270 BELL SYSTEM TECHNICAL JOURNAL 



As a filter is usually designed to match two fixed impedances between 

 which it must operate, a change in its impedance caused by element 

 variation will produce a mismatch between the filter and its termi- 

 nating impedances which w ill result in reflection loss in the transmitting 

 region. However, the reflection loss arising from impedance deviation 

 caused by element variation is usually much less troublesome than the 

 shift in the attenuation characteristic produced by this variation. 



A more complicated type of filter, such as the symmetrical "Con- 

 stant ^" band pass section exhibits a more involved relation between 

 the cut-off frequencies and the values of the elements. Li and Ci are 

 the series arm inductance and capacitance, while L2 and Ci are the 

 inductance and capacitance in the shunt arm. 



h 



2 1 _ j_ r /^_ j_ ri 



ij 27r VLiCo'^LiG'^VLiI 



In the equation as written L2 does not appear explicitly, but as in 

 this type of section LiCi = L2C2 the equation may be written with 

 L2C2 as the denominator of the second term in place of LiCi, if desired. 

 Therefore, three LC products influence each cut-off frequency; three 

 resonant frequencies, therefore, must be held constant if the cut-offs 

 are not to vary. The mid-band frequency of this section is given by 

 the equation 



^"^ ~ 2it\2 



' + ' 



L,\Cl i-'2^2 



from which it is seen that two LC products, LiCi and L2C2, must be 

 held constant if /m is not to vary. 



Element variation may cause a shift in the cut-off points and thus 

 a displacement of the attenuation or impedance characteristic of any 

 type of section, but it may have another effect on the characteristics of 

 M type sections. An M type section provides a peak of attenuation 

 at some finite frequency, which is determined, in most sections of this 

 type in common use, by a single pair of elements; either a series 

 resonant combination shunted across the filter or a parallel resonant 

 combination in a series arm. \^ariation in either of the elements 

 determining the location of the peak will cause a shift in the location 

 of this peak proportional to the element variation. Changes in these 

 elements would affect the cut-offs of the section as well as the peak or 

 peaks, but it may happen that variation in the opposite direction of 

 other elements in the section will result in negligible shift of the cut- 

 offs, while the peaks are shifted noticeably. Thus the attenuation 

 characteristic of an M type section may be distorted as well as dis- 

 placed by element variation. 



