ELECTRICAL WAVE FILTERS 



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actance is shown by the full line of Fig. 1 1 ; the dotted lines show the 

 reactance curves for the individual elements. It is evident that the 

 resonant frequency of the crystal is lowered, the anti-resonant, point 

 remains the same, and an additional resonance is added at a frequency 



Fig. 11 — ^Impedance characteristic of crystal and coil in series. 



above the anti-resonant frequency. For a crystal whose ratio of ca- 

 pacitances r is about 125 it is easily shown by calculation that if the 

 resonances are evenly spaced on either side of the anti-resonant fre- 

 quency the percentage frequency separation between the upper reso- 

 nance and the lower resonance is in the order of 9 per cent. 



Suppose now that this element is placed in the series arm of a lattice 

 network and another element of similar character is placed in the lat- 

 tice arm, the second element having its lowest resonance coincide 

 with the anti-resonance of the first element, and having the anti- 

 resonance of the second element coincide with the highest resonance of 

 the first element. This condition is shown by Fig. 12 C This network 

 will produce a band-pass filter whose band extends from the lowest 

 resonance of the series arm to the highest resonance of the lattice arm, 

 a total percentage frequency band width of 13.5 per cent. By design- 

 ing the impedances correctly the impedances of the two arms can be 

 made to coincide three times so that there is a possibility of three 

 attenuation peaks due to this section as shown by Fig. \2D. The loss 

 introduced by the filter is equivalent to that introduced by three simple 

 band-pass sections. Ordinarily the coils in the two arms are made 

 equal so that their resistances are equal and for this case one of the 

 peaks occurs at an infinite frequency. Since the resistances are 

 equal, then by the theorem illustrated by Fig. 10^ these resistances 

 can be brought out on the ends and incorporated with the terminal 



