336 



THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1954 



Singularities of Confluent Band Filter 



Recent work on insertion loss design and potential analog methods by 

 S. Darlington and others has fostered the practice of characterizing a 

 network by plotting its natural modes and infinite loss points in the 

 complex frequency plane. In the present case it is instructive to study the 

 effect that reducing dissipation will have on the singularities. A full 

 section confluent band filter has five infinite loss points and eight natural 

 modes. In Fig. 5 the singularities of the passive, confluent band filter 

 discussed earlier are plotted in the complex freciuency plane and identi- 

 fied by the digit one. A single infinite loss point or zero lies on the nega- 

 tive sigma axis, a pair falls at the origin, and a conjugate pair is located 

 near the midband frequency. The natural modes or poles consist of two 

 conjugate double pairs situated at about the upper and lower cut off 

 frequencies of the filter. The distance of the complex singularities from 



LOSS = -20 LOG,o 



2b 



_(a + l) +2b(a + l) 



5 LU 



ZERO LOSS b = 



2a 



ASYMPTOTE b = — 



Fig. 4. Transmission of symmetrical tee section. 



