ELECTRICAL WAVE FILTERS 



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with condensers and crystals make very acceptable band-pass filters 

 capable of moderate band widths. It is often desirable to obtain low 

 and high-pass filters having a very sharp selectivity. The filter of Fig. 

 12 can be modified to give a high-pass characteristic by leaving out 

 the coils in the series or lattice arms of the network. However, it will 

 be found that the cross-over points in the impedance curve of necessity 

 come very close to the pass band and hence no appreciable loss can be 

 maintained at frequencies remote from the pass band. A broader and 

 more useful characteristic is obtained by using a transformer having 

 a preassigned coefficient of coupling, in conjunction with crystals and 

 condensers, as the element for broadening the separation of resonances. 

 Such an element is shown by Fig. 15^. As is well known, a trans- 



fa A 



FREQUENCV 



Fig. 15 — Impedance characteristic of a transformer, condenser, and crystal. 



former with a specified coupling can be replaced by a T network of 

 three inductances as shown by Fig. \SB. The impedance character- 

 istic, as shown by Fig. 15 C, has two anti-resonant frequencies /i and /a, 

 and two resonant frequencies f^ and fi. 



Suppose now that an element of this type is placed in one arm of the 

 lattice and a similar element having a condenser in series with it is 

 placed in the other arm as shown by Fig. \6A. If the elements are so 

 proportioned that the anti-resonances of one arm coincide with the 

 resonances of the other arm and vice versa, as shown by Fig. \6B, the 

 impedances of the two arms are of opposite sign till the last resonance. 

 Hence, a low pass filter results. It is possible to make the two im- 

 pedance curves cross five times, so that an attenuation corresponding 

 to five simple sections of low-pass filter results. Other arrangements of 

 the resonances are also possible and are advantageous for special 

 purposes. For example, as shown by Fig. 16C we can make the last 

 resonance and anti-resonance of both arms coincide, and the other 

 resonances of one arm coincide with the anti-resonances of the second 

 arm. This arrangement results in a low-pass filter having an attenua- 

 tion corresponding to three simple low-pass filter sections and an 

 impedance which can be made nearly constant to a frequency very near 

 the cut-off frequency. This is advantageous for obtaining a filter with 



