416 BELL SYSTEM TECHNICAL JOURNAL. 



The use of more crystals than four, in any network configuration 

 employing only quartz crystals and condensers can be shown to result 

 in no wider bands than 0.8 per cent, although higher losses can be ob- 

 tained by the use of more crystals. Hence by the use of quartz crys- 

 tals and condensers alone, a limitation in band width to 0.8 per cent 

 is a necessary consequence of the fixed ratio of capacitances Co/Ci of 

 equation (3), 



Filter Sections Employing Crystals, Condensers and Coils 

 As was pointed out in the last section, filters employing only 

 crystals and condensers are limited to band pass sections whose band 

 widths do not exceed about 0.8 per cent. This band width is too nar- 

 row for a good many applications and hence it is desirable to obtain a 

 filter section allowing wider bands while still maintaining the essential 

 advantages resulting from the use of sharply resonant crystals. Such 

 filters can be obtained only by the use of inductance coils as elements. 

 Since the ratio of reactance to resistance of the best coils mounted in a 

 reasonable space does not exceed 400, attention must be given to the 

 effect of the dissipation. 



The effect of dissipation in a filter is two-fold. It may add a con- 

 stant loss to the insertion loss characteristic of the filter, and it may 

 cause a loss varying with frequency in the transmitting band of the 

 filter. The second effect is much more serious for most systems since 

 an additive loss can be overcome by the use of vacuum tube amplifiers 

 whereas the second effect limits the slope of the insertion loss frequency 

 curve. Hence, if the dissipation in the coils needed to widen the band 

 of the filter has only the effect of increasing the loss equally in the 

 transmitting band and the attenuating band of the filter, a satisfactory 

 result is obtained. The question is to find what configuration the 

 coils must be placed in with respect to the crystals and condensers in 

 order that their dissipation will not cause a loss varying appreciably 

 with frequency. 



Not every configuration will give this result, as is shown by the fol- 

 lowing example. The equivalent circuit of the crystal shown by Fig. 2A 

 can be transformed into the form shown by Fig. 8^ where the ratio 

 Ci/Co = 125. This gives the same reactance curve as before, limited 

 to a width of 0.4 per cent. Now suppose that we add an electrical 

 anti-resonant circuit in series with the crystal — Fig. 85 — resonating 

 at the same frequency and having the same constants as the anti- 

 resonant network representing the crystal. If this circuit were dissipa- 

 tionless we could combine the two resonant circuits into one with twice 

 the inductance and half the capacitance of that for the crystal alone 



