COAXIAL AND BALANCED TRANSMISSION LINES 



293 



has been used as a wide-band transformer and as a very narrow-band 

 filter, and experimental curves are given in the next section. The 

 equations connecting the output voltage and current with the input 

 voltage and current can easily be calculated by the methods given above 

 and are 



eo = ei 



Ci + C3 2 ^ 02 ( Ci -\- C 



„ cos" 



C2 



sm" — 



V 



. 2oil 



— jiiZoi 



2oil 



^2 + C3 , Zo? / Cl + C2 



C3 Zoj \ Cl 



to = II 



„ „ „ cos^— + Zooa)C2 sin^ 

 C0Z01C1C3 z' ' 2^ 



Cl -\- C2 2 Co/ Zoi / C2 + C3 \ -2^^ 



^ cos „ 



Cl V Z 



02 



C3 



. 2a)/ 

 sm — 



+ 



Cl + C2 + Cz 



(j^Zfy^C \Cz 



— Z01C0C2 



Zoj 



sm 



2co/ 



Cl 4" C2 . Zoi / C2 -\- Cz 

 Cl Z02 \ C3 



+ sin^ 



Cl + C2 + C: 



\- C2 -\- Cz\ , r^ ry 2 



ry r r + WC2Z01 cos^ 



Zo2C'lU3 J 



a)Z,02 



(47) 



In order that the structure shall transform uniformly over a band of 

 frequencies we must have 



Ci+ C2 

 Cl 



C3 \ _ Zq^ 



C2 + C3 / Z02 



= impedance transformation ratio. (48) 



