ELECTRICAL WAVE FILTERS 



415 



where Z\ is the impedance of the series arm (either 1, 2 or 3, 4 of Fig. 

 1A) and Z^ the impedance of the lattice arm (either 1, 3 or 2, 4 of 

 Fig. lA). Hence, if one pair of branches has a reactance whose sign 



A-ELECTRICAL STRUCTURE 



B- PHYSICAL STRUCTURE 



C-CHARACTERISTIC 

 ATTENUATION 



■CHARACTERISTIC 

 IMPEDANCE 



REACTANCE CURVES 

 FOR EACH ARM 



<0 



FREQUENCY 



/^1 



FREQUENCY 



Fig. 7 — Lattice network employing crystals and condensers. 



is opposite to that of the other pair, a pass band exists, while if they are 

 the same sign an attenuated band exists. Since the lattice is in the 

 form of a Wheatstone bridge an infinite attenuation exists when the 

 bridge is balanced, which occurs when both pairs of arms have the same 

 impedance. 



Let us consider a lattice filter with a crystal in each arm as shown 

 by Fig. IB. The crystals form two pairs of identical crystals, two 

 alike in the series arms and two alike in the lattice arms. In order that 

 a single band shall result it is necessary that the anti-resonant frequency 

 of one arm coincide with the resonant frequency of the other as shown 

 by Fig. IE. It is obvious that the band width will be twice the width 

 of the resonant region of the crystal or at most 0.8 per cent. Since the 

 attenuation peaks occur when the two arms have the same impedance, 

 they may be placed in any desired position by varying the impedance 

 of one set of crystals with respect to the other. If crystals alone are 

 used, these peaks will be symmetrical with respect to the pass band, 

 but if in addition condensers are used with these crystals, the peaks may 

 be made to occur dissymmetrically. In fact they may be made to 

 occur so that both are on one side of the pass band. A narrower band 

 results when capacitances are used in addition to crystals since the 

 ratio of capacitances becomes larger. This may be utilized to control 

 the width of the pass band to given any value less than 0.8 per cent. 



