According to the present proposal, to make it possible to obtain exact temperature compensation, one would add a component having a nonlinear stiffness to the mechanical load path and would place the entire resonator-and-compensator assembly on a thermoelectric controller, in an oven, or both. Then the temperature dependence of frequency would be approximately quadratic and the net derivative of frequency with respect to temperature would be given by
df/dT ≈ ∂f/∂T + (∂f/∂F)S2E2(α2 – α1) + AΔT
where A is a parameter that characterizes the nonlinearity to lowest order in temperature and ΔT is the difference between the present temperature and some other temperature, which could be a target temperature. To find the target temperature that gives exact temperature compensation, one sets the derivative equal to zero and solves for ΔT:
ΔTM ≈ –A–1[∂f/∂T + (∂f/∂F)S2E2(α2 – α1)]
The oven and/or the thermoelectric controller could be used to set the temperature to the exact compensation temperature. Even if the exact values of A, ∂f/∂T, ∂f/∂F, S2, E2, α1, and α2 were not known in advance, one could still determine the exact compensation temperature by measuring frequency as a function of temperature and finding the lowest point on the approximately quadratic frequency-versus-temperature curve.
This work was done by Anatoliy Savchenkov, Andrey Matsko, Dmitry Strekalov, Lute Maleki, Nan Yu, and Vladimir Iltchenko of Caltech for NASA’s Jet Propulsion Laboratory.
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Refer to NPO-44567, volume and number of this NASA Tech Briefs issue, and the page number.