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# Nonlinear Thermal Compensators for WGM Resonators

- Created on Tuesday, 01 September 2009

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*)*S*_{2}*E*_{2}(α_{2} – α_{1}) + *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*)*S*_{2}*E*_{2}(α_{2} – α_{1})]

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*, *S*_{2}, *E*_{2}, α_{1}, and α_{2}
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.*

*In accordance with Public Law 96-517, the contractor has elected to
retain title to this invention. Inquiries concerning rights for its commercial
use should be addressed to:*

*Innovative Technology Assets Management
JPL
Mail Stop 202-233
4800 Oak Grove Drive
Pasadena, CA 91109-8099
E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.*

*Refer to NPO-44567, volume and number of this *NASA Tech
Briefs* issue, and the page number.*

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