310 BELL SYSTEM TECHNICAL JOURNAL 



impedance characteristics. It contains those frequencies in the trans- 

 mitting bands where all image impedances become equal to R and 

 where the series impedances belonging to the different orders become 

 resonant. These resonant frequencies fu, f^r, etc., are the same as 

 those of Zik\ that is, where Zik = 0. The relation is 



fuhr "'fnr = V/1/2 ' ' ' /.„• (24) 



It may be noticed that relations (20) and (21) for Groups 1 and 2 are 

 the only ones which depend upon the parameter g. The proofs of all 

 these relations are to be found in Appendix I together with certain 

 reactance frequency theorems. 



Part 2. Formation of Terminal Wave-Filter Transducers 



2.1 General Design Method 



In the Introduction of this paper the method of forming the two 

 general kinds of transducers under consideration has been quite fully 

 discussed. Hence, only a brief repetition will be made here. 



The series terminal transducer is designed for connection to the 

 standard mid-series image impedance, Wn, and is formed by con- 

 necting in tandem an arbitrary number of single mid-half sections of 

 successively derived structures in Sequence 1, beginning with the 

 series il/-type. The image impedances are identical at each junction 

 and adjacent series or shunt impedances can be merged. The number 

 of arbitrary parameters in the final image impedance function is equal 

 to the number of mid-half sections which have been so united. This 

 impedance characteristic is then fixed to give a desired physical result, 

 whence the parameters of all intervening mid-half sections are like- 

 wise fixed. The attenuation peaks of successive sections are nearer 

 and nearer the critical frequencies. 



The shunt terminal transducer for connection to the standard mid- 

 shunt image impedance, W^k, is designed in a similar manner from the 

 wave-filters of Sequence 2, beginning with the shunt J/-type. 



From a theoretical standpoint the more mid-half sections used in 

 this composition to obtain a desired constant terminal impedance, the 

 better the possible approximation. The same method of solving for 

 the parameters can be used in all cases. But, in practice, two sections 

 appear to be sufficient. 



2.2 Transducers Having Tivo Parameters 



Proceeding on the above basis the two-parameter structures of 

 Fig. 10 are obtained. Their formation will be obvious from Figs. 



