ELECTRICAL WAVE FILTERS EMPLOYING CRYSTALS 225 



reactance while a solid line indicates a resistance. In the pass band 

 the filter has a resistive characteristic indicating a transmission of 

 energy, while in the attenuating band the characteristic impedance is 

 reactive indicating a reflection of energy. 



Filter No. 2 shows what characteristic will be obtained if an ideal 

 inductance is used in the lattice arm. As can be seen a band elimi- 

 nation filter will result with one attenuation peak. The width of the 

 suppression band will be the separation between the resonant and 

 anti-resonant frequencies. 



The use of a series resonant circuit results in a high-pass filter as 

 can be seen from filter No. 3. It is possible to obtain two dispositions 

 of the resonant frequencies which will give a single pass band as shown 

 by the two sets of curves. The first set gives a high-pass filter with 

 two attenuation peaks and a simple characteristic impedance. The 

 other arrangement gives one attenuation peak and a more complicated 

 type of characteristic impedance. The theory of this balancing of 

 characteristics obtainable with a lattice filter is well known/ and is 

 useful, when it is necessary on account of reflection efTects, to make 

 the characteristic impedance constant nearly to the cutoff. 



The use of an anti-resonant circuit results in a low-pass filter as 

 shown by filter No. 4. Two characteristics are possible. Filters No. 5 

 and 6 show the characteristics obtainable by using series resonant 

 circuits shunted by a capacitance or an inductance. In one case a 

 band-pass filter with two peaks results, and in the other either a band 

 suppression filter with two attenuation peaks or an all pass filter. 

 It will be noted that the configurations used in the lattice arm of 

 filter 5 is the equivalent circuit of the crystal and hence a crystal can 

 be used in this arm. In fact the circuit is similar to one discussed in 

 the former paper. ^ 



Since the crystal positive reactance region is very narrow (< .4%), 

 all of the band pass and band elimination filters obtained by using a 

 crystal in one arm will of necessity have very narrow band pass or 

 band suppression regions. For high and low-pass filters the attenua- 

 tion peaks will of necessity come close to the cutoff frequencies. 

 In the all-pass structure the phase shift will be very sharp in the 

 neighborhood of the crystal resonance. It was shown in the first 

 paper, ^ that wider pass bands and more general characteristics can be 

 obtained by employing inductance coils in series or parallel with the 

 crystal. Figures 3 and 4 show the possible types of filters obtained by 



^ Cauer, Siebschattungen VDI, Verlag Berlin, 1931. H. W. Bode, "A General 

 Theory of Electric Wave Filters," Jour, of Math, and Physics, Vol. XIII, pp. 275-362, 

 Nov. 1934. 



^ Loc. cit. 



