Out-of-Plane Tuning Fork Resonator for High-Q Miniaturization
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Solution Overview
Problem
Existing tuning fork resonators face challenges in miniaturization due to a decrease in quality factor Q with size, primarily due to thermoelastic damping, which limits their further downsizing.
Innovation Solution
A tuning fork resonator design with resonator beams having a thickness between 0.05% and 20% of the stem height, oscillating in an out-of-plane mode, and utilizing piezoelectric assemblies for actuation, made of materials like Z-cut quartz or langasite, to maintain a high quality factor Q.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Volume of moving object
If the size of tuning fork resonators is reduced, then the miniaturization objective is achieved, but the quality factor Q decreases due to thermoelastic damping
Solution Approach 1:
The patent changes the geometric parameters of the resonator, specifically making the beam thickness much smaller than the stem height (thickness between 0.05% and 20% of stem height). This parameter change modifies the thermal relaxation time τ, allowing it to remain sufficiently large even in miniaturized resonators, thereby maintaining ω•τ > 1 and preserving high quality factor Q while achieving miniaturization.
2Reliability
If grooves are etched into resonator beams to increase thermal insulation, then quality factor Q increases, but device complexity and machining difficulty increase
Solution Approach 1:
Instead of adding complex groove structures to increase thermal insulation, the patent extracts the thermal insulation function by simply reducing the beam thickness to be much smaller than the stem height. This geometric simplification naturally provides thermal isolation between the vibrating beam and the substrate, maintaining high quality factor without the need for additional grooves or complex machining.
3Object-generated harmful factors
If grooves are etched into resonator beams to homogenize electric field, then motional capacitance increases and resistance decreases, but device complexity and machining difficulty increase
Solution Approach 1:
The patent removes the need for groove structures to achieve electric field homogenization. By simply making the beam thickness much smaller than the stem height, the electric field naturally becomes more uniform across the beam cross-section, increasing motional capacitance and reducing resistance without requiring additional machining steps or design complexity.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
The design achieves reduced size while maintaining a quality factor Q greater than 5000, preferably 15000, by optimizing thermal and mechanical properties independently.
Implementation Method 1
The tines are generally provided with electrodes, as disclosed for example in EP3468037, or with piezoelectric strips, as disclosed for example in EP2278709. The electrodes or piezoelectric strips can be coupled to an alternative voltage causing the tines of the tuning fork to vibrate.
Implementation Method 2
A main issue in miniaturization of low frequency flexural mode resonators is the decreasing quality factor Q leading to increasing resistance due to thermoelastic damping. Thermoelastic damping is the highest when the time of thermal relaxation τ (tau) of a resonator beam in direction of oscillation is equal to the reciprocal of the angular frequency ω=2πf of the resonance, i.e. if ω•τ=1.
Implementation Method 3
On one hand, the grooves provide thermal insulation between the compressive and extensional side, which increases Q, lowering resistance.
Data Source
Figure 1~2
Figure 3~4b
Figure 5a~5b
AI summary
One aspect of the present invention is related to a tuning fork resonator having a design allowing reduced dimensions of resonators while maintaining a high quality factor.