METHOD AND SENSOR FOR DETERMINING A VALUE INDICATING THE IMPEDANCE OF A SUSPENSION

Abstract

A method for determining a value indicative of the impedance of a suspension in the framework of impedance spectroscopy comprises the following steps: generating an excitation current through the suspension, oscillating at an excitation frequency; determining a first impedance measurement value on the basis of the excitation current and a first voltage at a first pair of measurement electrodes; determining a second impedance measurement value on the basis of the excitation current and a second voltage at a second pair of measurement electrodes; determining the value indicative of the impedance of the suspension by correlating the first impedance measurement and the second impedance measurement.

Claims

1. A method for determining a value indicative of the impedance of a suspension in the framework of an impedance spectroscopy, comprising the following steps: generating an excitation current through the suspension, the excitation current oscillating at an excitation frequency, determining a first impedance measurement value on the basis of the excitation current and a first voltage at a first pair of measurement electrodes, determining a second impedance measurement value on the basis of the excitation current and a second voltage at a second pair of measurement electrodes, determining the value indicative of the impedance of the suspension by correlating the first impedance measurement value and the second impedance measurement value.

2. The method according to claim 1, wherein said first pair of measurement electrodes comprises a first measurement electrode and a second measurement electrode, and wherein said second pair of measurement electrodes comprises said first measurement electrode and a third measurement electrode, or wherein the first pair of measurement electrodes comprises a first measurement electrode and a second measurement electrode, and wherein the second pair of measurement electrodes comprises a third measurement electrode and a fourth measurement electrode.

3. (canceled)

4. The method according to claim 1, wherein determining the value indicative of the impedance of the suspension comprises determining the difference between the first impedance measurement value and the second impedance measurement value, or comprises determining the difference between a first adjusted impedance value and a second adjusted impedance value, wherein the first adjusted impedance value and the second adjusted impedance value are obtained by applying a correction function to the first impedance measurement value and the second impedance measurement value, the correction function preferably representing the transmission behavior of the measurement arrangement.

5. The method according to claim 1, wherein determining the value indicative of the impedance of the suspension comprises determining the difference between a first geometry factor and a second geometry factor, wherein the first geometry factor represents the measurement geometry of the first pair of measurement electrodes and wherein the second geometry factor represents the measurement geometry of the second pair of measurement electrodes.

6. The method according to claim 1, wherein determining the value indicative of the impedance of the suspension is carried out according to the following formula: ${Z=k\frac{1}{\left({\lambda }_1-{\lambda }_2\right)}{(G_{\mathrm{el}}^{-1}\left(Z_{\mathrm{sig}}\right).Math.}_1-G_{\mathrm{el}}^{-1}\left(Z_{\mathrm{sig}}\right).Math.}_2),$ wherein Z.sub.sig|.sub.1 denotes the first impedance measurement value, Z.sub.sig|.sub.2 denotes the second impedance measurement value, G.sub.el.sup.−1 denotes a correction function representing the transmission behavior of the measurement arrangement, λ.sub.1 denotes a first geometry factor representing the measurement geometry of the first pair of measurement electrodes, λ.sub.2 denotes a second geometry factor representing the measurement geometry of the second pair of measurement electrodes, and k denotes a proportionality constant.

7. The method according to claim 1, further comprising: measuring the first voltage at the first pair of measurement electrodes, and measuring the second voltage at the second pair of measurement electrodes, wherein measuring the first voltage and measuring the second voltage are performed substantially simultaneously, or further comprising: measuring the first voltage at the first pair of measurement electrodes, and measuring the second voltage at the second pair of measurement electrodes, wherein measuring the first voltage and measuring the second voltage are performed in a time-shifted manner.

8-9. (canceled)

10. The method according to claim 1, wherein determining the first impedance measurement value and determining the second impedance measurement value comprises: sampling the excitation current, sampling the first voltage, and sampling the second voltage wherein the method further comprises the steps of: setting a first sampling rate for sampling the excitation current, setting a second sampling rate for sampling the first voltage, and setting a third sampling rate for sampling the second voltage, wherein the first sampling rate, the second sampling rate and the third sampling rate are set to at least 4 times the excitation frequency of the excitation current, in particular to substantially 4 times the excitation frequency of the excitation current.

11-12. (canceled)

13. The method according to claim 10, wherein the step of determining the first impedance measurement value comprises performing a first complex Fourier transform on the basis of the sampling values of the excitation current and the sampling values of the first voltage, and wherein the step of determining the second impedance measurement value comprises performing a second complex Fourier transform on the basis of the sampling values of the excitation current and the sampling values of the second voltage.

14. The method according to claim 1, further comprising: determining a third impedance measurement value on the basis of the excitation current and a third voltage at a third pair of measurement electrodes, determining the value indicative of the impedance of the suspension by correlating the first impedance measurement value, the second impedance measurement value, and the third impedance measurement value.

15. The method according to claim 14, wherein determining the value indicative of the impedance of the suspension comprises determining a first difference between the first impedance measurement value and the second impedance measurement value and determining a second difference between the first impedance measurement value and the third impedance measurement value and determining a third difference between the second impedance measurement value and the third impedance measurement value, or wherein determining the value indicative of the impedance of the suspension comprises determining a first difference between a first adjusted impedance value and a second adjusted impedance value and determining a second difference between the first adjusted impedance value and a third adjusted impedance value and determining a third difference between the second adjusted impedance value and the third adjusted impedance value, wherein the first adjusted impedance value, the second adjusted impedance value and the third adjusted impedance value are obtained by applying a correction function to the first impedance measurement value, the second impedance measurement value and the third impedance measurement value, the correction function preferably representing the transmission behavior of the measurement arrangement.

16. The method according to claim 14, wherein determining the value indicative of the impedance of the suspension comprises determining a first difference between a first geometry factor and a second geometry factor and determining a second difference between the first geometry factor and a third geometry factor and determining a third difference between the second geometry factor and the third geometry factor, wherein the first geometry factor represents the measurement geometry of the first pair of measurement electrodes, the second geometry factor represents the measurement geometry of the second pair of measurement electrodes, and the third geometry factor represents the measurement geometry of the third pair of measurement electrodes, wherein determining the value indicative of the impedance of the suspension is carried out according to the following formula: $Z^2=k_2\frac{{{{\lambda }_3(G_{\mathrm{el}}^{-1}\left(Z_{\mathrm{sig}}\right).Math.}_2-G_{\mathrm{el}}^{-1}\left(Z_{\mathrm{sig}}\right).Math.}_1)}{\left({\lambda }_1-{\lambda }_2\right)\left({\lambda }_1-{\lambda }_3\right)\left({\lambda }_2-{\lambda }_3\right)}++\hspace{1em}{k}_2\frac{{{{\lambda }_2(G_{\mathrm{el}}^{-1}\left(Z_{\mathrm{sig}}\right).Math.}_1-G_{\mathrm{el}}^{-1}\left(Z_{\mathrm{sig}}\right).Math.}_3)}{\left({\lambda }_1-{\lambda }_2\right)\left({\lambda }_1-{\lambda }_3\right)\left({\lambda }_2-{\lambda }_3\right)}++k_2\frac{{{{\lambda }_1(G_{\mathrm{el}}^{-1}\left(Z_{\mathrm{sig}}\right).Math.}_3-G_{\mathrm{el}}^{-1}\left(Z_{\mathrm{sig}}\right).Math.}_2)}{\left({\lambda }_1-{\lambda }_2\right)\left({\lambda }_1-{\lambda }_3\right)\left({\lambda }_2-{\lambda }_3\right)},$ wherein Z.sub.sig|.sub.1 denotes the first impedance measurement value, Z.sub.sig|.sub.2 denotes the second impedance measurement value, Z.sub.sig|.sub.3 denotes the third impedance measurement value, G.sub.el.sup.−1 denotes a correction function that represents the transmission behavior of the measurement arrangement, λ.sub.1 denotes a first geometry factor that represents the measurement geometry of the first pair of measurement electrodes, λ.sub.2 denotes a second geometry factor that represents the measurement geometry of the second pair of measurement electrodes, λ.sub.3 denotes a third geometry factor that represents the measurement geometry of the third pair of measurement electrodes, and k2 denotes a proportionality constant.

17. (canceled)

18. A method for determining a value indicative of the impedance of a suspension in the framework of an impedance spectroscopy, comprising the following steps: generating an excitation voltage, oscillating at an excitation frequency, applied to the suspension, determining a first impedance measurement value on the basis of the excitation voltage and a first current through a first pair of measurement electrodes, determining a second impedance measurement value on the basis of the excitation voltage and a second current through a second pair of measurement electrodes, determining the value indicative of the impedance of the suspension by correlating the first impedance measurement value and the second impedance measurement value.

19. A method for deriving at least one characteristic property of a suspension, comprising the steps of: performing the method for determining a value indicative of the impedance of a suspension according to claim 1 a plurality of times, using a plurality of different excitation frequencies and determining a plurality of values indicative of the impedance of the suspension for the plurality of different excitation frequencies, deriving a plurality of values indicative of the permittivity of the suspension based on the plurality of values indicative of the impedance of the suspension, and deriving the at least one characteristic property of the suspension by correlating the plurality of values indicative of the permittivity of the suspension.

20. The method according to claim 19, wherein said method for determining a value indicative of the impedance of a suspension is performed for between 2 and 50 different excitation frequencies, in particular for between 10 and 40 different excitation frequencies, further in particular for between 20 and 30 different excitation frequencies, and/or wherein the different excitation frequencies are from a frequency range from 100 kHz to 10 MHz, in particular from a frequency range from 50 kHz to 20 MHz.

21. (canceled)

22. The method according to claim 19, wherein deriving the at least one characteristic property of the suspension includes generating a curve of the values indicative of the permittivity of the suspension over the different excitation frequencies, and/or wherein the suspension is a cell population and wherein the at least one characteristic property of the suspension comprises at least one property of number of living cells, size of the cells and homogeneity of the cells.

23. (canceled)

24. A sensor for determining a value indicative of the impedance of a suspension, comprising: an oscillator circuit, a pair of excitation electrodes coupled to the oscillator circuit, wherein an excitation current through the suspension, oscillating at an excitation frequency, can be generated across the pair of excitation electrodes by means of the oscillator circuit, at least three measurement electrodes for measuring a first voltage in the suspension between a first pair of the at least three measurement electrodes and a second voltage in the suspension between a second pair of the at least three measurement electrodes, and a data processing device configured to determine a first impedance measurement value on the basis of the excitation current and the first voltage, to determine a second impedance measurement value on the basis of the excitation current and the second voltage, and to determine the value indicative of the impedance of the suspension by correlating the first impedance measurement value and the second impedance measurement value.

25. The sensor according to claim 24, wherein the at least three measurement electrodes are arranged between the pair of excitation electrodes.

26. (canceled)

27. The sensor according to claim 24, wherein the at least three measurement electrodes are at least four measurement electrodes, wherein the first pair of the at least four measurement electrodes comprises a first measurement electrode and a second measurement electrode and wherein the second pair of the at least four measurement electrodes comprises a third measurement electrode and a fourth measurement electrode, wherein the third and fourth measurement electrodes are arranged between the first and second measurement electrodes and/or wherein the third and fourth measurement electrodes are arranged on a different side of the sensor than the first and second measurement electrodes.

28-29. (canceled)

30. The sensor according to claim 24, wherein the data processing device is configured to determine the value indicative of the impedance of the suspension via determining the difference between the first impedance measurement value and the second impedance measurement value, or wherein the data processing device is configured to determine the value indicative of the impedance of the suspension via determining the difference between a first adjusted impedance value and a second adjusted impedance value, wherein the data processing device is configured to determine the first adjusted impedance value and the second adjusted impedance value by applying a correction function to the first impedance measurement value and the second impedance measurement value, wherein the correction function preferably represents the transmission behavior of the measurement arrangement.

31. The sensor according to claim 24, wherein the data processing device is configured to determine the value indicative of the impedance of the suspension via determining the difference between a first geometry factor and a second geometry factor, wherein the first geometry factor represents the measurement geometry of the first pair of the at least three measurement electrodes and wherein the second geometry factor represents the measurement geometry of the second pair of the at least three measurement electrodes, wherein the data processing device is configured to determine the value indicative of the impedance of the suspension according to the following formula: ${Z=k\frac{1}{\left({\lambda }_1-{\lambda }_2\right)}{(G_{\mathrm{el}}^{-1}\left(Z_{\mathrm{sig}}\right).Math.}_1-G_{\mathrm{el}}^{-1}\left(Z_{\mathrm{sig}}\right).Math.}_2),$ wherein Z.sub.sig|.sub.1 denotes the first impedance measurement value, Z.sub.sig|.sub.2 denotes the second impedance measurement value, G.sub.el.sup.−1 denotes a correction function representing the transmission behavior of the measurement arrangement, λ.sub.1 denotes a first geometry factor representing the measurement geometry of the first pair of the at least three measurement electrodes, λ.sub.2 denotes a second geometry factor representing the measurement geometry of the second pair of the at least three measurement electrodes, and k denotes a proportionality constant.

32-39. (canceled)

40. The sensor according to claim 24, wherein the oscillator circuit is coupled to the pair of excitation electrodes via a transformer, wherein the transformer in particular has a parallel capacitance of 0.5 to 10 pF.

41-42. (canceled)

43. A sensor for determining a value indicative of the impedance of a suspension, comprising: an oscillator circuit, a pair of excitation electrodes coupled to the oscillator circuit, wherein an excitation voltage, oscillating at an excitation frequency, applied to the suspension can be generated across the pair of excitation electrodes by means of the oscillator circuit, at least three measurement electrodes for measuring a first current in the suspension between a first pair of the at least three measurement electrodes and a second current in the suspension between a second pair of the at least three measurement electrodes, and a data processing device configured to determine a first impedance measurement value on the basis of the excitation voltage and the first current, to determine a second impedance measurement value on the basis of the excitation voltage and the second current, and to determine the value indicative of the impedance of the suspension by correlating the first impedance measurement value and the second impedance measurement value.

44. A computer program comprising program instructions which, when executed on a data processing system, perform a method according to claim 1.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Further exemplary embodiments of the invention are described below with reference to the accompanying drawings.

[0064] FIG. 1 shows a sensor for determining a value indicative of the impedance of a suspension according to an exemplary embodiment of the invention in a side view;

[0065] FIG. 2 shows a sensor according to an exemplary embodiment of the invention, shown in part as a block diagram and in part as a circuit diagram;

[0066] FIG. 3 shows a sensor, modified as compared to FIG. 2, in accordance with a further exemplary embodiment of the invention, shown in part as a block diagram and in part as a circuit diagram;

[0067] FIG. 4 shows a sensor for determining a value indicative of the impedance of a suspension according to a further exemplary embodiment of the invention in a perspective view;

[0068] FIG. 5 shows a sensor for determining a value indicative of the impedance of a suspension according to a further exemplary embodiment of the invention in a side view;

[0069] FIG. 6 shows a sensor according to an exemplary embodiment of the invention, shown in part as a block diagram and in part as a circuit diagram;

[0070] FIG. 7 shows a sensor, modified as compared to FIG. 6, in accordance with another exemplary embodiment of the invention, shown in part as a block diagram and in part as a circuit diagram;

[0071] FIG. 8 shows a sensor for determining a value indicative of the impedance of a suspension according to a further exemplary embodiment of the invention in a side view; and

[0072] FIG. 9 shows an exemplary curve of permittivity values versus the excitation frequency and illustrates the derivation of characteristic properties of the suspension.

DETAILED DESCRIPTION

[0073] FIG. 1 shows a sensor 2 according to an exemplary embodiment of the invention in a side view. The sensor 2 is designed to determine a value indicative of the impedance of a suspension. The sensor 2 is designed for immersion in the suspension to be analyzed, in particular for immersion in a cell population to be analyzed. For this purpose, the sensor 2 has a rod-shaped sensor body 4, which is shown cut off in FIG. 1. The rod-shaped sensor body 4 can also be described as substantially cylindrical. The rod-shaped sensor body 4 may have a suitable length so that the analysis of the suspension can take place at a desired location in a container or reactor containing the suspension.

[0074] The rod-shaped sensor body 4 has six electrodes. In particular, the rod-shaped sensor body 4 has a pair of excitation electrodes, namely a first excitation electrode 8 and a second excitation electrode 10, a first pair of measurement electrodes, namely a first measurement electrode 11 and a second measurement electrode 12, and a second pair of measurement electrodes, namely a third measurement electrode 13 and a fourth measurement electrode 14. In the exemplary embodiment of FIG. 1, the six electrodes 8, 10, 11, 12, 13 and 14 are formed in a ring shape, i.e. they are formed circumferentially around the rod-shaped sensor body 4. It is emphasized that the six electrodes may also be present in other geometric configurations, for example in an elongated shape along the rod-shaped sensor body 4.

[0075] In the exemplary embodiment of FIG. 1, the six electrodes 8, 10, 11, 12, 13 and 14 are arranged in an end region of the rod-shaped sensor body 4. However, they may also be arranged in any other suitable region of the rod-shaped sensor body 4/of the sensor 2.

[0076] In the exemplary embodiment of FIG. 1, the first pair of measurement electrodes 11, 12 and the second pair of measurement electrodes 13, 14 are arranged between the excitation electrodes 8, 10. In particular, the first measurement electrode 11 is arranged adjacent to the first excitation electrode 8 and the third measurement electrode 13 is arranged adjacent to the first measurement electrode 11. Further in particular, the second measurement electrode 12 is arranged adjacent to the second excitation electrode 10 and the fourth measurement electrode 14 is arranged adjacent to the second measurement electrode 12. The second pair of measurement electrodes 13, 14 is arranged between the first pair of measurement electrodes 11, 12. The first measurement electrode 11 and the third measurement electrode 13 are closer to the first excitation electrode 8 than an imaginary centerline between the first excitation electrode 8 and the second excitation electrode 10. The second measurement electrode 12 and the fourth measurement electrode 14 are closer to the second excitation electrode 10 than an imaginary centerline between the first excitation electrode 8 and the second excitation electrode 10. By arranging the measurement electrodes 11, 12, 13, 14 between the excitation electrodes 8, 10 and in the vicinity of the excitation electrodes 8, 10, a comparatively high voltage can be measured when the excitation current is applied.

[0077] In operation, a first voltage Ui is measured between the first pair of measurement electrodes 11, 12 and a second voltage U2 is measured between the second pair of measurement electrodes 13, 14. This is shown schematically in FIG. 1 and will be described in detail below with reference to FIG. 2.

[0078] FIG. 2 shows a sensor 2 according to an exemplary embodiment of the invention, shown in part as a block diagram and in part as a circuit diagram. The components of the sensor 2 of FIG. 2 may be present in a sensor having the physical shape shown in FIG. 1. That is, the circuitry or signal processing structure of the sensor 2 of FIG. 2 may be the structure of the electrical components of the sensor 2 of FIG. 1. The components shown in FIG. 2 to the right of the circularly drawn coupling points can be accommodated in the sensor body 4 or in a component adjoining the same.

[0079] The sensor 2 comprises the first excitation electrode 8, the second excitation electrode 10, the first measurement electrode 11, the second measurement electrode 12, the third measurement electrode 13, and the fourth measurement electrode 14 described above. The six electrodes 8, 10, 11, 12, 13, 14 are accessible from the outside, i.e. they are in contact with the suspension when the sensor 2 is immersed in the suspension for analysis of the suspension. Furthermore, a temperature sensor 58 is provided, which is located outside the housing of the sensor 2.

[0080] The sensor 2 has an oscillator circuit 16, a signal detection and processing circuit 25, a data storage 36, a data processing device 40, a control unit 56, and a power management unit 38. The individual components and operation of these subsystems will be described in detail in the following.

[0081] The oscillator circuit 16 comprises an oscillator 18 coupled to an oscillation amplifier 20, which in turn is coupled to a transformer 22. The oscillator 18 is supplied with the desired excitation frequency EF via a control input. The excitation frequency EF is determined by the control unit 56, as described in detail below, and supplied to the oscillator 18. The oscillator 18 generates an oscillation having the excitation frequency EF, which is passed to the oscillation amplifier 20. The oscillation amplifier 20 generates an excitation current with the excitation frequency EF through the primary winding of the transformer 22. By induction, the excitation current is transferred to the secondary winding of the transformer 22, from where the current is applied to the first and second excitation electrodes 8, 10. One end of the secondary winding is connected to the first excitation electrode 8 via a first resistor 24 and the second end of the secondary winding is connected to the second excitation electrode 10 via a second resistor 26. Thus, there is formed a closed circuit from the first end of the secondary winding through the first resistor 24, via the first excitation electrode 8 through the suspension to the second excitation electrode 10, and through the second resistor 26 to the second end of the secondary winding. In this manner, an excitation current oscillating at the excitation frequency EF is generated through the suspension between the first excitation electrode 8 and the second excitation electrode 10. In the exemplary embodiment of FIG. 2, the excitation current is a sinusoidal excitation current oscillating at the excitation frequency EF. Further, in the exemplary embodiment of FIG. 2, the excitation current has an amplitude of 1 Vpp to 2 Vpp.

[0082] The transformer 22 provides for galvanic decoupling between the oscillation amplifier 20 and the first and second excitation electrodes 8, 10. A coupling capacitance may be provided in parallel with the transformer 22. The transformer 22 may then be said to have a parallel capacitance, which is present between the primary winding and the secondary winding. The parallel capacitance may be a discrete component or a parasitic capacitance of the transformer. The parallel capacitance, by being arranged parallel to the transformer, can counteract interfering influences from other coupling capacitances, such as coupling capacitances between the electrodes and the container of the suspension and/or coupling capacitances between the electrodes and other sensors present in the suspension. The parallel capacitance may be between 1 pF and 5 pF.

[0083] The excitation current between the first excitation electrode 8 and the second excitation electrode 10, oscillating at the excitation frequency EF, produces a first AC voltage between the first measurement electrode 11 and the second measurement electrode 12, and a second AC voltage between the third measurement electrode 13 and the fourth measurement electrode 14. Both the excitation current and the first voltage between the first pair of measurement electrodes 11, 12 and the second voltage between the second pair of measurement electrodes 13, 14 are detected and sampled by the signal detection and processing circuit 25. At the end of the signal processing in the signal detection and processing circuit 25, there are digital signals for the excitation current, the first voltage and the second voltage.

[0084] A first signal representing the excitation current is obtained in the following manner. The second resistor 26 acts as a measuring resistor for the excitation current. The voltage across the measuring resistor 26 is tapped by means of two conductors and supplied as the first signal to a first amplifier circuit 28. The amplified first signal is fed to the first analog-to-digital converter 32. There, the amplified first signal is converted into a digital signal, i.e. the amplified first signal is sampled and quantized. The resulting first sampling values are output to the data storage 36. It can be seen that the first resistor 24 is not required for obtaining the first signal. However, for reasons of symmetry, the first resistor 24 is provided nevertheless. Furthermore, it can be seen that tapping of a signal representing the excitation current can also take place at the first resistor 24. That is, the first amplifier circuit could also be coupled to the first excitation electrode 8 or the first resistor 24. For example, the first resistor 24 and the second resistor 26 may each have a value from 30Ω to 50Ω.

[0085] The voltage between the first measurement electrode 11 and the second measurement electrode 12 forms a second signal, which is fed to a second amplifier circuit 30. There, the second signal is amplified, and the amplified second signal is fed to a second analog-to-digital converter 33. The second analog-to-digital converter 33 generates, analogously to the first analog-to-digital converter 32, second sampling values which are discrete in time and quantized. The second sampling values are also output to the data storage 36.

[0086] The voltage between the third measurement electrode 13 and the fourth measurement electrode 14 forms a third signal, which is fed to a third amplifier circuit 31. There, the third signal is amplified, and the amplified third signal is supplied to a third analog-to-digital converter 34. The third analog-to-digital converter 34 generates, analogously to the first analog-to-digital converter 32, third sampling values io which are discrete in time and quantized. The third sampling values are also output to the data storage 36.

[0087] The first analog-to-digital converter 32, the second analog-to-digital converter 33, and the third analog-to-digital converter 34 also receive the information on the excitation frequency EF from the control unit 56. The first analog-to-digital converter 32, the second analog-to-digital converter 33 and the third analog-to-digital converter 34 use 4 times the excitation frequency EF for sampling the amplified first signal, the amplified second signal, and the amplified third signal. Thus, the first analog-to-digital converter 32, the second analog-to-digital converter 33, and the third analog-to-digital converter 34 generate first, second, and third sampling values for the excitation current, the first voltage, and the second voltage using 4 times the excitation frequency EF.

[0088] The first, second and third sampling values, output by the first analog-to-digital converter 32, the second analog-to-digital converter 33 and the third analog-to-digital converter 34, are temporarily stored or buffered in the data storage 36. Thus, the data storage 36 constitutes a buffer that holds the first sampling values, the second sampling values, and the third sampling values and can make them available for further data processing independent of real-time. Thus, from the data storage 36 onward, there are no longer any real-time requirements for the down-stream components. On the contrary, the downstream components can access a database accumulated over a period of time in the data storage 36. The data storage 36 may be, for example, a DPRAM or any other suitable type of data storage.

[0089] The data storage 36 is coupled to the data processing device 40 and outputs the first sampling values for the excitation current, the second sampling values for the first voltage between the first measurement electrode 11 and the second measurement electrode 12, and the third sampling values for the second voltage between the third measurement electrode 13 and the fourth measurement electrode 14 to the data processing device 40.

[0090] In the data processing device 40, the first, second and third sampling values are transferred to a Fourier transform module 42. The Fourier transform module 42 performs two discrete, complex Fourier transforms on the sampling values. In particular, the Fourier transform module 42 performs a first discrete complex Fourier transform with the first sampling values for the excitation current and the second sampling values for the voltage between the first measurement electrode 11 and the second measurement electrode 12, i.e., with the sampling values for the excitation current and the sampling values for the first voltage. Further in particular, the Fourier transform module 42 performs a second discrete complex Fourier transform with the first sampling values for the excitation current and the third sampling values for the voltage between the third measurement electrode 13 and the fourth measurement electrode 14, i.e. with the sampling values for the excitation current and the sampling values for the second voltage.

[0091] The Fourier transforms performed in the Fourier transform module 42 are discrete and complex, because the time-discrete sampling values for the excitation current and for the respective voltage are analyzed as interdependent quantities. The result of these complex Fourier transforms are the amplitudes of the excitation current and the respectively measured voltage for different frequencies as well as the phase shift a between the excitation current and the respectively measured voltage for the various frequencies. It is possible that the Fourier transforms perform a broad spectral analysis of the sampling values and that all spectral components except for the spectral components at the excitation frequency EF are discarded then. However, it is also possible for the Fourier transforms specifically determine the spectral component of the excitation current as well as the spectral component of the respective voltage between the respective measurement electrodes at the excitation frequency. In this context, the Goertzel algorithm can also be used to specifically determine the spectral components at the excitation frequency EF.

[0092] The amplitude of the spectral component of the excitation current at the excitation frequency EF and the amplitude of the spectral component of the respective measured voltage at the excitation frequency EF are passed to an impedance and permittivity determination module 48 via a first data transmission link 44. The phase shift a between the spectral component of the excitation current at the excitation frequency and the spectral component of the respective measured voltage at the excitation frequency is transferred to the impedance and permittivity determination module 48 via a second data transmission link 46.

[0093] The impedance and permittivity determination module 48 determines from the transferred parameters a first impedance measurement value Z.sub.sig|.sub.1, a second impedance measurement value Z.sub.sig|.sub.2, an impedance value Z, a capacitance value C and the permittivity c of the suspension at the excitation frequency. The first impedance measurement value Z.sub.sig|.sub.1 is obtained from the amplitude of the excitation current at the excitation frequency EF, the amplitude of the first voltage at the excitation frequency EF, and the phase shift a between the excitation current and the first voltage at the excitation frequency EF. The first impedance measurement value Z.sub.sig|.sub.1 is thus a complex impedance measurement value at the excitation frequency EF. The second impedance measurement value Z.sub.sig|.sub.2 is obtained from the amplitude of the excitation current at the excitation frequency EF, the amplitude of the second voltage at the excitation frequency EF and the phase shift a between excitation current and second voltage at the excitation frequency EF. The second impedance measurement value Z.sub.sig|.sub.2 is thus a complex impedance measurement value at the excitation frequency EF. As described above, the afore-mentioned amplitudes of excitation current, first voltage and second voltage as well as the afore-mentioned phase shifts are available as results of the first and second complex Fourier transforms. Thus, the first impedance measurement value Z.sub.sig|.sub.1 and the second impedance measurement value Z.sub.sig|.sub.2 can be conveniently calculated from the data present in the impedance and permittivity determination module 48.

[0094] It is emphasized that the first impedance measurement value Z.sub.sig|.sub.1 and the second impedance measurement value Z.sub.sig|.sub.2 may also be determined in other ways from the first signal, i.e., the voltage tapped at the second resistor 26, the second signal, i.e., the voltage tapped at the first pair of measurement electrodes 11, 12, and the third signal, i.e., the voltage tapped at the second pair of measurement electrodes 13, 14. Although the signal processing described in detail above permits a particularly accurate determination of the first impedance measurement value Z.sub.sig|.sub.1 and the second impedance measurement value Z.sub.sig|.sub.2, the manner of determining the first impedance measurement value Z.sub.sig|.sub.1 and the second impedance measurement value Z.sub.sig|.sub.2 is not decisive for the determination of the impedance value Z described below. In this respect, any suitable kind of signal processing can be used.

[0095] The impedance and permittivity determination module 48 determines the impedance value Z according to the following formula:

[00005]${Z=k\frac{1}{\left({\lambda }_1-{\lambda }_2\right)}{(G_{\mathrm{el}}^{-1}\left(Z_{\mathrm{sig}}\right).Math.}_1-G_{\mathrm{el}}^{-1}\left(Z_{\mathrm{sig}}\right).Math.}_2),$

wherein Z.sub.sig|.sub.1 denotes the first impedance measurement value and Z.sub.sig|.sub.2 denotes the second impedance measurement value, as described above. G.sub.el.sup.−1 denotes a correction function that represents the transmission behavior of the measurement arrangement. In the exemplary embodiment of FIG. 2, G.sub.el.sup.−1 corrects those artifacts that have been introduced into the signals between the respective electrodes and the associated analog-to-digital converters. These may include, for example, propagation time differences in the individual signal paths, non-linear gains in the amplifier circuits, etc. Accordingly, G.sub.el.sup.−1 fully or at least approximately restores those impedance measurement values that have been applied directly to the electrodes. Furthermore, λ.sub.1 denotes a first geometry factor representing the measurement geometry of the first pair of measurement electrodes 11, 12, and λ.sub.2 denotes a second geometry factor representing the measurement geometry of the second pair of measurement electrodes 13, 14. The first geometry factor λ.sub.1 and the second geometry factor λ.sub.2 describe the respective measurement cells underlying the voltage measurements at the first pair of measurement electrodes 11, 12 and at the second pair of measurement electrodes 13, 14. The nature of the first geometry factor λ.sub.1 and the second geometry factor λ.sub.2 will be described in detail further below. The variable k denotes a proportionality constant.

[0096] By using the first impedance measurement value Z.sub.sig|.sub.1 and the second impedance measurement value Z.sub.sig|.sub.2 and correlating the first impedance measurement value Z.sub.sig|.sub.1 and the second impedance measurement value Z.sub.sig|.sub.2 according to the above formula, an impedance value Z can be determined that is very robust with respect to interferences. In particular, by determining the difference between the impedance measurement values adjusted by way of the correction function G.sub.el.sup.−1 and by determining the difference between the geometry factors, it can be achieved that low-order interferences in the two measurements cancel each other out. The impedance value Z, obtained by the above formula, contains only higher order interferences, which are comparatively small in many applications. Thus, high measurement accuracy can be achieved.

[0097] The capacitance value C and the permittivity c are then calculated from the impedance value Z. In this way, the material property permittivity ε of the suspension is derived from the impedance value Z as a result. For deriving the permittivity c, perse known approaches and methods can be used. By obtaining the impedance value Z with high accuracy, as described herein, improved results can be obtained, compared to previous sensors, even when using known methods for deriving the permittivity ε.

[0098] Thus, the impedance value Z, the capacitance value C, and the permittivity c are available as results of the signal processing in the data processing device 40. In particular, these values are available as results for the excitation of the suspension with a specific excitation frequency. One or more of these values may be output for further processing. The output may be made to an external unit or, as shown in the exemplary embodiment of FIG. 2, to the control unit 56 provided in the sensor 2. In the exemplary embodiment of FIG. 2, the value determined for the permittivity ε is output to the control unit 56.

[0099] The data processing device 40 may be implemented in software or may be an arrangement of hardware components. It is also possible that the data processing device 40 is implemented partly in software and partly in hardware. The same applies to the control unit 56 described below.

[0100] The control unit 56 is connected to the power management unit 38, to the oscillator circuit 16, to the signal detection and processing circuit 25, and to the data processing device 40. The control unit 56 controls the method for determining a value indicative of the impedance of a suspension in accordance with exemplary embodiments of the invention. For this purpose, the control unit 56 is arranged to specify the excitation frequency EF for the method. In particular, the control unit is arranged to successively determine a plurality of excitation frequencies for a plurality of runs of the method in the framework of an impedance spectroscopy.

[0101] For a given run, the control unit 56 transmits the specified excitation frequency EF to the oscillator circuit 16, where the oscillator 18 generates an oscillation at the excitation frequency EF, to the signal detection and processing circuit 25, where the first analog-to-digital converter 32, the second analog-to-digital converter 33 and the third analog-to-digital converter 34 adjust the sampling rate based on the excitation frequency EF, and to the data processing device 40 where the Fourier transform module 42 analyzes the sampling values of excitation current, first voltage and second voltage with respect to the spectral signal components at the excitation frequency.

[0102] Further, in the exemplary embodiment of FIG. 2, the control unit 56 is coupled to the data processing device 40 in so far as the data processing device 40 transmits the permittivity ε, determined for the excitation frequency EF, to the control unit 56. The control unit 56 can then determine a new excitation frequency for the next run of the method in the framework of an impedance spectroscopy.

[0103] After determining a plurality of permittivity values for different excitation frequencies, the control unit 56 may derive one or more characteristic properties of the suspension from the plurality of permittivity values. To this end, the control unit may plot a curve through the plurality of permittivity values and derive the characteristic properties of the suspension from the curve, as described below with reference to FIG. 9. Such correlation of the plurality of permittivity values may also be performed externally of the sensor 2.

[0104] The control unit 56 is coupled to the power management circuit 38 in order to signal the start and end of a run of the method. Based on these signals, the power management circuit 38 supplies the oscillation amplifier 20 as well as the first amplifier circuit 28, the second amplifier circuit 30 and the third amplifier circuit 31 with the positive supply voltage V+ and the negative supply voltage V−, which are +4.5 V and −4 V in the present exemplary embodiment. At the end of a run of the method, the power management circuit 38 disconnects the positive and negative supply voltages and transmits a power down signal (“power down”) to the oscillator 18, the first analog-to-digital converter 32, the second analog-to-digital converter 33, the third analog-to-digital converter 34, and the data storage 36. In this manner, the sensor may conserve electrical energy between the runs of the method for determining the value indicative of the impedance.

[0105] The power management circuit 38 may obtain the electrical energy from outside the sensor 2 or via an internal energy reservoir, such as in the form of a battery.

[0106] To protect the sensor 2, the power management circuit 38 may open the voltage supply when the temperature sensor 58 measures a temperature above a predetermined threshold.

[0107] FIG. 3 shows a sensor 2 according to a further exemplary embodiment of the invention that is modified with respect to FIG. 2, again shown in part as a block diagram and in part as a circuit diagram. In particular, the modification relates to the signal processing in the signal detection and processing circuit 25. In general, corresponding components are provided with the same reference numerals as in FIG. 2. For their description, reference is made to the above explanations.

[0108] The signal detection and processing circuit 25 of the embodiment of FIG. 3 has no third amplifier circuit 31 and no third digital-to-analog converter 34. Instead, the second amplifier circuit 30 can be selectively connected to the first pair of measurement electrodes 11, 12 or to the second pair of measurement electrodes 13, 14. A first selection switch 29a and a second selection switch 29b are provided for this purpose. The first selection switch 29a connects either the first measurement electrode 11 or the third measurement electrode 13 to the second amplifier circuit 30. The second selection switch 29b connects either the second measurement electrode 12 or the fourth measurement electrode 14 to the second amplifier circuit 30. Thus, either the first voltage, i.e., the voltage between the first and second measurement electrodes 11, 12, or the second voltage, i.e., the voltage between the third and fourth measurement electrodes 13, 14, can be passed on to the second analog-to-digital converter 33 via the second amplifier circuit 30.

[0109] For the method for determining the value indicative of the impedance of the suspension, the modification of FIG. 3 means that the first impedance measurement value and the second impedance measurement value are determined on the basis of signals which are tapped with a time offset from each other. However, the method can be implemented with a sensor 2 having only one further amplifier circuit 30 in addition to the first amplifier circuit 28 and only one further analog-to-digital converter 33 in addition to the first analog-to-digital converter 32.

[0110] FIG. 4 shows a sensor 2 according to a further exemplary embodiment of the invention, modified with respect to FIG. 1, in a perspective view. The modification relates to the geometric arrangement of the first and second pairs of measurement electrodes. Compared to the embodiment of FIG. 1, the first measurement electrode 11, the second measurement electrode 12, the third measurement electrode 13 and the fourth measurement electrode 14 are not formed in a ring shape, but are formed in a partial ring shape. Each of the four measurement electrodes extends across a circular sector of slightly less than 180° along the cylindrical outer surface of the rod-shaped sensor body 4. In the view of FIG. 4, the first measurement electrode 11 and the second measurement electrode 12 are arranged on the left side of the sensor body 4, and the third measurement electrode 13 and the fourth measurement electrode 14 are arranged on the right side of the sensor body 4. In other words, the first pair of measurement electrodes 11, 12 and the second pair of measurement electrodes 13, 14 are arranged on different sides of the sensor 2. Such an arrangement allows a low mutual influence of the pairs of electrodes on each other, which could have a potentially negative effect on the measurement accuracy.

[0111] FIG. 5 shows a sensor 2 according to a further exemplary embodiment of the invention, modified with respect to FIG. 1, in a side view. The modification relates to the number and the geometric arrangement of the measurement electrodes. The sensor 2 of the exemplary embodiment of FIG. 5 has three measurement electrodes, a first measurement electrode 11, a second measurement electrode 12 and a third measurement electrode 13. The first measurement electrode 11 and the second measurement electrode 12 correspond in their arrangement to the first pair of measurement electrodes 11, 12 of the embodiment of FIG. 1. The third measurement electrode 13 of the embodiment of FIG. 5 is arranged where the fourth measurement electrode 14 was arranged in the embodiment of FIG. 1.

[0112] In the exemplary embodiment of FIG. 5, the first pair of measurement electrodes consists of the first measurement electrode 11 and the second measurement electrode 12. The second pair of measurement electrodes consists of the first measurement electrode 11 and the third measurement electrode 13. In operation, a first voltage U.sub.1 is measured at the first pair of measurement electrodes 11, 12, whereas a second voltage U.sub.2 is measured at the second pair of measurement electrodes 11, 13. In other words, the first measurement electrode 11 forms a potential reference point for both the measurement of the first voltage and the measurement of the second voltage. Two exemplary embodiments of the downstream signal processing of the sensor 2 of FIG. 5 are described below with reference to FIGS. 6 and 7.

[0113] FIG. 6 shows a sensor 2 according to a further exemplary embodiment of the invention, shown in part as a block diagram and in part as a circuit diagram. The components of the sensor 2 of FIG. 6 may be present in a sensor of the physical configuration shown in FIG. 5. That is, the circuitry or signal processing structure of the sensor 2 of FIG. 6 may be the structure of the electrical components of the sensor 2 of FIG. 5. Thus, FIG. 6 relates to FIG. 5 in the same way as FIG. 2 to FIG. 1. The sensor 2 of FIG. 6 is overall very similar and in large parts identical to the sensor 2 of FIG. 2. Corresponding components are provided with corresponding reference numerals. For the description of the components, reference is made to the description of FIG. 2 above.

[0114] The changes in the embodiment of FIG. 6 with respect to the embodiment of FIG. 2 take into account the fact that the sensor 2 of FIG. 6 has only three measurement electrodes 11, 12 and 13, as explained above with reference to FIG. 5. The first measurement electrode 11 can be selectively connected to the second amplifier circuit 30 or the third amplifier circuit 31 by means of a selection switch 29c. The second measurement electrode 12 is connected to the second amplifier circuit 30, and the third measurement electrode 13 is connected to the third amplifier circuit 31. Thus, either the first voltage can be supplied to the second analog-to-digital converter 33 via the second amplifier circuit 30, or the second voltage can be supplied to the third analog-to-digital converter 34 via the third amplifier circuit 31. For the method for determining the value indicative of the impedance of the suspension, this means that the first impedance measurement value and the second impedance measurement value are determined on the basis of signals which are tapped with a time offset from each other.

[0115] FIG. 7 shows a sensor 2 according to a further exemplary embodiment of the invention, modified with respect to FIG. 6, again shown in part as a block diagram and in part as a circuit diagram. In particular, the modification relates to the signal processing in the signal detection and processing circuit 25. In general, corresponding components are provided with the same reference numerals as in FIG. 6. For their description, reference is made to the above explanations.

[0116] The signal detection and processing circuit 25 of the embodiment of FIG. 7 has no third amplifier circuit 31 and no third digital-to-analog converter 34. Instead, the second amplifier circuit 30 is permanently connected to the first measurement electrode 11 and can be selectively connected to the second measurement electrode 12 or the third measurement electrode 13. A selection switch 29d is provided for this purpose. Thus, via the second amplifier circuit 30, either the first voltage, i.e. the voltage between the first and second measurement electrodes 11, 12, or the second voltage, i.e. the voltage between the first and third measurement electrodes 11, 13, can be passed on to the second analog-to-digital converter 33. For the method for determining the value indicative of the impedance of the suspension, this means that the first impedance measurement value and the second impedance measurement value are determined on the basis of signals which are tapped with a time offset from each other.

[0117] FIG. 8 shows a sensor 2 according to a further exemplary embodiment of the invention in a side view. Like the sensor 2 of FIG. 1, the sensor 2 of FIG. 8 has a first excitation electrode 8, a second excitation electrode 10, a first measurement electrode 11, a second measurement electrode 12, a third measurement electrode 13 and a fourth measurement electrode 14. The six electrodes are arranged in the sensor 2 of FIG. 8 in the same way as in the sensor 2 of FIG. 1. However, the four measurement electrodes 11, 12, 13, 14 of the sensor 2 of FIG. 8 form three pairs of measurement electrodes. In particular, a first pair of measurement electrodes consists of the first measurement electrode 11 and the second measurement electrode 12. A second pair of measurement electrodes consists of the first measurement electrode 11 and the fourth measurement electrode 14. A third pair of measurement electrodes consists of the third measurement electrode 13 and the fourth measurement electrode 14.

[0118] In operation, a first voltage U.sub.1 is measured at the first pair of measurement electrodes 11 and 12, a second voltage U.sub.2 is measured at the second pair of measurement electrodes 11 and 14, and a third voltage U.sub.3 is measured at the third pair of measurement electrodes 13 and 14. On the basis of the excitation current, the first voltage U.sub.1, the second voltage U.sub.2, and the third voltage U.sub.3, a first impedance measurement value, a second impedance measurement value, and a third impedance measurement value are determined. These three impedance measurement values are correlated with each other to determine an impedance value for the suspension. By using three pairs of measurement electrodes, which are created from a total of four measurement electrodes, interferences can be eliminated particularly well and a particularly accurate impedance value for the suspension can be determined.

[0119] The impedance value Z can be determined according to the following formula:

[00006]$Z^2=k_2\frac{{{{\lambda }_3(G_{\mathrm{el}}^{-1}\left(Z_{\mathrm{sig}}\right).Math.}_2-G_{\mathrm{el}}^{-1}\left(Z_{\mathrm{sig}}\right).Math.}_1)}{\left({\lambda }_1-{\lambda }_2\right)\left({\lambda }_1-{\lambda }_3\right)\left({\lambda }_2-{\lambda }_3\right)}++\hspace{1em}{k}_2\frac{{{{\lambda }_2(G_{\mathrm{el}}^{-1}\left(Z_{\mathrm{sig}}\right).Math.}_1-G_{\mathrm{el}}^{-1}\left(Z_{\mathrm{sig}}\right).Math.}_3)}{\left({\lambda }_1-{\lambda }_2\right)\left({\lambda }_1-{\lambda }_3\right)\left({\lambda }_2-{\lambda }_3\right)}++k_2\frac{{{{\lambda }_1(G_{\mathrm{el}}^{-1}\left(Z_{\mathrm{sig}}\right).Math.}_3-G_{\mathrm{el}}^{-1}\left(Z_{\mathrm{sig}}\right).Math.}_2)}{\left({\lambda }_1-{\lambda }_2\right)\left({\lambda }_1-{\lambda }_3\right)\left({\lambda }_2-{\lambda }_3\right)},$

wherein Z.sub.sig|.sub.1 denotes the first impedance measurement value, Z.sub.sig|.sub.2 denotes the second impedance measurement value and Z.sub.sig|.sub.3 denotes the third impedance measurement value. G.sub.el.sup.−1 denotes a correction function that represents the transmission behavior of the measurement arrangement, as described above. Furthermore, λ.sub.1 denotes a first geometry factor representing the measurement geometry of the first pair of measurement electrodes 11, 12, λ.sub.2 denotes a second geometry factor representing the measurement geometry of the second pair of measurement electrodes 11, 14, and λ.sub.3 denotes a third geometry factor representing the measurement geometry of the third pair of measurement electrodes 13, 14. The variable k.sub.2 denotes a proportionality constant.

[0120] The explanations given above with respect to FIGS. 2, 3, 6 and 7 concerning simultaneous or time-offset signal processing apply analogously to the sensor 2 of FIG. 8. For example, the four measurement electrodes can be coupled to two amplifier circuits and two analog-to-digital converters, so that partially simultaneous and partially time-offset signal processing takes place for the three measuring voltages. For example, the first voltage U.sub.1 and the third voltage U.sub.3 may be measured substantially simultaneously, while the second voltage U.sub.2 is measured thereafter. It is also possible, for example, that the four measurement electrodes are coupled to a single amplifier circuit and a single analog-to-digital converter by means of suitable selection switches, and the three voltages are measured one after the other.

[0121] It is emphasized furthermore that more than four measurement electrodes may be present and more than three pairs of measurement electrodes may be formed. Also, more than three impedance measurement values can be correlated for determining the value indicative of the impedance of the suspension. Two formulas are given above by which it is possible to determine a value indicative of the impedance of the suspension in the case of two impedance measurement values and in the case of three impedance measurement values. Some understanding aids to the formulas are provided below.

[0122] As described above, the objective of the method is to determine a value indicative of the impedance of a suspension. This value can be, for example, directly the impedance value Z.

[0123] In a real measurement setup, an impedance measurement value Z.sub.sig may be determined from a measured voltage U.sub.sig and measured current I.sub.sig. However, this impedance measurement value may differ from the impedance value Z.sub.mess present at the measurement electrodes due to the signal processing in the measurement arrangement. The conversion between the measured impedance value Z.sub.sig and the impedance value Z.sub.mess present at the measurement electrodes can be expressed by a transfer function G.sub.el of the measurement arrangement or a correction function G.sub.el.sup.−1 inverse to the same:

[00007]$\begin{array}{ccc}& G_{\mathrm{el}}& \\ Z_{\mathrm{sig}}& \rightleftarrows & Z_{\mathrm{mess}}\\ & G_{\mathrm{el}}^{-1}& \end{array}.$

[0124] In reality, the impedance value Z.sub.mess present at the measurement electrodes is not the sought impedance of the suspension, but is composed of an impedance value Z.sub.c.c., which depends on the measurement geometry, and a large number of interfering influences, such as parasitic capacitances, double layer formation on the electrode surfaces, contact resistances, etc. The interfering influences can be collectively referred to as parasitic influences Z.sub.par which distort the measurement. The totality of the parasitic influences can depend on a variety of parameters, such as temperature, conductivity of the solution, frequency of the excitation current, ion concentration in the solution, material and nature of the electrodes, etc. One can abbreviate the notation for these parameters to a parameter set {ψ.sub.i}. The parameters can contribute in different ways to Z.sub.par and thus be designated as different Z.sup.i−.sub.par({ψ.sub.i}). Thus, the impedance value Z.sub.mess present at the measurement electrodes can be expressed as a function F according to the following relationship:

[00008]$\begin{array}{ccc}& G_{\mathrm{el}}& \\ Z_{\mathrm{sig}}& \rightleftarrows & F\left(Z_{\mathrm{par}}^i\left(\left\{{\psi }_i\right\}\right),Z_{c.c.}\right).\\ & G_{\mathrm{el}}^{-1}& \end{array}$

[0125] The term Z.sub.c.c. is used because the impedance of a cell suspension can be described in a good approximation by the so-called Cole-Cole impedance.

[0126] As described above, the impedance value Z.sub.c.c. depends on the measurement geometry. The measurement geometry is also referred to herein as the geometry of the measurement cell of a pair of measurement electrodes. The impedance value Z sought is related to the measurement geometry dependent impedance value Z.sub.c.c. via the cell constant λ. The following relationship applies:

[00009]$Z_{c.c.}=\frac{{\lambda }_j}{i{\mathrm{\omega ϵ}}_{\mathrm{cole}\text{-}\mathrm{cole}}}={\lambda }_{j}Z.$

[0127] For the cell constant λ.sub.j of a j.sup.th pair of measurement electrodes holds:

[00010]${\lambda }_j=\frac{1}{{\sigma }_{\mathrm{solution}}\Delta {\varphi }^{\left[j\right]}}\int \stackrel{.fwdarw.}{J}d\stackrel{.fwdarw.}{A},$

wherein

∫{right arrow over (J)}d{right arrow over (A)}

is the area integral of the current densities and Δϕ.sup.(j) is the potential difference of the j.sup.th pair of measurement electrodes.

[0128] Thus, the impedance value Z.sub.mess present at the measurement electrodes can be expressed according to the following relationship:

[00011]$\begin{array}{cc}& G_{\mathrm{el}}\\ Z_{\mathrm{sig}}& \rightleftarrows \\ & G_{\mathrm{el}}^{-1}\end{array}F\left(Z_{\mathrm{par}}^i\left(\left\{{\psi }_i\right\}\right),{\lambda }_{j}Z\right).$

[0129] The function F can be expanded as polynomial of λ.sub.jZ. Thus, the result is:

[00012]$\begin{array}{cc}& G_{\mathrm{el}}\\ Z_{\mathrm{sig}}& \rightleftarrows \\ & G_{\mathrm{el}}^{-1}\end{array}\underset{n}{.Math.}\frac{1}{n!}{a}_n\left(Z_{\mathrm{par}}^i\left(\left\{{\psi }_i\right\}\right)\right){\lambda }_j^a{Z}^n.$

[0130] For the j.sup.th pair of measurement electrodes, the second order expansion results in:

G.sub.el.sup.−1(Z.sub.sig)|.sub.j=a.sub.0((Z.sub.par.sup.i))+λ.sub.ja.sub.1((Z.sub.par.sup.i))Z+O(2),

wherein O(2) is an abbreviation for the quadratic part of the polynomial expansion.

[0131] If one assumes that the prefactors a.sub.n and the parasitic influences Z.sup.i.sub.par are identical for different cell geometries, and if one assumes furthermore a series connection of parasitic influences and cell impedance, the difference for two impedance measurement values results as follows:

G.sub.el.sup.'11(Z.sub.sig)|.sub.1−G.sub.el.sup.−1(Z.sub.sig)|.sub.2=(λ.sub.1−λ.sub.2)a.sub.1((Z.sub.par.sup.i))Z+O(2),

wherein O(2) is an abbreviation for all quadratic parts of the polynomial expansions.

[0132] If one further assumes that O(2) as well as the portions of still higher order are negligible and that a.sub.1({Z.sub.par.sup.i}) in good approximation is a constant, one arrives at the above formula for the calculation of the value Z indicative of the impedance of the suspension from two impedance measurement values.

[0133] It has been found that under the assumptions described above, measurement results of very high accuracy are possible.

[0134] A further development of the above considerations leads to the additional above-mentioned formula for calculating the value Z indicative of the impedance of the suspension from three impedance measurement values.

[0135] FIG. 9 shows, purely qualitatively, the course 200 of the permittivity c of a cell population, plotted against the excitation frequency f. The course 200 is a purely exemplary curve derived from a plurality of permittivity values determined by the method described above. For example, the course 200 may have been derived from the plurality of permittivity values by means of a Cole-Cole fitting.

[0136] Characteristics of the cell population can be derived from the course 200 as follows. In FIG. 9, it is qualitatively shown that upstream of a frequency f.sub.ch, characteristic of the β-dispersion region 202, is a plateau region 204 in which the permittivity ε, compared to the region around the characteristic frequency f.sub.ch, changes only little with frequency, and that downstream of the characteristic frequency f.sub.ch, another plateau region 206 is located, which is different from the plateau region 204 upstream of the characteristic frequency f.sub.ch and in which the permittivity ε, again compared to the region around the characteristic frequency f.sub.ch, also does not change much with frequency.

[0137] Comparing a permittivity value ε.sub.1 representing the permittivity ε at an excitation frequency f.sub.1 in the plateau region 204 with a permittivity value ε.sub.2 at an excitation frequency f.sub.2 in the plateau region 206, a difference value Δε of the two permittivity values can be determined from the permittivity values ε.sub.1 and ε.sub.2 determined at the excitation frequencies f.sub.1 and f.sub.2, respectively. The difference value Δε is a measure for the number of living cells contained in the cell population. The alternative permittivity curve 210, indicated by two dots and three dashes, would result in an Δε at the respective excitation frequencies f.sub.1 and f.sub.2 that is larger in amount, permitting the conclusion that the cell population, for which the permittivity curve 210 was obtained, has more living cells in the same volume than the cell population underlying the permittivity curve 200.

[0138] A change in the characteristic frequency f.sub.ch indicates a change in the size of the cells or their physiology. A permittivity curve 220 with two points and one dash shows a higher characteristic frequency f.sub.ch in FIG. 9. The characteristic frequency f.sub.ch can be determined from the inflection point of the curve 200 between the plateau region 204 and the plateau region 206.

[0139] The slope of the permittivity curve at the point of its characteristic frequency f.sub.ch is a measure for the cell size distribution, with increasing slope indicating a more heterogeneous cell size distribution, and with flatter slopes of the permittivity curve 200 at the location of the characteristic frequency f.sub.ch indicating more homogeneous cell size distributions.

[0140] In particular, the permittivity curves shown in FIG. 9 may be the curves of the real parts of the permittivity values determined.

[0141] In the exemplary embodiment of FIG. 9, f.sub.1=50 kHz and f.sub.2=20 MHz. Sensors according to exemplary embodiments of the invention permit a highly accurate determination of permittivity values over such a broad frequency range, whereby for many cell populations the β-dispersion region can be described very extensively. In particular, the sensor and the method for determining a value indicative of the impedance of a suspension according to exemplary embodiments of the invention are suitable for cell populations with a conductivity of a few 0.1 mS/cm to 100 mS/cm and with a permittivity of a few pF/cm to several hundred pF/cm.

[0142] An exemplary application for the sensor and the method for determining a value indicative of the impedance of a suspension according to exemplary embodiments of the invention are fermentation processes, for example in brewing beverages. However, the invention is generally broadly applicable for determining values indicative of the impedance of a suspension and for a downstream determination of permittivity values.

[0143] Although the invention has been described with reference to exemplary embodiments, it is apparent to those skilled in the art that various modifications may be made and equivalents used without departing from the scope of the invention. The invention is not intended to be limited by the specific embodiments described. Rather, it includes all embodiments covered by the appended claims.