1230 THE BP:LL system technical JOUKNAL, SEPTEMBER 1957 



and the points of maximum power transfer are 



_ (2n + l)7r 



(67) 



where n is any integer. 



As is well known, complete power transfer from line to line 1 is 

 possible if and only if the (modified) phase constants (So and j8i are equal. 

 In general the maximum power transierred to line 1 depends on the ratio 

 of the coupling coefficient to the difference in phase constants, and if this 

 ratio is small, then 



(Pl)max ^ 4/c7(/3o - iSi)l (68) 



If the difference in phase constants is not large enough to prevent un- 

 desirable power loss from line 0, an alternative possibility, as Miller 

 has shown, is to increase the attenuation constant of line 1 while leaving 

 the attenuation constant of line as nearly unchanged as possible. We 

 can get an idea of the required attenuation difference from the following 

 approximate treatment. 



Let 



7o = ao + i^o , 

 7i = «i + i^i , 



(69) 



and assume that 



Then 



2/c/(7o -7i)|'«l. (70) 



2k' 



r ^ 7u - Ti - 7 X , (71) 



(To - 7i) 



and 



2 



mi ?t; -7i 



7^2 ^ — 70 + 



7o — 7i 



2 



k' 



7o - 7i 



(72) 



We are interested in the power in lineO. From the first of equations (60), 

 we have 



ao{z) 



2 



1+ " 



„"'2- "■ „">i^ (7'i) 



e — -, r-„e 



(7o - 7i)-J (7o - 7i)^ 



