286 BELL SYSTEM TECHNICAL JOURNAL 



transmitting bands. A study of this general problem has recently been 

 made, the results of which were presented in two papers both of 

 which appeared in the same issue of this Journal.^ The terminal 

 transducers there described consist of simple non-uniform ladder type 

 structures whose series and shunt impedances are each arbitrarily 

 proportional to the corresponding impedances of the "constant ^" 

 wave-filter and of two-terminal reactance networks added in series 

 or in shunt at the terminating end to complete them. A transducer 

 of this kind practically satisfies the ideal conditions in the transmitting 

 bands, but it does not have a standard image impedance in the atten- 

 uating bands as is desired here. Because of the latter fact, transmis- 

 sion loss calculations can not be made as readily as in a composite 

 wave-filter. 



This paper gives the solution of the terminal wave-filter impedance 

 problem by the logical extension of the use of the general systematic 

 methods of derivation which had led to the derivation of il/-type 

 sections, and the use of composite wave-filter principles. The solution 

 is obtained in two naturally related steps which are, first, the derivation 

 of sections having mid-point image impedances which are desirable as 

 terminal wave-filter impedances and, second, the formation of terminal 

 wave-filter transducers having these image impedances at terminals. 

 A brief outline of these steps will be given here before proceeding with 

 the details. 



The first step, the derivation of suitable terminal sections, is based 

 upon the use of two fundamental operations for deriving structures 

 already mentioned which are applicable to any ladder type network. 

 One of these, the mid-series derivation whose operation will be desig- 

 nated symbolically as Di{s), derives from any prototype a more general 

 ladder type structure whose series and shunt impedances are such 

 functions of the prototype impedances and of an arbitrary parameter, s, 

 that its mid-series image impedance is identical with that of the 

 prototype and thus independent of 5. Its mid-shunt image impedance 

 is, however, a function of this arbitrary parameter, where < 5 ^ 1, 

 and is thus more general than that of the prototype at the correspond- 

 ing termination. The other operation, the mid-shufit derivation desig- 

 nated as Di{s), derives from a prototype another more general structure 

 whose mid-shunt image impedance is identical with that of the proto- 

 type but whose mid-series image impedance depends upon 5. If both 

 of these prototypes, not necessarily the same, have identical transfer 

 constants, then both derived structures having the same value of 



^ "A Method of Impedance Correction," H. VV. Bode, B. S. T. /., October, 1930. 

 "Impedance Correction of Wave-Filters," E. B. Payne, B. S. T. J., October, 1930. 



