204 BKLL S YSTKM TECH NIC A L JOURNA L 



wide. A wider band was obtained in this case by combining the complex 

 lattice sections with hidder sections as shown in the figure. For this filter 

 a combination of sections was designed which gave physically realizable 

 crystal elements for a band width of 8.5 kc. This was the maximum band 

 width possible without increasing the distortion in the band. 

 Summarizing, the filter design process consists of: 



1. Design of wide band lattice sections which have quartz elements which 

 cannot be realized in practice. 



2. Design of electrical ladder sections of still wider band which introduce 

 little distortion at the pass band frequencies of the lattice section. 

 At this point the schematic is as shown in Fig. 8. 



3. Combination of like elements, electrical transformations, and replace- 

 ment of groups of elements consisting of an inductor and capacitor in 

 series shunted by a second capacitor by their equivalent crystal ele- 

 ments. This gives the final schematic shown in Fig. 1, in which the 

 crystal elements are physically realizable. 



The general steps in the design of lattice filters--'* are as follows: 



1. Choice of filter cut-oflfs. 



2. Determination of number and location of impedance controlling fre- 

 quencies to give a good match of image impedance to the termination. 



3. Location of peaks of infinite attenuation to give the necessary transfer 

 loss at frequencies removed from the pass band. 



4. Determination of impedance level which gives the most reasonable 

 element values. 



Theoretically a filter could be designed which contains only one lattice 

 section. The decision to split the filter into two sections was based on 

 a desire to simplify the design to ease the manufacturing problems. The 

 attenuation burdens of each section were reduced sufficiently to allow wider 

 tolerances to be placed on the filter components. The last design steps are 

 to determine the schematic of each section and to compute the theoretical 

 element values in accordance with previously dezcribed methods.-* 



Although the filter elements computed were physically realizable they 

 represented such extreme values as to introduce difficult problems. This 

 was true especially of the crystal elements where the equivalent inductances 

 of the eleven crystal elements in one section varied from 16 to 465 henries, 

 a range of 1 :29. A similar situation existed in the other section. 



Crystal elements of the -|-5 degree X-cut type vibrating in their funda- 

 mental longitudinal mode are used in this filter. The equivalent inductance 

 of such crystal elements varies directly with the thickness and inversely 

 with the width of the plate. Therefore the high inductance plates are thick 

 and narrow and the low inductance plates are thin and wide. In one sec- 

 tion of the filter the dimensions of the plates required varied in width from 



