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BELL SYSTEM TECHNICAL JOURNAL 



spectively to the lattice crystal filters of Fig. 8. The equivalent lattice 

 configurations are shown on Fig. 9. The first two filters have series 

 coils which inherently give low-impedance filters. The second of these 

 is equivalent to the filter of Fig. 8 (a) with one pair of the crystals 

 eliminated. If the inductance L^ were eliminated from Fig. 9 (a) or (b) 

 the filters will be resistance compensated, for all of the resistance will 

 be on the ends of the filter. Furthermore if a small amount of coupling 

 is allowed between the two end coils, the effect of this will be to intro- 

 duce the small coil L2/2 in the desired place as can be seen from the T 

 network equivalent of a coupled coil as shown on Fig. 10. Further- 

 more if the coils are air core, no dissipation is associated with the mutual 

 inductance and hence if coupled coils are used the networks still have a 

 resistance balance. Similarly the filters shown on Figs. 9 (c) and (d) are 

 equivalent to the high-impedance type filter shown on Fig. 8 (b) with all 

 crystals present or with crystals missing from the lattice arms. By 



-^WD^-i-^WO"^- 



PIM 



SIM 



PS-M 



PS-M 

 S+M 



PS-M 

 P+M 



Fig. 10 — T and tt network equivalences of a transformer. 



employing coils with a small amount of mutual inductance these types 

 can also be made with a resistance balance. They can also be made to 

 balance for physical coils by employing the resistances shown. It is 

 obvious from the equivalent lattice structures that these networks have 

 limitations on band widths and allowable attenuation which are not 

 present for the original lattice structures of Fig. 8. However, for filters 

 whose pass bands are less than the maximum pass bands, useful results 

 can be obtained. 



Another method for obtaining results similar to that obtainable in a 

 lattice network is to use a hybrid coil with series aiding secondaries 

 which are connected to a crystal and a condenser as shown on Fig. 11. 

 This circuit, which has been used extensively to provide a narrow band 

 crystal filter in telegraph work, was invented first by W. A. Marrison ^ 

 of the Bell Telephone Laboratories. Under certain circumstances this 

 configuration can be shown to give results similar to the narrow-band 



« Patent 1,994,658 filed June 7, 1927, granted March 19, 1935. 



