IDEAL FILTERS 



247 



FREQUENCY IN TERMS OF a 



Fig. 19 — Transfer, reflection, and interaction phase in the transition interval. 



tion. For this purpose the customary resolution of the total insertion 

 loss into transfer constant, reflections, and interaction is not very useful 

 because of the indeterminacies found at the cut-off. This difficulty 

 is avoided by expressing Z i and 6 in terms of the lattice impedances, 

 in which event 



gT = 



(26) 



where 7 is the total insertion loss. 



If iXx and iXy be written for Zx and Zy, the insertion loss and phase 

 shift are given by 



Ji. lA y R 



tan B^ = 



and 



R{Xx + Xy) 



e^y = 



yJ{R'-\-Xx')iR' + Xy^) 



R{X X — Xy) 



(27) 

 (28) 



Equation (27) can be used to confirm our previous choice of the 

 location of the cut-off. At this frequency one of the two reactances, 

 Xx and Xy, will be either resonant or anti-resonant. It is evident 

 from (27) that if the phase shift is to have the desired value, 

 {n -(- 3/4)7r, at the assumed cut-off the non-resonant impedance must 

 have the magnitude R. That this value is approximated follows from 

 the symmetrical spacing of transfer constant and image impedance 



