Electrical Wave Filters Employing Quartz Crystals as 



Elements 



By W. p. MASON 



This paper discusses the use of piezo-electric crystals as elements in wave 

 filters and shows that very sharp selectivities can be obtained by employing 

 such elements. It is shown that by employing crystals and condensers 

 only, very narrow band filters result. By using coils and transformers in 

 conduction with crystals and condensers, wide-band-pass and high and low- 

 pass filters can be constructed having very sharp selectivities. The circuit 

 configurations employed are such that the coil dissipation has only the effect 

 of adding a constant loss to the filter characteristic, this loss being indepen- 

 dent of the frequency. Experimental curves are given showing the degree of 

 selection possible. 



In the appendix, a study is made of the modes of motion of a perpen- 

 dicularly cut crystal, and it is shown that all the resonances measured can 

 be derived from the elastic constants and the density of the crystal. The 

 efTect of one mode of motion on another mode is shown to be governed by 

 the mutual elastic compliances of the crystal. By rotating the angle of cut 

 of the crystal, it is shown that some of the compliances can be made to 

 disappear and a crystal is obtained having practically a single resonant fre- 

 quency over a wide range of frequencies. Such a crystal is very advan- 

 tageous for filter purposes. 



Introduction 

 ■ FILTERS for communication systems must pass, without appreci- 

 -*- able amplitude distortion, waves with frequencies between certain 

 Hmits, and must attenuate adequately all waves with somewhat greater 

 or smaller frequencies. To do this efficiently, the change from the 

 filter loss in the transmission region, to that in the attenuation region, 

 must occur in a frequency band which is narrow compared to the use- 

 ful transmission band. At low frequencies, ordinary electrical coil 

 and condenser filters can perform this separation of frequencies well 

 because the percentage band widths (ratio of band width to the mean 

 frequency of the band) and the percentage separation ranges (ratio of 

 the frequency range required, in order that the filter shall change from 

 its pass region to its attenuated region, to the adjacent limiting fre- 

 quency of the pass band) are relatively large. 



For higher frequency systems, such as radio systems, or high fre- 

 quency carrier current systems, the band widths remain essentially the 

 same, and hence the percentage band widths become much smaller. 

 Here separation by coil and condenser filters becomes wasteful of 

 frequency space. For these filters, owing to the relatively low react- 

 ance-resistance ratio in coils (this ratio is often designated by the 

 letter Q) the insertion loss cannot be made to increase faster than a 



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