 



