The behavior of thickness/shear-mode quartz resonators is explained both mathematically and experimentally in terms of lateral standing-wave trapped-energy modes. A cutoff phenomenon, similar to that occurring in optical total internal reflection, results in energy trapping or the restriction of vibratory energy almost exclusively to the electroded region of a resonator, with an energy distribution decreasing exponentially with distance from the electrode edge. Consideration of boundary conditions at the electrode edges of an idealized two-dimensional model yields an expression for the eigenfrequencies of symmetric inharmonic overtone modes (lateral standing waves) that can exist in the electroded region of fundamental- and harmonic-mode resonators. Design formulas for the suppression of these unwanted modes are included. They show that electrode thickness and lateral dimensions can be traded off against one another to obtain a wide range of motional parameters. Previously, unwanted responses were eliminated by restricting the electrode diameter to empirically established values. The present understanding has led to a reduction in resonant resistance and an increase in motional capacitance by at least a factor of four with hf and vhf fundamental- and harmonic-mode filter crystals. Experimental data that verify results predicted by energy-trapping theory are given, and application to design of single- and multi-electrode resonators is considered. Specific examples in the 10- to 180-MHz frequency range are given.
XXSAbstract -This paper identifies the major sources of ontrack, self-induced, non-synchronous TMR (Track Mis-Registration) in a HDD (Hard-Disk Drive) with a track-density of 4400 TPI (Tracks Per Inch) and a rotational rate of 90 Hz. Experimental measurements of the drive's PES (Position-Error Signal) in ontrack mode are used to determine the spectrum of the perceived TMR, which is then broken down into component parts. The total RMS non-synchronous perceived TMR of 0.56% of a track is found to be composed of O.17%, due to torque disturbances, 0.33%, due to disk motions, 0.42% due to PES demodulation noise, with 0.04% unaccounted for (the total being the Root-Sum-of-Squares of the components). With the assumption of a doubling of the PES noise, a factor of two reduction in the disk vibrations, a quadrupling in the servo sample-rate, and a doubling of the loop bandwidth, the authors show that an RMS ontrack, non-synchronous, self-induced TMR of 1.67% of a track is possible with a track-density of roughly 72000 TPI.
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