1202 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1952 



Then the term i(ji-\/jH m (588) has a small real part, namely 



oid = IwVisV (tan <^2 + tan f), (590) 



where 



tan l = ^= '^\ + ^^ - '^^i ; (591) 



and Old is the part of the attenuation constant which is due to dielectric 

 and magnetic losses. If there were no dielectric or magnetic dissipation, 

 the second term on the right side of (588) would be purely real and would 

 represent the attenuation due to ohmic losses in the conducting layers. 

 We neglect the small change in this term when /I and e are complex, and 

 thus as usual regard the metal losses, the dielectric losses, and the magnetic 

 losses as additive. 



We observe that aa is the same for both plane and coaxial lines, and is 

 also independent of the mode number p. Although derived here for the 

 case of infinitesimally thin laminae, the same expression may be used for 

 lines with finite laminae, so long as the conducting layers are moderately 

 thin compared to the skin depth. The dielectric and magnetic losses do 

 not depend on the overall dimensions of the transmission line, but are 

 directly proportional to frequency provided that the loss tangents do not 

 vary with frequency. 



If it should be necessary to calculate the dielectric and magnetic losses 

 in a partially filled Clogston line where the dissipation factor of the main 

 dielectric is markedly different from the dissipation factoi* of the stacks, 

 ttd may be obtained, using the method described in Section VII, as half 

 the ratio of dissipated power per unit length to transmitted power. In this 

 calculation we may use the field components given in Sections IX and X 

 for the various modes in partially filled lines. 



ACKNOWLEDGMENTS 



Many people with whom I have discussed the theoretical and practical 

 aspects of the laminated transmission line problem at various times have 

 offered comments and suggestions which are reflected in this paper. I have 

 especially to express my appreciation to A. M. Clogston, H. S. Black, and 

 J. G. Ki'eer, Jr., for stimulating and helpful discussions. 



My thanks are also extended to Mrs. M. F. Shearer, Mrs. D. R. Furs- 

 don, and Miss R. A. Weiss for the extensive numerical computations which 

 they carried out in coimection with this study, and to Miss D. T. Angell 

 for preparation of the curves and diagrams. 



