28 BELL SYSTEM TECHNICAL JOURNAL 



k" wave-filter, a half-section being the minimum. Again, mid-series 

 and mid-shunt sections derived from prototypes other than the 

 "constant k" wave-filter, such as have already been indicated in con- 

 nection with the generalized M-type formulae, are other possible 

 units. The two different half-series impedances which join where 

 two mid-series sections are connected together can always be merged 

 into one impedance having the same impedance structure but in 

 general different magnitudes for all elements; a similar merging of 

 shunt impedances can be effected at the junction of two mid-shunt 

 sections. It is here from a structural standpoint that the ladder 

 type is much superior to other types, such as the lattice type over 

 which it has the additional advantage of a smaller number of elements 

 per section. For if one or more sections of the lattice type are in- 

 cluded in the composite network each section must be completely 

 constructed since there is no possibility of merging adjacent im- 

 pedances. 



It is known that among band pass wave-filters having equivalent 

 mid-point characteristic impedances some have positive phase con- 

 stants and others negative at the same frequencies in the transmitting 

 band. The question may be raised as to whether such sections 

 can not be combined in a manner which will give zero phase in addi- 

 tion to zero attenuation throughout the transmitting band. The 

 impossibility of this follows directly from the phase constant theorem 

 previously given, namely, that the phase constant increases with 

 frequency throughout the transmitting band, irrespective of its sign. 

 Combining sections increases the rate of total phase change with 

 frequency. 



Equivalent Substitutions 



There are equivalent structures for certain wave-filter sections as 

 well as for many of their impedances and impedance combimitions. 

 This is of practical importance in design where it is sometimes ad- 

 vantageous to use one form in preference to another. The number of 

 elements, their magnitudes, or both, are some of the determining 

 factors in this choice. 



The wave-filter sections here considered are of the band pass class 

 and their equivalence relations, both as regards current propagation 

 and impedance, are given by the following tabluation in which these 

 wave-filters are referred to by number as in Appendix II. The 

 subscripts 1 and 2 are omitted since it is to be understood that 

 the relations apply on the one hand to mid-series sections having those 

 numbers with a subscript 1 and on the other to mid-shunt sections 



