A method for optimizing the linearity of a quartz resonator

Abstract

The present invention discloses a method for optimizing the linearity of a quartz resonator, which belongs to the technical field of quartz resonators, and includes: selecting a cut type of quartz crystal, and determining a first value range of the angle corresponding to the selected cut type based on the elastic properties and piezoelectric properties of the quartz crystal; determining a second value range of the angle corresponding to the selected cut type based on the temperature-frequency characteristics of the quartz crystal, and forming a third value range together with the first value range; based on the influence of the angle on the temperature-frequency characteristics, narrowing the third value range to obtain a fourth value range; calculating the linearity corresponding to each angle within the fourth value range, and finding the angle value with the highest linearity as the optimal angle value, thereby completing the optimization design of the linearity of the quartz resonator. This method takes into account the key factors affecting the linearity, such as the temperature-frequency characteristics of the quartz crystal material itself, and can fundamentally improve the frequency stability of the resonator, so that the resonator has better linearity performance.

Description

Technical Field

[0001] The invention belongs to the technical field of quartz resonators, and in particular relates to a method for optimizing the linearity of a quartz resonator. Background Art

[0002] A quartz resonator is a device made by using the piezoelectric effect to produce resonance when the frequency of an electrical signal is equal to the natural frequency of a quartz crystal. It is a key component of crystal oscillators and narrowband filters. At present, the design and optimization of quartz resonators at home and abroad are mostly focused on sacrificing some linearity to give quartz resonators the performance advantages of high sensitivity and high consistency, but lack the requirement for high linearity.

[0003] Linearity is the key factor affecting the accuracy and precision of measurement. To improve it, it is necessary to optimize the core components of the quartz resonator, the quartz wafer and structural details, and adopt the method of micro-electromechanical systems, using micro-machining technologies such as lithography and anisotropic etching to improve the processing accuracy of the quartz wafer. Linearity reflects the linearity of the resonator frequency change when the external temperature changes. For a quartz resonator with good linearity, the frequency change is predictable and stable when the external conditions change, which plays a key role in improving the accuracy and precision of the resonator measurement.

[0004] In order to reduce the influence of external temperature on the quartz resonator, the existing method is usually to improve the frequency stability through peripheral circuits and temperature compensation.

[0005] However, the above existing methods have limited improvement on the frequency stability of the quartz resonator, thereby affecting the performance of the linearity of the quartz resonator. Summary of the invention

[0006] In order to solve the above problems existing in the prior art, the present invention provides a method for optimizing the linearity of a quartz resonator. The technical problem to be solved by the present invention is achieved through the following technical solutions:

[0007] The present invention proposes a method for optimizing the linearity of a quartz resonator, comprising:

[0008] Selecting a cut shape of the quartz crystal, and determining a first value range of the rotation angle corresponding to the selected cut shape based on the elastic properties and piezoelectric properties of the quartz crystal;

[0009] Based on the temperature-frequency characteristics of the quartz crystal, a second value range of the angle corresponding to the selected cut type is determined, and together with the first value range, a third value range is formed;

[0010] Based on the influence of the rotation angle on the temperature-frequency characteristic, the third value range is narrowed to obtain a fourth value range;

[0011] Calculate the linearity corresponding to each angle within the fourth value range, and find the angle value with the highest linearity as the optimal angle value;

[0012] The optimized design of the quartz resonator linearity is completed according to the optimal rotation angle value.

[0013] In one embodiment of the present invention, a cut shape of a quartz crystal is selected, and based on the elastic properties and piezoelectric properties of the quartz crystal, a first value range of a rotation angle corresponding to the selected cut shape is determined, including:

[0014] For the rotation angle corresponding to the selected cut type, obtain the relationship between the elastic compliance coefficient of the quartz crystal and the rotation angle, and the relationship between the piezoelectric coefficient of the quartz crystal and the rotation angle;

[0015] Constraints are imposed on the elastic compliance coefficient and the piezoelectric coefficient respectively, and the first value range is obtained by combining the relationship between the elastic compliance coefficient and the rotation angle and the relationship between the piezoelectric coefficient and the rotation angle.

[0016] In one embodiment of the present invention, the constraint imposed on the elastic compliance coefficient is expressed as:

[0017] ;

[0018] In the formula, represents the cross elastic compliance coefficient, represents the key elastic compliance coefficient, Indicates absolute value;

[0019] The constraints imposed on the piezoelectric coefficients are expressed as:

[0020] ;

[0021] In the formula, represents the key piezoelectric coefficient, Represents the unit of piezoelectric constant, The coulomb is the unit of charge. The unit of force is Newton.

[0022] In one embodiment of the present invention, based on the temperature-frequency characteristics of the quartz crystal, determining the second value range of the angle corresponding to the selected cut type includes:

[0023] Constraints are imposed on the first-order temperature-frequency coefficient, second-order temperature-frequency coefficient and third-order temperature-frequency coefficient of the quartz crystal, and the second value range is obtained by combining the relationship between the first-order temperature-frequency coefficient and the elastic compliance coefficient, the relationship between the second-order temperature-frequency coefficient and the elastic compliance coefficient, the relationship between the third-order temperature-frequency coefficient and the elastic compliance coefficient, and the relationship between the elastic compliance coefficient and the rotation angle.

[0024] In one embodiment of the present invention, constraints are imposed on the first-order temperature-frequency coefficient, the second-order temperature-frequency coefficient, and the third-order temperature-frequency coefficient of the quartz crystal, which are respectively expressed as:

[0025] ; ; ;

[0026] In the formula, represents the first-order temperature-frequency coefficient, represents the second-order temperature-frequency coefficient, represents the third-order temperature-frequency coefficient, represents the absolute value, Indicates the unit of temperature-frequency coefficient.

[0027] In one embodiment of the present invention, based on the influence of the rotation angle on the temperature-frequency characteristic, the third value range is narrowed to obtain a fourth value range, including:

[0028] According to the influence of the rotation angle on the temperature-frequency characteristic, the graphic area corresponding to the third value range is divided;

[0029] Based on the symmetry relationship of the divided graphic areas and the characteristic that the rotation angle does not affect the first-order temperature-frequency coefficient, the second-order temperature-frequency coefficient and the third-order temperature-frequency coefficient, the third value range is narrowed to obtain the fourth value range.

[0030] In one embodiment of the present invention, after obtaining the optimal rotation angle value, the method further includes:

[0031] The temperature range is divided into multiple temperature intervals. Based on the optimal rotation angle value, the optimal linearity is explored in different temperature intervals to find the global optimal temperature range.

[0032] Within the global optimal temperature range, each corner value within the fourth value range is used to perform optimal linearity exploration to find out whether there is a corner with a linearity higher than the linearity corresponding to the optimal corner value. If so, the found corner is updated to the optimal corner value.

[0033] In one embodiment of the present invention, the temperature range is divided into multiple temperature intervals, and based on the optimal rotation angle value, the linearity optimization exploration is performed in different temperature intervals to find the global optimal temperature range, including:

[0034] Select a certain temperature interval, and by changing the left and right interval values ​​of the temperature full scale, find the left and right interval values ​​of the temperature full scale corresponding to the highest linearity in the current temperature interval as the local optimal temperature range;

[0035] Traverse all temperature intervals to update the local optimal temperature range and finally obtain the global optimal temperature range.

[0036] In one embodiment of the present invention, the optimization design of the linearity of the quartz resonator is completed according to the optimal rotation angle value, including:

[0037] Based on the optimal rotation angle value, the aspect ratio of the tuning fork arm of the quartz resonator is optimized to obtain the optimal design values ​​of the tuning fork arm width and length;

[0038] According to the optimal rotation angle value and the optimal design values ​​of the tuning fork arm width and length, the optimal design of the quartz resonator linearity is completed.

[0039] In one embodiment of the present invention, based on the optimal rotation angle value, the aspect ratio of the tuning fork arm of the quartz resonator is optimized to obtain the optimal design values ​​of the width and length of the tuning fork arm, including:

[0040] Based on the optimal rotation angle value, by changing the width and length of the tuning fork arm of the quartz resonator, the width and length of the tuning fork arm corresponding to the error between the theoretical vibration fundamental frequency and the simulation frequency is less than the preset error threshold is found as the optimal design value of the width and length of the tuning fork arm; wherein, the theoretical vibration fundamental frequency is obtained according to the calculation formula of the vibration fundamental frequency.

[0041] Beneficial effects of the present invention:

[0042] 1. The optimization design method for the linearity of the quartz resonator provided by the present invention determines the value range of the angle corresponding to the selected cut type based on the elastic properties, piezoelectric properties and temperature-frequency characteristics of the quartz crystal itself, and on the other hand simplifies the angles within a large range of all possible values ​​according to the influence of the angle relationship between the angles on the temperature-frequency characteristics, narrows the angle value range, and finally selects the optimal angle value that meets the high linearity requirements. This method takes into account the key factors that affect linearity, such as the temperature-frequency characteristics of the quartz crystal material itself, and can fundamentally improve the frequency stability of the quartz resonator, so that the quartz resonator has better linearity performance; and it greatly saves the time of taking the angle value and reduces the workload of subsequent linearity calculations;

[0043] 2. When optimizing the linearity of the quartz resonator, the present invention not only finds the optimal design value of the width and length of the tuning fork arm by changing the width-to-length ratio of the tuning fork arm on the basis of the optimal rotation angle value, but also further improves the linearity of the quartz resonator.

[0044] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is a flow chart of a method for optimizing the linearity of a quartz resonator provided by an embodiment of the present invention;

[0046] Figure 2 is the turning angle provided by the embodiment of the present invention and Schematic diagram of the value range of ;

[0047] Figure 3 is the reduced turning angle provided by the embodiment of the present invention and Schematic diagram of the value range of . DETAILED DESCRIPTION

[0048] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0049] See also Figure 1 , Figure 1 1 is a flow chart of a method for optimizing the linearity of a quartz resonator provided by an embodiment of the present invention. The method mainly comprises the following steps:

[0050] Step 1: Select a cut shape of the quartz crystal, and determine a first value range of the rotation angle corresponding to the selected cut shape based on the elastic properties and piezoelectric characteristics of the quartz crystal.

[0051] In order to make the quartz resonator meet a single vibration frequency and work stably in the bending vibration mode, based on the elastic properties and piezoelectric characteristics of the quartz crystal, its elastic compliance coefficient and piezoelectric coefficient are constrained to obtain the value range of the rotation angle under this condition.

[0052] Specifically, first, a certain cut shape of quartz crystal is selected, and for the rotation angle corresponding to the selected cut shape, a relationship between the elastic compliance coefficient of the quartz crystal and the rotation angle, and a relationship between the piezoelectric coefficient of the quartz crystal and the rotation angle are obtained;

[0053] Then, constraints are imposed on the elastic compliance coefficient and the piezoelectric coefficient respectively, and the first value range is obtained by combining the relationship between the elastic compliance coefficient and the rotation angle and the relationship between the piezoelectric coefficient and the rotation angle.

[0054] It is understandable that for different cutting types, the angle has different relationships with the elastic compliance coefficient and the piezoelectric coefficient. Take this as an example for introduction.

[0055] Double corner cut It is the cutting symbol of quartz crystal in the IEEE (Institute of Electrical and Electronics Engineers) standard. Assuming that the quartz crystal is a rectangular plate, a three-dimensional coordinate system is defined using the right-hand rule, where: X The direction is the width direction of the quartz crystal. Y The direction is the length direction of the quartz crystal. Z The direction is the thickness direction of the quartz crystal, recorded as the initial coordinate system O-XYZ , rotate the coordinate system around X Axis rotation Angle, get the new coordinate system O-XY'Z'. Here is the first specified angle, representing the angle around X The axis rotates by a factor of 2. Y Axis and Z The axis will move to a new position, forming Axis and Axis. O-XY'Z' After the coordinate system, the next step is to go around the newly formed Axis rotation Angle, get the final double angle The cut coordinate system. The second specified angle, representing the The amount of rotation of the axis.

[0056] Double corner cut Corresponding to two corners, that is and , and its relationship with the elastic compliance coefficient can be expressed as:

[0057] ;

[0058] In the formula, , , , , are elastic constants, and their values ​​are as follows:

[0059] ;

[0060] ;

[0061] All cross-elastic compliance coefficients associated with anti-phase bending vibrations in the width direction include , , , and , and the elastic compliance coefficient The ratios must satisfy the following formula:

[0062] ;

[0063] In the formula, Indicates taking the absolute value.

[0064] The above formula imposes constraints on the elastic compliance coefficient, and the double rotation angle that satisfies a single vibration frequency can be obtained by synthesis: and The value range of .

[0065] Furthermore, Key piezoelectric coefficients of double-corner cut quartz crystals With double corner and The relationship is:

[0066] ;

[0067] in, , , Represents the unit of piezoelectric constant, The coulomb is the unit of charge. The unit of force is Newton.

[0068] In order to make the quartz tuning fork resonator work in the piezoelectric bending vibration mode, the minimum piezoelectric constant of the quartz tuning fork resonator for normal operation cannot be less than .

[0069] Therefore, the constraint on the piezoelectric coefficient is expressed as:

[0070] ;

[0071] From this we can get and The value range of .

[0072] The range of values ​​obtained by combining the elastic compliance coefficient and the piezoelectric coefficient can be used to obtain the double angle of the double-angle cut quartz crystal. and The first value range of .

[0073] Step 2: Based on the temperature-frequency characteristics of the quartz crystal, determine a second value range of the angle corresponding to the selected cut type, and form a third value range together with the first value range.

[0074] Specifically, considering the influence of the temperature-frequency characteristics (temperature-frequency characteristics) on the linearity of the quartz resonator, the first-order, second-order and third-order temperature-frequency coefficients (temperature-frequency coefficients) of the quartz crystal can be constrained to obtain the second value range, and then the angle value range of the basic factors such as the above-mentioned elastic properties and piezoelectric properties is combined to obtain the angle value range under high linearity conditions, which is recorded as the third value range.

[0075] Specifically, the first-order temperature-frequency coefficient of a quartz crystal is expressed as , whose expression is:

[0076] ;

[0077] In the formula,

[0078] ;

[0079] ;

[0080] ;

[0081] Represents the temperature coefficient of the first-order elastic compliance constant of the quartz crystal, in units of , K stands for Kelvin;

[0082] With the above , , , , Same as above, it also represents the elastic constant, and its value is ;

[0083] ;

[0084] ;

[0085] ;

[0086] Indicates that the quartz crystal The first-order linear expansion coefficient in the direction;

[0087] Indicates that the quartz crystal The first-order linear expansion coefficient in the direction.

[0088] Correspondingly, the second-order temperature-frequency coefficient of the quartz crystal is expressed as , whose expression is:

[0089] ;

[0090] In the formula,

[0091] ;

[0092] The temperature coefficient representing the second-order elastic compliance constant of a quartz crystal ;

[0093] ;

[0094] ;

[0095] ;

[0096] , indicating that the quartz crystal is The second-order linear expansion coefficient in the direction;

[0097] , indicating that the quartz crystal is The second-order linear expansion coefficient in the direction.

[0098] Correspondingly, the third-order temperature-frequency coefficient of the quartz crystal is expressed as , whose expression is:

[0099] ;

[0100] In the formula,

[0101] ;

[0102] The temperature coefficient representing the third-order elastic compliance constant of a quartz crystal ;

[0103] ;

[0104] ;

[0105] ;

[0106] , indicating that the quartz crystal is The third-order linear expansion coefficient in the direction;

[0107] , indicating that the quartz crystal is The third-order linear expansion coefficient in the direction.

[0108] From the above expressions of the first-order, second-order and third-order temperature-frequency coefficients, it can be seen that there is a functional relationship between the temperature-frequency coefficient and the elastic compliance coefficient. Since there is a functional relationship between the elastic compliance coefficient and the rotation angle, it can be concluded that there is a functional relationship between the temperature-frequency coefficient and the rotation angle.

[0109] Furthermore, the MATLAB program can be used to solve the first-order, second-order, and third-order temperature-frequency coefficients corresponding to different rotation angles. By observing the data calculated by the MATLAB program at different rotation angles, it is found that when the rotation angle changes, the second-order and third-order temperature-frequency coefficients have a significant impact on the change in the linearity of the quartz resonator. At the same time, under the constraint of satisfying the first-order temperature-frequency coefficient, the smaller the second-order and third-order temperature-frequency coefficients, the better the corresponding linearity.

[0110] Therefore, this embodiment preferably imposes constraints on the first-order temperature-frequency coefficient, second-order temperature-frequency coefficient and third-order temperature-frequency coefficient of the quartz crystal, and combines the relationship between the first-order temperature-frequency coefficient and the elastic compliance coefficient, the relationship between the second-order temperature-frequency coefficient and the elastic compliance coefficient, the relationship between the third-order temperature-frequency coefficient and the elastic compliance coefficient, and the relationship between the elastic compliance coefficient and the rotation angle to obtain a second value range.

[0111] Specifically, constraints are imposed on the first-order temperature-frequency coefficient, the second-order temperature-frequency coefficient, and the third-order temperature-frequency coefficient of the quartz crystal, which can be expressed as:

[0112] ; ; ;

[0113] In the formula, Indicates taking the absolute value, It is the unit of temperature-frequency coefficient.

[0114] This embodiment takes into account the temperature-frequency characteristics of the quartz crystal material itself when optimizing the linearity design of the quartz resonator, and can fundamentally improve the frequency stability of the quartz resonator, thereby making the quartz resonator have better linearity performance.

[0115] Step 3: Based on the influence of the rotation angle on the temperature-frequency characteristic, the third value range is narrowed to obtain a fourth value range.

[0116] On the basis of satisfying the constraint of the first-order temperature-frequency coefficient, by observing the second-order and third-order temperature-frequency coefficient data corresponding to different rotation angles, it is found that the second-order and third-order temperature-frequency coefficients show a periodic change law of 180° when the rotation angle changes. Therefore, this embodiment narrows the third value range obtained in step 2 based on this characteristic. First, according to the influence of the rotation angle on the temperature-frequency characteristic, the graphic area corresponding to the third value range is divided. Then, based on the symmetric relationship of the divided graphic area and the characteristic that the rotation angle does not affect the first-order, second-order and third-order temperature-frequency coefficients, the third value range is narrowed to obtain the fourth value range.

[0117] For details, see Figure 2 , Figure 2 is the turning angle provided by the embodiment of the present invention and Schematic diagram of the value range of . and The influence of the first-order, second-order and third-order temperature-frequency coefficients can be divided into four parts. According to the data in the graph presented by the MATLAB program, Figure 2 middle Above the axis is a positive value, Below the axis is negative, and the image is about The axis is completely symmetrical. According to the expressions of the first-order, second-order and third-order temperature-frequency coefficients, and The positive or negative value of will not affect the value of the first-order, second-order and third-order temperature-frequency coefficients, so we can only consider Below the axis The value of .

[0118] Figure 2 Region (1) and region (I) are exactly the same, and the angle between these two regions satisfies the following relationship:

[0119] ;

[0120] At this time, the corner in area (1) and The corresponding corner in region (I) and The first-order, second-order and third-order temperature-frequency coefficients are the same. Therefore, when discussing the linearity of the angle values ​​of these two regions, only one of the regions can be considered. Here, only the angle value of region (1) is considered.

[0121] Similarly, Figure 2 For region (2) and region (II), we can also first consider only the value of the corner of region (2). The value relationship of the corner is as follows:

[0122] ;

[0123] Area (1) is similar to area (2). We can also consider only the value of the angle of area (1). The relationship between the angles is as follows:

[0124] ;

[0125] Region (I) is similar to region (II), and the relationship between their rotation angles is as follows:

[0126] ;

[0127] According to the above formula, the turning angle of area (1) and The corresponding corner in region (2) and The first-order, second-order and third-order temperature-frequency coefficients are the same, and the turning angle of region (Ⅰ) and The corresponding corner in region (II) and The obtained first-order, second-order and third-order temperature-frequency coefficients are the same.

[0128] In summary, when discussing the linearity problem, Figure 2 The resulting angle and The eight value ranges of can be reduced to one value range that only considers the corner in the black part of region (1), such as Figure 3 shown.

[0129] This embodiment simplifies the angles within a large range of all possible values ​​based on the influence of the angular relationship between the angles on the temperature-frequency characteristics, thereby narrowing the range of the angle values, thereby reducing the task of screening out the optimal angle value that meets the high linearity requirement from a large number of values, greatly saving the time for taking the angle value and reducing the workload of subsequent linearity calculations.

[0130] Step 4: Calculate the linearity corresponding to each angle within the fourth value range, and find the angle value with the highest linearity as the optimal angle value.

[0131] Specifically, according to the narrowed fourth value range, the linearity corresponding to the angle is compared, that is, the nonlinear error value, and the angle value with the highest linearity in the fourth value range is obtained, and the new cut type at -180°C to 180°C is determined to be ZGar (52° / -47°), the optimal rotation angle is 52°, It is -47°.

[0132] Step 5: Complete the optimization design of the quartz resonator linearity according to the optimal rotation angle value.

[0133] Optionally, as an implementation method, this embodiment can use the optimal rotation angle value obtained in step 4 as the rotation angle design value of the quartz resonator to manufacture the quartz resonator, and the manufactured quartz resonator has good linearity.

[0134] In another embodiment of the present invention, in order to further improve the linearity of the resonator, after obtaining the optimal rotation angle value in step 4, the temperature measurement range is further narrowed to update the optimal rotation angle value, specifically including the following operations S1-S2.

[0135] S1: Divide the temperature range into multiple temperature intervals, and based on the optimal rotation angle value, perform optimal linearity exploration in different temperature intervals to find the global optimal temperature range.

[0136] First, a certain temperature interval is selected, and by changing the left and right interval values ​​of the temperature full scale, the left and right interval values ​​of the temperature full scale corresponding to the highest linearity in the current temperature interval are found as the local optimal temperature range;

[0137] Then, all temperature intervals are traversed to update the local optimal temperature range and finally obtain the global optimal temperature range.

[0138] S2: Within the global optimal temperature range, using each angle value within the fourth value range, perform optimal linearity exploration to find out whether there is a angle whose linearity is higher than the linearity corresponding to the optimal angle value. If so, update the found angle to the optimal angle value.

[0139] For example, in the temperature range of -180°C to 180°C, the best linearity cut ZGar (52° / -47°) is a reference cut. Within the temperature range of -180°C to 180°C, it can be divided into multiple temperature intervals. In this embodiment, only 10°C is the smallest temperature interval and 100°C is the largest temperature interval, and ten temperature intervals are recorded as , to explore the optimal linearity.

[0140] Select the smallest temperature range first By changing the left and right interval values ​​of the full range of the temperature, the test is carried out in this temperature range. The maximum linearity corresponds to the temperature range around the full scale. ZGar (52° / -47°) The nonlinearity error is the smallest in the temperature range of -20°C to -10°C, so this temperature range is recorded as the local optimal temperature range. After traversing all temperature ranges, it can be found that the global optimal temperature range is still -20°C to -10°C.

[0141] It is understandable that the selected ZGar The (52° / -47°) cut is not necessarily the one with the best linearity in the temperature range of -20°C to -10°C, so we need to find out whether there is a cut with a linearity higher than 0.01 in the global optimal temperature range within the fourth value range obtained in step 3. ZGar(52° / -47°) cut angle. If yes, replace the optimal angle value obtained in step 4 with the linearity higher than ZGar (52° / -47°) The corresponding angle of the cut type; if not, the optimal angle value is still ZGar (52° / -47°).

[0142] Finally, when the temperature interval is the minimum When the temperature is between -20℃ and -10℃, the optimal angle design value is obtained, and the new cut type with the best linearity is ZGar (52° / -47°).

[0143] By manufacturing the quartz resonator according to the optimal rotation angle value, better linearity can be obtained.

[0144] In another embodiment of the present invention, in order to further improve the linearity of the quartz resonator, after obtaining the final optimal angle design value, step 5 may further include the following steps ab:

[0145] Step a: Based on the optimal rotation angle value, the aspect ratio of the tuning fork arm of the quartz resonator is optimized to obtain the optimal design values ​​of the width and length of the tuning fork arm.

[0146] Specifically, based on the optimal rotation angle value, by changing the width and length of the tuning fork arm of the quartz resonator, the width and length of the tuning fork arm corresponding to the time when the error between the theoretical vibration fundamental frequency and the simulation frequency is less than a preset error threshold are found as the optimal design value of the width and length of the tuning fork arm; wherein, the theoretical vibration fundamental frequency is obtained according to the calculation formula of the vibration fundamental frequency.

[0147] The calculation formula of the vibration fundamental frequency is:

[0148] ;

[0149] In the formula, represents the fundamental frequency of vibration, as the theoretical fundamental frequency of vibration, Indicates the length of the tuning fork arm in meters ( m ), Indicates the width of the tuning fork arm in meters ( m ), Indicates the density of quartz crystal in units of kg / m 3 , It represents the elastic compliance coefficient, in units of m 2 / N , Represents the fundamental frequency coefficient, and its value is 4.73.

[0150] It should be noted that when the tuning fork arm width is continuously changed and length In the process, we find that the length of the tuning fork arm The change to the frequency is the greatest, so during the optimization process the main change is the length of the quartz tuning fork arm. To improve the modal vibration frequency.

[0151] By comparison, the tuning fork arm width of the quartz resonator is finally taken 0.38 mm , the length of the tuning fork arm of the resonator For 3 mm .

[0152] The above parameters and the quartz crystal material density 2560 kg / m 3 The elastic compliance coefficient of the quartz substrate after rotation is 1.3752×10 -11 m 2 / N Substitute the calculation formula of the vibration fundamental frequency into the vibration fundamental frequency of the quartz tuning fork resonator. 36375 Hz , and the frequency measured by simulation is 34637 Hz It is quite close, with a small error of nearly 5%, so this parameter meets the design requirements.

[0153] Step b: According to the optimal rotation angle value and the optimal design values ​​of the tuning fork arm width and length, the optimal design of the quartz resonator linearity is completed.

[0154] By using the optimal rotation angle value and the optimal design values ​​of the tuning fork arm width and length obtained above as the final design values ​​to manufacture the quartz resonator, better linearity can be obtained.

[0155] When optimizing the linearity of the quartz resonator, the present invention further ensures the selection of the optimal rotation angle value by narrowing the temperature measurement range. At the same time, by changing the width-to-length ratio of the tuning fork arm, the optimal values ​​of the width and length of the tuning fork arm are found as design values, thereby further improving the linearity of the quartz resonator.

[0156] The optimization design method for the linearity of the quartz resonator provided by the present invention determines the value range of the angle corresponding to the selected cut type based on the elastic properties, piezoelectric properties and temperature-frequency characteristics of the quartz crystal itself, and on the other hand simplifies the angles within a large range of all possible values ​​according to the influence of the angle relationship between the angles on the temperature-frequency characteristics, narrows the angle value range, and finally selects the optimal angle value that meets the high linearity requirements. This method takes into account the key factors that affect the linearity, such as the temperature-frequency characteristics of the quartz crystal material itself, and can fundamentally improve the frequency stability of the quartz resonator, so that the quartz resonator has better linearity performance; and it greatly saves the time of taking the angle value and reduces the workload of subsequent linearity calculations.

[0157] The effect of the present invention can be further illustrated by the following simulation experiment.

[0158] 1. Simulation conditions

[0159] The present invention uses ANSYS software developed by ANSYS company to perform simulation.

[0160] 2. Simulation content

[0161] According to the method provided by the present invention, the modal simulation of the quartz tuning fork resonator is performed in ANSYS software, and the results are shown in Table 1.

[0162] Table 1 Simulated vibration frequency

[0163]

[0164] It can be seen from Table 1 that the fundamental frequency of the quartz tuning fork resonator is 36375 Hz , and the frequency measured by simulation is 34637 Hz The results are relatively close, with an error as small as 5%, which proves the feasibility of the new angle-cut quartz tuning fork resonator designed by the method of the present invention.

[0165] The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the protection scope of the present invention.

Claims

1. A method for optimizing the linearity of a quartz resonator, characterized in that: include: Select a cut type of quartz crystal, and determine a first value range of the angle corresponding to the selected cut type based on the elastic properties and piezoelectric properties of the quartz crystal; wherein the method of determining the first value range of the angle corresponding to the selected cut type based on the elastic properties and piezoelectric properties of the quartz crystal is as follows: obtain a relationship between the elastic compliance coefficient of the quartz crystal and the angle, and a relationship between the piezoelectric coefficient of the quartz crystal and the angle; impose constraints on the elastic compliance coefficient and the piezoelectric coefficient respectively, and combine the relationship between the elastic compliance coefficient and the angle, and the relationship between the piezoelectric coefficient and the angle, to obtain the first value range; Based on the temperature-frequency characteristics of the quartz crystal, constraints are imposed on the first-order temperature-frequency coefficient, the second-order temperature-frequency coefficient and the third-order temperature-frequency coefficient of the quartz crystal, and combined with the relationship between the first-order temperature-frequency coefficient and the elastic compliance coefficient, the relationship between the second-order temperature-frequency coefficient and the elastic compliance coefficient, the relationship between the third-order temperature-frequency coefficient and the elastic compliance coefficient, and the relationship between the elastic compliance coefficient and the angle, a second value range of the angle corresponding to the selected cut is obtained, and a third value range is formed together with the first value range; wherein, constraints are imposed on the first-order temperature-frequency coefficient, the second-order temperature-frequency coefficient and the third-order temperature-frequency coefficient of the quartz crystal, respectively expressed as: In the formula, represents the first-order temperature-frequency coefficient, represents the second-order temperature-frequency coefficient, represents the third-order temperature-frequency coefficient, || represents the absolute value, C -1 Indicates the unit of temperature-frequency coefficient; Based on the influence of the rotation angle on the temperature-frequency characteristics, on the basis of satisfying the constraint of the first-order temperature-frequency coefficient, based on the fact that the second-order and third-order temperature-frequency coefficients present a 180° periodic change law when the rotation angle changes, the graphic area corresponding to the third value range is divided; based on the symmetric relationship between the values ​​of each rotation angle in the divided graphic area, and the characteristic that the rotation angle does not affect the first-order temperature-frequency coefficient, the second-order temperature-frequency coefficient and the third-order temperature-frequency coefficient, the third value range is narrowed to obtain a fourth value range; Calculate the linearity corresponding to each angle within the fourth value range, and find the angle value with the highest linearity as the optimal angle value; The temperature range is divided into multiple temperature intervals, and a certain temperature interval is selected. By changing the left and right interval values ​​of the temperature full scale, the left and right interval values ​​of the temperature full scale corresponding to the highest linearity in the current temperature interval are found as the local optimal temperature range; Traversing all temperature intervals, performing linear optimal exploration in different temperature intervals to update the local optimal temperature range, and finally obtaining the global optimal temperature range; In the global optimal temperature range, using each angle value in the fourth value range, performing optimal linearity exploration to find out whether there is an angle whose linearity is higher than the linearity corresponding to the optimal angle value, and if so, updating the found angle to the optimal angle value; The optimized design of the linearity of the quartz resonator is completed according to the optimal rotation angle value.

2. The method for optimizing the linearity of a quartz resonator according to claim 1, characterized in that: The cut type of the quartz crystal is selected, and based on the elastic properties and piezoelectric properties of the quartz crystal, a first value range of the rotation angle corresponding to the selected cut type is determined, including: For the rotation angle corresponding to the selected cut type, obtaining a relationship between the elastic compliance coefficient of the quartz crystal and the rotation angle, and a relationship between the piezoelectric coefficient of the quartz crystal and the rotation angle; Constraints are imposed on the elastic compliance coefficient and the piezoelectric coefficient respectively, and a first value range is obtained by combining a relationship between the elastic compliance coefficient and the rotation angle and a relationship between the piezoelectric coefficient and the rotation angle.

3. The method for optimizing the linearity of a quartz resonator according to claim 2, characterized in that: The constraint imposed on the elastic compliance coefficient is expressed as: In the formula, s' 2j represents the cross elastic compliance coefficient, s' 22 represents the elastic compliance coefficient, | | represents the absolute value; The constraints imposed on the piezoelectric coefficients are expressed as: |d’ 12 |≥1×10 -12 C / N; Where, d' 12 represents the key piezoelectric coefficient, C / N represents the unit of piezoelectric constant, C represents the unit of charge, Coulomb, and N represents the unit of force, Newton.

4. The method for optimizing the linearity of a quartz resonator according to claim 1, characterized in that: According to the optimal rotation angle value, the optimization design of the linearity of the quartz resonator is completed, including: Based on the optimal rotation angle value, the aspect ratio of the tuning fork arm of the quartz resonator is optimized to obtain the optimal design values ​​of the width and length of the tuning fork arm; According to the optimal rotation angle value and the optimal design values ​​of the tuning fork arm width and length, the optimized design of the linearity of the quartz resonator is completed.

5. The method for optimizing the linearity of a quartz resonator according to claim 4, characterized in that: Based on the optimal rotation angle value, the aspect ratio of the tuning fork arm of the quartz resonator is optimized to obtain the optimal design values ​​of the width and length of the tuning fork arm, including: Based on the optimal rotation angle value, by changing the width and length of the tuning fork arm of the quartz resonator, the width and length of the tuning fork arm corresponding to the error between the theoretical vibration fundamental frequency and the simulation frequency is less than a preset error threshold is found as the optimal design value of the width and length of the tuning fork arm; wherein, the theoretical vibration fundamental frequency is obtained according to the calculation formula of the vibration fundamental frequency.

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