. The Bell System technical journal . MECHANICAL AX(S = Y -ELECTRICAL AXIS=X Fig. I—Orientation of a Curie or perpendicular cut with respect to native crystal. or 30-degree cut in which the major surfaces of the crystal plate areparallel to both the optical and electrical axes. Since this cut resultsin a crystal vibrating along its smallest dimension, it is not of muchinterest for filter uses. When using a crystal as part of an electrical system, it is desirable 408 BELL SYSTEM TECHNICAL JOURNAL to know the constants of an electrical circuit which has the same im-pedance characteristic as the
. The Bell System technical journal . MECHANICAL AX(S = Y -ELECTRICAL AXIS=X Fig. I—Orientation of a Curie or perpendicular cut with respect to native crystal. or 30-degree cut in which the major surfaces of the crystal plate areparallel to both the optical and electrical axes. Since this cut resultsin a crystal vibrating along its smallest dimension, it is not of muchinterest for filter uses. When using a crystal as part of an electrical system, it is desirable 408 BELL SYSTEM TECHNICAL JOURNAL to know the constants of an electrical circuit which has the same im-pedance characteristic as the crystal. If attention is confined to thesingle prominent resonance, the electrical circuit representing thecrystal is as shown by Fig. 2. Some theoretical consideration has been r^Hh Co r-nnnp-n Ca --Hh cb. Ca-Co + C| fR = 06=1; (co+c,; Lb = c-i^r rv i-iC| C|C|Co 2Tr;L|C| 2Tr^ Fig. 2—Equivalent electrical circuit of piezo-electric crystal. given to the electrical network representing perpendicularly cut crys-tals by Cady,^ Van Dyke,^ Dye,^ Vigoureux ^ and others. Assuming aquartz plate to have only plane wave motion, Vigoureux has investi-gated the motion in such a plate, and has shown that there will beresonances at odd harmonics of a particular frequency determined bythe length, and mechanical constants of the plate. In the neighbor-hood of the fundamental resonance of the crystal, with the electricalplates placed on the crystal surfaces, he finds the equivalent circuitshown by Fig. 2A, the elements of which in practical units have thefollowing values: Co = :;—;—.. ^ ^, . ^fi = capacitance m larads, Ci = Li = Airle X 9 X IQiiloLSEdn TvHe X 9 X 10 lelmP X 9 X 10 SloEHn Yl = capacitance in farads,inductance in henries, (1) where /o, Im, h are respectively the lengths of the optical
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Keywords: ., bookcentury1900, bookdecade1920, booksubjecttechnology, bookyear1
