568 BELL SYSTEM TECIISICAL JOURNAL 



the advantage over other formulae and calculation methods of re- 

 quiring for every alteration in a composite wave-filter only a partial 

 recalculation rather than a more or less complete one. In addition, 

 by its use much of the otherwise necessarj' calculation can be elimi- 

 nated through the means of graphical representation. 



The main object of this paper is to present this chart calculation 

 method of determining composite wave-filter transmission losses, 

 giving its theory, the necessary charts, and an application of its use. 



Strtiditre of Wave-Filter Networks 



The ladder type of recurrent network having physical series and 

 shunt impedances 2i and S2, respectively, as shown in Fig. 1, is the 



Kig. 1 — Ladder Type Recurrent Network 



one most frequently employed for wave-filters. Also any passive 

 transducer having two pairs of terminals can theoretically be reduced 

 to the form of the ladder type. Hence, in what follows the ladder 

 type terminology will be used understanding, however, that other 

 structural types may also be included; for example, such as are deriv- 

 able from the ladder type by the substitution of an equivalent trans- 

 former with mutual impedance for T or n connected inductances, 

 or the lattice type. The figure illustrates, from left to right, one mid- 

 series section, one mid-half section (a dissymmetrical half section 

 terminated at mid-series and mid-shimt points), and one mid-shunt 

 section all connected so as to give a uniform structure.^ The charac- 

 teristic impedances of the ladder type at mid-series and at mid-shunt 

 points are K\ and Ki, respectively. 



The majority of wave-filter networks are mil miifunn iliroii^lmut 

 their length but have a composite structiu'e designeil as gi\en in the 

 paper (B. S. T. J., Jan., 1923) already mentioned. That is, the 

 interior or mid-part of a composite wave-filter consists of mid-series, 



' The same network may also be considered as made up in other ways; for e.\ample, 

 two mid-series and one mid-half sections, one niidhalf antl two mid-shunt sections, 

 or five mid-half sections. 



