. The Bell System technical journal . -1333, 1919. E. B. Sawyer, R. E., 19, No. 11, p. 2020, November, 1931. S. Ballantine. Proc. I. R. E., 21,No. 10, p. 1399, October, 1933. 718 ELECTRO-MECHANICAL REPRESENTATION OF CRYSTAL 719 the direction of the applied field. Two subdivisions of this case areusually of interest, the first when the crystal is supported at its centerand drives two symmetrical loads, and the second when the crystal issupported on one end and drives a load on the other end. The sym-metrical case is considered first. By employing the well known analogies between electri
. The Bell System technical journal . -1333, 1919. E. B. Sawyer, R. E., 19, No. 11, p. 2020, November, 1931. S. Ballantine. Proc. I. R. E., 21,No. 10, p. 1399, October, 1933. 718 ELECTRO-MECHANICAL REPRESENTATION OF CRYSTAL 719 the direction of the applied field. Two subdivisions of this case areusually of interest, the first when the crystal is supported at its centerand drives two symmetrical loads, and the second when the crystal issupported on one end and drives a load on the other end. The sym-metrical case is considered first. By employing the well known analogies between electrical and me-chanical systems, it is possible to obtain a simple network, expressed interms of electrical symbols, which represents the properties of a piezo-electric crystal. In this representation, force is the analogue of voltage,mechanical displacement of electrical charge, and velocity of electricalcurrent. When the electrodes are attached to the crystal faces, theequivalent network of the crystal is shown by Fig. 2, The voltage E. Fig. 2—Electromechanical representation of a symmetricalpiezoelectric crystal. is the voltage applied across the plates of the crystal, the force F isthe force applied to each end of the symmetrical crystal, Qi is the elec-trical charge flowing in the wires connected to the crystal and Q2 and Qzare the mechanical displacements of the ends of the crystal which areequal on account of the symmetry of the crystal. The constants of the crystal can be evaluated by considering limitingcases. The capacitance Co is the electrostatic capacitance of thecrystal clamped. The compliance Ce is the mechanical compliance ofthe crystal. In electrostatic and mechanical units, these havethe values 0 — —,—f- ; C-B — TT . K^) where K is the dielectric constant of the crystal clamped, h the dimen-sion of the crystal in centimeters perpendicular to the surfaces of theelectrodes, Im the length of the crystal in the direction of vibration, /o thelength of
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