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BELL SYSTEM TECHNICAL JOURNAL 



a sharp cut-off, for otherwise the mismatch of impedance near the 

 cut-off frequency causes large reflection losses which prevent the 

 possibility of obtaining a sharp discrimination. 



r^^H 



20 ^ 



Fig. 16 — Lattice network low-pass filter employing transformers, condensers, and 



crystals. 



The effect of dissipation in the transformer on the loss characteristic 

 is not so easy to analyze in this case as in the case of a series coil. The 

 effect can be obtained approximately as follows. Of the three coils of 

 Fig. \5B representing the transformer, the shunt coil has the least 

 dissipation since no copper losses are included in this coil. For an 

 air core coil, the Q of this shunt coil becomes very high and its dissipa- 

 tion can be neglected. The resistance of the primary winding can be 

 incorporated in the terminal resistance as in the series coil type of 

 filter and hence will cause only an added loss. The resistance of the 

 secondary will be in series with the crystal and condenser, and for a 

 reasonably good coil is of the same order of magnitude as the crystal 

 resistance at resonance. Hence its effect will be much the same as 

 cutting the Q of the crystal in half, so that instead of a crystal whose 

 Q is 10,000, we use one whose Q is 5000 and a dissipationless coil. 

 We see then that the Q of the crystal is still the most important factor 

 in determining the sharpness of cut-off in the filter as in the previous 



