TDR level measuring device and method for operating a TDR level measuring device
By using waveguide sections with reference reflectors formed by shape and size transitions, the TDR fill level measurement device addresses permittivity variation challenges, enhancing measurement reliability and accuracy.
Patent Information
- Application Number
- DE102017119502
- Authority / Receiving Office
- DE · DE
- Patent Type
- Patents
- Current Assignee / Owner
- Filing Date
- 2017-08-25
- Publication Date
- 2025-05-22
- Estimated Expiration
- 2037-08-25
AI Technical Summary
Existing TDR fill level measurement devices face challenges in accurately determining the fill level of a medium in a container due to variations in permittivity above the medium, which can occur with temperature gradients or other environmental factors.
The TDR fill level measurement device incorporates a waveguide with reference reflectors formed by transitions between waveguide sections of different shapes and/or sizes, allowing for the determination of permittivity distribution and correction of propagation speed, thereby enhancing measurement accuracy.
This approach significantly improves the reliability and accuracy of fill level measurements by accounting for permittivity variations, leading to more precise determination of the medium's fill level in the container.
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Abstract
Description
[0001] The invention is based on a TDR (Time Domain Reflectometry) level measuring device for measuring the level of a medium in a container, comprising at least one transmitting unit for transmitting a pulsed electromagnetic measuring signal, at least one receiving unit for receiving at least one reflection signal, at least one evaluation unit for evaluating the at least one reflection signal and at least one waveguide, wherein the waveguide has at least one conductor for guiding the measuring signal and the reflection signal, wherein the waveguide has at least two waveguide sections, wherein each waveguide section has at least one functional waveguide cross-sectional area, wherein the functional waveguide cross-sectional area corresponds to the cross-sectional area of the at least one conductor, wherein at least one reference reflector is present and wherein the reference reflector is designed and arranged in such a way,that during operation at least a part of the measurement signal is reflected at least once by the at least one reference reflector.,
[0002] Furthermore, the invention relates to a method for operating a TDR level measuring device for measuring the level of a medium in a container, wherein the TDR level measuring device has at least one transmitting unit for transmitting an electromagnetic measuring signal, at least one receiving unit for receiving at least one reflected reflection signal, at least one evaluation unit for evaluating the at least one reflection signal and at least one waveguide, wherein the waveguide has at least one conductor for guiding the measuring signal and the reflection signal, wherein the waveguide has at least two waveguide sections, wherein each waveguide section has at least one functional waveguide cross-sectional area, wherein the functional waveguide cross-sectional area corresponds to the cross-sectional area of the at least one conductor,wherein at least one reference reflector is present and wherein the reference reflector is designed and arranged such that during operation at least a part of the measurement signal is reflected at least once by the at least one reference reflector.
[0003] State-of-the-art TDR level measuring devices use the principle of time-domain reflectometry to measure the level of a medium, preferably a liquid, in a container. The distance between a transmitter unit and the surface of the medium to be measured is determined based on the propagation time of a measurement signal emitted by the transmitter unit and reflected by the surface. The measured distance, given the depth of the container, is then used to determine the level of the medium in the container. Knowledge of the propagation velocity of the measurement signal transmitted toward the medium is essential for correctly determining the level.
[0004] The propagation speed of the measuring signal depends in particular on the permittivity ε of the medium through which the measuring signal moves.
[0005] One type of TDR level measurement uses a waveguide that guides the measurement signal from the transmitter toward the medium and then carries the reflected signal from the medium's surface to the receiver. Depending on the application, particularly parameters of the measurement environment, and the medium being measured, the measurement signal may pass through regions with different permittivities above the medium. This is the case, for example, if a temperature gradient exists above the medium in the container.
[0006] To determine the permittivity distribution above the medium, it is known from the prior art of US Pat. No. 7,525,476 B1 to arrange reference reflectors in the form of cylindrical or otherwise shaped bodies at specified intervals along the waveguide. Due to the change in impedance, the measurement signal propagating along the waveguide is also reflected by the reference reflectors. Based on knowledge of the distance traveled between the transmitting unit or receiving unit and the respective reference reflector, as well as the propagation time of the measurement signal reflected by the reference reflector, the permittivity ε of the medium surrounding the waveguide above the reference reflector can be determined. This information can be used to correct the propagation velocity of the measurement signal along the waveguide and thus to correct the fill level determination of the medium.
[0007] From the document DE 20 2005 020 158 U1 it is also known to design the reference reflector as a local defect in the form of an opening, a notch, a protrusion or a diaphragm in the waveguide.
[0008] In addition, the document EP 0 534 654 B1 discloses the design of the reference reflector as a discontinuity in the form of, for example, a collar surrounding the waveguide or in the form of a connection of separately designed waveguide parts.
[0009] From the publication US 2014 / 0 104 099 A1, a TDR level measuring device with a waveguide is also known, wherein the waveguide has a geometric discontinuity which is used as a reference reflector during operation.
[0010] Further level measuring devices are known from the documents DE 101 60 688 A1, US 2015 / 0168203 A1, DE 10 2006 019 191 A1, US 2013 / 0061669 A1, WO 2003 / 016 835 A1, DE 22 42 723 A and US 2009 / 0303106 A1.
[0011] Based on this prior art, the present invention is based on the object of providing a TDR level measuring device that, on the one hand, is particularly reliable and, on the other hand, has a particularly simple design. Furthermore, the invention is based on the object of providing a corresponding method for operating such a TDR level measuring device.
[0012] According to a first teaching of the invention, the aforementioned object is achieved by a TDR level measuring device described above in that the at least one reference reflector is formed by a transition between two waveguide sections with different shapes and / or different sizes of the functional waveguide cross-sectional areas. According to the invention, it was recognized that a reference reflector can be designed particularly simply by the waveguide itself being designed as a reference reflector in at least one section. This advantageously eliminates the need for additional bodies attached to the waveguide to generate a reference reflection.
[0013] The at least two waveguide sections, between which the reference reflector is arranged, are arranged directly one after the other in the propagation direction of the measurement signal.
[0014] In addition, the waveguide cross-sectional areas between which the reference reflector is arranged are involved in guiding the measurement signal during operation.
[0015] According to a further embodiment, the transmitting unit and the receiving unit are designed as one unit, namely as a transmitting / receiving unit.
[0016] According to the invention, at least two reference reflectors are provided, wherein the at least two reference reflectors are designed as transitions between two waveguide sections each with different shapes and / or different sizes of the functional waveguide cross-sectional areas. According to this embodiment, the permittivity of the medium surrounding the waveguide can be determined in at least two regions, so that a permittivity distribution within the container can be detected particularly accurately.
[0017] The functional waveguide cross-sectional area can, for example, be rotationally symmetrical, in particular circular, or oval or quadrangular, in particular square.
[0018] According to one embodiment, the waveguide has exactly one conductor carrying the measurement signal.
[0019] According to a next embodiment, the waveguide has at least two conductors carrying the measurement signal.
[0020] According to the invention, the at least two reference reflectors are designed as a tapered portion of the at least one waveguide conductor involved in guiding the measurement signal, i.e., viewed in the propagation direction of the measurement signal, as a reduction in the size of the functional waveguide cross-sectional area while maintaining the shape of the functional waveguide cross-sectional area. Furthermore, a further reference reflector can also be designed as a thickened portion of the at least one waveguide conductor involved in guiding the measurement signal, i.e., viewed in the propagation direction of the measurement signal, as an enlargement of the size of the functional waveguide cross-sectional area while maintaining the shape of the functional waveguide cross-sectional area.
[0021] It is also conceivable that during operation at least one reference reflector is arranged within the medium so that a permittivity distribution within the medium, for example a multi-phase medium, can also be detected.
[0022] It is furthermore particularly advantageous if the transition in shape and / or size between the functional waveguide cross-sectional areas is at least partially discontinuous. In this embodiment, the reference reflection signal reflected at the transition is particularly narrow, whereby the determination of the propagation time and thus the determination of the permittivity of the medium surrounding the waveguide section is particularly precise. It is also conceivable that the transition in shape and / or size between the functional waveguide cross-sectional areas is at least partially stepped. According to this embodiment, the reference reflector generates, depending on the number and size of the steps, at least two directly successive reference reflection signals or one spatially or temporally extended reference reflection signal.This design has the advantage that the reference reflection signal can be particularly well distinguished from the reflection signal reflected on the surface of the medium during evaluation.
[0023] According to a further embodiment, the transition in shape and / or size between the functional waveguide cross-sectional areas is at least partially configured as a transition region, i.e., continuously. This embodiment has the advantage that the reference reflection signal is temporally and spatially extended and thus distinguishable from the reflection signal reflected at the surface of the medium.
[0024] Particularly advantageously, the transition in shape and / or size between the functional waveguide cross-sectional areas is spatially extended, at least partially, in the propagation direction of the measurement signal. For example, the transition can be designed in a stepped or offset manner.
[0025] According to the invention, at least two reference reflectors are provided, wherein the at least two reference reflectors are configured as a taper of the at least one waveguide conductor involved in guiding the measurement signal. It is also advantageous if at least three or more reference reflectors are provided, each of which is configured as a taper, preferably with a sudden transition, of the at least one waveguide conductor involved in guiding the measurement signal.
[0026] According to a further embodiment, at least two further reference reflectors are provided, wherein the at least two further reference reflectors are designed as a thickening of the at least one conductor of the waveguide involved in guiding the measurement signal. It is also advantageous if at least one reference reflector is designed as a taper and at least one reference reflector is designed as a thickening of the at least one conductor of the waveguide involved in guiding the measurement signal. According to an embodiment not according to the invention, at least three or more reference reflectors are provided, each of which is designed as a thickening, preferably with a sudden transition, of the at least one conductor of the waveguide involved in guiding the measurement signal.
[0027] According to a further embodiment, the position of a reference reflector on the waveguide is determined depending on the dimensions of the waveguide and the measurement environment and / or the temperature distribution expected in the container during operation. For example, it is advantageous if at least two reference reflectors are present, wherein the at least two reference reflectors are arranged at regular intervals along the waveguide. For example, the distance from the coupling of the measurement signal into the container to the first reference reflector, or the distance between the reference reflectors, is 1 m in each case.
[0028] According to a particularly preferred embodiment, the distance between the coupling of the measurement signal into the container or the distance between the individual reference reflectors is configured as a multiple of the wavelength of the measurement signal. Preferably, the forward measurement signal and the returning reflection signal are structurally superimposed.
[0029] According to a further embodiment, the distance between the coupling of the measurement signal into the container or the distance between the individual reference reflectors does not correspond to a multiple of the wavelength. This embodiment has the advantage that the reflection signal reflected at the surface of the medium is particularly easy to distinguish from the reference reflection signals.
[0030] According to a further embodiment of the level measuring device, at least two reference reflectors are provided, which are arranged at irregular intervals along the waveguide.
[0031] Furthermore, it is advantageous if at least the transition between the functional waveguide cross-sectional areas, which forms a reference reflector, is designed as a single piece. Particularly preferably, the at least one conductor has no material transitions or joints in the propagation direction of the measurement signal. The at least one conductor of the waveguide is preferably manufactured from a single workpiece.
[0032] Particularly preferably, the waveguide is made from a workpiece.
[0033] According to the invention, the waveguide is designed as a coaxial conductor comprising at least one inner conductor and at least one outer conductor, wherein at least one reference reflector is formed by the at least one inner conductor.
[0034] Furthermore, according to the invention, the waveguide is designed as a coaxial conductor, comprising at least one inner conductor and at least one outer conductor, wherein the at least two reference reflectors are formed by the at least one outer conductor.
[0035] It is also conceivable that the waveguide is designed as a coaxial conductor, comprising at least one inner conductor and at least one outer conductor, wherein at least two reference reflectors are formed by the at least one outer conductor and wherein at least one further reference reflector is formed by the at least one inner conductor.
[0036] Particularly preferably, the reference reflector formed by the inner conductor and the reference reflector formed by the outer conductor are arranged at the same height.
[0037] It is also advantageous if the reference reflector formed by the inner conductor and the reference reflector formed by the outer conductor are arranged at different heights.
[0038] Alternatively, the waveguide can be designed as a single monoprobe or as a double probe.
[0039] If the waveguide is designed as a double probe comprising a first and a second conductor, the at least one reference reflector is preferably formed by a conductor.
[0040] Alternatively, if the waveguide is designed as a double probe comprising a first and a second conductor, at least one reference reflector is formed by the first conductor and at least one reference reflector is formed by the second conductor.
[0041] Particularly preferably, the reference reflector formed by the first conductor and the reference reflector formed by the second conductor are arranged at the same height.
[0042] It is also advantageous if the reference reflector formed by the first conductor and the reference reflector formed by the second conductor are arranged at different heights.
[0043] According to a second teaching of the invention, the object derived at the outset is achieved by a method described at the outset for operating a TDR level measuring device for measuring the level of a medium in a container in that the at least one reference reflector is formed by a transition between two waveguide sections with different shapes and / or different sizes of the functional waveguide cross-sectional areas, wherein the waveguide is designed as a coaxial conductor comprising at least one inner conductor and at least one outer conductor, and wherein at least two reference reflectors are provided, wherein the at least two reference reflectors are designed as a taper of the outer conductor, and that the procedure comprises the following steps: - Emission of a measuring signal along the waveguide by the transmitting unit, - receiving at least one reflection signal by the receiving unit, wherein the reflection signal corresponds to at least one reflection of the measurement signal at at least one reference reflector, - receiving at least one further reflection signal by the receiving unit, wherein the further reflection signal corresponds to a reflection of the measurement signal at the surface of the medium to be measured, - Determining at least one permittivity ε of the medium surrounding a waveguide section from the propagation time of the at least one reflection signal by the evaluation unit, wherein the reflection signal corresponds to a reflection of the measurement signal at the at least one reference reflector, - Determining a correction factor of the propagation velocity of the measurement signal along the waveguide based on the at least one permittivity ε and - Determining the fill level of the medium in the container from the transit time and the corrected propagation speed of the at least one further reflection signal, wherein the further reflection signal corresponds to a reflection of the measurement signal at the surface of the medium to be measured.
[0044] The TDR level measuring device is particularly preferably designed according to one of the previously described embodiments.
[0045] In detail, there are numerous possibilities for designing and developing the level measuring device according to the invention and the method according to the invention. Reference is made to the claims subordinate to the independent claims as well as to the following description of preferred embodiments in conjunction with the drawings. The drawings show: Fig. 1 a first embodiment of a level measuring device, Fig. 2 a second embodiment of a waveguide, Fig. 3 a third embodiment of a waveguide, Fig. 4 a fourth embodiment of a waveguide, Fig. 5 a fifth embodiment of a waveguide, Fig. 6 a sixth embodiment of a waveguide, Fig. 7 a seventh embodiment of a waveguide, Fig. 8 an eighth embodiment of a waveguide and Fig. 9 a first embodiment of a method according to the invention.
[0046] In Fig. 1 shows a first embodiment of a TDR level measuring device 1 for measuring the level of a medium in a container, comprising at least one transmitting unit 3 for transmitting a pulsed electromagnetic measuring signal, a receiving unit 4 for receiving at least one reflection signal, an evaluation unit 5 for evaluating the at least one reflection signal and a waveguide 6 for guiding the measuring signal and the reflection signal.
[0047] The waveguide 6 is configured in sections as a reference reflector 7, with each reference reflector 7 being formed by a discontinuous transition between two waveguide sections with different sizes of the functional waveguide cross-sectional areas 8. In the illustrated embodiment, two reference reflectors 7 are present, each of which is configured as a taper of the waveguide 6. The functional waveguide cross-sectional areas 8 in the individual waveguide sections are each circular.
[0048] Due to the known position of the reference reflectors 7 or the known length of the individual waveguide sections and the measured transit time of the reflection signals reflected at the reference reflectors 7, the permittivity ε r3 or ε r2of the medium surrounding the corresponding waveguide sections, which can be used to correct the propagation velocity of the measuring signal and thus to determine the fill level of the medium in the container.
[0049] According to another embodiment, at least one reference reflector 7 is arranged in the medium, so that the permittivity ε rM of the medium can be determined.
[0050] Fig. 2 shows a second embodiment of a waveguide 6 with a reference reflector 7, wherein the transition of the size of the functional waveguide cross-sectional area 8 is designed as a spatially extended continuous transition region.
[0051] Fig. 3 shows a third embodiment of a waveguide 6 with two reference reflectors 7, wherein one reference reflector 7 is designed as a spatially extended taper of the waveguide 6 and wherein a second reference reflector 7 is designed as a thickening with a spatially extended transition region.
[0052] In Fig. 4 shows a further embodiment of a waveguide 6, wherein the reference reflector 7 is designed as a transition between two waveguide sections with different shapes of the functional waveguide cross-sectional areas 8. In detail, in a first waveguide section, the functional waveguide cross-sectional area 8 is circular, and in a second waveguide section, the functional waveguide cross-sectional area 8 is oval.
[0053] Fig. 5 shows a further embodiment of a waveguide 6 with a reference reflector 7, wherein the reference reflector 7 is designed as a step-like transition of the size of the functional waveguide cross-sectional areas 8 of a first and a second waveguide section.
[0054] In Fig. 6 shows a further embodiment of a waveguide 6 with a reference reflector 7, wherein the reference reflector 7, which is designed as a transition between two waveguide sections with different sizes of the functional waveguide cross-sectional areas 8, is designed in an offset, discontinuous manner and is thus designed as a spatially extended transition region.
[0055] The Fig. The waveguide 6 shown in Figure 7 is designed as a coaxial conductor comprising an inner conductor 16 and an outer conductor 17. The outer conductor 17 has holes 15 for the passage of the medium to be measured. The inner conductor 16 is partially designed as a reference reflector 7.
[0056] The Fig. The waveguide 6 shown in Figure 8 is also designed as a coaxial conductor comprising an inner conductor 16 and an outer conductor 17. The outer conductor 17 has holes 15 for the passage of the medium to be measured. Furthermore, the outer conductor 17 is partially designed as a reference reflector 7.
[0057] In Fig. Figure 9 shows a first embodiment of a method 2 according to the invention for operating a TDR level measuring device 1 for measuring the level of a medium in a container. The TDR level measuring device 1 is configured as shown in Fig.1. Method 2 comprises the following steps: - Transmission 9 of a measuring signal along the waveguide 6 by the transmitting unit 3, - receiving 10 a first reflection signal by the receiving unit 4, wherein the reflection signal corresponds to a reflection of the measurement signal at the first reference reflector 7, - receiving 10 a second reflection signal by the receiving unit 4, wherein the reflection signal corresponds to a reflection of the measurement signal at the second reference reflector 7, - Receiving 11 a further reflection signal by the receiving unit 4, wherein the reflection signal corresponds to a reflection of the measuring signal at the surface of the medium to be measured, - Determine 12 the permittivity ε r3 and ε r2 of the medium surrounding the respective waveguide sections from the transit time of the first and second reflection signals by the evaluation unit 5, - Determining 13 a correction factor of the propagation velocity of the measuring signal along the waveguide 6 based on the determined permittivities ε r3 and ε r2 and - Determining 14 the fill level of the medium in the container from the transit time and the corrected propagation speed of the at least one further reflection signal, wherein the further reflection signal corresponds to a reflection of the measurement signal at the surface of the medium to be measured.
[0058] The method 2 shown has the advantage that the determination of the fill level of the medium to be measured is particularly reliable due to the consideration of the permittivity distribution above the medium or the adaptation of the propagation speed of the measuring signal or the reflection signal to this permittivity distribution. Reference symbol 1 TDR level gauge 2 Procedure for operating a TDR level measuring device 3 Transmitter unit 4 Receiver unit 5 Evaluation unit 6 waveguides 7 Reference reflector 8 functional waveguide cross-sectional area 9 Sending a measurement signal 10 Receiving a first reflection signal 11 Receiving a second reflection signal 12 Determining the permittivity 13 Determining a correction factor 14 Determining the fill level 15 holes 16 inner conductors 17 outer conductors
Claims
[1] TDR level measuring device (1) for measuring the level of a medium in a container, comprising at least one transmitting unit (3) for transmitting a pulsed electromagnetic measuring signal, at least one receiving unit (4) for receiving at least one reflection signal, at least one evaluation unit (5) for evaluating the at least one reflection signal and at least one waveguide (6), wherein the waveguide (6) has at least one conductor for guiding the measuring signal and the reflection signal, wherein the waveguide has at least two waveguide sections, wherein each waveguide section has at least one functional waveguide cross-sectional area (8), wherein the functional waveguide cross-sectional area (8) corresponds to the cross-sectional area of the at least one conductor, wherein at least one reference reflector (7) is present and wherein the reference reflector (7) is designed and arranged in such a way,that during operation at least a part of the measurement signal is reflected at least once by the at least one reference reflector (7), wherein the at least one reference reflector (7) is formed by a transition between the two waveguide sections with different shapes and / or different sizes of the functional waveguide cross-sectional areas (8), wherein the waveguide (6) is designed as a coaxial conductor, comprising at least one inner conductor (16) and at least one outer conductor (17), characterized by , that at least two of the reference reflectors (7) are present, wherein the at least two reference reflectors (7) are designed as a taper of the outer conductor. [2] TDR level measuring device (1) according to claim 1, characterized by that the transition of the shape and / or size between the functional waveguide cross-sectional areas (8) is at least partially designed to be abrupt. [3] TDR level measuring device (1) according to claim 1 or 2, characterized by that the transition of the shape and / or size between the functional waveguide cross-sectional areas (8) is at least partially continuous in the form of a transition region. [4] TDR level measuring device (1) according to one of claims 1 to 3, characterized by that the transition of the shape and / or size between the functional waveguide cross-sectional areas (8) is at least partially spatially extended in the propagation direction of the measuring signal. [5] TDR level measuring device (1) according to one of claims 1 to 4, characterized by that the position of the at least two reference reflectors (7) on the waveguide (6) is determined as a function of the dimensions of the waveguide (6) and the measuring environment and / or of the temperature distribution in the container to be expected during operation. [6] TDR level measuring device (1) according to one of claims 1 to 5, characterized bythat the at least two reference reflectors (7) are arranged at regular intervals along the waveguide (6). [7] TDR level measuring device (1) according to one of claims 1 to 6, characterized by that at least the transition between the functional waveguide cross-sectional surfaces (8), which forms one of the reference reflectors (7), is designed in one piece. [8] TDR level measuring device (1) according to one of claims 1 to 7, characterized by that the waveguide (6) is designed as a coaxial conductor, comprising at least one inner conductor (16) and at least one outer conductor (17), wherein at least one of the reference reflectors (7) is formed by the at least one inner conductor (16). [9] Method (2) for operating a TDR level measuring device (1) for measuring the level of a medium in a container, wherein the TDR level measuring device (1) has at least one transmitting unit (3) for transmitting an electromagnetic measuring signal, at least one receiving unit (4) for receiving at least one reflected reflection signal, at least one evaluation unit (5) for evaluating the at least one reflection signal and at least one waveguide (6), wherein the waveguide (6) has at least one conductor for guiding the measuring signal and the reflection signal, wherein the waveguide (6) has at least two waveguide sections, wherein each waveguide section has at least one functional waveguide cross-sectional area (8), wherein the functional waveguide cross-sectional area (8) corresponds to the cross-sectional area of the at least one conductor,wherein at least one reference reflector (7) is present and wherein the reference reflector (7) is designed and arranged such that during operation at least a part of the measurement signal is reflected at least once by the at least one reference reflector (7), wherein the at least one reference reflector (7) is formed by a transition between the two waveguide sections with different shapes and / or different sizes of the functional waveguide cross-sectional areas (8), characterized by , that the waveguide (6) is designed as a coaxial conductor, comprising at least one inner conductor (16) and at least one outer conductor (17), and that at least two of the reference reflectors (7) are present, wherein the at least two reference reflectors (7) are designed as a taper of the outer conductor (17), and that the method (2) comprises the following steps: - transmitting (9) a measuring signal along the waveguide (6) by the transmitting unit (3), - receiving (10) the at least one reflection signal by the receiving unit (4), wherein the reflection signal corresponds to at least one reflection of the measurement signal at at least one of the reference reflectors (7), - receiving (11) at least one further reflection signal by the receiving unit (4), wherein the further reflection signal corresponds to a reflection of the measurement signal at the surface of the medium to be measured, - determining (12) at least one permittivity ε of the medium surrounding one of the waveguide sections from the propagation time of the at least one reflection signal by the evaluation unit (5), wherein the reflection signal corresponds to a reflection of the measurement signal at the at least one reference reflector (7), - determining (13) a correction factor of the propagation velocity of the measurement signal along the waveguide (6) based on the at least one permittivity ε and - determining (14) the fill level of the medium in the container from the transit time and the corrected propagation speed of the at least one further reflection signal, wherein the further reflection signal corresponds to a reflection of the measurement signal at the surface of the medium to be measured. [10] Method according to claim 9, characterized by that the TDR level measuring device (1) is designed according to one of claims 1 to 8.
Citation Information
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