2>2 BELL SYSTEM TECHNICAL JOURNAL 



= tV + 2 coth~^ ^ = -iTT + cosh 1 — 



l+i^ 



1 + - 7 

 = iV + log ^, . (15b) 



1 + I y 

 = i ^ — sinh~i —j i, (15c) 



1, o+r+(iy 



where y = a -{- i ^. 



In these formulas Z1/Z2 = 7^ and Zi Z2 = k"^ might be expressed 

 in terms of the resonant and anti-resonant complex frequencies of 

 Zi and Z2, the frequencies being made complex quantities so as to 

 include the damping. Where there is no damping, that is, where all 

 network impedances are devoid of resistance, the simplified forms 

 of these expressions are given by formulas (8) and (9). The use of 

 these formulas for designing wave filters having assigned pass bands 

 is explained at page 23. 



