COAXIAL AND BALANCED TRANSMISSION LINES 

 when li = h = l 



289 



'02 



'Ol 



CO 



. wl I 



, Oo , , W, 



eo = Ct \ 1 + ^ cos jiiZai sin — 1 — ~ cot 



Z, 



Oi V 



Oil . er . co/ 

 to = ii cos — — 7 ^— sin — . 



(35) 



For this case 



oj/ 



.^2 = ^ ; cosh 6 ^ ; i^i = Zo^^p Jl -f^^cot^- . (36) 



J , Zo2 ^ ' \ Zoi Z^ ^ 



Zoj 



The band width of the filter for narrow bands is given approximately by 



fi -fi ^ 4<p 



Fig. 7 — A wide-band transformer constructed from coaxial conductors. 

 The design equations for the transformer are 



Zoi = Ri/^; Zo, = Riil - ^')lip'; 



l^v/4fm; Ro = Ril<p\ (37) 



1 + 



Zo2 



The first transformer discussed is a step-down transformer while the 

 one considered here has a step up from the input of the line to the 

 output. The first filter had a mid-shunt impedance characteristic on 

 each end, i.e., the impedance of the band is infinity at the two edges; 

 whereas the transformer with the series open-circuited line has a mid- 

 series impedance, since the impedance given by the last expression in 

 equation (36) goes to zero at the two cut-off frequencies. The range 

 of transformation is about the same for each and hence one type has 

 no particular advantage over the other. 



It is often desirable in filter work to be able to have the impedance 

 of one end of the filter somewhat different from that of the other, i.e., 

 to have the filter act as a transformer of a moderate ratio. An example 

 of this occurs when using a structure composed of short lengths of 



