NDLI: Nonlinearities for parametric pumping of quartz UHF oscillators

Content Provider	IEEE Xplore Digital Library
Author	Kubena, R.L. Yong, Y.-K. Kirby, D.J. Joyce, R.J.
Copyright Year	2011
Description	Author affiliation: HRL Laboratories, Malibu, California, U.S.A. (Kubena, R.L.; Kirby, D.J.; Joyce, R.J.) \|\| Rutgers University, Piscataway, New Jersey, U.S.A. (Yong, Y.-K.)
Abstract	The feasibility of a parametric amplification method for improving the Q of UHF quartz oscillators is considered. A fundamental thickness shear resonator operating at about 500 MHz was studied for estimating the magnitude of fractional change in stiffness, Δk/k that could be obtained at resonance and off-resonance. The Δk/k is employed in a parametric pumping of the thickness shear mode of vibration. A relationship between the Δk/k at resonance and Δk/k at off-resonance was derived. For a 532 MHz fundamental thickness shear resonator, a Δk/k = $3.8×10^{−4}$ /V at resonance, and a Δk/k = $1.6×10^{−7}$ /V at off-resonance was found. The off-resonance data compares well with measured data of Δk/k = $1.7×10^{−7}$ /V. Our off-resonance study of Δk/k established that it is independent of the sign of electric potential drive that is Δk/k is a rectified excitation and therefore appears at twice the excitation frequency. The parametric amplification phenomenon is governed by the Mathieu equation. MATLAB Simulink models of the Mathieu equation were developed to establish the baseline criteria for parametric amplification to improve the resonator Q. The resonator model was excited at a frequency ωA over a range that included the natural frequency ω0 and the third overtone ω3. The parametric drive frequency ωP was set equal to 2ωA/n (n=1, 2, 3, ….). The model results showed that for parametric drive frequencies of ωP = ωA (for fundamental mode operation), and ωP = ωA/3 (for third overtone operation), the Δk/k needed for parametric amplification is in the range of 0.001 to 0.003 for a resonator Q of 9,000 to 15,000. It was observed that there was shift of the resonance frequency with the parametric amplification resulting from the change in dc stiffness Δk/k of the thickness shear mode.
Starting Page	1
Ending Page	7
File Size	715170
Page Count	7
File Format	PDF
ISBN	9781612841113
ISSN	10756787
e-ISBN	9781612841120
DOI	10.1109/FCS.2011.5977315
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2011-05-02
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Mathematical model Resonant frequency Equations Electric potential Strain Admittance Frequency modulation
Content Type	Text
Resource Type	Article

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