428 BELL SYSTEM TECHNICAL JOURNAL 



even approximately constant and hence the filter cannot be resistance 

 compensated throughout the band of the filter. It can, however, be 

 compensated at the frequencies of infinite attenuation and high losses 

 can be obtained at these frequencies. 



The effect of the lack of resistance compensation throughout the 

 band can best be shown by a numerical computation of the loss of an 

 electrical filter as compared to that for a crystal filter. A practical 

 example has been taken of a filter whose band width is 12 kilocycles 

 wide with the mean frequency at 465 kilocycles. In order to obtain the 

 best (2's with reasonably sized coils an arrangement suggested by R. A. 

 Sykes is used. The coils L\ are obtained by using the two equal wind- 

 ings of a coupled coil series aiding so that Li equals the primary induct- 

 ance plus the mutual inductance. Since in an air core coil all of the 

 dissipation is associated with the primary inductance and none with the 

 mutual this gives a high Q for Li. The inductance L2 neutralizes the 

 negative mutual inductance —M and supplies in addition a small 

 positive inductance. The Q of this combination is poor but it makes 

 unnecessary the use of a high resistance Rx for balancing purposes. By 

 this method a much higher effective Q is obtained than can be obtained 

 by a single coupled coil or by three separate coils. 



The calculated curve for the electrical filter assuming Q's of 150 for all 

 the coils is shown on Fig. 7 by the dotted lines. A similar curve for a 

 crystal filter is shown on Fig. 7 by the full lines. As is evident the 

 effect of the coil dissipation is to round off the edges of the pass band 

 and to limit the effective discrimination between the passed and 

 attenuated bands. 



This result does not agree with that given by Landon,"* who in a 

 recent paper makes a comparison between the results obtained with 

 crystal and electrical filters which appears to be somewhat misleading. 

 It is stated in this paper that the electrical filter circuits given are com- 

 pletely resistance compensated and "in crystal filters in which the 

 crystal is confined to the rejector meshes of the network, the limitation 

 is about the same as for electrical filters." By referring to the curves 

 of Fig. 7 it is readily seen that high losses can be obtained outside the 

 pass band with resistance compensated electrical filters, ^ but that the 



*"'M Derived' Band-Pass Filters with Resistance Cancellation," Vernon D. 

 Landon, R. C.A. Review, Oct. 1936, Vol. 1, No. 2, Page 93. 



* The use of resistance for compensating and balancing the attenuation in electrical 

 filters has been worked out bv H. W. Bode and S. Darlington (see U. S. patents 

 2,002,2 16, 1 ,955,788, 2,029,014,'2,035,258). The first work was done for low- and high- 

 pass filters but it was later extended also to band-pass filters. Some of these results 

 are analogous to those of Landon, while others give a better compensation within the 

 transmitted band. The use of the resistance in the crystal filter of Fig. 1 was sug- 

 gested by Mr. Darlington. 



