_{3}Substrate

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A new micro gyroscope based on the surface acoustic wave (SAW) gyroscopic effect was developed. The SAW gyroscopic effect is investigated by applying the surface effective permittivity method in the regime of small ratios of the rotation velocity and the frequency of the SAW. The theoretical analysis indicates that the larger velocity shift was observed from the rotated X-112°Y LiTaO_{3} substrate. Then, two SAW delay lines with reverse direction and an operation frequency of 160 MHz are fabricated on a same X-112°Y LiTaO_{3} chip as the feedback of two SAW oscillators, which act as the sensor element. The single-phase unidirectional transducer (SPUDT) and combed transducers were used to structure the delay lines to improve the frequency stability of the oscillator. The rotation of a piezoelectric medium gives rise to a shift of the propagation velocity of SAW due to the Coriolis force, resulting in the frequency shift of the SAW device, and hence, the evaluation of the sensor performance. Meanwhile, the differential structure was performed to double the sensitivity and compensate for the temperature effects. Using a precise rate table, the performance of the fabricated SAW gyroscope was evaluated experimentally. A sensitivity of 1.332 Hz deg^{−1} s at angular rates of up to 1,000 deg s^{−1} and good linearity are observed.

Recently, the surface acoustic wave (SAW) based gyroscope has provided a new method for angular rate detection with excellent inherent shock robustness, very larger dynamic testing range, small size, low cost, simplicity and long working life [^{−1} [_{3} with high temperature coefficients.

To overcome the shortcomings of SAW gyroscopes based on the standing wave mode, another gyroscope mode was reported utilizing the SAW gyroscopic effect, which originates from the rotation effect of a wave that is a rotation vector perpendicular to the propagating axis, causing a velocity change proportional to the input rotation through the Coriolis force [

Until recent years, the theoretical work on gyroscopic effect was not confirmed by the experiments. Lee ^{−1} s was observed at angular rates up to 2,000 deg/s, and this is far away from any real application. To improve the detection sensitivity, some other meaningful research works on such gyroscope were also done [

The first purpose of this study is to establish a comprehensive theoretical model dealing with the SAW based gyroscopic effect. A surface effective permittivity method based on the function of acoustic waves in piezoelectric materials and the boundary conditions was introduced to the gyroscopic effect analysis [_{3} piezoelectric substrate.

The second aim of this study is to develop a valuable SAW gyroscope based on an X-112°Y LiTaO_{3} piezoelectric substrate. It was composed of a dual-delay line oscillator, in which, two parallel delay lines with opposite propagation direction wer fabricated on the same chip as the feedback element. The schematic of the sensor is shown in

When the device was subjected to rotation around the x-axis, Ω_{x}, the Coriolis force acts on the particles along the SAW propagation path, the induced pseudo-SAW couples with the initial SAW, resulting in the SAW velocity change. Then the SAW velocity in one delay line increases and that of the other one decreases due to the opposite rotation around the x-axis. Hence, the differential scheme doubles the sensitivity of the sensor and compensates for the temperature effect, as indicated in _{out}. To ensure the excellent frequency stability, the single phase unidirectional transducers (SPUDT) and combed transducers were used to structure the SAW device [

A plane SAW is propagated along the surface of an anisotropic piezoelectric substrate occupying the half space as shown in

In this section, the SAW gyroscopic effect is described by solving the piezoelectric medium equations of motion and surface effective permittivity method. Consider an anisotropic and piezoelectric medium occupying a half-space (_{3} ≤ 0) with no mechanical load about the plane (_{3} = 0) and rotating at a constant angular rate (Ω_{i}_{i}-axis (_{1}, _{2}, _{3}, denote the Cartesian coordinates _{ijk} is the Levi-civita symbol, and we denote by _{i}_{ijkl}_{kij}_{ij} stand for the elastic, piezoelectric and dielectric constants, and ρ for the mass density of the substrate, respectively. The summation convention for repeated tensor indices and the convention that a comma followed by an index denotes partial differentiation with respect to the coordinate associated with the index are adopted. The indices _{ijkl}_{ijk}_{pq}_{ip}_{ij} and the stress tensor _{ij}_{p}_{q}

First, we assume a general solution of the _{s}_{1} direction and the time frequency, respectively. _{s}_{3} direction. _{j}_{4} are wave amplitudes. Substitution of _{j}_{4} as follows:

Then, for nontrivial solutions of _{j}_{4}, the determinant of the coefficient matrix of the linear algebraic equations must vanish, and this leads to a polynomial equation of degree eight for _{s}_{i}_{s}_{s}_{j}_{4}(_{m}

The solutions of the motion equation satisfy both the mechanical boundary condition, and the electrical boundary condition respectively.

The mechanical boundary condition:
_{i3}

The electrical boundary conditions were considered in case of free surface and metallic surface.

For a free surface, the effect of the electric field in the surrounding space can be considered by requiring the electrical potential cross the interface continuously:
_{1}) created by the interdigital transducers (IDT) electrodes equal to the incontinuity of the normal component _{3} of the dielectric displacement vector cross the interface:

And then, substituting

Here, the _{0} is the dielectric constant in vacuum. Usually, after solving _{s}_{3}) is the electrical potential distribution in slowness domain of the piezoelectric substrate. _{s}

Then, the weight factors _{s}_{0} is the determinant value of the matrix in left side of _{4n} is the algebraic complement of matrix elements _{4n} in the matrix of [_{in}]. The _{s}_{i}_{s}_{i}/ω.

As a numerical example, the gyroscopic effect of the SAW propagating along some common piezoelectric substrates like ST-X quartz, 128°YX LiNbO_{3} and X-112°Y LiTaO_{3} was considered. The mechanical parameters like the density, elastic constants, piezoelectricity and dielectric constants of the above mediums are listed in

Using Equations (_{s}_{3} substrate in the case of a normalized rotation of 2,000 ppm (Ω/_{1}-axis was depicted as shown in _{s}^{−4} s/m), and the image part of _{s}_{s}_{mR}_{mR}_{mR}_{s}_{oR}_{oR}_{s}

Thus, the velocity shift induced by the external rotation Δ_{s}_{OR0}_{mR0}

Using the surface effective permittivity method described as above and the corresponding mechanical parameters listed in _{3} piezoelectric substrate.

In this section, the fabrication process of the SAW sensor is described. It was composed of two delay lines with opposite direction on a same chip, and the corresponding oscillation circuit.

EWC/SPUDT and a combed transducer were utilized to structure the SAW delay lines on X-112°Y LiTaO_{3} substrate to improve the frequency stability of the oscillator. The SAW velocity on the X-112°Y LiTaO_{3} substrate with 110 nm Al metallization was 3,295 m/s. The operation frequency of the SAW delay line is specifically given by 160 MHz, thus, the wavelength λ of the SAW is given by 20.6 μm. Two delay line patterns with opposite direction were fabricated on a same LiTaO_{3} wafer by standard photolithography techniques. Each delay line consists of a launching transducer and readout transducers; the length of the launching transducer was set to 195λ with four groups, which was about 80% of the center-to-center distance between the launching and readout transducers. The distance between the transducers was 135λ. In order to limit the total number of Al fingers in each transducer to about 60, the launching transducer was thinned into a comb structure. To keep the uniformity of the acoustic velocity, many pseudo-fingers are distributed between the SPUDT cells of the comb transducer. It means each group was composed of 15 SPUDT cells and some pseudo-fingers with length of 45λ, as shown in

Using the HP 8753D network analyzer, the amplitude and phase response of the SAW delay lines were measured under matched conditions, as shown in

Next, the fabricated SAW device chip was loaded into a standard metal base, as shown in

After mounting the SAW sensor onto the PCB board, the performance of the SAW rate sensor was evaluated. The experimental apparatus setup for performance evaluations was composed of a precision rate table [^{−1}; a very clear frequency shift of 620 Hz was observed. The sensitivity and linearity of the present SAW gyroscope with rotation in the ^{−1} s and 0.967, respectively, as shown in

The SAW gyroscopic effect was analyzed theoretical by solving the piezoelectric medium equations of motion and the surface effective permittivity method. The calculated results indicate that among the common piezoelectric substrates a larger sensor response was observed from the rotated X-112°Y LiTaO_{3}. Based on the theoretical analysis, a new SAW gyroscope on X-112°Y LiTaO_{3} substrate with operation frequency of 160 MHz was developed, \composed of two SAW delay line oscillators with opposite direction. Using a precise rate table, the sensor performance was evaluated experimentally. Sensitivity of 1.332 Hz deg^{−1} s over a large dynamic testing range (over 900 deg s^{−1}), and good linearity were obtained.

The author gratefully acknowledges the support of the National Natural Science Foundation of China: No. 10974171, 10911140269, and Alexander von Humboldt Foundation.

The schematic of the present SAW gyroscope.

The coordinate system used in this study.

The surface effective permittivity curve on X-112°Y LiTaO_{3} with and without rotation.

The PCB packaged with SAW gyroscope

The measured amplitude

The measured long-term frequency stability of the fabricated SAW oscillator, insert: short-term frequency stability testing.

SAW gyroscope signal output depending on the different rotations

Sensitivity evaluation of the fabricated SAW gyroscope.

The mechanical parameters of some common substrates.

^{3}) |
^{2}) |
^{2}) |
_{0}) | ||
---|---|---|---|---|---|

Quartz | ST-X (0°,132.75°,0°) | 2,651 | c_{11}:8.674; c_{33}:10.72;c_{44}:5.794; c_{12}:0.699; c_{13}:1.191; c_{14}:−1.791 |
e_{11}:0.171; e_{14}:−0.0436; e_{36}:0.14 |
ε_{11}:4.5; ε_{33}: 4.6 |

ST-X (0°,132.75°,33.3°) | |||||

128°YX LiNbO_{3} |
(0°,37.86°,0°) | 4,700 | c_{11}:20.3;c_{33}:24.5;c_{44}:6.0; c_{12}:5.3; c_{13}:7.5; c_{14}:0.9 |
e_{15}:3.7; e_{22}: 2.5; e_{31}: 0.2; e_{33}: 1.3 |
ε_{11}:44; ε_{33}: 29 |

X-112°Y LiTaO_{3} |
(90°,90°,112.2°) | 7,450 | c_{11}:23.3; c_{33}:27.5; c_{44}:9.4; c_{12}:4.7; c_{13}:8.0; c_{14}:−1. 1 |
e_{15}:2.6; e_{22}: 1.6; e_{31}: 0.0; e_{33}: 1.9 |
ε_{11}:41; ε_{33}: 29 |

The calculated gyroscopic effect for SAW along various substrates.

^{3}) |
^{−1} s) |
||
---|---|---|---|

ST-X quartz (Euler(0°,132.75°,0°)) | 2,651 | −0.15/0.024 in _{2}-axis |
−0.14 [ |

ST-X quartz (Euler (0°,132.75°,33.3°)) | 2,651 | −0.19/0.03 in _{2}-axis |
−0.73 [ |

128° YX LiNbO_{3} (Euler (0°, 37.86°, 0°)) |
4,700 | −0.08/0.012 in _{2}-axis |
−0.094 [ |

X-112° Y LiTaO_{3} (Euler(90°,90°,112.2°)) |
7,450 | −0.38/0.06 in _{1}-axis |
−0.39 [ |