LAMINATED TRANSMISSION LINES. I 941 



The avoraso rule of enorj>;y dissipation por unit volume in a lossy di- 

 cloctric hy a harmonically xaryinji; elect lic field of maximum amplitudes 

 A' is just \u)t"l'j~, since the imaginary part e" of the complex dielectric 

 constant coti-esponds to a conductivity ij = we". Similarly the average 

 rate of energy dissipation per vuiit volume in a lossy majj;netic mateiial 

 by a harmonically varying magnetic field of maximum amplitude // is 

 ^o:n"H'. The part of the attenuation constant which arises from di- 

 electric and magnetic dissipation is one-half the ratio of power dissipated 

 per- unit IcMigth of line to total transmitted power, provided of course 

 that the attenuation per wavelength is small. Since the loss tangents 

 of the various materials are assumed small, we can use the fields found 

 for the lossless case to calculate the transmitted and dissipated power. 



If the volume occupied by currents in the stacks is small compared 

 to the volume of the main dielectric, so that we can neglect the power 

 flow in the stacks in the direction of wave propagation compared to the 

 power flow in the main dielectric, then the part of the attenuation 

 constant which is due to dielectric and magnetic dissipation is given by 

 equation (51) of Section II, namely 



ad = lo^VM^Ctan 00 + tan fo) = "" V"'"'"' ^^an <Ao + tan To), (249) 



Aw 



where X„ is the vacuum wavelength and Mor , eor are the real parts of the 

 relative permeability and relative dielectric constant of the main di- 

 electric. This equation will be derived from energy considerations pres- 

 ently. It should be noted that the part of the attenuation constant 

 given by (249) is directly proportional to frequency, provided that the 

 loss tangents are independent of frequency; but it is the same for both 

 plane and coaxial geometry and is independent of all the geometrical 

 factors which describe the size and the relative proportions of the line. 



Equation (249) will probably be sufficiently accurate for all Clogston 

 1 lines having the proportions (stacks thin compared to main dielectric) 

 which we have considered in Part I. As an example wherein we also take 

 into account the power flow in the stacks, however, we shall treat a 

 parallel-plane line with infinitesimally thin laminae backed by high- 

 impedance walls. Then, according to equations (120) and (121) of 

 Section IV, the principal field components in the main dielectric are 



Hi ^ Ho , 



Ey ^ - ViU^oHo , (250) 



and in the stacks, 



