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Temperature compensation of silicon resonant pressure sensor
ELSEVIER
Sensorsand ActuatorsA 57 (1996) 179-182
Temperature compensation of silicon resonant pressure sensor Jan V~h~ Czech Technical University in Prague. Department of Measurement K338. Technickd 2.16627 Prague, 6. Czech Republic
Received 19 April 1996;revised2 July 1996;accepted5 August 1996
Abstract In this article, a new method of temperature compensation for resonant pressure sensors is described and preliminary experimental results are presented. The proposed method is based on measurement of resonance frequencies for two different oscillation modes of a single resonator. From these two values, the actual pressure including non-linearity and temperature correction can be calculated. Keywords: Resonantpressuresensors;Silicon;Temperaturecompensation
1. Introduction Resonant pressure sensors have been developed in which the frequency of the output signal is a function of the measured pressure [ 1,2]. They have high accuracy, outstanding stability and negligible hysteresis. Their output signal is suitable for direct processing in digital systems without the need for analog to digital (AD) conversion. In order to achieve sufficient accuracy, correction of nonlinearity and temperature drift of the sensor has to be calculated during the measurement. While non-linearity correction causes no significant problems, temperature correction requires an additional temperature sensor and AD converter. In this article, a new method of temperature correction for resonant pressure sensors is described. The proposed method is based on the measurement of resonance frequencies for two different oscillation modes of a single resonator. From these two values, the actual pressure, including non-linearity and temperature correction, can be calculated. Experimental results presented at the end of the article were obtained by measurement on a RFT100 resonant pressure sensor manufactured by Druck Ltd., UK.
2. The sensor The detailed description of the RPTI00 resonant pressure sensor can be found in Ref. [ 3 ]. Its sensing element is shown on Fig. 1; it consists of a resonator chip and a substrate chip, which are bonded together by a layer of reflowed glass. Both resonator and substrate chips are manufactured from silicon wafers. 0924-4247/96/$15.00 © 1996ElsevierScienceS.A. All fightsrescued PIIS0924-4247(96)01376-3
Fig. I. RI~IOB~mk~ngelement.
The outer surface of the diaphragm on the resonator chip is exposed to the measured pressure, while the inner cavity containing the resonator is evacuated. The mechanical f o r e induced by the measured pressure is transferred through the girders and increases the tensile stress in the resonator structure. The resonance frequency of the resonator is a function of the tension and therefore varies with pressure. The resonator is made to oscillate at its resonance point using a system of electrodes on the substrate chip, which are connected to a wide-band amplifier. The resonator can exhibit several modes of oscillation, and can therefore have several resonance frequencies. The mode excited is determined by the electrode layout and the phase shift of the amplifier. With the current electrode layout two basic oscillation modes can be excited (Fig. 2).
J. Vd:H/ SensorsandActuatorsA 57 (1996) 179-182
18o
OSCILLATION MODE 1
wheref = frequency,j~ = nominal frequency, Ud = diode voltage and Udo = nominal diode voltage. The set of coefficients ai~ is different for every sensor. Coefficients are calculated by making a least-squares fit of Eq. ( 1) to the data measured during calibration. 2.2. Temperature correction using two oscillation modes As mentioned earii~r, oscillation in two basic modes can be excited in the resonator. Each resonance frequencyfis a function g of two independent variables: pressure p and temperature T:
OSCILLATION MODE 2
f,=g,(p,T)
(2)
f2 = g2(p, T)
(3)
Eqs. (2) and (3) form the system of equations. If the fimctions g~ and g2 fulfil certain criteria, the independent variables pressure p and temperature Tcan be expressed from Eqs. (2) and (3) in the form
Fig. 2. Oscillationmodesof RPTIO0resonator.
(5)
p= ~ ~.~-~o)'~-~o)' i-oj-o
Resonant pressure sensors are inherently non-linear and exhibit temperature drift. In order to obtain the actual pressure, the resonance frequency is measured and a corrected output is calculated in a microprocessor unit. Temperature is sensed by an external sensor, from which the output signal is converted by an analog to digital converter (ADC) and the corresponding digital value is transmitted into the microprocessor. For the RPTI00 sensor a two-dimensional polynomial in frequency and temperature, represented by diode voltage, is used to calculate the actual pressure [4]: ~.~a#(f-fo)'( Ud-- Udo)'
(4)
Y=g4(f,,f2)
Although it would be generally possible to express Eqs. (2) and (3) as a two-dimensional polynomial, for example, and to solve the system of equations, the easier way is to suppose Eq. (4) to be in the form of two-dimensional polynomial:
2.1. Temperature correction u~ing external temperature sensor
pressure = ~
P----g3(fl,f2)
(1)
i=Oj=O
(6)
wheref~ = frequency for the mode l,flo = nominal frequency for the mode 1, f2=frequency for the mode 2 and f2o = nominal frequency for the mode 2. The coefficients b o can be calculated again by making a least-squares fit of Eq. (6) to the calibration data.
3. Experimental results The method described above was verified by experimental measurements on the RPT100 resonant pressure sensor. The oscillation of the resonator was excited by a wide-band amplifier with automatic gain control, which was connected between the sensing and exciting electrodes. Oscillation
Table i Averageparametet~of a RPTI00 sensingelement Parameter
Mode 1
Mode 2
Nominalfreq. at 100kPa.20°(3 Frequencyversuspressure Frequencyversustemperature
36 to 40 kHz + 25 to + 30 Hz kPa- i - 0.2 to + 0.2 Hz °C- i,
55 to 60 kHz + 100 to + 140 Hz kPa- t - 0.8 to + 0.8 Hz °C- z=
=Temperaturecoefficientsvarywith pressure,and device-to-devicedramatically(even in the sign).
.i. V&h'~l Sensors and Actuators A 57(1996) 179-182
181
0.0
.0.1
~,m,c ---X-- m'c
"0.2
-0.3 20
40
60
80
100
140
120
~ ' e . u m ~Pa] Fig. 3. Residual error without temperature conecfion.
0.0-
.0.1-
~ ' c ~m'c
-Q.2
-0.3
'
2O
t
40
'
I
60
'
I
°
I
8O 100 Pressure ~Pa]
'
I
'
120
i
140
Fig. 4. Residualerrorwitht©mpera~,reconectiQn. mode 1 or 2 was selected by switching the phase shift of the amplifier to 0 ° or 180 °. Resonance frequeuciesf~,f2 versus pressure and temperature were measured. Readings were taken at 20 kPa steps from 20 to 140 kPa and at 0,10, 20, 30, 40 and 60°C. Average parameters e r a RPT100 sensing element are summarized in Table 1. The measured data were fitted by a polynomial fit. The order of the fit is a compromise of the required accuracy, number of measured data, their noise and the numerical stability of the calculation. The calibration data will not be perfectly represented by the algorithm and the deviation is the curve-fit error. Fig. 3 shows an example of the residual error after the non-linearity has been corrected by a simple polynomial fit (fourth order) in frequency but not in temperature. The temperature drift of the sensor is obvious. Fig. 4 shows the residual error after the calibration data have been fitted by the two-dimensional polynomial (6) with m = n = 3. The temperature drift is reduced almost four times compared with that of the uncorrected sensor.
4. Conclusions Experimental results show that the proposed method can be successfully used for temperature correction of the RPTI00 resonant pressure sensor. The temperature drift figures after correction are preliminary and will be improved using a modified measurement set-up. The method has two significant advantages over the method of correction using an external temperature sensor. First, there is no need for an external temperature sensor, signal-conditioning circuit or analog to digital converter, which simplifies the design of the electronics. Secondly, there are no errors caused by the temperature difference between the external temperature sensor and resonator itself, which occurs, for example, during fast ambient temperature changes. The disadvantage of the proposed method is the inherently slower readout during measurement, since one pressure readout requires measurement of two frequencies and time is
182
J. vi:fi /Sensors and Actuators A 57 (1996) 179-182
necessary for oscillation mode switching. Exciting both the oscillation modes simultaneously has not yet been tested.
Acknowledgements I would like to thank Mr John Greenwood from Druck Ltd., UK, for valuable advice and support o f this research project.
[2] E. Stemmeand G. Stemme,Capacitivelyexcited and detectedresonant pressuresensor with temperaturecompensation,Sensors and Actuators A, 32 (1992) 639--647. [3] J.C. Greenwood and D.W. Satchell, A miniature silicon resonant pressuresensor,lEE Prec., 135 (1988) 369-372. [41 J.C. Greenwood and T. Wray, High accuracy presst,re measurement with a silicon resonantsensor, Sensors and Actuators A, 37-38 (1993) 82-85. Biography J a n V ~ i ~ was born in 1971 and received his degree in elec-
References [ l ] R. Langdom, Resonant Sensors - - a review, .L Phys. Electrotechnics: Sci. lnstrum., 18 (1985) 103.
trical engineering from the Czech Technical University in Prague, Czech Republic in 1995. In the same year he joined the Department of Measurement at the Faculty o f Electrical Engineering at the same institution, where he is now a Ph.D. student.
Sensorsand ActuatorsA 57 (1996) 179-182
Temperature compensation of silicon resonant pressure sensor Jan V~h~ Czech Technical University in Prague. Department of Measurement K338. Technickd 2.16627 Prague, 6. Czech Republic
Received 19 April 1996;revised2 July 1996;accepted5 August 1996
Abstract In this article, a new method of temperature compensation for resonant pressure sensors is described and preliminary experimental results are presented. The proposed method is based on measurement of resonance frequencies for two different oscillation modes of a single resonator. From these two values, the actual pressure including non-linearity and temperature correction can be calculated. Keywords: Resonantpressuresensors;Silicon;Temperaturecompensation
1. Introduction Resonant pressure sensors have been developed in which the frequency of the output signal is a function of the measured pressure [ 1,2]. They have high accuracy, outstanding stability and negligible hysteresis. Their output signal is suitable for direct processing in digital systems without the need for analog to digital (AD) conversion. In order to achieve sufficient accuracy, correction of nonlinearity and temperature drift of the sensor has to be calculated during the measurement. While non-linearity correction causes no significant problems, temperature correction requires an additional temperature sensor and AD converter. In this article, a new method of temperature correction for resonant pressure sensors is described. The proposed method is based on the measurement of resonance frequencies for two different oscillation modes of a single resonator. From these two values, the actual pressure, including non-linearity and temperature correction, can be calculated. Experimental results presented at the end of the article were obtained by measurement on a RFT100 resonant pressure sensor manufactured by Druck Ltd., UK.
2. The sensor The detailed description of the RPTI00 resonant pressure sensor can be found in Ref. [ 3 ]. Its sensing element is shown on Fig. 1; it consists of a resonator chip and a substrate chip, which are bonded together by a layer of reflowed glass. Both resonator and substrate chips are manufactured from silicon wafers. 0924-4247/96/$15.00 © 1996ElsevierScienceS.A. All fightsrescued PIIS0924-4247(96)01376-3
Fig. I. RI~IOB~mk~ngelement.
The outer surface of the diaphragm on the resonator chip is exposed to the measured pressure, while the inner cavity containing the resonator is evacuated. The mechanical f o r e induced by the measured pressure is transferred through the girders and increases the tensile stress in the resonator structure. The resonance frequency of the resonator is a function of the tension and therefore varies with pressure. The resonator is made to oscillate at its resonance point using a system of electrodes on the substrate chip, which are connected to a wide-band amplifier. The resonator can exhibit several modes of oscillation, and can therefore have several resonance frequencies. The mode excited is determined by the electrode layout and the phase shift of the amplifier. With the current electrode layout two basic oscillation modes can be excited (Fig. 2).
J. Vd:H/ SensorsandActuatorsA 57 (1996) 179-182
18o
OSCILLATION MODE 1
wheref = frequency,j~ = nominal frequency, Ud = diode voltage and Udo = nominal diode voltage. The set of coefficients ai~ is different for every sensor. Coefficients are calculated by making a least-squares fit of Eq. ( 1) to the data measured during calibration. 2.2. Temperature correction using two oscillation modes As mentioned earii~r, oscillation in two basic modes can be excited in the resonator. Each resonance frequencyfis a function g of two independent variables: pressure p and temperature T:
OSCILLATION MODE 2
f,=g,(p,T)
(2)
f2 = g2(p, T)
(3)
Eqs. (2) and (3) form the system of equations. If the fimctions g~ and g2 fulfil certain criteria, the independent variables pressure p and temperature Tcan be expressed from Eqs. (2) and (3) in the form
Fig. 2. Oscillationmodesof RPTIO0resonator.
(5)
p= ~ ~.~-~o)'~-~o)' i-oj-o
Resonant pressure sensors are inherently non-linear and exhibit temperature drift. In order to obtain the actual pressure, the resonance frequency is measured and a corrected output is calculated in a microprocessor unit. Temperature is sensed by an external sensor, from which the output signal is converted by an analog to digital converter (ADC) and the corresponding digital value is transmitted into the microprocessor. For the RPTI00 sensor a two-dimensional polynomial in frequency and temperature, represented by diode voltage, is used to calculate the actual pressure [4]: ~.~a#(f-fo)'( Ud-- Udo)'
(4)
Y=g4(f,,f2)
Although it would be generally possible to express Eqs. (2) and (3) as a two-dimensional polynomial, for example, and to solve the system of equations, the easier way is to suppose Eq. (4) to be in the form of two-dimensional polynomial:
2.1. Temperature correction u~ing external temperature sensor
pressure = ~
P----g3(fl,f2)
(1)
i=Oj=O
(6)
wheref~ = frequency for the mode l,flo = nominal frequency for the mode 1, f2=frequency for the mode 2 and f2o = nominal frequency for the mode 2. The coefficients b o can be calculated again by making a least-squares fit of Eq. (6) to the calibration data.
3. Experimental results The method described above was verified by experimental measurements on the RPT100 resonant pressure sensor. The oscillation of the resonator was excited by a wide-band amplifier with automatic gain control, which was connected between the sensing and exciting electrodes. Oscillation
Table i Averageparametet~of a RPTI00 sensingelement Parameter
Mode 1
Mode 2
Nominalfreq. at 100kPa.20°(3 Frequencyversuspressure Frequencyversustemperature
36 to 40 kHz + 25 to + 30 Hz kPa- i - 0.2 to + 0.2 Hz °C- i,
55 to 60 kHz + 100 to + 140 Hz kPa- t - 0.8 to + 0.8 Hz °C- z=
=Temperaturecoefficientsvarywith pressure,and device-to-devicedramatically(even in the sign).
.i. V&h'~l Sensors and Actuators A 57(1996) 179-182
181
0.0
.0.1
~,m,c ---X-- m'c
"0.2
-0.3 20
40
60
80
100
140
120
~ ' e . u m ~Pa] Fig. 3. Residual error without temperature conecfion.
0.0-
.0.1-
~ ' c ~m'c
-Q.2
-0.3
'
2O
t
40
'
I
60
'
I
°
I
8O 100 Pressure ~Pa]
'
I
'
120
i
140
Fig. 4. Residualerrorwitht©mpera~,reconectiQn. mode 1 or 2 was selected by switching the phase shift of the amplifier to 0 ° or 180 °. Resonance frequeuciesf~,f2 versus pressure and temperature were measured. Readings were taken at 20 kPa steps from 20 to 140 kPa and at 0,10, 20, 30, 40 and 60°C. Average parameters e r a RPT100 sensing element are summarized in Table 1. The measured data were fitted by a polynomial fit. The order of the fit is a compromise of the required accuracy, number of measured data, their noise and the numerical stability of the calculation. The calibration data will not be perfectly represented by the algorithm and the deviation is the curve-fit error. Fig. 3 shows an example of the residual error after the non-linearity has been corrected by a simple polynomial fit (fourth order) in frequency but not in temperature. The temperature drift of the sensor is obvious. Fig. 4 shows the residual error after the calibration data have been fitted by the two-dimensional polynomial (6) with m = n = 3. The temperature drift is reduced almost four times compared with that of the uncorrected sensor.
4. Conclusions Experimental results show that the proposed method can be successfully used for temperature correction of the RPTI00 resonant pressure sensor. The temperature drift figures after correction are preliminary and will be improved using a modified measurement set-up. The method has two significant advantages over the method of correction using an external temperature sensor. First, there is no need for an external temperature sensor, signal-conditioning circuit or analog to digital converter, which simplifies the design of the electronics. Secondly, there are no errors caused by the temperature difference between the external temperature sensor and resonator itself, which occurs, for example, during fast ambient temperature changes. The disadvantage of the proposed method is the inherently slower readout during measurement, since one pressure readout requires measurement of two frequencies and time is
182
J. vi:fi /Sensors and Actuators A 57 (1996) 179-182
necessary for oscillation mode switching. Exciting both the oscillation modes simultaneously has not yet been tested.
Acknowledgements I would like to thank Mr John Greenwood from Druck Ltd., UK, for valuable advice and support o f this research project.
[2] E. Stemmeand G. Stemme,Capacitivelyexcited and detectedresonant pressuresensor with temperaturecompensation,Sensors and Actuators A, 32 (1992) 639--647. [3] J.C. Greenwood and D.W. Satchell, A miniature silicon resonant pressuresensor,lEE Prec., 135 (1988) 369-372. [41 J.C. Greenwood and T. Wray, High accuracy presst,re measurement with a silicon resonantsensor, Sensors and Actuators A, 37-38 (1993) 82-85. Biography J a n V ~ i ~ was born in 1971 and received his degree in elec-
References [ l ] R. Langdom, Resonant Sensors - - a review, .L Phys. Electrotechnics: Sci. lnstrum., 18 (1985) 103.
trical engineering from the Czech Technical University in Prague, Czech Republic in 1995. In the same year he joined the Department of Measurement at the Faculty o f Electrical Engineering at the same institution, where he is now a Ph.D. student.