LAMINATIOD TRANSMISSION LINES. I 913 



infiiiitosimally thin laminae approacli validity for laminae of finite 

 thickness as the frequency is reduced, provided of course that we do not 

 go to such extremely low frequencies that the attenuation per wave- 

 lonoth becomes large. We shall show in the next section tiiat the effect 

 of finite lamina thickness is to introduce a frequency dependence into 

 the attenuation and phase constants, in addition to the variations (if 

 any) which av\sv from the fr(M|uencv dependence of the coi-e and sheath 

 impedances. 



We next writc^ down approximate expr(\ssions for Wiv field components 

 in a })lan(^ Clogston 1 line with infinitesimally thin laminae. In the 

 main dielectric we have, from eciuations (22) of Section II, 



(120) 

 ^ 2Zoiyo)Hoy -y, 



111, 1^^ 6 J 



for —\b^ u ^ \h, where i/o is an arbitrary amplitude factor and 

 Z(i(7o) is given by (105). In the stacks the fields are 



Ey 



y^^ Holl + gZo{yo)ihb T ijW, (121) 



E, ^ ±Zo(To)i^oe~"^ 



for 56 ^ I 7/ I ^ ha, where in cases of ambiguous sign the upper sign 

 refers to the upper stack (y > 0) and the lower sign to the low^er stack 

 {y < 0). It should be noted that whereas the tangential field components 

 Hj: and E, are continuous through the stack, the normal field component 

 Ey is discontinuous at layer boundaries. From equation (52) we have, in 

 th(> conducting layers, 



Ey = -(y/g,)H,, (122) 



while in the insulating layers, 



Ey = -(7Aco62)7/.. (123) 



To our approximation, therefore, the only contributions to the average 

 field Ey come from the insulating layers. 



The average current density .A in either stack is iniiform, being 



