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BELL SYSTEM TECHNICAL JOURNAL 



in effect we have to use crystals with twice the ratio of capacitances 

 than can be used in the balanced case. 



APPENDIX 



A Determination of the Resonant Frequencies 

 OF Lattice Filters 



In order to obtain the element values of the filters shown in this 

 paper it is necessary to determine the resonant frequencies of the 

 elements in terms of the desired characteristics of the filter. It is the 

 purpose of this appendix to show how these resonant frequencies may 

 be derived. 



The simplest type of band-pass filter section — referred to as the 

 elementary section — is one in which there is one resonance in each 

 arm of a lattice filter as shown in Fig. 23A. The impedance of the 



A B 



Fig. 23 — Lattice filter configuration for elementary band pass sections. 



series and lattice arms takes the form 



Zi 





Zo = 



0)C2 



1 



CO" 

 COfi- 



(10) 



where co is It times the frequency /, /a the resonant frequency of the 

 series arm which also is the lower cutoff of the filter, and/^ the resonant 

 frequency of the lattice arm which is also the upper cutoff. 



The characteristic impedance and propagation constant are from 

 equation (3) 



Z„=4z:z, = J--vV[l-^]('-~.). 



\ C(;-CiC2 L '^-i' J \ ^B" J 



It is desirable to correlate the value of m with the frequency of infinite 

 attenuation in the filter. Since the filter will have an infinite attenua- 



