Coaxial microwave sensor for measuring complex dielectric constant of liquid

Abstract

The invention relates to a coaxial microwave sensor for liquid complex dielectric constant measurement. The coaxial microwave sensor comprises a cylindrical metal conductor, a transmission medium wrapping the cylindrical metal conductor and a defect conductor arranged on the outer surface of the transmission medium. The winding structure is adopted as a defect conductor sensing structure and used for detecting the dielectric property of the material to be detected, and different from a traditional coaxial dielectric sensor designed through a reflection method, the novel method reconstructs field distribution by actively etching the defect structure on the outer conductor of the coaxial structure. The axial sensitive area around the central axis of the coaxial structure is effectively utilized, and the interaction between the electromagnetic field and the to-be-detected material is remarkably enhanced, so that high-sensitivity detection of the dielectric property is realized.

Description

Technical Field

[0001] This application relates to the field of liquid complex permittivity measurement technology, and in particular to a coaxial microwave sensor for measuring the liquid complex permittivity. Background Technology

[0002] The complex permittivity of a liquid is a core physical parameter characterizing its polarization behavior and electromagnetic energy dissipation mechanism, and is widely used in industry to determine the quality of petroleum products (such as crude oil, fuel, and lubricating oil). The real part of the permittivity describes the ability of a liquid medium to polarize under an applied electric field, characterizing the material's ability to confine microwaves; the imaginary part represents the energy dissipation efficiency within the electric field, reflecting a combination of various loss mechanisms, and also characterizing the ease with which the material absorbs microwaves. Based on these properties, as one of the key physical parameters affecting the dynamic response behavior of liquid media under external electromagnetic fields, permittivity characterization technology has demonstrated extremely important research and application value in fields such as biomedical engineering, chemical processes, and industrial engineering.

[0003] However, the inherent fluidity of liquid media leads to highly complex dynamic behavior, variability, and sensitivity to minute concentration changes in their dielectric properties. This presents a significant challenge to achieving high-precision, real-time, in-situ dielectric sensing. Although traditional measurement methods (such as the parallel-plate capacitor method) are widely used, their stringent sample geometry requirements and precise control of electrode spacing limit their ability to handle dynamic continuous fluids. While resonator and resonant perturbation methods can provide high-precision dielectric characterization through variations in resonant frequency and quality factor, their enclosed measurement areas greatly limit their application range, especially in handling flowing liquids. Furthermore, non-resonant methods (such as the coaxial transmission line method) offer the possibility of contact measurement, but their weak signal amplitude and susceptibility to environmental noise limit their ability to detect subtle dielectric changes, thus restricting their detection accuracy. In recent years, dielectric sensors based on planar microwave structures (such as coplanar waveguides and microstrip lines) have been widely studied due to their non-contact characteristics, ease of integration, and miniaturization advantages. However, they struggle to effectively capture local perturbations in the fluid flow field when faced with local dielectric changes within complex fluids. Summary of the Invention

[0004] To overcome, to some extent, the problem in related technologies that it is difficult to balance measurement sensitivity, anti-interference ability, and structural integration in flowing or continuous liquid environments, thus making it impossible to perform high-precision, real-time, in-situ characterization of minute changes in the complex permittivity of liquids, this application provides a coaxial microwave sensor for measuring the complex permittivity of liquids.

[0005] The proposed solution is as follows: A coaxial microwave sensor for measuring the complex permittivity of a liquid, comprising: Cylindrical metal conductors and transmission media, as well as defective conductors fabricated using flexible printed circuit board technology; The metal conductor is disposed inside the transmission medium and is coaxial with the transmission medium, serving as the inner core of the transmission medium; The defective conductor is bent into a cylindrical shape along the width of the rectangular array and wrapped around the outside of the transmission medium. After the wrapping is completed, the defective conductor is coaxial with the transmission medium. One end of the metal conductor is connected to a microwave matching load, and the other end is connected to a microwave network test unit; the microwave network unit is used to measure the return loss parameter of the coaxial microwave sensor immersed in the liquid being tested, and the return loss parameter is used to calculate the complex permittivity of the liquid being tested.

[0006] Preferably, the defective conductor is a rectangular array composed of multiple conductor units with regular octagonal structures; The conductor units are arranged in a rectangular array with a first interval along the length of the rectangular array and with a second interval along the width of the rectangular array. The length of the rectangular array is the same as the height of the transmission medium; the width of the rectangular array is the same as the perimeter of the cross-section of the transmission medium. In the rectangular array, vertical connecting arms are provided between adjacent conductor units in the same column; Only one horizontal connecting arm is provided between two adjacent columns, and each end of the horizontal connecting arm is connected to a conductor unit.

[0007] Preferably, with the sides along the length of the rectangular array as the top and bottom sides and the sides along the width as the left and right sides, the defective conductor further includes: First and second edge conductor strips are set on the left and right sides of the rectangular array; The first and second edge conductor strips are connected to the conductor units located on the left and right sides of the rectangular array.

[0008] Preferably, the conductor units on the left and right sides of the rectangular array are both half of a regular octagonal structure; The conductor unit on the left side of the rectangular array is the right half of a regular octagonal structure; The conductor unit on the right side of the rectangular array is the left half of a regular octagonal structure.

[0009] Preferably, two adjacent horizontal connecting arms are arranged with a conductor unit spaced vertically from each other.

[0010] Preferably, the first interval is greater than the second interval.

[0011] Preferably, the horizontal connecting arm and the vertical connecting arm have the same width; The width of the first edge conductor strip and the second edge conductor strip is half the width of the horizontal connecting arm and the vertical connecting arm, respectively.

[0012] Preferably, the radius of the metal conductor is smaller than that of the transmission medium.

[0013] Preferably, the length of the rectangular array is 29.5 mm; the width of the rectangular array is 15.16 mm. The radius of the metallic conductor is 0.95 mm; The radius of the transmission medium is 2.41 mm; The width of the horizontal connecting arm and the vertical connecting arm is 0.5mm; The widths of the first and second edge conductor strips are 0.25 mm; The center-to-center distance between two adjacent metal conductors in the same column is 3.79 mm; The distance between two adjacent vertical connecting arms is 5.4mm; The distance between any two opposite corners of a metallic conductor is 3 mm.

[0014] The technical solution provided in this application may include the following beneficial effects: This application utilizes a rectangular defect conductor array, consisting of multiple rows of regular octagonal conductor units and their vertical and horizontal connecting arms, arranged around the outer periphery of a cylindrical transmission medium. This array is then bent and wrapped into a cylindrical structure coaxial with the transmission medium using flexible printed circuit board technology. The defect conductor array participates in resonance as a defect structure within the outer conductor of the coaxial transmission line, significantly lengthening the equivalent electromagnetic path and enhancing the local electric field distribution within a limited size. This results in more sensitive resonant frequency and amplitude perturbations to changes in the complex dielectric constant of the liquid. The application employs a meandering structure reconstructed from regular octagons as the sensing structure to detect the dielectric properties of the test material. Unlike traditional coaxial dielectric sensors designed using reflection methods, this novel method reconstructs the field distribution by actively etching defect structures onto the outer conductor of the coaxial structure. This effectively utilizes the axially sensitive region around the central axis of the coaxial structure, significantly enhancing the interaction between the electromagnetic field and the test material, thereby achieving highly sensitive detection of dielectric properties.

[0015] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and do not limit this application. Attached Figure Description

[0016] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0017] Figure 1 This is an overall structural diagram and cross-sectional view of a coaxial microwave sensor used for measuring the complex permittivity of liquids; Figure 2 This is a schematic diagram of the unfolded state of a defective conductor; Figure 3 This is a comparison chart of the electromagnetic simulation results and the equivalent circuit simulation results of the S11 scattering parameters of the coaxial microwave sensor. Figure 4 This is a schematic diagram of the surface current distribution of a defective conductor under encapsulation conditions; Figure 5 It is a geometric decomposition of a defective conductor and its equivalent circuit diagram; Figure 6 This is the equivalent circuit diagram of a coaxial microwave sensor based on a defective conductor structure. Figure 7 The figures show the electromagnetic simulation results and equivalent circuit simulation results of the S11 scattering parameters of the coaxial microwave sensor under different relative permittivity conditions. Figure 8 This is a simulation environment of a coaxial microwave sensor and its electric field intensity distribution in the area to be measured at a frequency of 975MHz. Figure 9 These are the results of the sensitivity surface and average sensitivity curve of the coaxial microwave sensor under different simulation environments; among them... Figure 9 a represents the results under different penetration depth conditions; Figure 9 b. Results under different sample radii; Figure 10 The figure shows the scattering parameters S11 of the coaxial microwave sensor under different relative permittivity and different loss tangent conditions. Figure 11 This is a graph showing the relative frequency shift (Rf) and frequency concentration (FCR) of the coaxial microwave sensor at its operating frequency relative to the loss tangent of the measured material; where, Figure 11 a is a graph showing the relative frequency offset as a function of the MUT loss tangent; Figure 11 b is a graph showing the change in frequency concentration as a function of the loss tangent of the liquid medium under test. Figure 12 Simulation results and fitted curves of the slope and intercept of the relative frequency shift and frequency concentration of a coaxial microwave sensor relative to the loss tangent of the measured material at the operating frequency are presented; among them, Figure 12 'a' represents the slope result based on the relative frequency offset; Figure 12 b represents the intercept result based on the relative frequency offset; Figure 12 c represents the slope result based on frequency concentration; Figure 12 d represents the intercept result based on frequency concentration; Figure 13 The image shows the surface plot of the complex permittivity inversion model for a coaxial microwave sensor; where, Figure 13 a is the fitted surface plot of the relative frequency shift; Figure 13 b is the fitted surface plot of the frequency concentration; Figure 14 Error analysis diagram for the complex permittivity inversion model of a coaxial microwave sensor; Figure 14 a is the relative error diagram of the relative permittivity; Figure 14 b is the absolute error diagram of the loss tangent; Figure 15 S11 scattering parameter diagrams when different test materials are loaded onto a coaxial microwave sensor; Figure 16 The graph shows the relative frequency shift versus sensitivity variation of the coaxial microwave sensor. Figure 17 A comparison chart of the performance of various microwave test sensors.

[0018] Figure reference numerals: Metallic conductor-1; Transmission medium-2; Defective conductor-3. Detailed Implementation

[0019] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.

[0020] Figure 1 This application provides an overall structural diagram and a cross-sectional view of a coaxial microwave sensor for measuring the complex permittivity of a liquid, according to one embodiment of the present application. Figure 2 This is a development diagram of a defective conductor provided in one embodiment of this application, with reference to... Figures 1-2 A coaxial microwave sensor for measuring the complex permittivity of a liquid, comprising: Cylindrical metal conductors and transmission media, as well as defective conductors fabricated using flexible printed circuit board technology; The metal conductor is placed inside the transmission medium, coaxial with the transmission medium, and serves as the inner core of the transmission medium; The defective conductor is bent into a cylindrical shape along the width of the rectangular array and wrapped around the outside of the transmission medium. After the wrapping is completed, the defective conductor is coaxial with the transmission medium. One end of the metal conductor is connected to a microwave matching load, and the other end is connected to a microwave network test unit; the microwave network unit is used to measure the return loss parameter of the coaxial microwave sensor immersed in the liquid being tested, and the return loss parameter is used to calculate the complex permittivity of the liquid being tested.

[0021] Preferably, refer to Figures 1-2The defective conductor is a rectangular array composed of multiple conductor units with regular octagonal structures; The conductor units are arranged in a rectangular array with a first interval along the length of the rectangular array and a second interval along the width of the rectangular array. The length of the rectangular array is the same as the height of the transmission medium; the width of the rectangular array is the same as the perimeter of the cross-section of the transmission medium. In a rectangular array, vertical connecting arms are provided between adjacent conductor units in the same column; Only one horizontal connecting arm is set between two adjacent columns, and each end of the horizontal connecting arm is connected to a conductor unit.

[0022] The coaxial microwave sensor in this technical solution consists of a high-conductivity copper inner conductor, a polytetrafluoroethylene transmission medium with a relative permittivity of 1.24 and a dielectric loss tangent of 0.001, and a defective conductor fabricated using flexible printed circuit board technology. Its specific structure is as follows: Reference Figure 2 With the sides along the length of the rectangular array as the top and bottom sides, and the sides along the width as the left and right sides, the defective conductor also includes: First and second edge conductor strips are set on the left and right sides of the rectangular array; The first and second edge conductor strips are connected to the conductor units located on the left and right sides of the rectangular array.

[0023] Reference Figure 2 In the rectangular array, the conductor units on the left and right sides are both half of a regular octagon structure; The conductor unit on the left side of the rectangular array is the right half of a regular octagonal structure; The conductor unit on the right side of the rectangular array is the left half of a regular octagonal structure.

[0024] Reference Figure 2 The two adjacent horizontal connecting arms are set with a conductor unit spaced one vertically between them.

[0025] It should be noted that the first interval is larger than the second interval.

[0026] The horizontal connecting arm and the vertical connecting arm have the same width; The width of the first edge conductor strip and the second edge conductor strip is half that of the horizontal connecting arm and the vertical connecting arm, respectively.

[0027] The radius of a metallic conductor is smaller than that of the transmission medium.

[0028] The specific dimensional parameters of the coaxial microwave sensor in this technical solution are as follows: The length of the rectangular array is 29.5 mm; the width of the rectangular array is 15.16 mm. The radius of the metallic conductor is 0.95 mm; The radius of the transmission medium is 2.41 mm; The width of the horizontal connecting arm and the vertical connecting arm is 0.5mm; The widths of the first and second edge conductor strips are 0.25 mm; The center-to-center distance between two adjacent metal conductors in the same column is 3.79 mm; The distance between two adjacent vertical connecting arms is 5.4mm; The distance between any two opposite corners of a metallic conductor is 3 mm.

[0029] The dimensional parameters of each part of the structure can also be referenced. Figure 2 Compare with Table 1.

[0030] Table 1. Dimensional parameters of coaxial microwave sensor and its sensing structure

[0031] The geometric dimensions of the coaxial microwave sensor proposed in this application are given in Table 1. Based on these dimensions, the following can be obtained: Figure 3 The electromagnetic simulation results for the S11 scattering parameters are shown. The results indicate that the proposed coaxial microwave sensor can operate at three frequencies: 975 MHz, 1.28 GHz, and 2.26 GHz. However, the resonant characteristics at the 2.26 GHz operating frequency show a significant decrease as the relative permittivity of the measured liquid medium increases. This phenomenon is particularly pronounced for measured liquid media with a relative permittivity greater than 2, while the other two operating frequencies remain unaffected. Furthermore, when measuring measured liquid media with low permittivity, the 3 dB bandwidth at 975 MHz is easier to extract. Therefore, subsequent explanations will focus solely on the 975 MHz operating frequency.

[0032] The defect conductor proposed in this application constructs a sufficiently large irregular cross-section by reconstructing a regular octagonal structure at the nodes of the meandering structure and at the center positions between longitudinal nodes, such as... Figure 2 As shown, this design reconstructs the conduction current path and enhances electromagnetic field variations at the boundaries. Of particular note is the fact that the sharp vertices of these regular octagonal structures induce charge accumulation, significantly enhancing the edge effect. This effect not only strengthens the local electric and magnetic fields but also steepens the spatial gradient of the electromagnetic field, ultimately significantly improving the sensitivity of the coaxial microwave sensor to changes in the surrounding medium. Correspondingly, this phenomenon can be confirmed by the surface current distribution on the defective conductor layer, such as... Figure 4As shown, the surface current distribution of the regular octagonal structure reveals a significantly higher surface current intensity in its edge regions. Consequently, the electromagnetic field distribution in these edge regions is correspondingly more concentrated, enhancing the polarization effect on the surrounding medium. Stronger polarization means that the medium exhibits a more significant dielectric response when the electric field changes, thus significantly improving the sensing sensitivity of the proposed coaxial microwave sensor. Furthermore, the surface current intensity between the nodes of the proposed defective conductor is also quite significant, generating a strong electromagnetic coupling effect between the edges and nodes. Simultaneously, a significant electric field gradient will form around these regions. This phenomenon helps enhance the interaction between the sensing structure and the medium, thereby improving the sensor's ability to detect minute changes in certain parameters.

[0033] from Figure 2 As can be seen from the defective conductor shown, the structure is formed by connecting a semi-regular octagonal structure and a complete regular octagonal structure through a meandering structure. Based on Figure 5 Different classifications and combinations of SRO and IRO structures allow for the decomposition of the geometric structure of defective conductors and their representation using a lumped circuit model, thereby constructing... Figure 6 The equivalent circuit shown.

[0034] L1=0.233nH, L2=0.313nH, L3=34.354nH, L4=14.993nH, L5=0.032nH, L6=0.033nH, L7=0.183nH, L8=0nH, L9=14.8nH, L10=142.58nH, L11=2.72nH, L12=0nH, L13=0.078nH, L14=0.217nH, L15=199.97nH, L16=199.96nH, L17=0.0095nH, L18=199.998nH, L19=0.0002nH, L20=0nH L21=14.49nH, L22=0.118nH, L23=0.924nH, L24=1.0085nH, L25=1.417nH, L26=2.845nH, L27=1.143nH, L28=0nH, L29=2.387nH, L30=0.0051nH, L31=9.139nH, L32=0.0734nH, C1=1.508pF, C2=0.181pF, C3=1.55pF, C4=0.83pF, C5=2.097pF, C6=0.152pF, C7=0pF, C8=0.864pF, C9=2.444pF, R1=497.296Ω, R2=497.55Ω, R3=479.061Ω, R4=177.49Ω, R5=141.569Ω, R6=1.448Ω, R7=61.474Ω, ZL=50Ω。

[0035] Figure 5The method for constructing the equivalent circuits of the first and fourth structures is to treat the terminal interfaces of the regular octagonal structure as equivalent inductor models to characterize the phase changes of the electromagnetic field. Specifically, for the equivalent inductances corresponding to the left and right IRO connection interfaces in the first structure, and the SRO and IRO connection interfaces in the fourth structure, parallel resistors are connected to characterize their loss characteristics. For the IRO structure in the second structure, since there are only two terminal interfaces, its electromagnetic field phase change is represented by a single equivalent inductor model, with parallel resistors to reflect the loss characteristics. The IRO structures discussed above are all non-edge structures of the wrapped defect conductor. According to the characteristics of coaxial cables, these structures will generate a capacitance effect with the inner conductor, so it is necessary to connect equivalent capacitance models at each terminal interface to characterize this effect. However, since the SRO of the fourth structure is an edge structure, its terminal interface will be connected to the third structure, which is also at the edge. Therefore, the capacitance effects formed by the third structure and the inner conductor, and the fourth structure and the inner conductor, can be equivalently regarded as a single capacitor and characterized in the equivalent circuit of the fourth structure. Meanwhile, the SRO of the third structure only needs to be characterized by a single equivalent inductance model to represent the phase change of the electromagnetic field, and its loss characteristics will be characterized by the resistance model in the equivalent circuit of the fourth structure together with the loss characteristics of the fourth structure.

[0036] When the liquid medium to be measured is within the sensor's detection area, it is affected by an external electromagnetic field. This causes polarization of the molecules and atoms within the medium, resulting in a rearrangement of the electric dipole moments and thus altering the original electric field distribution. Furthermore, the defective conductor structure etched into the outer conductor layer of the proposed coaxial microwave sensor further enhances its interaction with the liquid medium, leading to changes in the electromagnetic field distribution within the sensor, primarily manifested in changes in capacitance, inductance, and resistance values ​​in the equivalent circuit structure. It is particularly noteworthy that a complex capacitance distribution appears within the liquid medium due to the influence of the polarization electric field generated by polarization charges. This phenomenon is especially pronounced for materials with high dielectric constants. To simplify the analysis, an equivalent circuit model of the coaxial microwave sensor is used, through... Figure 5 The parallel capacitance in the first, second, and fourth structure resistor-inductor parallel model is used to characterize the capacitance effect in the liquid medium under test. Figure 7This paper compares the results of electromagnetic simulation and equivalent circuit simulation when loading liquid media with different relative permittivity. The results show a high degree of agreement, proving that the equivalent circuit structure can effectively characterize the external response of the proposed coaxial microwave sensor in materials with low relative permittivity. However, when detecting materials with high relative permittivity, this parallel connection method cannot fully characterize the external response. This is mainly because liquid media with different relative permittivity will form significantly different electromagnetic field distributions under external electromagnetic field excitation. Therefore, to achieve equivalent characterization, it is necessary to appropriately adjust the characterization method of capacitance effect in the equivalent circuit according to the electromagnetic characteristics of the liquid medium under test, such as redesigning the connection form of the external capacitor and adjusting the construction method of the external sensing circuit.

[0037] Analyze the simulation environment parameters (1) The effect of “depth” variation on the sensitivity of the proposed coaxial microwave sensor The simulation environment of the proposed coaxial microwave sensor at 975 MHz and its electric field intensity distribution under no-load conditions are shown below. Figure 8 As shown, the electric field distribution demonstrates the electromagnetic simulation results at a penetration depth of 81.5 mm and a sample radius of 49 mm. It can be seen that a significant electric field gradient exists between the medium surrounding the sensing structure and other regions. This phenomenon effectively amplifies the influence of changes in the dielectric properties of the liquid medium on the local electric field distribution, thereby improving the sensing performance of the coaxial microwave sensor. To more clearly analyze the influence of different environmental variables on the sensing performance, this application uses sensitivity surfaces and average sensitivity curves to analyze the sensitivity characteristics of the proposed coaxial microwave sensor under different environments. The calculation methods are shown in Equations (1) and (2), respectively, where var represents the environmental variable and N represents the number of environmental configurations.

[0038] (1); (2); from Figure 9 As can be seen, when the penetration depth is less than 40 mm, the sensing structure is basically located outside the liquid medium being measured. As it gradually approaches the liquid medium, the liquid medium exhibits polarization under the influence of the external electromagnetic field, and this phenomenon shows an increasing trend, resulting in an increase in sensor sensitivity. However, at this point, the response of the liquid medium to the external electromagnetic field is still relatively weak, so the overall sensor sensitivity remains low.

[0039] When the penetration depth is between 40 mm and 60 mm, it can be seen that the change in penetration depth has a relatively small impact on the sensor sensitivity. This is because at this depth, the sensing structure is located at the interface between the liquid medium being measured and the air, and the liquid medium is simultaneously affected by the electromagnetic fields excited by the sensing structures located inside and outside it. As the penetration depth increases, the polarization phenomenon caused by the sensing structure located outside the liquid medium weakens, while the polarization phenomenon caused by the sensing structure located inside the liquid medium strengthens, keeping the polarization phenomenon in the liquid medium relatively stable. With the continued increase in penetration depth, the polarization phenomenon caused by the sensing structure located inside the liquid medium gradually becomes dominant, making the polarization phenomenon more and more obvious. Therefore, the sensor sensitivity generally shows an increasing trend, but this increasing trend is not significant.

[0040] When the penetration depth exceeds 60 mm, the sensing structure is almost entirely located within the liquid medium being measured. With increasing penetration depth, the electromagnetic field excited by the sensing structure acts over a wider area of ​​the liquid medium, causing more molecules in the liquid medium to cooperatively respond to the electric field, thus making the polarization phenomenon more pronounced. This phenomenon is strong and sensitive, resulting in a rapid increase in sensor sensitivity.

[0041] (2) The effect of the change in "radius" on the sensitivity of the proposed coaxial microwave sensor like Figure 9 Figure b shows the sensitivity surface and average sensitivity curve of the proposed coaxial microwave sensor under different sample radii. It can be seen that when the sample radius is within 40 mm, the sensor sensitivity increases with increasing sample radius. However, when the sample radius exceeds 40 mm, the change in sample radius has a relatively small impact on the sensor sensitivity.

[0042] The reason for this phenomenon is as follows. For sample radii less than 40 mm, some of the electric field lines excited by the defective conductor will penetrate the liquid medium and enter the air. This makes the polarization in the liquid medium much smaller than when the sample radius is large enough to confine almost all the electric field lines within the liquid medium. This further leads to a significant effect of sample radius variation on sensor sensitivity. However, when the sample radius exceeds 40 mm, the liquid medium essentially confines the electric field lines excited by the defective conductor within it. Therefore, as the sample radius increases, the change in polarization within the liquid medium becomes less pronounced. This results in the sensor sensitivity no longer fluctuating as dramatically as when the sample radius is less than 40 mm, but rather remaining in a relatively stable state.

[0043] The simulation results of the coaxial microwave sensor in this application are as follows: like Figure 10As shown, the scattering parameters S11 of the proposed coaxial microwave sensor under different relative permittivity and loss tangents are presented. It can be seen that when no liquid medium is applied, the first peak of the scattering parameter S11 of the sensor appears at 975 MHz. After applying the liquid medium, the scattering peak continuously shifts to lower frequencies as the relative permittivity of the liquid medium increases. Clearly, this operating frequency exhibits a monotonically decreasing trend.

[0044] It can also be seen that when the relative permittivity of the liquid medium under test increases from 1 to 80, the maximum frequency shift of the sensor reaches 804 MHz, and its relative frequency shift reaches 82.46%. In addition, it is worth noting that when the relative permittivity of the liquid medium under test is fixed and the loss tangent increases from 0 to 0.1, the operating frequency of the sensor still shows a decreasing trend, but this phenomenon is not significant.

[0045] Constructing a complex permittivity inversion model for a coaxial microwave sensor: The complex permittivity inversion model constructed in this application is based on the relative frequency shift at the sensor's operating frequency and the frequency concentration derived from the 3dB bandwidth at that operating frequency. The formula for calculating the relative frequency shift is given by equation (3), where This indicates the operating frequency of the proposed coaxial microwave sensor when no liquid medium is loaded. This indicates the operating frequency of the proposed coaxial microwave sensor when the liquid medium to be measured is loaded: (3); Frequency concentration is used to quantify the system frequency selectivity at the sensor's operating frequency, and its calculation formula is shown in (4). Where, This indicates that when the relative permittivity is 1 The loss tangent is When testing liquid media, the proposed coaxial microwave sensor exhibits a 3dB bandwidth at its operating frequency. It should be noted that the numerator in the Frequency Concentration (FRC) formula corresponds to the sensor's operating frequency.

[0046] When the operating frequency coincides with the sensor's resonant frequency, the frequency concentration is equivalent to the quality factor (Q value), indicating that they have exactly the same physical meaning. However, in this paper, the operating frequency is not the resonant frequency, but rather the peak frequency of the proposed coaxial microwave sensor's scattering parameter S11.

[0047] Figure 11Figure a shows the curves of the relative frequency shift of the proposed coaxial microwave sensor at the operating frequency as a function of the loss tangent of the measured liquid medium. It can be observed that for all measured materials, the correlation coefficient between the relative frequency shift and the loss tangent remains above 0.99, exhibiting a significant linear relationship. Furthermore, the slope and intercept of this linear relationship change with the relative permittivity of the measured liquid medium. Therefore, the relationship between the relative frequency shift of the proposed coaxial microwave sensor and the loss tangent of the measured liquid medium can be expressed by equation (5).

[0048] (5); In addition, from Figure 11 As can be observed in b, the correlation coefficient between frequency concentration and loss tangent consistently remains above 0.98, indicating a significant linear relationship between the two. It is noteworthy that the linear relationship between frequency concentration and loss tangent weakens as the relative permittivity of the tested liquid medium increases. However, when the relative permittivity of the tested liquid medium is below 20, the two still maintain a significant linear relationship. Furthermore, from... Figure 11 As can be seen from b, both the slope and intercept of this linear relationship change with the relative permittivity of the liquid medium being measured. Therefore, the relationship between the frequency concentration of the proposed coaxial microwave sensor and the loss tangent of the liquid medium being measured can be expressed by equation (6).

[0049] (6); Figure 12 Simulation results and fitted curves of the relative frequency shift and frequency concentration of the proposed coaxial microwave sensor relative to the slope and intercept of the loss tangent of the measured material at the operating frequency are presented. Figure 12 It can be observed that the slope of the relative frequency shift generally decreases with the increase of the relative permittivity of the liquid medium under test. It should be noted that this change process exhibits local fluctuations, but no significant deviations are observed. Therefore, by using the nonlinear curve fitting method, the functional relationship between the slope of the relative frequency shift and the relative permittivity of the liquid medium under test can be approximately characterized by equation (7), and the coefficient of determination of this fitted curve is 0.9575.

[0050] (7); from Figure 12As can be seen from b, the intercept of the relative frequency shift generally increases with the increase of the relative permittivity of the liquid medium under test. Throughout the entire data range, its change exhibits a monotonically increasing characteristic, without significant fluctuations or abnormal data. Therefore, by using the nonlinear curve fitting method, the functional relationship between the intercept of the relative frequency shift and the relative permittivity of the liquid medium under test can be approximately characterized by equation (8), and the coefficient of determination of its fitting curve reaches 0.9990.

[0051] (8); like Figure 12 As shown in Figure c, the absolute value of the correlation coefficient between the frequency concentration slope and the relative permittivity of the measured liquid medium reaches 0.9917, indicating a significant linear correlation between the two, which can be described by a linear function. However, through observation... Figure 9 The trend of the simulated slope data in c shows that when the relative permittivity of the measured liquid medium is in the range of 8 to 12, the slope change is relatively gentle. Furthermore, analysis of the slope trend shows no anomalies in the current dataset. Clearly, although linear fitting can reasonably approximate the slope change trend, there is still room for improvement. Therefore, using a nonlinear curve fitting method, the functional relationship between the slope of the frequency concentration and the relative permittivity of the measured liquid medium can be approximated by equation (9), and the coefficient of determination of its fitted curve reaches 0.9902.

[0052] (9); from Figure 12 As can be observed, the correlation coefficient between the intercept of the frequency concentration and the relative permittivity of the liquid medium under test reaches 0.9933, indicating that there is a significant linear relationship between the two. Similar to the relationship between the slope of the frequency concentration and the relative permittivity of the liquid medium under test, although the linear function can reasonably fit the trend of the intercept changing with the relative permittivity, Equation (10) can better describe its functional relationship, and the coefficient of determination of the fitted curve reaches 0.9971.

[0053] (10); Substituting equations (7) and (8) into equation (5), and substituting equations (9) and (10) into equation (6), we can construct... Figure 13 The surface plot of the complex permittivity inversion model is shown. As the relative permittivity of the test liquid medium increases, both the relative frequency shift and frequency concentration show an upward trend. When the loss tangent of the test liquid medium increases, the relative frequency change is not significant, while the frequency concentration shows an overall downward trend. Specifically, for test liquid media with high relative permittivity, the frequency concentration decreases rapidly with the increase of its loss tangent; while for test liquid media with low relative permittivity, the change in frequency concentration is not obvious.

[0054] During the construction of the complex permittivity inversion model, slight fluctuations may occur in the edge data of the measurement range. Therefore, to avoid the influence of these undesirable data, the measurement range of the relative permittivity is limited to [7, 19], and the measurement range of the loss tangent is limited to [0.01, 0.09].

[0055] like Figure 14 As shown, by simultaneously solving the coaxial microwave sensor complex permittivity inversion model proposed in equations (5) and (6), the relative error of the relative permittivity and the absolute error of the loss tangent of the liquid medium under test are obtained. Their calculation formulas are given by equations (11) and (12), respectively.

[0056] (11); (12); It should be noted that solving these equations simultaneously yields equation (13), which is only related to the relative permittivity. This equation may have no solution or multiple solutions, so the range of solutions must be constrained during the solution process. When there is no solution, the value of the function in equation (13) that is closest to zero is taken as the final solution.

[0057] (13); Through analysis Figure 14 It can be seen that, regarding the relative error of the relative permittivity, the inversion accuracy reaches its highest point in the central region of the measurement range and gradually decreases towards the edge region. Quantitative analysis shows that, throughout the entire measurement range, the relative error of the relative permittivity remains below 2.17%, with an average relative error of only 0.92%. This proves that the proposed inversion model can achieve high-precision reconstruction of the relative permittivity. Regarding the absolute error of the loss tangent, the maximum absolute error is 0.0108, while the average absolute error is 0.0052. Furthermore, the inversion model shows that the absolute error increases accordingly when the loss tangent approaches zero. This phenomenon mainly stems from the fact that low-loss dielectric materials are affected by various factors such as mesh generation, convergence tolerance, and iteration settings, which mask subtle changes in relative frequency shift and frequency concentration, making it difficult for the fitted curve to accurately capture these minute changes.

[0058] The experimental setup used to characterize the proposed coaxial microwave sensor included a support fixture, a sample container, the analyte, a coaxial transmission line, a matched load, and a vector network analyzer. Oil-based samples with a relative permittivity below 11 were used as the liquid medium for measurement to evaluate the sensor performance. The corresponding results are summarized in Table 2, and representative graphical data are shown in [the table / incomplete]. Figure 15 .

[0059] Table 2 Measurement data of coaxial microwave sensor when loading different test materials

[0060] like Figure 15 As shown, the experimentally measured S11 scattering parameters exhibit a systematic frequency shift across a wide bandwidth compared to the simulation results, rather than a local deviation. This phenomenon primarily stems from the combined effects of multiple factors, including differences in material properties, sensor manufacturing tolerances, measurement environmental variables, and idealized assumptions in the simulation model. Specifically, manufacturing errors (such as defect width deviations or changes in material properties) directly alter the distributed capacitance and inductance parameters, causing frequency shifts. Furthermore, simulations typically simplify the conductor surface to an ideal, smooth model, while actual surfaces exhibit microscopic roughness due to manufacturing processes and oxidation, introducing additional distributed inductance and capacitance effects. This further perturbs the high-frequency response of the proposed coaxial microwave sensor, exacerbating the frequency shift. Additionally, differences in the feed structure and experimental conditions between simulation and measurement also affect the sensor response, collectively contributing to the observed frequency shift phenomenon.

[0061] Table 2 presents the measurement results and analysis of the relative frequency shift and frequency concentration of the proposed coaxial microwave sensor at the operating frequency. It can be observed that as the relative permittivity of the tested liquid medium increases, both the operating frequency and its 3dB bandwidth exhibit a monotonically decreasing trend, while the relative frequency shift shows a monotonically increasing trend. When the relative permittivity of the tested liquid medium reaches 10.09, the relative frequency shift reaches 55.19%. Furthermore, the frequency concentration generally increases with the increase of the relative permittivity of the tested liquid medium, but slight fluctuations exist in certain regions.

[0062] Figure 16 The results of the relative frequency shift and sensitivity analysis of the coaxial microwave sensor for the processed part are presented, with an average sensitivity of 9.51%. Figure 17 Furthermore, a comparative analysis is provided between the proposed coaxial microwave sensor and several existing dielectric sensors. It can be seen that, leveraging the defective conductor sensing structure in this application, the coaxial microwave sensor can achieve high-precision dielectric property characterization. Experimental data demonstrate that this coaxial microwave sensor has significant engineering application value in materials science and engineering testing, providing a new approach to dielectric property characterization techniques.

[0063] Figure 17This paper compares the performance of various microwave sensors in measuring the complex permittivity of liquids. For example, a uniquely designed complementary resonator sensor achieves leading sensitivity and reliability in measuring the permittivity of materials. Other noteworthy designs include: a high-sensitivity dual-frequency resonant sensor based on a complementary square helical resonator with a square patch, enabling accurate characterization of materials with low permittivity as low as 1.19; a non-destructive testing technique that solves the challenge of characterizing conductor backing materials by integrating a novel planar resonator with a sample backplate; and a high-sensitivity metamaterial sensor employing a bent groove CSRR structure with integrated microchannels, providing a cost-effective solution for characterizing the dielectric properties of solids and liquids. Compared to these planar structures, the sensor proposed in this study is based on a defective conductor structure on a coaxial outer conductor. This design features a compact structure, full immersion in liquid operation, and high structural utilization, achieving a 55.19% relative frequency shift within the measurement range of relative permittivity 1–10.

[0064] In summary, this application proposes a high-sensitivity coaxial microwave sensor based on a defective conductor structure. This coaxial microwave sensor achieves dielectric sensing functionality by etching a defective conductor structure into the outer conductor layer of a coaxial cable, exhibiting excellent dielectric sensing performance at an unloaded operating frequency of 886 MHz. Experimental results show that, within a relative permittivity range of 1.015 to 10.09, the proposed coaxial microwave sensor achieves a maximum frequency shift of 55.19% and an average sensitivity of 9.51%. Compared with existing dielectric sensors, this coaxial microwave sensor demonstrates significant advantages in dielectric sensing applications and has important engineering application value in materials science and engineering testing.

[0065] It is understood that the same or similar parts in the above embodiments can be referred to each other, and the contents not described in detail in some embodiments can be referred to the same or similar contents in other embodiments.

[0066] It should be noted that in the description of this application, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance. Furthermore, in the description of this application, unless otherwise stated, "a plurality of" means at least two.

[0067] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0068] Although embodiments of this application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting this application. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of this application.

Claims

1. A coaxial microwave sensor for liquid complex permittivity measurements, characterized by, The application relates to a coaxial microwave sensor for measuring the complex permittivity of a liquid. The coaxial microwave sensor comprises: a cylindrical metal conductor and a transmission medium, and a defect conductor made through a flexible printed circuit board process; the metal conductor is arranged inside the transmission medium coaxially with the transmission medium as an inner core of the transmission medium; the defect conductor is bent into a cylindrical shape along the width direction of a rectangular array and is wrapped outside the transmission medium, and after the wrapping is completed, the defect conductor is coaxial with the transmission medium; one end of the metal conductor is connected with a microwave matching load, and the other end is connected with a microwave network test unit; the microwave network unit is used for measuring the return loss parameter of the coaxial microwave sensor immersed in a measured liquid, and the return loss parameter is used for calculating the complex permittivity of the measured liquid.

2. The defect conductor is a rectangular array composed of a plurality of conductor units in a regular octagonal structure; the conductor units are arranged in a first interval along the length direction of the rectangular array and in a second interval along the width direction of the rectangular array in the rectangular array; the length of the rectangular array is the same as the height of the transmission medium; and the width of the rectangular array is the same as the cross-sectional circumference of the transmission medium; in the rectangular array, vertical connecting arms are arranged between conductor units in the same column and adjacent to each other; 3. The coaxial microwave sensor of claim 1, wherein, only one horizontal connecting arm is arranged between two adjacent columns, and the horizontal connecting arm is connected with one conductor unit at each end. with the edges in the length direction of the rectangular array as the upper and lower sides and the edges in the width direction as the left and right sides, the defect conductor further comprises: first and second edge conductor strips arranged on the left and right sides of the rectangular array; 4. The coaxial microwave sensor of claim 3, wherein, the first and second edge conductor strips are connected with the conductor units on the left and right sides of the rectangular array. the conductor units on the left and right sides of the rectangular array are each half of a regular octagonal structure; the conductor unit on the left side of the rectangular array is the right half of a regular octagonal structure; 5. The coaxial microwave sensor of claim 3, wherein, the conductor unit on the right side of the rectangular array is the left half of a regular octagonal structure.

6. The coaxial microwave sensor of claim 1, wherein, two horizontal connecting arms adjacent to each other are arranged with one conductor unit in between.

7. The coaxial microwave sensor of claim 3, wherein, the first interval is greater than the second interval. the width of the horizontal connecting arm is the same as that of the vertical connecting arm; 8. The coaxial microwave sensor of claim 7, wherein, the width of the first and second edge conductor strips is half of that of the horizontal and vertical connecting arms.

9. The coaxial microwave sensor of claim 8, wherein, the radius of the metal conductor is smaller than that of the transmission medium. the length of the rectangular array is 29.5 mm; and the width of the rectangular array is 15.16 mm; the radius of the metal conductor is 0.95 mm; the radius of the transmission medium is 2.41 mm; the width of the horizontal and vertical connecting arms is 0.5 mm; the width of the first and second edge conductor strips is 0.25 mm; the distance between the centers of two metal conductors adjacent to each other in the same column is 3.79 mm; the distance between two vertical connecting arms adjacent to each other is 5.4 mm; the distance between any two opposite corners of the metal conductor is 3 mm.

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