COAXIAL AND BALANCED TRANSMISSION LINES 



285 



Combining these equations we have 



Co 



coll ■ ry . ^l\ 



ei COS Pi^ox sin — , 



to — ll COS — 



V 



Zoi tan 



1 + 



Zo, tan 



(jil\ 



co^a 



Sin 



J^i 



Zoi cot 

 Z02 tan 



oil 



ioh 



(20) 



In order to interpret this equation in terms of transformer theory, it can 

 be shown that equations (20) are identical to the equations for a perfect 

 transformer and a symmetrical filter. To show this, consider the 

 circuit of Fig. 6, which consists of two half-sections of a symmetrical 



Fig. 6 — Transformer and filter. 



filter separated by a perfect transformer having an impedance step- 

 down (p^ to 1. The characteristic impedance of the first filter is (p- 

 times that of the second filter. The equations for the first section, the 

 transformer, and the last section are respectively 



ei = ei cosh -^ — iiKi sinh -z\ ii = ii cosh -^ — -^ sinh — ; 

 L L L Ai / 



ii = ipii\ ei = ei/<p; (21) 



eo — ei cosh ^ — iiKi sinh - ; ^ = ii cosh ^ — -^ sinh ^ • 

 LI z A2 L 



Combining these equations on the assumption that KijKi = ip^, we 

 have 



Co = - \_ei cosh r — ijKi sinh F] ; 



io = (p\ 



ij cosh r — 



ei sinh F 

 Ki 



(22) 



