288 BELL SYSTEM TECLINICAL JOURNAL 



and the critical frequencies belonging to any of these derived sections; 

 there is a slightly different relation for each of the four general groups 

 into which all the different classes of multiple band pass wave-filters 

 may be divided. The MM'-types, etc., are structurally more com- 

 plicated than ilf-types and therefore have preferential value from an 

 impedance standpoint primarily. 



The second step of this solution, the formation of terminal wave- 

 filter transducers, is related to the first step. The method of deriving 

 sections which possess desirable terminal image impedances furnishes 

 through the successive operations the necessary means whereby the 

 final impedance section can be joined to the standard "constant ^" 

 wave-filter without impedance irregularity. There are two such 

 general transducers, the series terminal transducer which connects to 

 the standard mid-series image impedance and the shunt terminal 

 transducer which connects to the standard mid-shunt image impedance. 

 Obviously the series terminal transducer is obtained from the wa\-e- 

 filters of Sequence 1 and is formed by connecting in tandem mid- 

 half sections of successive derived structures, beginning with the 

 series .l/-type and ending in the one having the desired image imped- 

 ance. At each junction point, always between dissimilar sections, the 

 image impedances are identical and in every case it is possible to merge 

 the adjacent series or shunt impedances, thereby considerably reducing 

 the total number of elements in the entire network. This composite 

 wave-filter has the same number of dissimilar mid-half sections as there 

 are arbitrary parameters in the final image impedance function and the 

 sections are functions of one or more of these same parameters, con- 

 taining in succession m, m and ni' , m and m' and m", etc., the final 

 terminal section containing all parameters. The image impedance at 

 one end of this transducer is entirely independent of all these parame- 

 ters, being equal at any frequency to the mid-series image impedance 

 of the standard "constant ^" wave-filter; that at the other end depends 

 upon them all. Fixing the final impedance characteristic determines 

 all these arbitrary parameters and therefore all the sections making up 

 the transducer. The propagation characteristics of these sections, 

 while similar in form, are all different in frequency placement, being like 

 those of il/-types having successive parameters equal to the products m, 

 mm', mm'm", etc. Since m, m', m", etc., are each less than unity, these 

 products form a decreasing sequence. As a result, the attenuation 

 peaks of successive sections are progressively nearer the critical fre- 

 quencies and their combination builds up desirable attenuation 

 characteristics. 



The shunt terminal transducer is obtained in an exactly similar 



