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BELL SYSTEM TECHNICAL JOURNAL 



a transformer. As usually used, however, the impedance of the trans- 

 former is much lower than that of the filter and as a consequence the 

 band-pass characteristic of the filter is lost. As a result the network 

 passes only a single frequency and gives results similar to those obtain- 

 able with a very sharply tuned circuit. By placing a crystal in the 

 other arm of the network as shown by Fig. 14, '^ this configuration can 

 be made equivalent to the filter shown in -'ig. 12. 



It is obvious from the equivalence of Fig. 13 that the configurations of 

 Fig. 11 and Fig. 14can also be used togiveawide-bandfilter. This follows 

 since the series inductances can be taken inside the lattice and the low- 

 impedance crystal filter of Fig. 8 (a) results. The Q of the coils included 

 in the filter will ordinarily not be high since the inductance is obtained 

 by a difi"erence of primary and mutual inductances, and a better result 

 will be obtained by making the secondary coupling high and including 

 physical coils in series with the crystals. 



Fig. 14 — A three-winding transformer crystal filter with two crystals. 



We see then that all of the resistance compensated wide-band filters 

 are equivalent to the lattice filters of Figs. 8 and 12, and all their design 

 equations are known when the design equations of the equivalent 

 lattices are calculated. This requires two steps, first the calculation of 

 the spacing of the resonant frequencies of the network to give the 

 required attenuation and secondly the calculation of the element values 

 from the known resonances by means of Foster's theorem. Such 

 calculations are familiar in filter theory and hence only the results are 

 given here. The results are given in Tables I, II, and III for the 

 network of Figs. 8 (a) , 8 (b) and 12 respectively. These values are given 

 in terms of the characteristic impedance Zo of the filter at the mean 

 frequency, the lower and upper cut-ofif frequencies /i and/2 respectively 

 and the 6's of the network. These last are parameters which specify 



' This configuration is covered by patent 2,001,387 issued to C. A. Hansell. 



