406 BELL SYSTEM TECHNICAL JOURNAL 



certain percentage rate with frequency. Hence an abrupt frequency 

 discrimination cannot be obtained between the passed frequency range 

 and the attenuated frequency range. In present radio systems, 

 double or triple demodulation is often used to supplement the selectiv- 

 ity of filter circuits. 



If, however, elements are employed which have large reactance- 

 resistance ratios, filters can be constructed which have small percent- 

 age bands and which attenuate in small percentage separation ranges. 

 Such high Q elements are generally obtainable only in mechanically 

 vibrating systems. Of these elements, probably the most easily used 

 is the piezo-electric crystal, for it possesses a natural driving mechan- 

 ism. 



It is the purpose of this paper to describe work which has been done 

 in utilizing these crystals as elements in filters.^ Since the quartz 

 crystal appears to be the most advantageous piezo-electric crystal, all 

 of the work described in this paper is an application of this type of 

 crystal. The possibilities and limitations are discussed and experi- 

 mental data are given showing that these filters are realizable in a 

 practical form. 



Piezo-electric Crystals and Their Equivalent Electrical 



Circuits 



When an electric force is applied to two plates adjacent to a piezo- 

 electric crystal, a mechanical force is exerted along certain directions 

 which deforms the crystal from its original shape. On the other hand 

 deformations in certain directions in the crystal produce a charge on 

 the electric plates. Hence the crystal is a system in which a mechanical 

 electrical coupling exists between the mechanical and electrical parts 

 of the system. 



Quartz crystals, particularly when vibrating along their smallest 

 dimension, as they do for high frequency oscillators, have a large num- 

 ber of resonances which do not differ much in frequency from the prin- 

 cipal resonance. While this is no great disadvantage for an oscillator, 

 since an oscillator can pick out the strongest resonance and utilize it 

 only, the large number of resonances is a great disadvantage when using 



1 The development of ideas in the direction of employing crystals as elements of 

 selecting circuits dates back to Cady who in patent — Re. 17,358 issued July 2, 1929, 

 original filed January 28, 1920 — showed various types of tuned circuits of which 

 crystals formed a part. Subsequently Espenschied in patent 1,795,204, issued 

 March 3, 1931, filed January 3, 1927 — patented broadly the use of crystals as ele- 

 ments of true filter structures. More recently a patent of the writer's — 1,921,035 

 issued August 8, 1933, filed Sept. 30, 1931 — describes the use of crystals in lattice 

 structures, and this patent, together with several others pending, forms the basis 

 for the filters discussed in this paper. It is only within the last few years that filter 

 structures including crystal elements have been practically realized. 



