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BELL SYSTEM TECHNICAL JOURNAL 



and throughout the band the value of ip does not differ much from this 

 value for narrow-band filters. 



Hence the structure of Fig. 8 acts as a narrow-band coupling unit 

 which introduces a transformation from input to output. For narrow 

 bands it is easily shown that the image impedance at the middle of the 

 pass band is given by the expression 



K,= 



(fm) 



^ (f f\ VZ01Z03 -^r- 



^ U2 — Jl) Z03 



(45) 



The design equations for this transforming filter are 



h = 



4/2* 



l2 = 



1-1 



/l /2 



Zoi — "T 



^Riih-h) 



Zt)i — 



xi?r(/2-/i) 



fm<P 



Zoo — 



4 V^/m 



TRT(f2-fl) . 



4/„<^Hl + <p) ' 



Rr 

 Ri 



= <P 



(46) 



V. Filters and Transformers Employing Transmission Lines 



AND Condensers 



Condensers can be constructed for high radio frequencies which have 

 little dissipation and hence they can be combined with short sections 

 of transmission lines to produce filters and transformers. Combina- 



V/J/J^^/^?^?.'. 



zo, 





Fig. 9 — A transformer or filter using condensers and coaxial conductors. 



tions of lines with condensers have the advantages that much more 

 isolated bands can be obtained, in general narrower pass bands can 

 be obtained, and at the lower frequencies shorter sections of lines can 

 be employed if they are resonated by capacities. Also, when such 

 structures are used as interstage coupling units working between 

 vacuum tubes, they usually will have to incorporate the grid to fila- 

 ment and plate to filament capacities as part of the coupling circuit. 

 Hence it is desirable to consider combinations of transmission lines 

 and condensers as filters and transformers. 



One of the simplest and most useful types of band-pass filter using 

 transmission lines and condensers is shown in Fig. 9. This structure 



