Method for operating a resonator and measuring arrangement therefor

Abstract

The invention relates to a method (300) for operating a resonator, the method comprising: exciting (310) a resonator by means of a periodic excitation signal with a pulse repetition frequency prf; determining (320) signal components (E(k, prf)) of the excitation signal for at least two frequencies which include (2k-1). prf, where k >= 1 and k ϵ ℕ. determining (330) signal components (A(k, prf)) of a response signal of the resonator for the at least two frequencies; and calculating (340) model parameters of a parametric model of the resonator, as a function of the signal components of the response signal and of the excitation signal, wherein the periodic excitation signal comprises a rectangular pulse with the pulse repetition frequency prf.

Description

[0001] Method for operating a resonator and measuring arrangement therefor

[0002] The present invention relates to a method for operating a resonator and a measuring arrangement therefor.

[0003] The vibration properties of a resonator can be characterized using model parameters of a parametric model of the resonator, whereby the physical properties of the resonator and its environment are determined based on the model parameters. Such resonators can, for example, be oscillating cantilevers that are capacitively excited. Based on the quality factor and eigenfrequency of a resonator vibration mode, the viscosity and density of a medium exposed to the resonator can be determined. The medium can, in particular, be a gas or a liquid. The measurement can be affected by parasitic capacitances of the resonator. Therefore, approaches are known to eliminate the influence of parasitic capacitances.

[0004] A relevant measurement arrangement with a cantilever exhibiting a parasitic capacitance is described, for example, in Appl. Phys. Lett. 107, 053506 (2015). The reference branch has a reference cantilever with the same capacitance, but which is not capable of oscillation. The similar capacitance allows the effect of the parasitic capacitance to be compensated within certain limits. However, this solution has the disadvantage of varying parasitic capacitance, for example, due to varying dielectric properties of the analyte. In this case, the parasitic capacitance cannot be determined, and thus, the dielectric properties of the medium cannot be deduced. Further resonator measurement arrangements are disclosed in WO 2011 040 678 A1 and WO 2012 129 098 A2.Another approach is described in DE 10 2015 120 596 A1, in which the resonator is excited with a limited number of integer multiples of its fundamental natural frequency, and the response signals at the excitation frequencies are evaluated. Based on this data, the resonator can be characterized. However, controlling and providing the multitude of excitation frequencies is energy-intensive. The signal generators available for this purpose have a power consumption on the order of approximately half a watt. This requires considerable additional effort in terms of explosion protection, and it also imposes limits on the miniaturization of the measurement setup.It is therefore the object of the invention to remedy this situation, i.e. to provide a method and a measuring arrangement for carrying it out, which overcome the disadvantages of the prior art and in particular have a reduced cross-sensitivity to temperature and a lower power consumption.

[0005] The object is achieved according to the invention by the method according to independent patent claim 1 and the measuring arrangement according to independent patent claim 10.

[0006] The inventive method for operating a resonator comprises: exciting a resonator by means of a periodic excitation signal with a pulse repetition frequency prf; determining signal components E(k, prf) of the excitation signal for at least two frequencies, which comprise (2k-1) • prf, where k >= 1 and ke H; determining signal components A(k, prf) of a response signal of the resonator for the at least two frequencies; and determining model parameters of a parametric model of the resonator, depending on the signal components of the response signal and the excitation signal, wherein the periodic excitation signal has a rectangular pulse with the pulse repetition frequency prf.

[0007] In a further development of the invention, the signal components and the model parameters are determined for k = 1 and k = 2.

[0008] In a further development of the invention, the excitation signal comprises a voltage signal or a current signal which is supplied to the resonator, wherein the excitation signal is provided by means of a voltage-controlled oscillator or a digitally controlled oscillator.

[0009] In a further development of the invention, the pulse repetition frequency prf is set such that a signal component of the response signal with the pulse repetition frequency prf and a signal component of the excitation signal with the pulse repetition frequency prf have a defined phase relationship to one another, so that, for example, there is a phase difference of 0° between the phase of the signal component of the excitation signal with the pulse repetition frequency prf and the signal component of the response signal with the pulse repetition frequency prf.

[0010] In a further development of the invention, the signal components of the excitation signal and response signal are determined by means of signal component extraction, in particular by means of a Goertzel algorithm, wherein the signal component extraction comprises sampling the excitation signal and the response signal generated by the resonator at the frequencies (2k-1) • prf.

[0011] In a further development of the invention, the method further comprises calculating the model parameters of the resonator, wherein the model parameters comprise the complex admittance of the resonator at the pulse repetition frequency prf, adjusted for parasitic effects, from the signal components with the frequencies (2k-1) • prf of the excitation signal and signal components with the frequencies (2k-1) • prf of the response signal.

[0012] In a further development of the invention, the method serves to measure a viscosity and / or a density of a medium by means of a resonator acted upon by the medium, wherein the resonator is operated with the method described above, wherein the method further comprises calculating a viscosity measured value and / or a density measured value of the medium based on the model parameters of the parametric model.

[0013] According to a further development of the invention, the medium comprises a fuel gas mixture, wherein the method serves to determine, on the basis of viscosity and density of the fuel gas mixture and, if applicable, its thermal conductivity, one or more of the variables from a list which includes: calorific value, Wobbe index, methane number, inert gas content.

[0014] The measuring arrangement according to the invention comprises: a resonator, and a measuring and operating circuit coupled to the resonator with a processor, which is configured to carry out the method according to one of the preceding claims. In a development of the invention, the measuring and operating circuit comprises a processor which is configured to determine signal components (E(k, prf)) of the excitation signal for at least two frequencies, which comprise (2k-1) • prf, where k >= 1 and k € H, and to determine signal components (A(k, prf)) of a response signal of the resonator for the at least two frequencies, where in particular k = 1 and k = 2.

[0015] In a further development of the invention, the processor is further configured to calculate the model parameters of the resonator for the frequencies (2k-1) • prf from the signal components of the excitation signal (E(k, prf)) and the response signal (A(k, prf)) at the frequencies (2k-1) • prf, wherein the model parameters comprise the complex admittance of the resonator at the pulse repetition frequency prf, adjusted for parasitic effects.

[0016] In a further development of the invention, the processor is configured to determine a density measurement value and a viscosity measurement value of the medium based on the admittance of the resonator, adjusted for parasitic effects, at the pulse repetition frequency prf.

[0017] In a further development of the invention, the processor is configured to: determine one or more measured variables based on viscosity and density of the fuel gas mixture and optionally its thermal conductivity under the assumption that the medium comprises a fuel gas mixture, wherein the measured variable or the measured variables are selected from a list which includes: calorific value, Wobbe index, methane number, inert gas content.

[0018] According to a further development of the invention, the medium comprises a fuel gas mixture, wherein the processor is configured to determine, on the basis of viscosity and density of the fuel gas mixture and, if applicable, its thermal conductivity, one or more of the variables from a list which includes: calorific value, Wobbe index, methane number, inert gas content.

[0019] The invention will now be explained in more detail with reference to the exemplary embodiments illustrated in the drawings. In the drawings: Fig. 1: a schematic circuit diagram of an exemplary embodiment of a measuring arrangement according to the invention;

[0020] Fig. 2: a schematic representation of a structure for signal processing when carrying out the method according to the invention; and

[0021] Fig. 3: a flowchart of an embodiment of the method according to the invention.

[0022] The exemplary embodiment of a measuring arrangement 100 according to the invention, shown schematically in Fig. 1, comprises an excitation circuit 110, a reference path 120, a sensor path 140, and a processor 200. The excitation circuit 110 comprises a pulse generator 112 with a fixed frequency and pulse width modulation (PWM), wherein the pulse width is controlled by the processor 200 via a feedback line 296. The reference branch 120 comprises a reference capacitor 122. This is followed by a first transimpedance converter 124, which is followed by a third low-pass filter 126 and a first A / D converter. The output of the first A / D converter 128 is connected to an input of the processor 200. The measuring branch 140 has a similar structure to the reference branch 120. The essential and only difference is that instead of the reference capacitor 122, a resonator 142 with a cantilever or with a tuning fork in MEMS technology is arranged.In the following, for the sake of readability of the text, only the cantilever is mentioned, although the tuning fork can equally be used as an alternative.

[0023] The equivalent circuit diagram according to a Butterworth-Van Dyke model is sketched here. A series connection of a measuring capacitance c m , a measuring resistor R m and a measuring inductance L m forms a measuring branch, where a parasitic capacitance c P is effective as if it were connected in parallel with the measuring branch. The parasitic capacitance varies within certain limits and its exact value is unknown. The reference capacitance c qHowever, it should correspond to the value of the parasitic capacitance to within approximately + / - 20%. The sensor path 140 has a second transimpedance converter 144 connected to the resonator 142, to which a fourth low-pass filter 146 and a second A / D converter 148 are connected, the output of the second A / D converter being fed to an input of the processor 200. The two transimpedance converters 124, 144 have essentially the same structure and serve to convert an incoming current signal into a current-proportional voltage signal. They each comprise an operational amplifier, to whose inverting input the current signal to be converted is applied, which is supplied here in the reference path 120 from the reference capacitor 122 and in the sensor path from the resonator 142. A resistance element with a converter resistance Rf and a capacitor with a converter capacitance et are each connected in parallel to one another and in parallel to the operational amplifier.To determine the current excitation frequency, the output signal of the voltage-controlled oscillator 116 is fed to the processor 200 via a pulse signal path 150.

[0024] The cantilever of resonator 142 is not shown in detail here. It can be excited piezoelectrically, for example, and has a fundamental bending vibration mode with a resonant frequency on the order of a few tens of kHz, for example, 30 kHz. The exact value of the resonant frequency depends on the density of the medium surrounding the cantilever. The quality factor Q of the resonator depends in particular on the viscosity of the medium surrounding the cantilever, especially the gas.

[0025] The structure of the information flow when carrying out the method according to the invention by means of the processor 200 is explained below with reference to Figs. 1 and 2. The processor 200 comprises a data buffer area 220 with a first data buffer 228 for output values ​​128' of the first A / D converter 128, i.e., for a first sequence of voltage values ​​of the reference path 120, and a second data buffer 248 for output values ​​148' of the second A / D converter 148, i.e., for a second sequence of voltage values ​​of the sensor path 140. A sequence of pulses 150', which reach the processor 200 via the pulse signal path 150 from the output of the voltage-controlled oscillator 116, is counted by a counter 152, wherein a value for the pulse repetition frequency prf is calculated based on the number of pulses by reference to a clock signal of the processor 200. This pulse repetition frequency prf corresponds to the current excitation frequency of the resonator.

[0026] This is followed by a transformation block 240 to transform the two temporal sequences of voltage values ​​128' 148' into the frequency domain using the Görtzel algorithm. The frequencies considered here are (2k-1) • prf for k = 1 and k = 2, i.e., the single and triple pulse repetition or excitation frequency. This yields both the complex spectral components E(k, prf) 2281 , 2283 of the reference path 120 and the complex spectral components A(k, prf) 2481 , 2483 of the sensor path 140 at these two frequencies.

[0027] This is followed by an admittance calculation block 260, which includes the calculation 262 of the complex admittance of the resonator Y, adjusted for the influence of the parisitic capacitance, according to:

[0028] The basic idea of ​​this calculation is that the current signal component in the sensor path 140, before being converted into a voltage signal by the transimpedance converter 144 at k = 2, i.e., at three times the excitation frequency, is essentially dominated by the parasitic capacitance path parallel to the resonator. By subtracting the capacitance-dominated ratio of the current signal components at three times the excitation frequency from the ratio of the current signal components at the fundamental frequency prf, the resulting admittance Y at the fundamental frequency is largely freed from the influence of the parasitic capacitance. Calculating 264, amplitude A and phase <p der Admittanz Y schließt sich an.

[0029] A control and evaluation block 280 includes an amplitude evaluation 282 and a phase evaluation 284. The phase evaluation 284 involves a comparison of the current phase with a target value, for example, 0°. To control and, if necessary, correct the phase, signal 294 is output via the feedback line 296 to the pulse generator 112, whereby the excitation frequency is controlled via the input voltage of the voltage-controlled oscillator 116.

[0030] In the case of resonance, i.e. correctly adjusted phase position, the amplitude evaluation 282 can calculate the quality factor Q of the resonator depending on the amplitude A and the pulse repetition frequency prf according to:

[0031] Here, G is a constant that can be determined, for example, by calibration.

[0032] The viscosity and density of the medium are determined based on the quality factor Q and the pulse repetition frequency prf.

[0033] If the medium is a fuel gas, the fuel gas mixture can be characterized with regard to its calorific value, its Wobbe index, its methane number and its hydrogen content on the basis of its viscosity and density and, if applicable, its thermal conductivity, as described in the European patents EP 3 362 790 B1, EP 3 535 581 B1 and DE 10 2017 106 904 A1.

[0034] The steps of an embodiment of the method 300 according to the invention are summarized in Fig. 3 and are briefly explained below. The method 300 for operating a resonator begins with the excitation 310 of the resonator with rectangular pulses of a pulse repetition frequency prf. This is followed by the determination 320 of signal components E(k, prf) of the excitation signal using the Goertzel algorithm for two frequencies comprising (2k-1) • prf, where k = 1 and k = 2, and the determination 330 of signal components (A(k, prf)) of a response signal of the resonator for the at least two frequencies using the Goertzel algorithm, as explained above. For this purpose, a sequence of values ​​of the excitation signal and the response signal is recorded in each case.Based on the above signal components, model parameters of a parametric model of the resonator are calculated 340, whereby the model parameters here include the amplitude and phase of the resonator's admittance adjusted for the influence of the parasitic capacitance. Finally, in step 350, a phase adjustment is performed, the result of which is a feedback signal 355 that is sent to control the resonator's excitation frequency. Specifically, the feedback signal is used to control the pulse width of a pulse generator, the output of which, via a low-pass filter, defines the input voltage of a voltage-controlled oscillator that outputs the rectangular pulses at the pulse repetition frequency prf. In a subroutine 342, the quality factor of the resonator can be determined 344 based on the amplitude of the admittance and the pulse repetition frequency in the case of resonance. This is followed by the determination 346 of the density and viscosity of a medium surrounding the resonator.In the case of a fuel gas as the medium, the following steps are taken: 348 determination of the calorific value, Wobbe index, methane number, hydrogen content, and inert gas content of the fuel gas mixture, if necessary using additional parameters such as thermal conductivity. Naturally, the state variables pressure and temperature of the fuel gas mixture are included in these calculations.

Claims

Patent claims 1. A method (300) for operating a resonator, comprising: Exciting (310) a resonator by means of a periodic excitation signal with a pulse repetition frequency prf; Determining (320) signal components (E(k, prf)) of the excitation signal for at least two frequencies comprising (2k-1) • prf, where k >= 1 and ke H. Determining (330) signal components (A(k, prf)) of a response signal of the resonator for the at least two frequencies; and Calculating (340) model parameters of a parametric model of the resonator as a function of the signal components of the response signal and the excitation signal, wherein the periodic excitation signal comprises a rectangular pulse with the pulse repetition frequency prf.

2. The method according to claim 1, wherein k = 1 and k = 2.

3. The method according to claim 1 or 2, wherein the excitation signal comprises a voltage signal or a current signal supplied to the resonator, the excitation signal being provided by means of a voltage-controlled oscillator or a digitally controlled oscillator.

4. The method according to claim 3, wherein the excitation signal is provided by means of a voltage-controlled oscillator, wherein an input voltage of the voltage-controlled oscillator is provided by averaging a PWM signal by means of a low-pass filter.

5. Method according to one of claims 1 to 4, in which the pulse repetition frequency prf is set such that a signal component of the response signal with the pulse repetition frequency prf and a signal component of the excitation signal with the pulse repetition frequency prf have a defined phase relationship to one another, so that, for example, there is a phase difference of 0 between the phase of the signal component of the excitation signal with the pulse repetition frequency prf and the signal component of the response signal with the pulse repetition frequency prf.

6. The method according to any one of claims 1 to 4, wherein the signal components of the excitation signal and response signal are determined by means of signal component extraction, in particular by means of a Goertzel algorithm, wherein the signal component extraction comprises sampling the excitation signal and the response signal generated by the resonator at the frequencies (2k-1) • prf.

7. The method according to any one of claims 1 to 6, further comprising: calculating the model parameters of the resonator, the parameters comprising the complex admittance of the resonator at the pulse repetition frequency prf, corrected for parasitic effects, from the signal components with the frequencies (2k-1) • prf of the excitation signal and signal components with the frequencies (2k-1) • prf of the response signal.

8. A method for measuring a viscosity and / or a density of a medium by means of a resonator acted upon by the medium, wherein the resonator is operated by the method according to one of the preceding claims, further comprising: calculating a viscosity measurement value and / or a density measurement value of the medium based on the model parameters of the parametric model.

9. The method according to claim 8, wherein the medium comprises a fuel gas mixture, the method further comprising: determining one or more measured variables based on viscosity and density of the fuel gas mixture and optionally its thermal conductivity, wherein the measured variable or the measured variables are selected from a list which includes: calorific value, Wobbe index, methane number, inert gas content.

10. A measuring arrangement comprising: a resonator, and a measuring and operating circuit coupled to the resonator with a processor, which is configured to carry out the method according to one of the preceding claims.

11. Measuring arrangement according to claim 10, wherein the measuring and operating circuit comprises a processor which is configured to determine signal components (E(k, prf)) of the excitation signal for at least two frequencies comprising (2k-1) • prf, where k >= 1 and ke H, and to determine signal components (A(k, prf)) of a response signal of the resonator for the at least two frequencies.

12. Measuring arrangement according to claim 11, wherein the processor is further configured to calculate the model parameters of the resonator for the frequencies (2k-1) • prf from the signal components of the excitation signal (E(k, prf)) and the response signal (A(k, prf)) at the frequencies (2k-1) • prf, wherein the model parameters comprise the complex admittance of the resonator at the pulse repetition frequency prf, corrected for parasitic effects.

13. Measuring arrangement according to claim 12, wherein the processor is configured to determine a density measurement value and a viscosity measurement value of the medium based on the admittance of the resonator, corrected for parasitic effects, at the pulse repetition frequency prf.

14. Measuring arrangement according to claim 13, wherein, assuming that the Medium comprises a fuel gas mixture, the processor is configured to: determine one or more measured variables based on viscosity and density of the fuel gas mixture and optionally its thermal conductivity, wherein the measured variable or variables are selected from a list which includes: calorific value, Wobbe index, methane number, inert gas content.

15. Measuring arrangement according to claim 10 to 14, wherein the resonator comprises a MEMS oscillator, in particular a cantilever.

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