JP2022061671A - Resonator characteristic measurement method - Google Patents

Abstract

To provide a resonator characteristic measurement method capable of easily obtaining characteristics of a resonator.SOLUTION: A resonator characteristic measurement method includes: a first step of evaluating a sensitivity coefficient and uncertainty relative to resonator dimensions and determining resonator dimensions such that the sensitivity coefficient becomes small; a second step of measuring passage characteristics of a resonator having resonator dimensions determined in the first step and calculating a resonance frequency of the resonator and a non-load Q value; a third step of calculating a relative dielectric constant of the resonator by a resonance frequency calculated in the second step and an actual measurement value of resonator dimensions; and a fourth step of calculating a conductivity of a wide wall surface of the resonator, a conductivity of a narrow wall surface, and a dielectric tangent by the non-load Q value calculated in the second step, the relative dielectric constant calculated in the third step, and the actual measurement value of resonator dimensions.SELECTED DRAWING: Figure 4

Description

The present invention relates to a method for measuring resonator characteristics.

There is a waveguide excitation resonator as one of the resonators used in the high frequency band such as the millimeter wave band. The waveguide excitation resonator can be used, for example, as an antenna or a waveguide in a high frequency band. Patent Document 1 discloses a technique relating to a laminated waveguide line. Further, Patent Document 2 discloses a technique relating to a high-frequency conductivity measuring device capable of easily measuring the conductivity of a conductor plate to be measured.

Japanese Unexamined Patent Publication No. 2010-34826 Japanese Unexamined Patent Publication No. 2015-227850

When designing a resonator applicable to a given device, it is necessary to determine the conductivity and dielectric loss tangent of the resonator in the high frequency band. For example, in the case of a rectangular parallelepiped resonator, it is necessary to obtain the conductivity of a wide wall surface, the conductivity of a narrow wall surface, and the dielectric loss tangent. However, in the technique disclosed in Patent Document 2, since these values cannot be obtained at once, there is a problem that it becomes complicated when obtaining the characteristics of the resonator.

In view of the above problems, an object of the present invention is to provide a resonator characteristic measuring method in which the characteristics of the resonator can be easily obtained.

The resonator characteristic measuring method according to one aspect of the present invention is
The first step of evaluating the sensitivity factor and uncertainty with respect to the resonator size and determining the resonator size such that the sensitivity factor becomes smaller.
The second step of measuring the passage characteristics of the resonator having the resonator dimension determined in the first step and calculating the resonance frequency and the no-load Q value of the resonator.
The third step of calculating the relative permittivity of the resonator using the resonance frequency calculated in the second step and the measured value of the resonator dimensions,
Using the no-load Q value calculated in the second step, the relative permittivity calculated in the third step, and the measured value of the resonator size, the wide wall surface of the resonator is used. A fourth step of calculating the conductivity of the narrow wall surface, the conductivity of the narrow wall surface, and the dielectric loss tangent.

In the above-mentioned resonator characteristic measurement method,
The resonator may be a rectangular parallelepiped resonator, and when the width direction dimension of the resonator is a, the thickness direction dimension is b, and the longitudinal dimension is d.
In the first step, the sensitivity coefficient formula of the relative permittivity and the dimension a, the sensitivity coefficient formula of the relative permittivity and the resonance frequency, the sensitivity coefficient formula of the dimension d and the dimension a, and the sensitivity coefficient formula of the dimension d and the resonance frequency are obtained. make,
Assuming the standard uncertainty of the no-load Q value, the standard uncertainty of the dimensions a, b, d, the standard uncertainty of the resonance frequency, and the standard uncertainty of the relative permittivity.
The sensitivity coefficient when the dimensions a, b, and d are changed may be calculated.

In the first step, after setting the interval of the adjacent resonance frequencies so that the error of the no-load Q value is equal to or less than a predetermined value, the resonator size may be determined so that the sensitivity coefficient becomes small. ..

In the first step,
Assuming a resonator parallel circuit with two or more resonators,
The resonance frequency and the no-load Q value Qu are given to calculate the passing characteristics.
The no-load Q value Qum is calculated from the passage characteristics, and the load Q value is calculated.
The interval between adjacent resonance frequencies is set so that the difference between the Qu and the Qum is equal to or less than a predetermined value.
The resonator size may be determined so that the sensitivity coefficient becomes small.

In the second step, the first and second conductor substrates arranged so as to face each other and the metal vias arranged between the first conductor substrate and the second conductor substrate are formed. The passage characteristic of the resonator in which the space surrounded by the first conductor substrate, the second conductor substrate, and the plurality of metal vias functions as a waveguide may be measured.

In the third step,
Resonator dimensions a, b, d, and relative permittivity ε _r are unknown, and resonance frequency f _mnl , resonance mode order m, l, and magnetic permeability μ _r are known numbers.
The relative permittivity of the resonator may be calculated using the measured value of the resonator dimensions and the following linear equation (however, x ₁ , x ₂ , x ₃ , and x ₄ are defined as follows. ).

In the fourth step,
Resonator dimensions a, b, d, magnetic permeability μ, wave number k, angular frequency ω, with unknowns being the conductivity σ _f on the wide wall surface of the resonator, the conductivity σ _{r, t} on the narrow wall surface, and the dielectric tangent tan δ. Let the no-load Q value Qu and the resonance mode order l be known numbers.
The following linear equation may be used to calculate the conductivity of the wide wall, the conductivity of the narrow wall, and the dielectric loss tangent of the resonator (where a ₁ = l ² a ³ d + ad ³ , a ₂ = 2l). ² a ³ b + 2 bd ³ and x ₅ , x ₆ and x ₇ are defined as follows).

INDUSTRIAL APPLICABILITY According to the present invention, it is possible to provide a resonator characteristic measurement method in which the characteristics of a resonator can be easily obtained.

It is a perspective view which shows an example of the resonator which concerns on embodiment. It is a perspective view which shows the structural example of the resonator which concerns on embodiment. It is a top view which shows the structural example of the resonator which concerns on embodiment. It is a flowchart for demonstrating the resonator characteristic measuring method which concerns on embodiment. It is a flowchart for demonstrating the details of the operation of step S1 of FIG. It is a graph which shows an example of the measurement result of the passage characteristic in step S2 of FIG. It is a graph for demonstrating the calculation method of the Q value in step S2 of FIG.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.
First, a resonator to which the resonator characteristic measuring method according to the present embodiment is applied will be described. FIG. 1 is a perspective view showing an example of a resonator according to the present embodiment. As shown in FIG. 1, the resonator 1 is a rectangular parallelepiped resonator, and has a structure having a length in the x-axis direction of a, a length in the y-axis direction of b, and a length in the z-axis direction of d. ..

Coupling slots 11 and 12 are formed on the xz plane of the resonator 1. Specifically, the coupling slot 11 is provided on the negative side in the z-axis direction of the resonator 1, and the coupling slot 12 is provided on the positive side in the z-axis direction of the resonator 1. The sizes of the coupling slots 11 and 12 are l in the x-axis direction and w in the z-axis direction. For example, the inside of the resonator 1 is hollow, and the high frequency introduced from the coupling slot 11 propagates inside the resonator 1 and then is derived from the coupling slot 12.

2 and 3 are a perspective view and a top view showing a configuration example of the resonator according to the present embodiment. The resonator 2 shown in FIGS. 2 and 3 is a waveguide excitation SIW (Substrate Integrated Waveguide) resonator, which is configured by using two conductor substrates 31 and 32 and a plurality of metal vias (through conductors) 33. Has been done. The conductor substrate 31 is arranged on the upper side (plus side in the y-axis direction), and the conductor substrate 32 is arranged on the lower side (minus side in the y-axis direction). A plurality of metal vias 33 are arranged between the conductor substrate 31 and the conductor substrate 32 so as to form a waveguide. That is, in the resonator 2 shown in FIGS. 2 and 3, the space surrounded by the conductor substrate 31, the conductor substrate 32, and the plurality of metal vias 33 functions as a waveguide. The space sandwiched between the two conductor substrates 31 and 32 may be hollow, or a dielectric material may be arranged.

Coupling slots 21 and 22 are formed on the surface of the resonator 2 on the conductor substrate 32 side. Specifically, the coupling slot 21 is provided on the negative side in the z-axis direction of the resonator 2, and the coupling slot 22 is provided on the positive side in the z-axis direction of the resonator 2. A waveguide 35 is connected to the coupling slot 21, and a waveguide 36 is connected to the coupling slot 22. The negative side of the waveguides 35 and 36 in the y-axis direction is connected to a network analyzer (not shown). For example, the high frequency generated by the network analyzer is introduced into the resonator 2 via the waveguide 35 and the coupling slot 21. The high frequency introduced into the resonator 2 passes through the resonator 2 and then is transmitted to the network analyzer via the coupling slot 22 and the waveguide 36. In step S2 of FIG. 4 described below, the passage characteristic of the resonator is measured by using the resonator 2 having such a configuration.

Next, the resonator characteristic measuring method according to the present embodiment will be described. FIG. 4 is a flowchart for explaining the resonator characteristic measuring method according to the present embodiment. The resonator characteristic measuring method according to the present embodiment includes the following first to fourth steps.

The first step is to evaluate the sensitivity coefficient and uncertainty with respect to the resonator size, and determine the resonator size so that the sensitivity coefficient becomes smaller (step S1 in FIG. 4).
The second step is a step of measuring the passing characteristics of the resonator having the resonator dimensions determined in the first step, and calculating the resonance frequency and the no-load Q value of the resonator (step S2 in FIG. 4). ).
The third step is a step of calculating the relative permittivity of the resonator using the resonance frequency calculated in the second step and the measured value of the resonator size (step S3 in FIG. 4).
The fourth step uses the no-load Q value calculated in the second step, the relative permittivity calculated in the third step, and the measured value of the resonator size, and the wide wall surface of the resonator is used. This is a step of calculating the conductivity, the conductivity of the narrow wall surface, and the dielectric loss tangent (step S4 in FIG. 4).

Hereinafter, the resonator characteristic measurement method according to the present embodiment will be described in detail with reference to the flowchart shown in FIG. In the following, a method of measuring the characteristics of the resonator 1 having the structure shown in FIG. 1 will be described.

In step S1 of FIG. 4, the sensitivity coefficient and uncertainty with respect to the resonator size are evaluated (step S1-1), and the resonator size is determined so that the sensitivity coefficient becomes small (step S1-2). Specifically, hypothetical conditions are determined, and the sensitivity coefficient and uncertainty for the resonator 1 having the structure shown in FIG. 1 are evaluated.

FIG. 5 is a flowchart for explaining the details of the operation of step S1 of FIG. As shown in FIG. 5, in step S1, first, a sensitivity coefficient equation is created (step S11).

The following formula is a general formula of synthetic uncertainty, _{u fi} is the synthetic uncertainty of fi, and u _xj is the uncertainty of _xj . ∂f _i / ∂x _j is a sensitivity coefficient. Further, a, b, and d are the dimensions of the resonator 1 shown in FIG. 1, ε _r is the relative permittivity, σ _f is the conductivity of the wide wall surface, and σ _{r, t} is the conductivity of the narrow wall surface. Yes, tan δ is a dielectric loss tangent, and _Qu is a no-load Q value.

Moreover, the following formula is a general formula of the sensitivity coefficient.

In step S11, a sensitivity coefficient formula for each parameter is created using the above-mentioned general formula for synthetic uncertainty and the general formula for the sensitivity coefficient.

Specifically, the sensitivity coefficient equations of the relative permittivity ε _r and the dimension a are as follows.

The sensitivity coefficient equations for the relative permittivity ε _r and the resonance frequency f are as follows.

Further, the sensitivity coefficient equations of the dimension d and the dimension a are as follows.

The sensitivity coefficient equations for the dimension d and the resonance frequency f are as follows.

Next, the standard uncertainty of the measured value is assumed in order to obtain the uncertainty (step S12). As an example, the standard uncertainty of the no-load Q value _Qu is 0.3%, the standard uncertainty of the dimensions a, b, and d is 0.01%, and the standard uncertainty of the resonance frequency f is 0.01%. The standard uncertainty of the relative permittivity is assumed to be 0.3%.

Then, the sensitivity coefficient when each parameter is changed is calculated (step S13). As an example, as analysis conditions, the frequency is 57 to 95 GHz, the relative permittivity is 2.18, the dielectric loss tangent is 0.001, the conductivity of the wide wall surface is 1.82 × ¹⁰⁷ S / m, and the conductivity of the narrow wall surface. The sensitivity coefficient is calculated by setting the rate to 1.12 × ¹⁰⁷ S / m.

After that, the resonator size is determined so that the sensitivity coefficient becomes small (step S1-2 in FIG. 4). For example, the resonator dimension a is set small. The resonator dimension b does not affect the relative permittivity ε _r and the dimension d, but when it is increased, the uncertainty of the conductivity of the narrow wall surface and the uncertainty of the dielectric loss tangent decreases, and the uncertainty of the conductivity of the wide wall surface increases. Increasing the resonator dimension d reduces uncertainty at all parameters. However, when the resonator dimension d is increased, the number of modes increases, so that the difference in resonance frequency becomes small, and the Q value changes under the influence of the adjacent frequency.

Hereinafter, the case of determining the resonator size so that the sensitivity coefficient becomes small will be described with reference to steps S14 to S19 of FIG. In steps S14 to S19, the influence of the adjacent resonance frequency interval on the no-load Q value is evaluated. That is, when the resonator length d is increased, the difference in resonance frequency becomes smaller and the Q value changes under the influence of the adjacent resonance frequency. Therefore, the influence of the interval between adjacent resonance frequencies on the unloaded Q value is evaluated. do.

First, a two resonator parallel circuit is assumed (step S14). Next, the resonance frequency and the no-load Q value Qu are given, and the passing characteristics are calculated (step S15). Then, the no-load Q value Qum is calculated from the passing characteristics (step S16). Then, the difference between Qu and Qum due to the interval Δf between two or more resonance frequencies is evaluated (step S17). Then, the resonance frequency interval Δf is set so as to satisfy a predetermined error range (step S18). For example, the resonance frequency interval Δf is set so that the error of the no-load Q values Qu and Qum is 0.1% or less. Under the above conditions, in order to reduce the error of the no-load Q value to 0.1% or less, the resonance frequency interval Δf is set to satisfy Δf> 0.02. In the present embodiment, the processes of steps S15 to S18 are repeated so that the error between Qu and Qum satisfies a predetermined error range. After that, the resonator size is determined so that the sensitivity coefficient becomes small (step S19). In this embodiment, at least a two-resonator parallel circuit may be used to evaluate the adjacent resonance frequency. For example, a parallel circuit having a larger number of parallels than the two resonators, that is, a resonator parallel circuit having two or more resonators may be used. good.

Next, the passage characteristics of the resonator having the resonator dimensions determined in step S1 are measured, and the resonance frequency of the resonator and the no-load Q value are calculated (step S2 in FIG. 4). For example, a resonator 2 having the configurations shown in FIGS. 2 and 3 is prepared. At this time, the resonator 2 is configured to have the resonator dimensions a, b, and d determined in step S1. Then, the passing characteristics of the resonator 2 are measured (step S2-1).

Specifically, the waveguide 35 is connected to the coupling slot 21 provided in the resonator 2, and the waveguide 36 is connected to the coupling slot 22. Further, a network analyzer (not shown) is connected to the negative side of the waveguides 35 and 36 in the y-axis direction. Then, a high frequency is generated by a network analyzer, and this high frequency is introduced into the resonator 2 via the waveguide 35 and the coupling slot 21. The high frequency introduced into the resonator 2 passes through the resonator 2 and then is transmitted to the network analyzer via the coupling slot 22 and the waveguide 36. Using the resonator 2 having such a configuration, the passage characteristics of the resonator are measured.

Next, the resonance frequency of the resonator and the no-load Q value are calculated using the measured passage characteristics of the resonator (step S2-2). FIG. 6 is a graph showing an example of the measurement result of the passage characteristic in step S2. As shown in FIG. 6, the resonance frequency is a frequency at which the passing amount S21 peaks.

FIG. 7 is a graph for explaining the method of calculating the Q value in step S2. As shown in FIG. 7, when the frequency on the low frequency side is f ₁ and the frequency on the high frequency side is f ₂ at a value 3 dB smaller than the peak value of the resonance frequency f ₀ , the load Q value Q _l uses the following equation. Is required. In other words, the load Q value Q _l is obtained using the pass characteristic of the 3 dB bandwidth.

Further, the insertion loss IL ₀ of the coupling slots 21 and 22 and the waveguides 35 and 36 is obtained by using the following equation.

Then, the no-load Q value Q _{u, m} can be expressed by the following equation using the load Q value Q _l and the insertion loss IL ₀ .

The no-load Q value Q _{u, m} is a value indicating the sharpness of resonance, and the larger the Q _{u, m,} the smaller the loss.

Next, the relative permittivity of the resonator is calculated using the resonance frequency calculated in step S2 and the measured value of the resonator dimensions (step S3 in FIG. 4). Specifically, the relative permittivity of the resonator is calculated using the following method.

As a precondition, the resonator dimensions a, b, d, and the relative permittivity ε _r are unknown. Further, the resonance frequency f _mnl , the resonance mode order m, l, and the magnetic permeability μ _r are set as known numbers.

In the resonator 1 having the configuration shown in FIG. 1, the resonance frequency _fmnl is expressed by the following equation. In addition, c is the speed of light.

The above equation is modified as the following equation.

Then, x ₁ , x ₂ , x ₃ , and x ₄ are defined as follows.

Then, the above equation is expressed as follows using x ₁ , x ₂ , x ₃ , and x ₄ .

Here, since n = 0, the above equation is expressed as follows.

Here, the resonator dimensions a, b, and d are obtained by mechanically measuring the dimensions of the resonator used in step S2. Therefore, x ₁ and x ₃ are known values. Therefore, since the above equations result in simultaneous linear equations, an exact solution can be calculated when N = 2 and a least squares solution can be calculated when N> 2. As described above, in step S3, the relative permittivity ε _r of the resonator can be calculated by using the measured value of the resonator dimension and the above-mentioned linear equation.

Next, using the no-load Q value calculated in step S2, the relative permittivity calculated in step S3, and the measured value of the resonator size, the conductivity of the wide wall surface and the conductivity of the narrow wall surface of the resonator are used. The rate and the dielectric loss tangent are calculated (step S4 in FIG. 4). Specifically, the conductivity of the wide wall surface of the resonator, the conductivity of the narrow wall surface, and the dielectric loss tangent are calculated using the following methods.

As preconditions, the conductivity σ _f of the wide wall surface of the resonator, the conductivity σ _{r, t} of the narrow wall surface, and the dielectric loss tangent tan δ are unknown. Further, the resonator dimensions a, b, d, magnetic permeability μ, wave number k, angular frequency ω, no-load Q value Qu, and resonance mode order (z-axis direction) l are known numbers.

In the resonator 1 having the configuration shown in FIG. 1, the no-load Q values Q _{u and a} are expressed by the following equations. From the following equation, it can be said that the no-load Q value is determined according to the current flowing on the wall surface of the resonator. Note that k is the wave number, η is the impedance in free space, and _{Ri, j} , σ _{i, and j} are the skin resistance and conductivity with respect to the current flowing in the j direction in the i-plane.

Further, the no-load Q value _Qu has the following relationship.

Further, 1 / Q _c is expressed as follows.

At this time, x ₅ and x ₆ are defined as shown below, (l ² a ³ d + ad ³ ) is set to a ₁ , and (2 l ² a ³ b + 2 bd ³ ) is set to a _2. As a result, 1 / Q _c = a ₁ x ₅ + a ₂ x ₆ .

Further, 1 / Q _d is expressed as follows.

Therefore, 1 / _Qu is eventually expressed by the following linear equation.

When N resonance modes are measured, N linear equations are obtained. Therefore, in this case, since there are three unknowns x ₅ , x ₆ , and x ₇ , an exact solution can be obtained when N = 3, and a least squares solution can be obtained when N> 3. Moreover, the error can be absorbed by measuring 4 or more resonance modes. Note that x ₅ is the square root of the reciprocal of the conductivity σ _f of the wide wall surface, x ₆ is the square root of the reciprocal of the conductivity σ _{r and t} of the narrow wall surface, and x ₇ is the dielectric loss tangent tan δ.

In the resonator characteristic measurement method according to the present embodiment described above, the characteristics of the resonator can be obtained at once for the conductivity of the wide wall surface, the conductivity of the narrow wall surface, and the dielectric loss tangent with a single resonator. Is easily requested. That is, in the resonator characteristic measuring method according to the present embodiment, the conductivity of the wide wall surface, the conductivity of the narrow wall surface, and the dielectric loss tangent can be obtained at once without measuring a plurality of resonators. Characteristics are easily determined. Further, in the resonator characteristic measurement method according to the present embodiment, since the passage characteristics of the resonator are measured using the resonators having the configurations shown in FIGS. 2 and 3 in step S2, the passage characteristics are close to the practical embodiment. The electrical properties can be evaluated by the shape.

Although the present invention has been described above in accordance with the above-described embodiment, the present invention is not limited to the configuration of the above-described embodiment, and is within the scope of the claimed invention within the scope of the claims of the present application. Of course, it includes various modifications, corrections, and combinations that can be made by a person skilled in the art.

1, 2 Resonator 11, 12 Coupling slot 21, 22 Coupling slot 31, 32 Conductor substrate 33 Metal via (through conductor)
35, 36 Waveguide

Claims (7)

The first step of evaluating the sensitivity factor and uncertainty with respect to the resonator size and determining the resonator size such that the sensitivity factor becomes smaller.
The second step of measuring the passage characteristics of the resonator having the resonator dimension determined in the first step and calculating the resonance frequency and the no-load Q value of the resonator.
The third step of calculating the relative permittivity of the resonator using the resonance frequency calculated in the second step and the measured value of the resonator dimensions,
Using the no-load Q value calculated in the second step, the relative permittivity calculated in the third step, and the measured value of the resonator size, the wide wall surface of the resonator is used. The fourth step of calculating the conductivity of the narrow wall surface, the conductivity of the narrow wall surface, and the dielectric loss tangent.
Resonator characteristic measurement method. The resonator is a rectangular parallelepiped resonator, and when the width direction dimension of the resonator is a, the thickness direction dimension is b, and the longitudinal dimension is d.
In the first step, the sensitivity coefficient formula of the relative permittivity and the dimension a, the sensitivity coefficient formula of the relative permittivity and the resonance frequency, the sensitivity coefficient formula of the dimension d and the dimension a, and the sensitivity coefficient formula of the dimension d and the resonance frequency are obtained. make,
Assuming the standard uncertainty of the no-load Q value, the standard uncertainty of the dimensions a, b, d, the standard uncertainty of the resonance frequency, and the standard uncertainty of the relative permittivity.
Calculate the sensitivity coefficient when the dimensions a, b, and d are changed.
The resonator characteristic measuring method according to claim 1. Claimed in the first step, after setting the interval of adjacent resonance frequencies so that the error of the no-load Q value is equal to or less than a predetermined value, the resonator size is determined so that the sensitivity coefficient becomes small. The resonator characteristic measuring method according to 1 or 2. In the first step,
Assuming a resonator parallel circuit with two or more resonators,
The resonance frequency and the no-load Q value Qu are given to calculate the passing characteristics.
The no-load Q value Qum is calculated from the passage characteristics, and the load Q value is calculated.
The interval between adjacent resonance frequencies is set so that the difference between the Qu and the Qum is equal to or less than a predetermined value.
Determine the resonator dimensions such that the sensitivity coefficient is small.
The resonator characteristic measuring method according to any one of claims 1 to 3. In the second step, the first and second conductor substrates arranged so as to face each other and the metal vias arranged between the first conductor substrate and the second conductor substrate are formed. One of claims 1 to 4, wherein the space surrounded by the first conductor substrate, the second conductor substrate, and the plurality of metal vias measures the passage characteristics of a resonator that functions as a waveguide. The method for measuring resonator characteristics according to item 1. In the third step,
Resonator dimensions a, b, d, and relative permittivity ε _r are unknown, and resonance frequency f _mnl , resonance mode order m, l, and magnetic permeability μ _r are known numbers.
The relative permittivity of the resonator is calculated using the measured value of the resonator dimension and the following linear equation.
The resonator characteristic measuring method according to any one of claims 1 to 5.

However, x ₁ , x ₂ , x ₃ , and x ₄ are defined as follows.

In the fourth step,
Resonator dimensions a, b, d, magnetic permeability μ, wave number k, angular frequency ω, with unknowns being the conductivity σ _f on the wide wall surface of the resonator, the conductivity σ _{r, t} on the narrow wall surface, and the dielectric tangent tan δ. Let the no-load Q value Qu and the resonance mode order l be known numbers.
Using the following linear equation, the conductivity of the wide wall surface, the conductivity of the narrow wall surface, and the dielectric loss tangent of the resonator are calculated.
The resonator characteristic measuring method according to any one of claims 1 to 6.

However, a ₁ = l ² a ³ d + ad ³ , a ₂ = 2 l ² a ³ b + 2bd ³ , and x ₅ , x ₆ , and x ₇ are defined as follows.

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