504 BELL SYSTEM TECHNICAL JOURNAL 



It will be recalled in the case of the telephone circuit that the intro- 

 duction of inductance coils at regular intervals in the circuit produced a 

 remarkable change in the transmission characteristic. Over a broad 

 band of frequencies the attenuation was reduced and made fairly uni- 



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c, 4= i Z„ 



Fig. 8 — Electrical equiv^ilent of simple low pass type of network which occurs fre- 

 quently in this work 



form over that range while beyond a critical frequency called the cut-oft" 

 frequency the attenuation became very high. In the ideal filters with 

 zero dissipation the transmission characteristics are of the same nature 

 but more clear cut. Structures of this type with infinitely repeated 

 sections will have one or more transmission bands of zero attenuation 

 and one or more bands having infinite attenuation. The impedance 

 characteristics of such a structure measured from certain characteristic 

 points will be pure resistance more or less uniform in the transmission 

 bands, and pure reactance in the attenuation bands. These termina- 

 tions are mid-series; that is, the entering element being one-half of 

 the normal series element; or mid-shunt; that is, the entering element 

 being twice the impedance of the normal shunt element. The cor- 

 responding impedances are called the mid-series and mid-shunt 

 characteristic or iterative impedances. 



If we retain the first few sections of such a structure and terminate 

 them with a resistance which is equal to the resistance impedance of the 

 infinite line from which they were taken, the characteristics are sub- 

 stantially unchanged. It is understood, of course, that this resistance 

 equals approximately the resistance impedance of the remainder of the 

 infinite line at most of the frequencies in the transmission band in 

 which we are interested. 



The presence of small amounts of damping in the various elements 

 also has but slight effect on the general characteristics. These results 

 could in general be readily applied to the various telephone transmis- 

 sion problems because the source and load between which the filter sys- 

 tem was inserted generally had or could be made to have a resistance 

 impedance nearly equalling the mid-series or mid-shunt impedance 

 of the filter within the transmission band. The filter and terminating 

 impedances may then be said to be matched. Where adjacent sections 



