Pressure measuring device and method using quartz resonators

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BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates generally to a device and method for measuring pressures, and more particularly, to a method for performing more accurate measurement at low cost.

2. Background of the Invention

One type of conventional pressure measuring device receives an analog output produced by a semiconductor strain gauge and converts it to a digital output. This type of device has a resistor layer formed on a surface of a semiconductor such as silicon and measures a change in resistance caused by an induced strain on the semiconductor by an applied pressure. An output is obtained through a bridge circuit configured with a plurality of resistor layers for temperature compensation. The pressure measuring device utilizing a semiconductor strain gauge provides a measurement of high accuracy by means of the bridge circuit. A drawback of the device, however, is that it is very expensive to manufacture because of high cost of a strain gauge and AD converter.

Another type of pressure measuring device, which can be manufactured at a reduced cost, measures a frequency of a quartz resonator. More particularly, this type of device measures the difference in oscillation frequency between two quartz resonators: one placed in a reference pressure such as vacuum or air atmosphere and the other placed under an applied pressure to be measured. This type of devices are disclosed in, for example, Japanese laid-open patents SHO 54-158275, SHO 57-12342, SHO 59-67437, and HEI 3-248028. Although these devices can be manufactured at low cost, they do not necessarily provide an accurate pressure measurement on account of temperature characteristics of the quartz resonators. Particularly, if inexpensive quartz resonators are used, measurement wildly varies.

A method for improving temperature characteristics of pressure measuring devices utilizing quartz resonators is demonstrated in Japanese laid-open patent HEI 3-189528. In this method difference in oscillation frequency between two oscillation circuits, one having a quartz resonator placed in vacuum and the other having another quartz resonator in an atmospheric pressure, is counted by a counter. A pressure measuring unit computes the pressure using the measured count and also performs temperature calibration in use of a linear mathematical formula, which has been determined in advance from four count measurements under two known pressures and two known temperatures. The calibration formula is obtained from the four pairs of data on the assumption that the difference in frequency between the two oscillation circuits is linear with temperature and that the formula itself is a linear function of temperature.

However, the temperature characteristic varies depending on different intrinsic physical properties of individual quartz resonators and on different behaviors of quartz resonators under an air atmospheric pressure and vacuum. Therefore, even the aforementioned linear calibration formula does not provide accuracy of 1 hPa, which is needed for an atmospheric pressure measurement. Further, according to this method frequencies of a quartz resonator at different pressures and temperatures must be counted and calibration factors must be determined before shipment, resulting in increased cost. If one measures the characteristic of a typical quartz resonator at different pressures and temperatures only once, and applies the same calibration factors to every product, the temperature calibration will not allow for good accuracy because of variation of characteristics of individual quartz resonators assembled in pressure measuring devices.

What is needed then is a method for improving the accuracy of pressure measurement performed in use of quartz resonators by means of appropriate temperature calibration and for implementing the temperature calibration at lower cost.

SUMMARY OF THE INVENTION

The present invention relates to a pressure measuring device utilizing a pair of quartz resonators, which provides pressure difference based on measured difference in oscillation frequency between the two quartz resonators placed under different pressures. This pressure measuring device exhibits large temperature dependence caused by temperature dependence of the quartz resonators. Therefore, appropriate temperature calibration is needed for accurate measurement of pressure difference. The present invention provides a method for accurate calibration by using a quadratic calibration formula with parameters easily obtained. The present invention also provides a simple, reliable temperature compensation method by inserting temperature dependent resistors in at least one of the oscillation circuits having a quartz resonator.

An object of the present invention is to improve performance of a method or device for measuring a pressure by measuring a difference in oscillation frequency between two oscillation circuits each having a quartz resonator (first resonator and second resonator) which is placed under a different pressure from each other. The first method of the present invention demonstrates is to calibrate a measured pressure value derived from a measured difference in oscillation frequency between the first and second quartz resonators which change their characteristics according to ambient temperatures, using a temperature calibration formula of a quadratic or higher order. This method compensates the temperature characteristics resulting from the variations of turning points and quadratic temperature coefficients of quartz resonators under different pressures. It also compensates the temperature characteristics caused by variation in intrinsic physical properties (that is, turning points and quadratic temperature coefficients) of individual quartz resonators.

The temperature calibration formula is preferably determined by placing each of the first and second quartz resonators under a pressure which the resonator is ordinarily to be placed under (For example, if one crystal resonator is intended to be placed in vacuum and the other under a pressure to be measured, one quartz resonator should be placed in vacuum and the other under the range of a pressure to be measured.) and by measuring differences in oscillation frequency between the two oscillation circuits at least three different temperatures. In this case, since the pressures under which the quartz resonators are placed remain the same, the determination of the calibration formula is simpler.

The hardware configuration to implement this method comprises a measuring means for outputting a measured value corresponding to difference in oscillation frequency between the two oscillation circuits, a temperature sensing means for sensing an ambient temperature of the first and second quartz resonators, a storage means for storing calibration parameters (that is, three sets of data corresponding to a given pressure, two sets of relative data with reference to the data associated with one temperature, a table of temperature calibration values computed using the above-mentioned three sets of data for a given rage of temperatures, or a table of pressures calibrated with respect to the temperatures) determined by the measurements of differences between the oscillation frequencies at minimum three temperatures, and a calibration computing means for computing calibration using the calibration parameters and the ambient temperature. In this method temperature compensation is carried out using the calibration parameters which essentially correspond to the differences of oscillation frequencies measured at minimum three temperatures. Therefore, it can compensate the different temperature dependencies of turning points and quadratic temperature coefficients of the quartz resonators under different pressures. It can also compensate the variation of temperature dependence caused by the variation in intrinsic physical properties of the individual quartz resonators.

A preferable calibration computing means obtains a temperature calibrated value for a measured value by substituting an ambient temperature for a temperature in a calibration formula of quadratic or a higher order with regard to temperature, where the calibration formula is determined with the calibration parameters. In this case, since the calibration computing means obtains a temperature calibrated value for a measured value by substituting an ambient temperature for a temperature in the calibration formula of quadratic or higher order with regard to temperature, the amount of data to be stored is minimal.

A preferable storing means for storing calibration parameters has a table of temperatures vs. temperature calibrated values, after-calibration measured values, or after-calibration measured pressures. These tables are associated with the calibration formula of quadratic or higher order with regard to temperature, which is determined with the calibration parameters. Further, a preferable calibration computing means determines a calibrated value, after-calibration measured value, or after-calibration measured pressure for a given ambient temperature in referring to the table. In this case temperature calibration is carried out by using a measured ambient temperature and referring to the table that corresponds to the temperature calibration formula of a quadratic or higher order with regard to temperature. Therefore, more data must be stored, but temperature calibration can be carried out without a computing means.

Furthermore, it is desirable to select first and second quartz resonators so that their turning point difference caused by variation in intrinsic physical properties cancels an amount of variation caused by pressure difference which the two quartz resonators are exposed to. In this case, since the difference in turning point caused by variation in intrinsic physical properties cancels their difference caused by the pressure difference which the two quartz resonators are exposed to, the difference in turning point between the two quartz resonators arranged for an actual pressure measurement is reduced. As a result, the symmetry of the temperature calibration formula is improved and a calibration value is reduced. A value of a turning point of a quartz resonator varies according to a cut angle of a quartz crystal. Using appropriate cut angles one may obtain two quartz resonators so that the difference between their turning points significantly reduces. In particular, it is possible for a turning point of one quartz resonator to almost completely cancel that of the other. A plate having a plane perpendicular to the optical axis (referred to as the Z-axis) of a quartz crystal is referred to as the Z-plate. The cut angle .theta. is defined as an angle of the counterclockwise rotation of the Z-plate by the Electrical axis (referred to as the X-axis). Quartz resonators are cut out from quartz crystals with these various cut angles to control values of turning points.

The second method which the present invention demonstrates includes a means for producing an output corresponding to a measured difference in oscillation frequency between the two oscillation circuits and one or more temperature dependent resistors connected to at least one of the two oscillation circuits so that it modifies the temperature dependence of the oscillation frequency of that oscillation circuit and reduces the temperature dependence of the oscillation frequency difference between the two oscillation circuits. In this case the temperature dependencies of the oscillation frequencies of the first and/or second quartz resonators are modified by the temperature dependent resistors connected to the oscillation circuits, and accordingly, the temperature dependence of the oscillation frequency difference is reduced. As a result, measurement errors can be reduced inexpensively without complex calibration processes.

A preferable temperature dependent resistor is a thermistor having a negative thermal coefficient or a monolithic resistor having a positive thermal coefficient. In particular, an FET channel resistor is desirable as a monolithic resistor. In this case the temperature dependence of the oscillation frequency difference can be reduced reliably. When a monolithic resistor is used as a temperature dependent resistor, integration of a measuring circuit is simplified. When an FET channel resistor is used as a temperature dependent resistor, a measuring circuit can be configured with a general-purpose integrated circuit.

It is preferable to have the temperature dependent resistor to be connected in parallel to another temperature dependent resistor having different temperature dependence. In this case the temperature dependence of the resultant resistance can be adjusted to the temperature dependence of the oscillation circuit. This allows for accurate temperature calibration.

The third method of the present invention comprises a means for producing an output corresponding to a measured oscillation frequency difference between the two oscillation circuits, one or more temperature dependent resisters connected to at least one of the two oscillation circuits so that it modifies the temperature dependence of the oscillation frequency of that oscillation circuit and reduces the temperature dependence of the oscillation frequency difference, a means for measuring an ambient temperature of the first and second quartz resonators, and a means for performing temperature calibration on the measured value for the ambient temperature using a given mathematical calibration formula. This scheme of temperature calibration, based on the mathematical formula in addition to insertion of a temperature dependent resistor in the oscillation circuit to reduce the temperature dependence, makes selection of temperature dependent resistors easier and reduces an amount of calibration and its rate of change obtained from the mathematical formula. This further allows for reduction of measurement errors.

A preferable temperature calibration means calibrates a measured value using a mathematical formula of quadratic or higher order with regard to temperature. In this case, since the calibration is performed using the mathematical formula of quadratic or higher order with regard to temperature, it calibrates temperature dependencies of both the differences in turning point and second order temperature coefficient between the quartz resonators placed under different pressures. It also calibrates different temperature dependencies of the quartz resonators caused by variation in intrinsic physical properties.

In the three methods mentioned above a preferable means for measuring the difference in oscillation frequency between the first and second oscillation circuits includes a beat generation means for forming a beat signal based on the signals from both the oscillation circuits and a counting means for measuring the beat frequency. Since the frequency of the beat signal obtained by the beat generating means is low, neither high frequency processing nor high frequency circuit such as a high speed counter is needed. This reduces manufacturing cost and power consumption.

A preferable beat generating means detects and holds a state of the signal from one of the two oscillation circuits in synchronizing with the signal from the other oscillation circuit and outputs the state value. In this case, since the beat signal is generated by detecting and holding a state of the signal from one of the two oscillation circuits in synchronizing with the signal from the other oscillation circuit and by outputting the state value, the circuit for the beat generating means that maintains the beat cycle information can be made simpler.

A preferable counting means of beat cycles detects a state of the beat signal at a given phase of every beat cycle and rechecks the state of the beat signal at a predetermined period of time shorter than the beat period after that detection. In this case, since the beat cycles are counted in rechecking the state of the beat signal at a predetermined time shorter than the beat period after that detection, signal processing for the beat signal is not necessary and accurate counting is performed regardless noise and a wave form of the beat signal, as far as the beat signal includes the information of the beat cycles.

Other objects and attainments together with a fuller understanding of the invention will become apparent and appreciated by referring to the following description and claims taken in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a block diagram of a pressure measuring device using quartz resonators described in Embodiment 1 of the present invention.

FIG. 2 shows typical temperature dependence of oscillation frequency of a quartz resonator used in Embodiment 1 of the present invention.

FIG. 3 is a diagram illustrating difference in temperature dependence between quartz resonators placed under vacuum and an ordinary atmosphere as described in Embodiment 1 of the present invention.

FIG. 4 is a diagram showing oscillation frequency as a function of pressure for a quartz resonator used in Embodiment 1 of the present invention.

FIG. 5 is a diagram showing turning point as a function of pressure for a quartz resonator used in Embodiment 1 of the present invention.

FIG. 6 is a diagram showing distribution of turning points of quartz resonators used in Embodiment 1 of the present invention.

FIG. 7 is a diagram showing distribution of second order temperature coefficients of quartz resonators used in Embodiment 1 of the present invention.

FIG. 8 is a diagram showing temperature dependence of difference in oscillation frequency between two quartz resonators with their turning point difference as parameter when difference in second order temperature coefficient between the two quartz resonators is positive.

FIG. 9 is a diagram showing temperature dependence of difference in oscillation frequency between two quartz resonators with their turning point difference as parameter when difference in second order temperature coefficient between the two quartz resonators is negative.

FIG. 10 is a diagram showing variation of turning point as a function of cut angle for forming a quartz resonator from a quartz crystal.

FIG. 11 is a diagram showing temperature dependence of difference in oscillation frequency between two quartz resonators, each having a significantly different turning point from the other.

FIG. 12 is a diagram showing temperature dependence of resistance of a thermistor.

FIG. 13 is a diagram showing temperature dependence of difference in oscillation frequency between two quartz resonators which are modified with thermistor.

FIG. 14 is a circuit diagram showing configuration of an oscillation circuit employing a quartz resonator used in Embodiment 2 in the present invention.

FIG. 15 shows an example of compound resistors substituted for a resistor R.sub.c in FIG. 14.

FIG. 16 illustrates general relations between oscillation frequency difference and resistors R.sub.a, R.sub.b, and R.sub.c shown in FIG. 14.

FIG. 17 is a diagram showing temperature dependencies of resistance of a thermistor and combined resistors.

FIG. 18 is a diagram showing temperature dependencies of oscillation frequency differences for cases: (A) no modification, (B) modification with a thermistor, and (C) modification with compound resistors.

FIG. 19 is a circuit diagram showing configuration of an oscillation circuit employing different temperature dependent resistors.

FIG. 20 is a block diagram showing a major part of Embodiment 2 in the present invention.

FIG. 21 is a block diagram showing actual hardware configuration.

FIG. 22 is a timing chart showing (a) output signal from a reference oscillation circuit in Embodiment 2, (b) output signal from a measuring oscillation circuit, (c) beat signal formed by those two signals, and (d) wave form of actual beat signal including noise.

FIG. 23 is a flow chart showing procedure of a wave-form analyzing circuit implemented with software.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Embodiments of the present invention are described with reference to the drawings.

Embodiment 1

FIG. 1 indicates a circuit block diagram showing the entire configuration of the pressure measuring device of Embodiment 1 according to the present invention. Reference numeral 1 represents an oscillation circuit accommodating a reference quartz resonator placed in vacuum and 2 another oscillation circuit including a measurement quartz resonator placed in an atmosphere, oscillator circuits 1 and 2 oscillating at frequencies f.sub.1 and f.sub.2, respectively. The oscillation pulses are led to an IC including a four-bit MPU. The IC comprises counters 3 and 4 that count numbers of the input oscillation pulses for a predetermined period, and a subtracter 5 that subtracts the counts from counter 4 from those from counter 3. The output of subtracter 5 that corresponds to the difference in oscillation frequency between oscillation circuits 1 and 2, .DELTA.f=f.sub.1 -f.sub.2, is sent to MPU 6.

A temperature sensor 7 made of a thermistor, for example, measures an ambient temperature of quartz resonators 1 and 2. The measured value is sent to MPU 6 through an AD converter 8. MPU 6 performs a pressure calibration computation based on the temperature measured by temperature sensor 7 and the temperature calibration values provided from a ROM 9. MPU 6 then adds the obtained pressure calibration to the measured pressure provided by subtracter 5 to obtain a calibrated pressure value, which is fed to a display device 11 such as a Liquid crystal display through an output circuit 10.

Quartz resonators used for oscillation circuits 1 and 2 are tuning fork type resonators having a negative second-order temperature coefficient as shown in FIG. 2. A quartz resonator in this example is designed to have a taming point, which is an apex of the parabola, at approximately 25.degree. C. in taking consideration of using the oscillator at room temperature. This quartz resonator is less expensive and consumes less power. It exhibits, however, a poorer temperature characteristic than an AT cut quartz resonator that has an improved temperature characteristic.

FIG. 3 shows pressure dependence of the temperature characteristic of an oscillation circuit utilizing a quartz resonator. For a typical quartz resonator placed in vacuum and connected to an oscillation circuit, the oscillation frequency f.sub.1 =32.768 kHz, the turning point T.sub.1 =25.0.degree. C., a coefficient a.sub.1 =-0.035 ppm/.degree. C.sup.2. Let the oscillation frequency, the taming point, and the second-order temperature coefficient be f.sub.2, T.sub.2, and a.sub.2, respectively, for the same quartz resonator placed in an atmosphere. Then we have:

f.sub.1 -f.sub.2 =.DELTA.f=122 ppm(.about.4Hz)

T.sub.1 -T.sub.2 =.DELTA.T.sub.p =-0.5.degree.C

a.sub.1 -a.sub.2 =.DELTA.a=0.005 ppm/C.degree..sup.2.

Quartz resonators of this type show the variation of .DELTA.T.sub.p from a few tenths to a few tens of .degree. C in the negative sign. The variation of .DELTA.a is small and in the positive sign. The axes of ordinates in FIGS. 2 and 3 indicate frequency f relative to f.sub.1 in the ppm unit.

FIG. 4 shows pressure dependence of oscillation frequency of a quartz resonator placed in the environment maintained at 25.degree. C., while FIG. 5 shows pressure dependence of turning point T.sub.p. As seen in the figures both the oscillation frequency and turning point vary almost linearly with pressure. Pressure measurement using quartz resonators takes advantage of variation of oscillator frequency with pressure as shown in FIG. 4, but the variation is also very sensitive to a change in temperature as shown in FIG. 2. Therefore, in the configuration in which the quartz resonator of the oscillation circuit 1 is placed in vacuum in FIG. 3 as a reference oscillator, and that of the oscillation circuit 2 is placed in an atmosphere to be measured as a measuring oscillator, the difference between the two frequencies cancels the temperature dependencies of the two quartz resonators and provides an improved, somewhat temperature independent pressure measurement For example, if the differences in turning point .DELTA.T.sub.p and in second-order temperature coefficient .DELTA.a between the two quartz resonators are zero, then the temperature characteristics of the two resonators are identical. Consequently, the temperature dependencies are completely canceled out. Actually, however, there is a difference between the turning points of the quartz resonators placed at vacuum and atmospheric pressures as shown in FIG. 5. In this case, if the difference between the second-order temperature coefficients .DELTA.a is zero, then the measured pressure varies as a linear function of temperature. Therefore, calibration may be made by a linear function as described in the Japanese laid-open patent HEI 3-189528.

It was discovered that there is always a finite difference in second-order temperature coefficients .DELTA.a in the pressure measurement scheme mentioned above and that the difference in second-order temperature coefficients .DELTA.a significantly contributes to the aforementioned atmospheric pressure measurement. That is, the difference between the two frequencies (.DELTA.f=f.sub.1 -f.sub.2) is expressed as a quadratic function of temperature as shown below: ##EQU1##

Therefore, the second-order calibration according to the equation (1) is required in order to obtain an accuracy needed for measurement of an atmospheric pressure. Since the above-mentioned temperature characteristic of the quartz resonator induces a larger error for a larger temperature variation, the accuracy of the temperature calibration described in the Japanese laid-open patent HEI 3-189528 rapidly deteriorates for a large temperature variation.

The physical properties, such as the turning point and the second-order temperature coefficient, of the quartz resonators of oscillation circuits 1 and 2 may be different when they have been manufactured. Thus, these variations of the intrinsic physical parameters must also be taken into account for pressure calibration, when the aforementioned scheme is applied to a pressure measurement. For example, FIGS. 6 and 7 indicate distributions of turning points and second-order temperature coefficients of a typical lot of quartz resonators, respectively. Both the distributions show larger variations than that due to pressure difference between vacuum and an atmosphere. Therefore, if two arbitrary quartz resonators are chosen from this lot to measure pressure difference of vacuum and an atmosphere, a larger calibration is needed than when two quartz resonators having an identical temperature characteristic are used for the same pressure measurement.

The difference between the oscillation frequencies due to variation of intrinsic physical parameters also depends on the differences in turning points and second-order temperature coefficients between two quartz resonators. Thus, Equation (1) also holds to this case by interpreting those parameters in the equation as parameters characterizing differences of intrinsic physical parameters between the two quartz resonators. That is, the temperature dependence of frequency difference due to the variation in intrinsic physical parameters of the quartz resonators is expressed by the same formula as Equation (1), which describes the temperature dependence of frequency difference due to pressure difference.

Taking the above-mentioned facts into consideration for this embodiment the temperature calibration for quartz resonators is done as follows: first, after a device is assembled, the frequency difference .DELTA.f between quartz resonator 1 placed in vacuum and quartz resonator 2 in the atmosphere is measured at three different temperatures. The desirable temperatures for the measurement are a temperature each near, below, and above the turning points of oscillation circuits 1 and 2. One may store those temperatures in the ROM and use them for the measurement, or one may input the temperatures measured with the temperature sensor 7 when the measurement is carded out. The measured frequency differences .DELTA.f together with the temperatures are stored as three sets of 8-bit digital data in ROM 9 configured with an EEPROM, for example. Instead, the measured values and the temperatures may be stored as the relative values to those near the turning points as two sets of data.

The measurement at practically three different temperatures determines the coefficients of the quadratic Equation (1): .DELTA.a, C, and D. From these values one can obtain the following calibration formula:

.DELTA.f.sub.s =.DELTA.f(.DELTA.aT.sub.s.sup.2 +CT.sub.s +D)/(.DELTA.at.sup.2 +Ct+D), (2)

where T.sub.s is a reference temperature used for calibration of a measured value. The temperature calibration formula, Equation (2), provides a reference measured value .DELTA.f.sub.s, which corresponds to the difference between the oscillation frequencies at the temperature T.sub.s. The .DELTA.f.sub.s is expressed as a function of an ambient temperature t temperature sensor 7 measures as well as a measured oscillation frequency difference .DELTA.f. FIG. 4 shows a linear relation between pressure and oscillation frequency. Therefore, the difference in oscillation frequency between the two quartz resonators is proportional to the difference between the pressures that the two quartz resonators are exposed to, and hence the calibrated pressure is obtained by multiplying a constant value into .DELTA.f.sub.s.

Now the quadratic equation (1) is rewritten as:

.DELTA.f=.DELTA.at.sup.2 +Ct+D=.DELTA.a(t-c).sup.2 +d.

If the reference temperature T.sub.s is set to be T.sub.s =c (c takes on a different value for a different device.), then the reference measured value is given as:

.DELTA.f.sub.t =.DELTA.f(d/(.DELTA.a(t-c).sup.2 +d)) (3)

Once the coefficients of the quadratic equation (1) and T.sub.s are determined, MPU 6 computes the calibration formula (2) or (3) using those values on every pressure measurement. FIG. 1 does not show a means for setting a pressure for the display. However, when the aforementioned temperature calibration values are input, the measured pressure itself is also input by a setting means (a device to input data from a pressure gauge; not shown in FIG. 1 ) and the proportional constant for converting a measured reference value .DELTA.f.sub.s or .DELTA.f.sub.t to a pressure is determined. Another calibration method based on the quadratic (1) is described in Embodiment 2.

In the present embodiment the oscillation frequency difference between oscillation circuits 1 and 2 is expressed in a quadratic formula of temperature. Therefore, the temperature dependence of oscillation frequency difference between the two quartz resonators caused by different pressures the two quartz resonators exposed to and the temperature dependence of oscillation frequency difference between the two quartz resonators having different intrinsic physical properties are able to be calibrated simultaneously. Thus, inexpensive tuning fork type resonators can be used for highly accurate pressure measurements.

FIGS. 8 and 9 show the temperature dependence of oscillation frequency difference .DELTA.f between two quartz resonators, one placed in vacuum and the other in an atmosphere, for cases in which the difference of their second-order temperature coefficients .DELTA.a is+0.005.times.10.sup.-6 ppm/.degree. C.sup.2 and -0.005.times.10.sup.-6 ppm/.degree. C.sup.2, respectively, with the difference of their turning points as parameter. The differences of turning points and second-order temperature coefficients results from difference in pressure between the two quartz resonators and variation in their intrinsic physical parameters.

These figures show that when the difference in turning point between the two quartz resonators .DELTA.T .sub.p =0.degree. C. (drawn with heavy curves), the oscillation frequency difference .DELTA.f is a symmetrical curve of second order around the training point. However, when a magnitude of .DELTA.T.sub.p increases, the symmetry is lost and the .DELTA.f rapidly varies in either the higher or lower temperature side. Therefore, if two quartz resonators having the same turning points are used, then computation for calibration is simplified. Furthermore, the temperature calibration measurements may be carried out at only two temperatures not equal to the turning point. Since this provides the least sum of calibrated values in an ordinary temperature region, the temperature calibration is the most reliable.

A pair of quartz resonators may be selected so that the difference of their turning points due to variation in intrinsic physical properties cancels the variation in turning point due to pressure difference. For example, consider the same case as above where one quartz resonator is placed in vacuum (reference pressure) and the other in an atmosphere (pressure to be measured). If the turning point increases by +0.5.degree. C. when the pressure changes from vacuum to one atmospheric pressure, a pair of quartz resonators having turning point difference of 0.5.degree. C (under the same pressure) are selected, and the one with the lower turning point is used as a measuring resonator.

Instead of a strict selection as above, a crude selection may be applied: quartz resonators are grouped in two groups, one having higher turning points, while the other having lower turning points, and then two resonators are taken from each of the two groups. That is, in this embodiment a quartz resonator for measuring an atmospheric pressure is taken from the group having lower turning points and a reference quartz resonator from the other group having higher turning points. This selection scheme allows for cancellation of variation due to pressure difference and variation in intrinsic physical properties with each other. This results in a smaller difference in turning points on measurement, an improvement in the symmetry of the calibration quadratic, and a smaller amount of calibration as a whole. All these contribute to an easier temperature calibration.

FIG. 10 shows how turning point changes when cut angle of a tuning fork type quartz resonator is varied. The quartz resonator is formed as a plane tuning fork by etching a substrate (so called the Z-plate) using a photo mask made by photolithography, the substrate being produced from a quartz crystal cut perpendicular to its optical axis (Z-axis). The single crystal may be rotated by the electrical axis (X-axis) and then cut. The angle .theta. in FIG. 10 is an angle of that rotation with reference to the Z-plate. FIG. 10 shows that changing the cutting angle produces different turning points. Accordingly, two groups of quartz resonators may be prepared alternatively by using two different angl