. The Bell System technical journal . RESISTANCE COMPENSATED BAND-PASS CRYSTAL FILTERS 427 possible to take these resistances outside the lattice and combine themwith the terminating impedance, leaving all the elements inside thelattice dissipationless. The two remaining arms of the lattice have theimpedance characteristic shown on Fig. 6A. A lattice filter has a passband when the two impedance arms have opposite signs and an at-tenuation band when they have the same sign. When the impedanceof two arms cross, an infinite attenuation exists. Hence the character-istic obtainable with this networ
. The Bell System technical journal . RESISTANCE COMPENSATED BAND-PASS CRYSTAL FILTERS 427 possible to take these resistances outside the lattice and combine themwith the terminating impedance, leaving all the elements inside thelattice dissipationless. The two remaining arms of the lattice have theimpedance characteristic shown on Fig. 6A. A lattice filter has a passband when the two impedance arms have opposite signs and an at-tenuation band when they have the same sign. When the impedanceof 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 condenserstake the place of the essentially dissipationless crystal. In this case thedissipation due to Li and L2 can be balanced as before and the onlyquestion to consider is the effect of the dissipation associated with L3and 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 asecond series tuned circuit having the same resonant frequency as thefirst 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 arethe same and therefore the value of Q equal, it is possible to replace theseries resistance by a shunt resistance and hence compensate it byvarying the resistance Rx. Since, however, the reactance of the tunedcircuit varies from a negative value through zero to a positive valueover the pass band of the filter, the value of this shunt resistance is not 428 BELL SYSTEM TECHNICAL JOURNAL even approximately constant and hence the filter cannot be resistancecompensated throughout the band of the filter. It can, however, becompensated at the frequencies of infinite attenuation and high lossescan be obtained at these frequencies. The eff
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