DE102022133018B3 - Method and measuring system for carrying out an impedance spectroscopic measurement - Google Patents

Abstract

The invention relates to a method for carrying out an impedance spectroscopic measurement on a test object. For this purpose, a broadband test signal is generated which consists of several test signal components in the form of binary pseudo-noise sequences, with a predetermined bandwidth (b) of the test signal being divided into at least two adjacent sub-bands of the test signal components. The test object is then excited by simultaneously impressing all test signal components in their sub-bands. The reaction of the excited test object is recorded, with at least one associated sensor on the test object recording partial measurement signals in the respective sub-band for each of the sub-bands. The partial measurement signals are processed in parallel measurement channels by Fourier transformation. Finally, the processed partial measurement signals are combined to form a measurement signal which characterizes the test object. The invention also relates to a measurement system for carrying out an impedance spectroscopic measurement on a test object.

Description

The present invention relates to a method and a measuring system for carrying out an impedance spectroscopic measurement.

Different technical possibilities for measuring impedances on test objects are known. What the usual methods have in common is that test signals are generated and their effects on the material to be examined are recorded as a measurement signal. The invention deals with the aspects of such signal generation and signal recording and is therefore generally applicable to various methods of impedance measurement.

Impedance spectroscopy is a well-known method for determining the electrical response of solid and liquid materials. The parameters determined can then be used to draw conclusions about material composition, material quality, etc. To carry out an impedance spectroscopic measurement, the test object to be examined is exposed to a weak alternating electrical field and the electrical resistance that the test object offers to a current flow at a given frequency of the alternating field is measured. The resistance depends on many internal, molecular and structural effects, the frequency-dependent effects of which can be determined over a very broad frequency band. In order to record the parameters of the material to be examined as completely as possible, measurements over an extremely broad frequency spectrum are required. Such measurements are traditionally carried out using sinusoidal signals, the frequency of which is changed step by step over the relevant frequency band. Two measurement concepts are used, which are regularly referred to as impedance analyzers and network analyzers. For frequencies below 10 - 100 MHz, impedance analyzers are usually used. Above 100 MHz, network analyzers are usually used. These are typically laboratory devices that are not suitable for use as industrial sensors. Signal generation is complex and causes a long measurement time, since the measurement frequencies are run through sequentially.

The EN 10 2004 047 042 A1 explains a method for spectrum analysis of a signal in several frequency bands, each with a different frequency resolution. The method comprises a data acquisition step and a subsequent data evaluation step for each frequency band. The data acquisition step and the subsequent data evaluation step run cyclically without interruption for each frequency band of the spectrum analysis. The associated device for spectrum analysis of a signal cyclically stores a sampling sequence of the signal for each frequency band in a ring buffer. A discrete Fourier transformer cyclically calculates the spectral values belonging to the respective frequency band from the cyclically stored sampling sequences.

The EP 3 141 898 A1 describes an impedance spectroscopy system for bioimpedance measurement in which a signal with a broadband frequency spectrum is generated and an analog injection current is derived from the signal. The analog injection current has a high-pass frequency characteristic. An amplifier is used to measure a voltage in response to the analog injection signal, which includes biopotential information (eg ECG or EEG) from which a bioimpedance spectrum and other parameters can be obtained. This system uses an injection current with a high-pass frequency characteristic so that the injection current increases with frequency. This compensates for the typical bioimpedance behavior so that the signal-to-noise ratio of the system is more uniform across frequency.

The characterization and analysis of the composition of materials or, in general, of substances to be examined using impedance spectroscopy allows continuously operating measurement methods or measurement systems that are non-destructive and do not require sampling. The method uses the material-specific transport or displacement mechanisms of free or bound electrical charge carriers. From a macroscopic point of view, the behavior of the charge carriers is described by the frequency-dependent permittivity number ε(f). The permittivity (dielectric conductivity) of a substance is a complex-valued function depending on the frequency, which is typically represented as the product of the permittivity of the vacuum ε ₀ and the relative permittivity ε _r (f) of the substance under consideration. The size and frequency dependence of the permittivity depend on the material in question or on its composition of basic materials, impurities, contamination, etc. Thus, the impedance spectroscopic measurement requires that the composition or quality of a substance (test object) can be deduced retrospectively from the permittivity measurement. This requires the solution of an inverse problem. Such problems tend to lead to ambiguous and contradictory solutions. To counteract this, as much information as possible and as diverse as possible must be collected about the test object. Applied to the method of impedance spectroscopy, this means that the interaction of an electric field with the test object must be observed over as wide a frequency band as possible in order to be able to record several physical interaction mechanisms. In the case of impedance spectroscopy, one usually restricts oneself to frequencies in the microwave range and below. Within these frequency ranges, the typical interactions are based on relaxation phenomena with specific relaxation times.

One object of the invention is to provide an improved method for carrying out an impedance spectroscopic measurement. This method should in particular allow the impedance spectroscopic measurement to be carried out more quickly than with conventional methods, with simple technical means and, above all, over an extremely wide frequency band, so that material-specific parameters of the test object can be determined with high accuracy.

To better understand the invention, some of the key findings on which the invention is based are first presented. In many potential fields of application, such as inline monitoring of flowing liquids, the time to record a complete impedance spectrum is very limited. This quickly pushes conventional measurement methods (impedance analyzer, network analyzer) to their limits, as these devices run through the required frequency range in sequential steps, which leads to a long measurement time and also requires complex sine signal generators that can cover a broadband frequency band. One approach to significantly reducing the measurement time is to excite the test object to be examined with a large number of frequencies at the same time. This requires a broadband test signal that contains all spectral components at the same time; the test signal should therefore have a large "instantaneous bandwidth". At the same time, however, it must be ensured that the total power of the test signal does not exceed certain values in order to avoid overheating or destruction of the test object. The desired permittivity ε _r of the test object (usually a solid or liquid substance) is a material parameter that cannot be measured directly. One measurable quantity is, for example, the frequency-dependent admittance Y (f) of a capacitor whose dielectric is formed by the substance being measured. If, for the sake of simplicity, we initially assume that the permittivity of the test material is frequency-independent, there is a range of variation in the admittance amplitude within the frequency band, with the range of variation of the measured value being in the same order of magnitude as the range of variation of the frequency. For a desired frequency interval of, for example, 12 decades, we would therefore need a measuring device that can also measure an admittance over 12 orders of magnitude. Since all frequencies are to occur simultaneously, it is not possible to switch the measuring range for the admittance measuring device. The precise measurement of an admittance over 12 decades in a single measuring range is physically impossible with today's components.

Surprisingly, the invention makes it possible to meet these seemingly contradictory requirements physically and technically. It thus creates completely new measurement possibilities and fields of application for the impedance spectroscopic measurement of materials or substances.

Based on these considerations, the above-mentioned object is achieved by a method according to the appended claim 1 and by a measuring system according to claim 9. Preferred embodiments are mentioned in the dependent subclaims, although this does not represent an exhaustive list of possible variations.

According to the invention, in a first step a broadband test signal with a large instantaneous bandwidth is generated, which is broken down into several test signal components in the form of binary pseudo-noise sequences. There are several ways of generating very broadband signals. A very simple, cost-effective and power-saving method is the generation of binary pseudo-noise sequences, e.g. an M-sequence. The invention is described below using M-sequences as a test signal, but this does not exclude the applicability of other binary pseudo-noise sequences. In addition to the term M-sequence, the term MLBS (maximum length binary sequence) is also used. The generation of an M-sequence is relatively easy up to high frequencies, preferably by a stable clock generator triggering a digital, linear feedback shift register (LFSR). Such a shift register consists of a number n of flip-flops that are suitably fed back in order to generate an M-sequence (in Individual: J. Sachs, Handbook of Ultra-Wideband Short-Range Sensing - Theory, Sensors, Applications. Berlin: Wiley-VCH, 2012 ). n also denotes the order of the M-sequence.

An M-sequence is a periodic signal whose period consists of apparently randomly distributed positive and negative elementary pulses - so-called chips.

The number N of chips per period is determined by the order n of the M-sequence, i.e. the number of flip-flops in the LFSR: $$N=2^n-1$$

The duration of an elementary pulse is determined by the clock rate of the generator: $$t_c={ƒ}_c^{-1}.$$

The duration of an M-sequence period is therefore: $$T_P=N\cdot t_c$$

If you subject an M-sequence to a Fourier transformation, you get a line spectrum. A signal with a line spectrum can also be understood as a superposition of several sinusoidal signals of different frequencies; in this case, these are the desired sinusoidal frequencies $${ƒ}_i=i\cdot \mathrm{\Delta }ƒ\mathrm{=}\frac{i}{T_P}=\frac{i}{N}{ƒ}_c;i=\mathrm{0,1,2,3,}\cdots$$

The amplitudes of the corresponding sine components follow a sinc ² function. It can be seen that all spectral components (sine components) with frequencies less than f _c /2 have almost the same power, while spectral components above this become weaker and weaker. They would therefore hardly be suitable for stimulating a test object. Therefore, according to a particularly preferred embodiment, all frequencies greater than f _c /2 are excluded when generating the test signal. In order to be able to guarantee this in practice, the undesirable spectral components are suppressed by a low-pass filter. For the sake of simplicity, an ideal rectangular low-pass filter with the cut-off frequency f _c /2 is assumed below.

verfügt, ohne dass aufwendige Sweep-Vorgänge oder Frequenzregelschleifen benötigt werden. Je nach geforderter relativer Bandbreite b kann die nötige Länge des Schieberegisters gewählt werden. Im Falle der bevorzugten Tiefpassfilterung ist die Signalamplitude der M-Sequenz im Wesentlichen gleichmäßig über die gesamte Periode verteilt. Spannungsspitzen, die zu Überlastungen des Testobjektes oder zur Übersteuerung einer Messelektronik führen könnten, sind damit ausgeschlossen. Damit umfasst das Spektrum der M-Sequenz eine Anzahl von N_F nutzbaren, nicht redundanten Spektrallinien $$N_F=\frac{N-1}{2}=2^{n-1}-1$$

The M-sequence (or a comparable binary pseudo-noise sequence) is therefore initially available as a test signal, which simultaneously has the frequencies $$e_i=i\cdot \mathrm{\Delta }e;i=\mathrm{1,2,}\cdots \frac{N-1}{2}$$

without the need for complex sweep processes or frequency control loops. The required length of the shift register can be selected depending on the required relative bandwidth b. In the case of the preferred low-pass filtering, the signal amplitude of the M-sequence is distributed essentially evenly over the entire period. Voltage peaks that could lead to overloading of the test object or overloading of the measuring electronics are thus excluded. The spectrum of the M-sequence thus comprises a number of N _F usable, non-redundant spectral lines $$N_F=\frac{N-1}{2}=2^{n-1}-1$$

The use of M-sequences (or comparable binary pseudo-noise sequences) simplifies both the generation of the test signal and the acquisition and processing of the measurement signals obtained from the test object to be examined, as will be described below.

It is essential for the invention that the test signal with the desired large bandwidth b is divided into at least two test signal components that lie in adjacent sub-bands. For this purpose, at least two parallel channels are implemented in a measuring system that are fed with the same clock, but limit the large bandwidth b to a predetermined narrower frequency band (sub-band) and form an M-sequence for each of them, which is then available as a test signal component.

In the next step of the method according to the invention, the multiple M-sequences (or comparable binary pseudo-noise sequences) are impressed on a test object for the purpose of measurement, ie the The test object is excited by the test signal, which is represented by at least two, preferably numerous test signal components. The test object is, for example, a solid or liquid substance, in particular a material mixture to be examined with regard to its parameters. Such test objects are regularly embedded in a measuring circuit.

The reaction of the test object to the test signal (test signal components) represents the measurement signal, which must be recorded in a suitable form in the next step. According to preferred embodiments, Nyquist sampling, interleaved sampling or oversampling with optional low-pass filtering are used as methods for recording the measurement signal. All of these methods require the band limitation of the test signal to half the respective clock rate of the LFSR. This is achieved by a low-pass filter, which can in principle be arranged anywhere between the LSFR and an analog/digital converter (ADC). With oversampling, a digital implementation is also possible, so that analog filters can be omitted. Division into several filters is also possible.

The above-mentioned and similar variants of measured value acquisition provide a data stream of N=2 ⁿ -1 digitized voltage values per measurement. For further processing, the measurement signals obtained must be subjected to a Fourier transformation (in the practical case an FFT - Fast Fourier Transformation) in order to obtain the spectral composition of the measurement signal. This procedure ultimately corresponds to a (virtual) excitation of the test object with sinusoidal signals (test signal).

In particular, the LFSR components and the required clock dividers, which divide the clock signal and feed it to the parallel channels, can be implemented as real circuits or can be mapped by an algorithm in a freely programmable digital circuit (e.g. FPGA or DSP). However, the latter remains limited to clock rates below a few 10 MHz with currently common components.

By applying the preferred band limitation mentioned above, the technical effort can be reduced and a particularly stable operation of the overall system can be ensured, since all time-critical subcomponents can be operated from a common clock source. The Nyquist sampling theorem states that the clock rate of the analog/digital converter (ADC) must be (at least) twice as large as the bandwidth of the measurement signal. In this case, LFSR and ADC can therefore be operated from the same clock generator. In addition, the strict temporal coupling between the test and measurement signals enables their mutual phase to be determined without the need for a reference channel to record the test signal. This reduces the technical effort, power consumption and data volume.

As explained above, in the impedance spectroscopic measurement (hyper-broadband measurement), the test object, which is embedded in a measurement environment, is to be excited with test signals in a large frequency range, namely over a frequency band with the relative bandwidth b. For b, e.g. 8, 10 or 12 decades can be assumed (b= [10 ⁸ 10 ¹⁰ 10 ¹² ]). Such signals can be generated with an LFSR of order 28, 35 or 41. Chaining such a number of flip-flops to form an LFSR is not technically a problem. The associated data volumes that are to be recorded per measurement result in 268 million, 34 billion or 2.2 trillion measured values, each typically 12 ... 16 bits, for the three cases. For a conventional sensor system, these would be unmanageable data volumes - without application of the invention. In addition, it must be ensured that the total power of the test signal generally does not exceed 1 mW (in many cases even less) in order to prevent damage to the test object. This power is distributed evenly across all spectral lines, so that in conventional sensor systems there would no longer be any reasonably measurable power available for each spectral component.

This problem of hyper-broadband measurement with its contradictory requirements is solved by the method according to the invention by dividing the processing into sub-bands. The processing of the measurement signals obtained is cascaded or parallelized so that a quasi-logarithmic gradation of the spectral lines of the test or excitation signal is obtained. For conceptual understanding, it should be noted that the measurement channels used to carry out the method according to the invention work in parallel, but they are cascaded in terms of frequency. Within a sub-band, the frequency spacing is equidistant (i.e. linear). The center frequencies of the individual sub-bands are scaled logarithmically, so that one can speak of a quasi-logarithmic gradation. This means that at low frequencies the distance between two spectral lines is relatively small, while at high frequencies their distance becomes ever larger. Since the distance between the spectral lines of an M-sequence is necessarily always equidistant, no continuous increase in distance can be achieved, but only in jumps gen - hence the term quasi-logarithmic. This advantageously leads to a reduction in the amount of data and an increase in the signal power per spectral line compared to a purely linear scaling of the measurement frequencies. In this sense, the resulting measurement signal shows a quasi-logarithmic frequency axis, which results from the interaction of shift registers and clock dividers.

The aforementioned detection of the reaction of the excited test object is carried out by sensors adapted to the test object. Each channel of the measuring system, which operates in a sub-band as described, is assigned at least one sensor that is adapted to the frequency range of this sub-band. The person skilled in the art is familiar with numerous sensors from which he can make a selection. Each sensor detects partial measurement signals on the test object in the associated sub-band, which are then sent for further processing. The sensor, the test object and any other components required to obtain the measurement signals can be referred to as a whole as a measurement environment that is to be set up for each channel and of which at least two are provided to work in parallel according to the invention.

In a subsequent process step, the recorded partial measurement signals are processed in parallel in parallel measurement channels, namely by a Fourier transformation, preferably an FFT. Finally, the processed partial measurement signals are combined to form a final measurement signal, which represents the parameters of the test object being examined. The measurement signal has a quasi-logarithmic frequency axis and can be output to other units and/or displayed on a display unit.

The measuring system according to the invention for carrying out an impedance spectroscopic measurement on a test object is particularly suitable for carrying out the method described above or one of its embodiments. The measuring system initially comprises a clock generator for generating a clock signal f _c and at least one clock divider to divide the clock signal into at least two clock signal components. At least two measuring channels operating in parallel each receive a clock signal component. Each measuring channel operates in its own sub-band, with the frequency ranges of the neighboring sub-bands adjacent to one another or possibly partially overlapping in the border areas. Each of these parallel measuring channels comprises a linear feedback shift register (LFSR), which generates a partial test signal in the form of a binary pseudo-noise sequence from the clock signal component. Each measuring channel has a measuring environment with a sensor that detects a partial measurement signal in the sub-band of the measuring channel on the test object, and an analog/digital converter (ADC) that converts the partial measurement signal. Finally, the measuring system has a computing unit which receives the partial measurement signals from the measuring channels and, using a parallel Fourier transformation, combines them into a measurement signal with a quasi-logarithmic frequency axis.

• 1 ein Blockschaltbild einer ersten Ausführungsform eines Hyper-Breitband-Messsystems mit kaskadierten/parallelen Pseudo-Rausch-Einheiten zur Ausführung des erfindungsgemäßen Verfahrens;
• 2 ein Blockschaltbild einer zweiten Ausführungsform eines Hyper-Breitband-Messsystems mit kaskadierten/parallelen Pseudo-Rausch-Einheiten;
• 3 ein Blockschaltbild einer dritten Ausführungsform eines Hyper-Breitband-Messsystems mit zwei separat getakteten 2-Kanal-Analog/Digital-Wandlern.

Further advantages and details of the invention emerge from the following description of preferred embodiments, with reference to the drawing. They show:

• 1 a block diagram of a first embodiment of a hyper-broadband measuring system with cascaded/parallel pseudo-noise units for carrying out the method according to the invention;
• 2 a block diagram of a second embodiment of a hyper-wideband measurement system with cascaded/parallel pseudo-noise units;
• 3 a block diagram of a third embodiment of a hyper-broadband measuring system with two separately clocked 2-channel analog/digital converters.

1 shows a simplified block diagram of a first embodiment of a hyper-broadband measuring system which is suitable for carrying out the method according to the invention. The measuring system uses a cascading or parallel connection of pseudo-noise units. The desired quasi-logarithmic frequency scaling is achieved by dividing the frequency band b to be recorded into K sub-bands: $$b=b_0^K$$

For the sake of simplicity, only an even distribution across the various sub-bands is considered here; however, by choosing the appropriate LFSR order and the divider factors, other combinations or distributions can also be generated.

In the embodiment shown, K=4 is selected. A clock generator 11 provides a clock signal with a clock frequency f _c , which is then provided, partly via clock dividers 12, to the four parallel measuring channels ❶❷❸❹. Each measuring channel has a linear feedback shift register 13 (LFSR), which consists of a number n of flip-flops that are suitably fed back to generate an M sequence. The clock dividers 12 ensure that each LFSR 13 operates in a different sub-band. Within a sub-band, the distance between the spectral lines is equidistant. A separate measuring channel is used for each sub-band. The binary pseudo-noise sequence generated by the LFSR is preferably filtered by an adapted low-pass filter 14 and then fed to a measuring environment 15. Depending on the embodiment, the low-pass filtering can be carried out before or after the measurement object (the measuring environment). In the case of oversampling, it can also be implemented digitally and be part of the downsampling. Therefore, the filter blocks in channels ❸ and ❹ are missing in 1 and in channel ❹ in the 2 and 3 . At high measurement frequencies, i.e. where subsampling or Nyquist sampling is used, low-pass filtering must be carried out using analog filters. Each measurement environment includes the test object, a sensor and other components required to carry out the measurement.

The signal generation is technically not very complex and enables a time-parallel measurement across all frequencies. This requires K sensor electrodes, which are part of the respective measurement environment 15 and are preferably placed spatially close to one another, especially if spatial inhomogeneity of the test object to be examined is to be expected. The various sensor electrodes do not necessarily have to be identical. Each measurement environment 15 supplies a partial measurement signal for the respective sub-band, which is fed via an associated analog/digital converter 16 (ADC) to a computing unit 17, in which the partial measurement signals are subjected to a parallel (fast) Fourier transformation and combined to form a final measurement signal. The ADCs 16, which can be combined all or in groups to form a multi-channel ADC, are preferably fed by the same clock signal as one of the LFSRs 13.

• - alle LFSR sind von der gleicher Ordnung n;
• - alle Taktteiler sind ebenfalls von der Ordnung n;
• - ein Multi-Kanal ADC erfasst parallel alle Teilmesssignale; er wird mit der Frequenz f_s getaktet;
• - die Messwerterfassung in allen Sub-Bändern (Messkanälen) umfasst die gleiche Zeitdauer T_R.

To explain how it works, we will use the simplest of conditions as an example, as follows:

• - all LFSRs are of the same order n;
• - all clock dividers are also of order n;
• - a multi-channel ADC records all partial measurement signals in parallel; it is clocked with the frequency f _s ;
• - the measured value acquisition in all sub-bands (measurement channels) covers the same time period T _R .

1 shows a 4-channel embodiment, where in each measuring channel the clock rate of the corresponding LFSR 13 is reduced by a factor of 2 ⁿ . Due to the same order of all LFSR 13, the same number of usable spectral lines is generated in all four channels, although their frequency position and spacing decrease with each level.

Preferably, a track and hold (T&H) circuit 18 is provided upstream of the ADC 17 in channel ❶, particularly when the analog input bandwidth of the AD converter is not large enough for the bandwidth of the M-sequence. This is typically the case in the subsampling operating mode.

$\left[\mathrm{1,2,3}\cdots 2^{n-1}-1\right]\frac{{ƒ}_c}{\left(2^n-1\right)2^{n\left(K-1\right)}}$

❹ $\left[\mathrm{1,2,3}\cdots 2^{n-1}-1\right]\frac{{ƒ}_c}{\left(2^n-1\right)2^{3n}}$

f_min 9.8 KHz 145 mHz f_max 148 KHz 37 Hz ❸ $\left[\mathrm{1,2,3}\cdots 2^{n-1}-1\right]\frac{{ƒ}_c}{\left(2^n-1\right)2^{2n}}$

f_min 315 KHz 75 Hz f_max 4.7 MHz 20 KHz ❷ $\left[\mathrm{1,2,3}\cdots 2^{n-1}-1\right]\frac{{ƒ}_c}{\left(2^n-1\right)2^n}$

f_min 10 MHz 38 KHz f_max 151 MHz 10 MHz ❶ $\left[\mathrm{1,2,3}\cdots 2^{n-1}\right]\frac{{ƒ}_c}{\left(2^n-1\right)}$

f_min 320 MHz 20 MHz f_max 4.8 GHz 5 GHz Relative Bandbreite b=2^nK-1 5 10⁵ 3.4 10¹⁰ Datenumfang N_HW=K(2ⁿ-1) 124 2044 Anzahl Spektrallinien $N_{F,HW}=K\left(2^{n-1}-1\right)\approx \frac{1}{2}{N}_{HW}$

60 1020 The following Table 1 summarizes the frequencies of all occurring spectral lines and illustrates the frequency range of the individual channels using examples. A clock rate of f _c =10GHz is assumed. Table 1: channel Spectral lines Order of LFSR and divisor n = 5 n =9

$\left[\mathrm{1,2,3}\cdots 2^{n-1}-1\right]\frac{{ƒ}_c}{\left(2^n-1\right)2^{n\left(K-1\right)}}$

❹ $\left[\mathrm{1,2,3}\cdots 2^{n-1}-1\right]\frac{{ƒ}_c}{\left(2^n-1\right)2^{3n}}$

f _min 9.8KHz 145 MHz _fmax 148KHz 37Hz ❸ $\left[\mathrm{1,2,3}\cdots 2^{n-1}-1\right]\frac{{ƒ}_c}{\left(2^n-1\right)2^{2n}}$

f _min 315KHz 75Hz _fmax 4.7MHz 20KHz ❷ $\left[\mathrm{1,2,3}\cdots 2^{n-1}-1\right]\frac{{ƒ}_c}{\left(2^n-1\right)2^n}$

f _min 10MHz 38KHz _fmax 151MHz 10MHz ❶ $\left[\mathrm{1,2,3}\cdots 2^{n-1}\right]\frac{{ƒ}_c}{\left(2^n-1\right)}$

f _min 320MHz 20MHz _fmax 4.8GHz 5GHz Relative bandwidth b= ^2nK-1 5 10 ⁵ 3.4 10 ¹⁰ Data scope N _HW =K(2 ⁿ -1) 124 2044 Number of spectral lines $N_{F,HW}=K\left(2^{n-1}-1\right)\approx \frac{1}{2}{N}_{HW}$

60 1020

The advantages of splitting into sub-bands are evident from the examples in Table 1. In a single-stage or 1-channel process (i.e. only one M-sequence stage), for example, a number of N≈10 ⁶ measured values would have to be recorded for a relative bandwidth of b=5 10 ⁵ if the invention is not used. Instead, according to the invention, only N _HW =124 need to be recorded in the 4-channel process. The improvement becomes more and more apparent with increasing bandwidth, because instead of N≈6.8·10 ¹⁰ data samples to achieve a relative bandwidth of b=3.4·10 ¹⁰ in one stage, only N _HW =2044 voltage values need to be recorded in the 4-channel process.

Regarding the measurement data acquisition, in the embodiment according to 1 It is assumed that a 4-channel ADC is available for this purpose, the input voltages of which are typically all recorded at the same clock rate (a time offset in the measured value recording between the channels would not play a role; simultaneous recording is therefore not necessary). Since the highest frequency to be measured should be around 5 GHz, a sampling rate of 10 GHz would be required for the ADC in measuring channel ❶ of the hyper-broadband sensor operating according to the invention. The ADC required for this would be technically complex and one therefore opts for sequential sampling at this stage (in the general case for interleaved sampling). For the case n=9, this leads to an actual sampling rate of the ADC of f _s =2 ^-9 f _c ≈20 MHz , which also corresponds to the clock rate of the shift register in measuring channel ❷. ADCs for this measuring rate are commercially available.

zum Erfassen aller Datensamples im Kanal ❹ am längsten dauert. Sie entspricht der Periodendauer der M-Sequenz mit der niedrigsten Taktrate. Aus praktischer Sicht ist es sinnvoll, dass alle Messkanäle über eine gleiche Messzeit arbeiten und nur die physikalisch sinnvollen Datensamples einer Weiterverarbeitung, z. B. Fourier-Transformation, zugeführt werden. Im Ergebnis dessen soll also jeder Messkanal N = 2ⁿ -1 Spannungssamples pro Zeitintervall T_R4 liefern.Since this clock rate also applies to all other channels of the ADC, the measuring channel ❷ works in “Nyquist sampling” mode and the channels ❸ and ❹ work in “over sampling” mode. For the channels working in “over sampling” mode, it is assumed that the band limitation on the digital side is taken over by the down sampling, so that analog filters can be dispensed with. It should also be noted that the time $T_R$$4_{}={\mathrm{<figure-callout\; id="4"\; label="T\; P"\; filenames="DE102022133018B3\_0022.png,DE102022133018B3\_0023.png"\; state="\{\{state\}\}">T</figure-callout>}}_P=\left(2^n-1\right)\cdot 2^{3n}\cdot {ƒ}_c^{-1}$

to record all data samples in channel ❹ takes the longest. It corresponds to the period of the M sequence with the lowest clock rate. From a practical point of view, it makes sense for all measurement channels to work for the same measurement time and for only the physically meaningful data samples to be sent for further processing, e.g. Fourier transformation. As a result, each measurement channel should therefore deliver N = 2 ⁿ -1 voltage samples per time interval T _R4 .

benötigt. Man kann deren Messung also 2²ⁿ-fach innerhalb des Zeitintervalls T_R4 wiederholen und die erfassten Werte synchron mitteln. In 1 ist das durch ${\mathrm{\Sigma }}^{2^{2n}}$

symbolisiert. Im Kanal ❸ benötigt die Erfassung aller Werte eine Zeit von $T_{R3}=\left(2^n-1\right)2^{2n}\cdot f_c^{-1}.$

$$

Hier kann man die Messungen 2ⁿ-mal wiederholen und synchron mitteln. Gleichzeitig wird um den Faktor 2ⁿ höher als nach dem Nyquist-Theorem nötig abgetastet, so dass durch ein Down-Sampling um den Faktor 2ⁿ schließlich die resultierende Anzahl N=2ⁿ-1 von Spannungswerten zur Verfügung steht. Die Reihenfolge von Mitteln oder Down-Sampeln ist dabei unerheblich. Im letzten Kanal ❹ muss dann nur noch die um den Faktor 2²ⁿ zu hohe Abtastung durch ein entsprechendes Down-Sampling kompensiert werden.To record all data samples of a period, only one time of ${\mathrm{<figure-callout\; id="1"\; label="T\; R"\; filenames="DE102022133018B3\_0022.png,DE102022133018B3\_0023.png"\; state="\{\{state\}\}">T</figure-callout>}}_R={\mathrm{<figure-callout\; id="2"\; label="T\; R"\; filenames="DE102022133018B3\_0022.png,DE102022133018B3\_0023.png"\; state="\{\{state\}\}">T</figure-callout>}}_R=\left(2^n-1\right)2^n\cdot e_c^{-1}$

required. The measurement can be repeated 2 ²ⁿ times within the time interval T _R4 and the recorded values can be averaged synchronously. In 1 is that through ${\mathrm{<figure-callout\; id="2"\; label="\Sigma "\; filenames="DE102022133018B3\_0022.png,DE102022133018B3\_0023.png"\; state="\{\{state\}\}">\Sigma </figure-callout>}}^{2^{2n}}$

In channel ❸, the recording of all values takes a time of ${\mathrm{<figure-callout\; id="3"\; label="T\; R"\; filenames="DE102022133018B3\_0022.png,DE102022133018B3\_0023.png"\; state="\{\{state\}\}">T</figure-callout>}}_R=\left(2^n-1\right)2^{2n}\cdot e_c^{-1}.$

$$

Here, the measurements can be repeated 2 ⁿ times and averaged synchronously. At the same time, sampling is carried out by a factor of 2 ⁿ higher than required according to the Nyquist theorem, so that by down-sampling by a factor of 2 ⁿ , the resulting number N=2 ⁿ -1 of voltage values is finally available. The order of averaging or down-sampling is irrelevant. In the last channel ❹, only the sampling that is too high by a factor of 2 ²ⁿ needs to be compensated by appropriate down-sampling.

Die so entstandenen Teilmesssignale werden anschließend parallel durch eine Fourier-Transformation in vier komplexwertige Spektren umgerechnet und schließlich zu einem quasi-logarithmisch skaliertem Spektrum vereiniget. Jeder der einzelnen Datenpunkte resultiert aus 2²ⁿ Messwerten, die vom ADC eingesammelt wurden und durch synchrones Mitteln oder/und Down-Sampling auf jeweils einen Wert reduziert wurden. Somit hat jeder der Datenpunkte ein um den Faktor $$\begin{array}{l}Q=\sqrt{2^{2n}}=2^n\\ Q\left[\text{dB}\right]=10\text{lg}{2}^n\approx 10n+3\end{array}$$

geringeres Rauschen als ein einzelner mit dem ADC erfasster Messwert.In this way, the same number of data points are made available in each measurement channel of the hyper-broadband system within the time period T _R4 . The time T _R4 , i.e. the time of a complete measurement, is determined by the smallest frequency to be measured ${\mathrm{<figure-callout\; id="4"\; label="T\; R"\; filenames="DE102022133018B3\_0022.png,DE102022133018B3\_0023.png"\; state="\{\{state\}\}">T</figure-callout>}}_R={\mathrm{<figure-callout\; id="4"\; label="T\; P"\; filenames="DE102022133018B3\_0022.png,DE102022133018B3\_0023.png"\; state="\{\{state\}\}">T</figure-callout>}}_P={\mathrm{<figure-callout\; id="4"\; label="ƒ"\; filenames="DE102022133018B3\_0022.png,DE102022133018B3\_0023.png"\; state="\{\{state\}\}">ƒ</figure-callout>}}_{4\text{min}}^{-1}.$

The resulting partial measurement signals are then converted into four complex-valued spectra in parallel using a Fourier transformation and finally combined to form a quasi-logarithmically scaled spectrum. Each of the individual data points results from 2 ²ⁿ measured values that were collected by the ADC and reduced to one value each by synchronous averaging and/or down-sampling. Thus, each of the data points has a value that is increased by a factor of $$\begin{array}{l}Q=\sqrt{2^{2n}}=2^n\\ Q\left[\text{dB}\right]=10\text{<figure-callout id="2n" label="lg" filenames="DE102022133018B3\_0022.png,DE102022133018B3\_0023.png" state="{{state}}">lg</figure-callout>}{2}^n\approx 10\mathrm{<figure-callout\; id="3"\; label="n\; +"\; filenames="DE102022133018B3\_0022.png,DE102022133018B3\_0023.png"\; state="\{\{state\}\}">n</figure-callout>}+3\end{array}$$

less noise than a single measurement value acquired with the ADC.

2 shows a block diagram of a second embodiment of a hyper-broadband measuring system with cascaded pseudo-noise units, which is also suitable for carrying out the method according to the invention. In this embodiment, the clock rate of the ADC 16 is higher than that in 1 shown embodiment. Even simpler ADCs can therefore be used. Here, the two measuring channels ❶ and ❸ operate in sequential sampling mode. Both channels are equipped with suitable track-and-hold (T&H) circuits 18 to take account of the analog bandwidth in both measuring channels. The lower clock rate of the ADC 16, however, only allows smaller averaging and down-sampling factors, so that the noise suppression is worsened. In modified embodiments, the analog low-pass filter in channel ❹ can be omitted, since it is also handled by the down-sampling in the computing unit 17.

3 Finally, shows an embodiment of the measuring system with two separately clocked two-channel ADC 16.

All in the 1-3 The embodiments shown assume, in simplified terms, that the frequency bands in the individual sub-bands of the measurement channels are arranged seamlessly. This requires that the low-pass filters 14 have an ideal rectangular shape for band limitation, which is an assumption that is practically impossible to realize. Due to the finite edge steepness of real low-pass filters, there will therefore be a small frequency gap between successive channels. Since the relaxation effects of the test objects are very broad-band, such frequency gaps can be accepted. If this is not acceptable for special requirements, a frequency overlap between the sub-bands can be achieved by choosing the LFSR order of n+1 and the divider order of n, within which the low-pass filter can go into its stop band.

The numbers listed for the order of LFSR and divider as well as synchronous averaging and down-sampling are only to be regarded as examples. There is a lot of scope for adapting these numbers to the circumstances, especially if the measurement data of the individual subsystems do not have to be available at the same time after synchronous averaging and down-sampling.

The 1-3 The embodiments shown serve in particular to clarify the signal flow and do not refer to a specific technical implementation. This can be done by directly interconnecting electronic components (LFSR, divider, etc.) in hardware. However, it is also possible to map the structures and signals in software and have them executed by an FPGA, for example. Combinations of both implementation concepts are also conceivable, although those system components that work at very high frequencies are preferably built in hardware. In software implementations, it is important to ensure that the M-sequences generated are to be viewed as analog signals, even if they were generated using digital means. This means that random interference on the signals, such as that which occurs through coupling with other digital signals within an FPGA, must be avoided or subsequently eliminated.

Claims (10)

Method for carrying out an impedance spectroscopic measurement on a test object, comprising the following steps: - generating a broadband test signal which consists of several test signal components in the form of binary pseudo-noise sequences, wherein a predetermined bandwidth (b) of the test signal is divided into at least two adjacent sub-bands of the test signal components; - exciting the test object by simultaneously impressing all test signal components in their sub-bands; - detecting the reaction of the excited test object, wherein for each of the sub-bands at least one associated sensor on the test object detects partial measurement signals in the respective sub-band; - parallel processing of the partial measurement signals in parallel measurement channels by Fourier transformation; - combining the processed partial measurement signals into a measurement signal which characterizes the test object. Procedure according to Claim 1 , characterized in that an M-sequence is generated as the test signal component. Procedure according to Claim 2 , characterized in that the M-sequence is generated by means of a digital, linear feedback shift register (LFSR) which receives a clock signal (f _c ) or a clock signal component derived therefrom from a clock generator. Procedure according to Claim 3 , characterized in that the test signal component is low-pass filtered in the generating step in order to filter out frequencies above half the clock frequency (f _c /2) of the clock generator. Method according to one of the Claims 1 until 4 , characterized in that one of the following methods is used to detect the partial measurement signal: - Nyquist sampling, - interleaved sampling, - oversampling. Method according to one of the Claims 1 until 5 , characterized in that the generation of the test signal components and the processing of the partial measurement signals are carried out using a common clock source, using differently stepped clock dividers (12) in order to generate M-sequences over a wide frequency interval of the sub-bands. Method according to one of the Claims 1 until 6 , characterized in that the frequencies of the test signal components partially overlap at the boundaries of the adjacent sub-bands. Method according to one of the Claims 1 until 7 , characterized in that the predetermined bandwidth (b) of the test signal is divided into at least K sub-bands of the test signal components, with K ≥4. Measuring system for carrying out an impedance spectroscopic measurement on a test object, comprising: - a clock generator (11) for generating a clock signal (f _c ); - a clock divider (12) to divide the clock signal into at least two clock signal components; - at least two measuring channels operating in parallel, each of which receives and processes a clock signal component, each measuring channel comprising: ◯ a linear feedback shift register (13) (LFSR), which generates a partial test signal in the form of a binary pseudo-noise sequence in a sub-band, ◯ a measuring environment (15) with a sensor that detects a partial measurement signal on the test object in the sub-band of the measuring channel, ◯ an analog/digital converter (16) (ADC), which converts the partial measurement signal; - a computing unit which receives the partial measurement signals from the measuring channels and, using a parallel Fourier transformation, combines them into a measurement signal with a quasi-logarithmic frequency axis. Measuring system according to Claim 9 , characterized in that it is suitable for carrying out a method according to one of the Claims 1 until 8th is configured.

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