RESISTANCE COMPENSATED BAND-PASS CRYSTAL FILTERS 427 



possible to take these resistances outside the lattice and combine them 

 with the terminating impedance, leaving all the elements inside the 

 lattice dissipationless. The two remaining arms of the lattice have the 

 impedance characteristic shown on Fig. 6A . A lattice filter has a pass 

 band when the two impedance arms have opposite signs and an at- 

 tenuation band when they have the same sign. When the impedance 

 of two arms cross, an infinite attenuation exists. Hence the character- 

 istic obtainable with this network is that shown on Fig. 6B. 



Next let us consider an electrical filter in which coils and condensers 

 take the place of the essentially dissipationless crystal. In this case the 

 dissipation due to Li and L2 can be balanced as before and the only 

 question to consider is the effect of the dissipation associated with L3 

 and C3. In a similar manner to that employed for the coil we can show 



Fig. 6 — Characteristics obtainable with the crystal filter of Fig. 1. 



that a series tuned circuit with a series resistance Ri is equivalent to a 

 second series tuned circuit having the same resonant frequency as the 

 first shunted by a resistance Ri where 



where Q = 



1 



C0C4 



CO 



1 - -— 



2 



R, 



(3) 



At two frequencies for which the absolute values of the reactances are 

 the same and therefore the value of Q equal, it is possible to replace the 

 series resistance by a shunt resistance and hence compensate it by 

 varying the resistance Rx. Since, however, the reactance of the tuned 

 circuit varies from a negative value through zero to a positive value 

 over the pass band of the filter, the value of this shunt resistance is not 



