426 BELL SYSTEM TECHNICAL JOURNAL 



Defining Q, the ratio of reactance to resistance, asQ — ooLijRi, we have 



R, = i?i(l + Q') ; L2 = Li(l + 1/(32). (2) 



This relation holds strictly only for a single frequency, but over a 

 narrow-band filter the relation holds quite accurately. 



Employing this conception, the lattice network can be reduced to 

 that of Fig. 4 in which a resistance R parallels each arm of the lattice. 



Fig. 4 — Filter showing paralleling resistance. 



This is made possible by the adjustable resistance Rx which is fixed at 

 such a value that the parallel resistance associated with the inductance 

 Li + 2L2 is equal to that associated with Li. Then by employing the 

 two lattice equivalents shown on Fig. 5, first proved by the writer,' it is 



c 



c 



A/W-- 



(a) 



r V^ 1 



"l V\A ^ 



(b) 



Fig. 5 — Lattice network equivalences. 

 ' Reference 1, page 418. 



