JP2006010431A - Mass detector - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a highly sensitive, versatile and compact mass detector of high measuring precision capable measuring quickly a specified substance in a solution or a state of the solution by a simple method. <P>SOLUTION: This mass detector using the QCM method by a quartz oscillator 1 is constituted to compute changes of signal levels in a plurality of frequencies indicating different output characteristics in the vicinity of a resonance frequency of the quartz oscillator 1 and to measure a very small change of a mass. The change of the signal level is computed using Expression 1 and Expression 2. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a mass detector, and more particularly to measuring the mass of a substance fixed on a surface of a crystal resonator electrode in a solution by a simple method, specifically, a QCM (Quartz Crystal Microbalance) method.

  Conventionally, a method of measuring a mass change of a substance fixed on an electrode surface by using a quartz crystal resonator is known for measuring a specific substance such as a measurement of moisture in a solvent or a viscosity of a liquid. Measurement using such a crystal resonator can be roughly divided into two methods, an oscillation method and an impedance method.

  As shown in FIG. 10, the oscillation method is composed of an oscillation circuit 11 and a frequency counter 12 using a crystal resonator (Xtal) 1 as a feedback element, and an output of the oscillation circuit is connected to an input terminal of the frequency counter 12. In this method, the oscillation frequency generated in the oscillation circuit 11 is counted, and the counting result is displayed or connected to and output from an external data processing device. That is, when the mass of the electrode surface of the crystal unit 1 is changed, the oscillation frequency is changed, and a minute mass is detected by relating the change of the oscillation frequency to the change of the mass. The method of FIG. 10 is an analog signal whose frequency is the input signal, but a digital numerical result can be obtained by using the frequency counter 12, so that a method such as AD conversion is unnecessary, which is advantageous.

  On the other hand, the impedance method refers to a method in which an AC signal of an arbitrary frequency is applied to a crystal resonator and the main resonance frequency value of the crystal resonator is obtained from the frequency characteristics of the impedance of the crystal resonator. A circuit, V-F converter, current-voltage converter, and peak hold circuit are applied to the crystal unit, and an alternating current signal that periodically sweeps a predetermined frequency range is applied to the crystal unit. Then, a method has been proposed in which the peak value of the voltage is measured and the impedance characteristics of the quartz crystal resonator at resonance are measured in real time (for example, Patent Document 1).

In addition, regarding the measurement of the impedance or resonance frequency of the crystal resonator, the number of measurement points is reduced by using a network analyzer as the resonance frequency calculation means based on the reactance of the complex impedance from the resonance frequency calculation method based on the phase curve, and A measuring device and a measuring method for impedance and resonance frequency of a crystal resonator with little resonance frequency calculation error have been proposed (for example, Patent Document 2).
Japanese Patent Laid-Open No. 06-109676 Japanese Patent Laid-Open No. 08-248072

  However, the measurement method or measurement apparatus described above may have the following problems.

  That is, in the oscillation method, in general, 1 second, which is a unit time, is required from the count value per unit time to detect a change of 1 Hz with respect to the detection response time, and a response speed higher than this is required. However, a special device was required for the frequency counter, which caused the device to be complicated and expensive. Further, when it is necessary to detect a minute mass change of the vibrator, such as a biological reaction, high detection sensitivity is required. Increasing the detection sensitivity is possible by increasing the counting time, but the problem arises that the response speed is sacrificed.

厳密には発振周波数がＲ_１、Ｃ_０の影響を受けるので、電極表面に付着した物質の質量だけでなく、粘弾性、温度、ストレス、振動子に接する液体との物理的、および化学的相互作用等、さまざまな要因に影響を受けることが明らかになってきた。つまり、発振周波数は水晶振動子の等価定数（Ｌ_１、Ｃ_１、Ｒ_１、Ｃ_０）の変動影響を受けるため、接液中ではＲ_１が大きくなる。従って、Ｒ_１の影響を少なくするためには、溶液の温度を一定にする必要があり、例えば±０．１℃以下の正確な温度制御が必要であり、装置のコスト高の原因になっていた。 Further, the oscillation type QCM method is a method of detecting an oscillation frequency change as a mass change because the oscillation frequency oscillates at a frequency close to the main resonance frequency f ₀ of the crystal resonator as shown in the following formula 4. But,

Strictly speaking, since the oscillation frequency is affected by R ₁ and C ₀ , not only the mass of the substance attached to the electrode surface but also the physical and chemical interaction with the viscoelasticity, temperature, stress, and the liquid in contact with the vibrator. It has become clear that it is influenced by various factors, such as action. That is, the oscillation frequency to receive the effect of a variation in the equivalent constants of the crystal oscillator _{(L 1, C 1, R} 1, C 0), R 1 becomes larger in wetted. Therefore, in order to reduce the influence of R ₁ , it is necessary to make the temperature of the solution constant. For example, accurate temperature control of ± 0.1 ° C. or less is necessary, which causes high cost of the apparatus. It was.

  On the other hand, the conventional measuring apparatus using the impedance method has a drawback that the circuit configuration is very complicated and cannot meet the demands of various applications. In particular, in the current-voltage conversion circuit used, since the crystal resonator is a crystal resonator of 10 MHz or less, it is difficult to realize an accurate current-voltage conversion circuit for a crystal resonator having a frequency higher than this. It was. In addition, the measuring apparatus and measuring method using a network analyzer have a drawback that the measuring apparatus itself must be expensive because an expensive network analyzer is required. In addition, it is necessary to use a complicated circuit technique to obtain a strict resonance frequency, and in particular, advanced technology such as high-frequency RF signal processing is required for practical use, resulting in a more complicated circuit configuration. . In addition, the cost is high and there is a problem in terms of energy efficiency.

  Therefore, the present invention solves the above-described problems, and is a compact, high-sensitivity, rapid, versatile, and high-accuracy measuring device that uses a crystal resonator to solve the above-described problems. An object of the present invention is to provide a mass detection device for measuring a specific substance in a solution or a state of the solution. That is, an object is to measure a minute mass increase of a substance fixed on the surface of a crystal resonator electrode in a solution by a mass detection device having a simple configuration.

  As a result of intensive studies, the present inventors have found that the above object can be achieved by a mass measuring apparatus shown below, and have completed the present invention.

  The present invention is a mass detection apparatus using a QCM method using a crystal resonator, which calculates a change in signal amount at a plurality of frequencies indicating different output characteristics in the vicinity of the resonance frequency of the crystal resonator, and performs a minute change in mass. Is measured.

As mentioned above, larger influence on the ambient temperature in addition the value is increased in the equivalent series resistance R ₁ in particular solutions of the crystal oscillator, the output characteristic of the crystal oscillator is likewise in solution, the effect of ambient temperature Will be greatly affected. The present inventor calculated the output characteristics of the crystal resonator in the vicinity of the resonance frequency, the frequency at which the change in the equivalent constant of the crystal resonator is the largest, and the frequency appearing in the measurement result, which is calculated by the elements forming the equivalent circuit It was in good agreement with the theoretical characteristics, and it was judged that the constant of the crystal unit would not change for a short time.

Therefore, if the output characteristics at two frequencies in the vicinity are calculated simultaneously, the resonance frequency can be determined from the calculation result, and it is divided into L ₁ related to the mass of the vibration part and R ₁ related to the internal friction of the vibration part. the operation result can be obtained with, mass change does not include a theoretical equivalent series resistance R ₁ - it is possible to obtain output characteristics. In other words, without being affected by the theoretical equivalent series resistance R _1, directly, it becomes possible to detect the mass or mass change. It has been confirmed that characteristics close to this theory can be obtained even in actual measurement of a specific substance or solution state in a solution using a mass detector, and by using such a simple configuration or method, It has become possible to accurately measure the state of a specific substance or solution. In the conventional impedance method, it is necessary to find the resonance frequency from the measurement results at many frequencies, and it takes time to measure. However, in this method, the resonance frequency is determined from the minimum two measurement results, so the measurement time is shortened. can do. Of course, the frequency to be selected is not limited to two, and it is needless to say that selecting a plurality of frequencies in consideration of other error factors in actual measurement is effective in improving accuracy.

The present invention is the above-described mass detection device, wherein the change in the signal amount is calculated using the following formulas 1 and 2. Where z is impedance, e is potential, f is frequency, j is imaginary, ω = 2πf, L ₁ is the mass of the vibrating part, C ₁ is the compliance of the crystal piece, R ₁ is the internal friction of the vibrating part, C ₀ Represents the parallel capacity.

In other words, from the knowledge of the present inventor as described above, by analyzing a simultaneous equation based on the output characteristics represented by the above equation for a plurality of selected frequencies, the equivalent constant of the crystal resonator is obtained, An output corresponding to a change in mass fixed to the electrode can be obtained. Therefore, it is possible to provide a mass detection device with a high measurement accuracy that is simple in configuration, low cost, and capable of obtaining a large amount of information with low power consumption. Specifically, as shown in the above formula, the change in the mass of the electrode surface is separated from L ₁ corresponding to the mass of the vibration part and the vibration energy loss R ₁ due to friction or the like, so that the result is obtained. By measuring the minute mass increase of the substance fixed on the surface of the crystal resonator electrode caused by the substance, the concentration of the specific substance can be measured by a mass detection device having a simple configuration. In addition, with this method, the resonance frequency can be determined from the measurement results of a minimum of two points, and the optimum frequency can be selected and measured in a very short time, resulting in fluctuations in the drive circuit, detection circuit, etc. Little affected by drift due to factors.

Furthermore, the present invention is the above-described mass detection device, wherein the change in the signal amount is calculated using the following Equation 1 and Equation 3. Here, z is impedance, e is potential, a is sensitivity correction coefficient, b is drift correction coefficient, f is frequency, j is imaginary number, ω = 2πf, L ₁ is the mass of the vibrating part, and C ₁ is the compliance of the crystal piece , R ₁ represents the internal friction of the vibrating part, and C ₀ represents the parallel capacity.

  In other words, in Equation 2 above, the factors of sensitivity and drift may still not be negligible with respect to the output characteristics. For these two factors, the sensitivity correction coefficient and the drift correction coefficient are added to the arithmetic expression to further measure. The accuracy can be improved.

  As described above, the present invention enables a mass detection apparatus using a crystal resonator having a simple configuration, high sensitivity, quickness, high versatility, and high measurement accuracy. In addition, the hardware aspect has the advantage of low cost and energy saving. That is, by measuring the minute mass increase of the substance fixed on the surface of the crystal resonator electrode caused by the specific substance in the solution, the concentration of the specific substance can be measured by a mass detection device having a simple configuration.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings.

FIG. 1 shows an example of the configuration of a mass detection apparatus using a QCM method using a crystal resonator according to the present invention. An AC voltage having a predetermined frequency is applied to the crystal unit 1 from an AC power source 2 through a constant impedance (Z ₁ ) 3 and converted into a detection signal by a digital multimeter 5 through a rectifier circuit 4. 6 is processed. At this time, it is possible to measure a minute change in mass on the surface of the crystal unit 1 by calculating a change in signal amount at a plurality of frequencies indicating different output characteristics in the vicinity of the resonance frequency f ₀ of the crystal unit 1. it can. In other words, the computer 6 obtains an equivalent constant of the crystal resonator 1 by analyzing simultaneous equations from the measured voltage values obtained with the configuration shown in FIG. 1, and the substance immobilized on the electrode surface of the crystal resonator 1. The result corresponding to the mass change of can be obtained.

AC voltage applied, the output characteristic of the crystal oscillator 1 is, at its resonance frequency f ₀ near, since that matches well with the characteristics of the theoretical calculated by elements forming the equivalent circuit, the resonance frequency f ₀ near A plurality of frequencies are selected. In addition, since the change in the equivalent constant of the crystal resonator is the largest and the frequency that appears in the measurement result, the resonance frequency can be determined from the measurement result by simultaneous calculation of the output characteristics at two frequencies in the vicinity. In addition, it is possible to obtain a calculation result divided into L ₁ related to the mass of the vibrating portion and R ₁ related to the internal friction of the vibrating portion, and to obtain a mass change-output characteristic that does not theoretically include the equivalent series resistance R _1. Can do.

  Further, in the conventional oscillation method or impedance method, it is necessary to insulate the terminal of the crystal resonator electrode from the circuit COM. However, in this method, one electrode terminal can be connected to the circuit COM and noise is reduced. , An output with excellent stability can be obtained.

Furthermore, since the result is obtained separately from L ₁ related to mass and R ₁ related to energy loss, temperature control or the like for the purpose of reducing the influence of R ₁ seen in the oscillation equation as described above becomes unnecessary, and low cost and energy saving are achieved. It becomes possible.

In addition, since the obtained equivalent series inductance value L ₁ is related to the mass of the vibration part, the mass change was conventionally calculated from the frequency deviation using the Sauerbrey's formula. However, in this method, the direct mass or mass change is calculated. Can be obtained.

  In addition, the conventional method is affected by the stray capacitance between crystal resonator terminals, specifically the capacitance and input capacitance when connected to the detection circuit. However, in this method, since the stray capacitance value does not affect the measurement result, a simple configuration is possible. Furthermore, probe-type products that connect the crystal resonator and the detection circuit with a probe can be assembled, and expansion of applications can be desired.

Here, the characteristics of the crystal unit are displayed by an electric circuit model as shown in FIG. That is, in FIG. 2, L ₁ corresponds to the mass of the vibrating part, C ₁ corresponds to the compliance of the crystal piece, R ₁ corresponds to the internal friction of the vibrating part, the mechanical friction of the support system, and C ₀ corresponds to the parallel capacity. Such a vibration model and electric circuit model of a crystal unit in a liquid contact state in the air have already been established, but in the present invention, a method of driving such a circuit and a frequency characteristic obtained thereby are analyzed. -By calculating, a mass detection device having high measurement accuracy can be formed with a simple configuration.

  In addition, since the sensor unit in which the crystal resonator is disposed is mainly mainly for a solution, it is easy to install the sensor unit at the lower part or the side part of the container-like body that allows easy sample introduction. The flow-through method is preferable when there is little or when continuous measurement is performed. Specifically, in the sensor structure illustrated in FIG. 3, a sample flow path 8 including a sample introduction path 8a, a detection unit 8b, and a sample discharge path 8c is formed, and terminals 7 are provided at both ends of the detection unit 8b. The plate-shaped quartz crystal resonator 1 connected with is detecting a change corresponding to a specific component in the sample. This sensor structure has the advantage that the sample liquid can be measured in a flow state by being close to a flat structure, and the sample liquid can be easily replaced and can be stably measured. . In other words, error factors such as contamination can be eliminated by smooth sample flow and replacement, and high-precision measurement with continuity is possible.

  The calculation formulas of the impedance z and the measurement voltage e, which are the basis of the present invention, are derived as follows based on the electric circuit model of FIG.

(1) In the QCM method, the crystal resonator characteristic change due to the change in L ₁ due to the increase in vibration mass due to the substance adhering to the surface of the crystal resonator electrode Can be said to be a method of detecting a minute mass increase.

  (2) On the other hand, the frequency characteristics obtained by the oscillation method as described above are the effects of the increase in mass fixed on the electrode surface and the increase in equivalent series resistance due to internal friction caused by vibration of the fixed material. This is considered to be the result of both the effects.

(3) Then, considering the impedance method in the present invention,
1. As shown in FIG. 1, the equivalent circuit model of the crystal unit is constant. 2. It can be considered that the measurement time can be measured in a short time and the condition of the crystal unit does not change during the measurement time. The frequency of the drive signal is stable Based on the above conditions, an appropriate impedance z ₁ is determined by the circuit of FIG. 1, and the crystal is measured from the measurement voltages (e ₀₁ , e ₀₂ ) at two measurement frequencies (f ₁ , f ₂ ). It is possible to analytically determine the equivalent circuit constants L ₁ and R ₁ of the vibrator. Specifically, unknown 2 points _{(L 1, R} 1), by solving the simultaneous equations consisting of the obtained results two points _{(e 01,} e _02), determine the unknowns two points _{(L 1, R} 1) be able to. Here, f ₁ is a frequency at which R ₁ can be easily calculated, and f ₂ is a frequency at which L ₁ can be easily calculated.

(4) Formula 1 is a formula obtained from the AC circuit theory for the voltage e ₀ across the crystal resonator. Where z is impedance, e is potential, f is frequency, j is imaginary, ω = 2πf, L ₁ is the mass of the vibrating part, C ₁ is the compliance of the crystal piece, R ₁ is the internal friction of the vibrating part, C ₀ Represents the parallel capacity.

(5) by the upper Equation 1 and 2, the result _{e 01} = _{e 0 (f 1),} 2 single equation as the voltage measurement at frequency _{f 2 e 02 = e 0 (} f 2) of the voltage measured at the frequency _{f 1} And L ₁ and R ₁ can be obtained analytically from these two equations.

  Further, in the configuration of FIG. 1, if there is a possibility that the characteristics of the crystal unit 1 and the characteristics of the rectifier circuit cause interference with each other, the influence of this interference is eliminated by providing an amplifier 9 as shown in FIG. It is possible. That is, the buffer function of the amplifier 9 can cut off the direct connection between the crystal resonator 1 and the rectifier circuit and eliminate the influence of mutual interference.

In the above description, the unknown constants are set to two points L ₁ and R ₁ for ease of analysis. However, if the number of measurement frequency points is increased, it is possible to measure unknown constants, which is simpler than the conventional method. The accuracy can be improved by a simple method. That is, the frequency to be selected is not limited to two, and it is effective to improve the accuracy to select a plurality of frequencies in consideration of other error factors in actual measurement.

  In the impedance method according to the present invention, a measurement value in accordance with the analysis principle as described above can be obtained. However, strictly speaking, the actually obtained measurement value includes the signal level drift of the drive signal source and the detection circuit. Sensitivity errors such as sensitivity drift, and offset errors of the detection circuit are included. These become analysis errors, but if an unknown sensitivity term and offset term are added to Equation 2, and this is made unknown and the number of measurement frequency points is increased and analysis is performed using the same algorithm, these error factors can be reduced. It becomes.

Specifically, by using the following mathematical formulas 1 and 3, the crystal vibration from the measurement voltages (e ₀₁ , e ₀₂ , e ₀₃ , e ₀₄ ) at four measurement frequencies (f ₁ , f ₂ , f ₃ , f ₄ ) It is possible to analytically determine the equivalent circuit constants L ₁ and R ₁ of the child. Here, a represents a sensitivity correction coefficient, and b represents a drift correction coefficient.

That is, as shown in FIG. 5, around the resonance frequency of the crystal oscillator, the result _{e 01 = e 0 (f 1} ) of the voltage measured at the frequency _{f 1,} the voltage measurement at frequency _{f 2 e 02} = _e The voltage measurement result e ₀₃ = e ₀ (f ₃ ) at ₀ (f ₂ ), the frequency f ₃ , and the voltage measurement result e ₀₄ = e ₀ (f ₄ ) at the frequency f ₄ are created, and four equations are created. L ₁ and R ₁ can be analytically determined from the four equations.

  Here, the above calculation method was verified as follows assuming actual use conditions. For verification, Formula 1 and Formula 3 were used.

(1) When the quartz crystal equivalent constant is put into the transfer function, and the frequency calculation result of the point when the quartz crystal equivalent series resistance value R1 is 10, 20, 40, ₁₀₀ , 200, 400 is analyzed, FIG. As a frequency characteristic as shown in (A), it was hardly calculated as a change in the main resonance frequency.

(2) Further, when calculated as a change in the same manner equivalent series inductance L _1, as shown in FIG. 6 (B), little change was calculated.

  From the above verification results, the QCM method using this algorithm is capable of separately detecting the influence on the oscillation frequency due to the vibrational frictional resistance: R in the solution seen in the conventional oscillation type QCM. I understood.

  Examples and the like specifically showing the configuration and effects of the present invention will be described below. In addition, the evaluation items in Examples and the like were measured as follows. In addition, it cannot be overemphasized that this invention is not limited to this Example and evaluation method.

<Example 1>
(1) Configuration The configuration shown in FIG. 1 of the present invention was used as a method for obtaining the crystal resonator resonance frequency.

(2) Implementation conditions As the crystal resonator, 20 MHz manufactured by Kyocera Kinseki Co., Ltd. was selected. FIG. 7 shows the result of the voltage across the crystal resonator based on the circuit calculation when R ₁ is set to 200Ω, which is the equivalent constant of the crystal resonator, which is close to the time of liquid contact. As an equivalent constant of a crystal unit,
L ₁ : 3.202 × 10 ⁻³ H
C ₁ : 18.9 × 10 ⁻¹⁵ F
R ₁ : 200Ω
C _0: 4.107 × ^{10 -12} F
A crystal resonator having 20.45873 MHz as a main resonance frequency f ₀ is used, and f ₁ : 20.46 MHz and f ₂ : 20.475 MHz are selected as measurement frequencies, and voltages e ₁ : 0.204 V and e _{2 at} this time are selected. The voltage was 0.79V.

(3) Results When other crystal resonator equivalent constants are known, two equations are established from Equation 1, and L ₁ and R ₁ are obtained by numerical calculation software (the analysis procedure is omitted).
L ₁ : 3.202 × 10 ⁻³ H
R ₁ : 200.000663Ω
I was able to ask.
If the resonance frequency f ₀ is obtained based on this result, the difference between the given L ₁ and the resonance frequency obtained from C ₁ is 7.403 × 10 ⁻³ Hz, and a minute resonance frequency difference is obtained by this method. I got a result that was possible.

<Example 2>
(1) Configuration The configuration shown in FIG. 1 of the present invention was used as a method for obtaining the crystal resonator resonance frequency.

(2) Implementation conditions The crystal unit is manufactured by Kyocera Kinseki Co., Ltd. as in Example 1. In FIG. 1, Z ₁ is set to 200Ω, the equivalent constant of the crystal unit is set to the constant shown above, and R ₁ is connected. FIG. 8 shows the result of the voltage across the crystal resonator based on the circuit calculation when 200 ± 20Ω close to that of the liquid. In other words, as the quartz crystal equivalent constant,
L ₁ : 3.202 × 10 ⁻³ H
C ₁ : 18.9 × 10 ⁻¹⁵ F
R ₁ : 200 ± 20Ω (a: 200, b: 220, c: 180)
C _0: 4.107 × ^{10 -12} F
A crystal resonator having 20.45873 MHz as a main resonance frequency f ₀ is used, and f ₁ : 20.46 MHz and f ₂ : 20.475 MHz are selected as measurement frequencies, and voltages e ₁ : 0.204 V and e _{2 at} this time are selected. The voltage was 0.79V.

(3) Result As shown in FIG. 8, when the frequency characteristic is seen, the minimum peak voltage is seen at a frequency close to the crystal resonator resonance frequency.
Although it is possible to easily obtain the crystal resonator resonance frequency by this method, if the circuit calculation is strictly performed, it can be seen that the frequency indicating the peak voltage is affected by the equivalent resistance.
FIG. 9 shows characteristics obtained by differentiating the characteristics shown in FIG. It can be seen from FIG. 9 that the frequency at which the differential frequency characteristic indicating the peak voltage indicates zero changes due to the equivalent resistance.

It is explanatory drawing which shows the example of 1 structure of the mass detection apparatus which concerns on this invention. It is explanatory drawing which expressed the crystal oscillator by the equivalent circuit. It is explanatory drawing which shows the sensor structural example of the mass detection apparatus which concerns on this invention. It is explanatory drawing which shows the other structural example of the mass detection apparatus which concerns on this invention. It is explanatory drawing which shows the output characteristic of the crystal oscillator based on this invention. It is explanatory drawing which shows the result of having verified the output characteristic of the crystal oscillator based on this invention. FIG. 6 is an explanatory diagram illustrating output characteristics of the crystal resonator according to the first embodiment. 6 is an explanatory diagram showing output characteristics of a crystal resonator according to Example 2. FIG. 6 is an explanatory diagram illustrating details of output characteristics of a crystal resonator according to Example 2. FIG. It is explanatory drawing which shows the structural example of the mass detection apparatus which concerns on a prior art.

Explanation of symbols

1 Crystal Unit 2 AC Power Supply 3 Impedance 4 Rectifier Circuit 5 Digital Multimeter 6 Computer

Claims (3)

  A mass detection device using a QCM method using a crystal resonator, which calculates a change in signal amount at a plurality of frequencies exhibiting different output characteristics in the vicinity of the resonance frequency of the crystal resonator and measures a minute change in mass. A mass detector characterized by the following. The mass detection apparatus according to claim 1, wherein the change in the signal amount is calculated using the following formula 1 and formula 2.

Where z is impedance, e is potential, f is frequency, j is imaginary, ω = 2πf, L ₁ is the mass of the vibrating part, C ₁ is the compliance of the crystal piece, R ₁ is the internal friction of the vibrating part, C ₀ Represents the parallel capacity. The mass detection device according to claim 1, wherein the change in the signal amount is calculated using the following formulas 1 and 3.

Here, z is impedance, e is potential, a is sensitivity correction coefficient, b is drift correction coefficient, f is frequency, j is imaginary number, ω = 2πf, L ₁ is the mass of the vibrating part, and C ₁ is the compliance of the crystal piece , R ₁ represents the internal friction of the vibrating part, and C ₀ represents the parallel capacity.

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