ELECTRIC WA VE-FILTERS 



299 



1.4 Sequence 1 



As already stated in the Introduction to this paper, the successive 

 wave-filter structures of any class which comprise Sequence 1 are 

 derived from the known "constant ^" wave-filter taken as the initial 

 prototype by performing in succession the operations Di(m), then 

 D^im'), Di(m"), etc. They may be considered as wave-filters of 

 higher and higher order since they contain a greater and greater 

 number of arbitrary parameters. The parameters of the alternate 

 operations Di(s) and D2{s) are in the order oi s = m, m' , m" , etc. 



The small letter m with superscripts is used as the notation for all 

 the parameters in order to denote their association with "mid" of mid- 

 point impedances, since mid-points are under consideration here in 

 ladder type networks. Where the initial prototype is the "constant k " 

 wave-filter, as it is here, I have used a terminology for the derived 

 structures whose basis is the capital letter M with superscripts to 

 correspond with those of the associated small letter parameters. 

 Thus, I have shortened the expression "mid-series derived, parameter 

 m ladder type" to "series .l/-type"; similarly for the other structures. 



"jCormlafrd, h"^ SatJbc^ M-yfypB SMimh M M-^-pe Seri£^M MM-ytype 



_D/m^l 



•Sequence 1. 



The wave-filters of Sequence 1, so designated, can be expressed 

 concisely in the following symbolic manner where any part within 

 brackets represents a ladder type structure. Each operation is to be 

 performed upon the structure within brackets to its right; therefore, to 

 obtain the actual series and shunt impedances which result in any 

 particular case when two or more operations are involved, these 

 operations would begin at the right with Di{m) on [_k], the "constant ^ " 

 wave-filter. 



"Constant ^" = [k~\, 

 Series i/-type = Di{m)[k'], 

 Shunt MM'-ty^e = D2{m%Di{m)\ik']'], 

 Series i/MM/"-type = D,{m")lD.{m')lD,{m)[_k']']'], etc. 



(7) 



A diagram which illustrates this process and gives as well the 

 notation of the resulting image impedances in the successive structures 



