9-12 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1952 



H, ^ Ihiha T y)/s, 



(251) 



Ey ^ - \/^i'/i'II.aa T /y)/.s, 



the propagation factor g~i'' + '"'' being understood throughout. To take 

 account of dielectric and magnetic dissipation in the stacks, we write 



i = i' - ii" = [4/(1 _ e)\ - /[el'/d - e)], 



(252) 



M = m' - /m" = [^Mi + (1 - ^)M2] - ?[^Ml' + (1 - d)A 



The average power Po transmitted through the main dielectric is 

 obtained by integrating the real pant of the ^-component of the com- 

 plex Poynting vector |E X H* over unit width of the line; thus 



Po = I f" VJANoHoHtdy = W]U^,H,Hth. (253) 



Similarly, the average power Pi transmitted per unit width of either 

 stack is 



Pi = I £" WVN HoHtiha - y)'/^] dy ^^54) 



= WVJi'H,Hts. 



The average power APo dissipated in the main dielectric per unit length 

 and width of the line is 



APo = ho: r Uo'eX + noHMt]dy 

 J-ib 



* ^255) 



= ^w[eo (mo/co) + Mo ]HoHo b 



= h^iioHoHob(tan 0o + tan fo), 



while the average power APi dissipated per iniit length and width of 

 either stack is 



APi = Ic r [i'EyE* + il"lhH*A dy 

 Jib 



= ^oifi'HoHoS (tan 02 + tan f), 



(25G) 



where 



tan f = — = , . T— r • ^^^0 



M Qixi + (1 — 0)m2 



The attenuation constant due to dielectric and magnetic dissipation is 



