Sensor for detecting underground buried objects based on metamaterial resonance

Abstract

An underground buried object detection sensor based on metamaterial resonance is mainly composed of three layers which are a metal grounding layer, a dielectric layer and a metal patch layer from bottom to top. Two complementary slotted metal rings (CSRR) are etched on a metal grounding layer, and a metal patch layer is formed by combining a circular ring and two microstrip lines. The sensor can achieve the purpose of detecting the dielectric constant of the dielectric plate in different detection modes in double frequency bands. In other words, the detection of the dielectric constant is realized by monitoring the amplitude change in the frequency band of 1.25-2.00 GHz, and the detection sensitivity is 2.10 dB / permittivity unit; the detection of the dielectric constant is realized by monitoring the frequency change in the frequency band of 2.00 to 3.00 GHz, and the detection sensitivity of the dielectric constant sensor is 39.8 MHz / permittivity unit. The method has the characteristics of high sensitivity, dual-band detection and dual detection modes, and has potential application prospects in buried target detection.

Description

Technical Field

[0001] The present invention relates to the technical field of electromagnetic metamaterials, and in particular to a metamaterial sensor with a dual-band and dual-measurement mode and applications thereof. Background Art

[0002] With rapid economic development and population growth, the demand for urban underground space development and infrastructure construction continues to rise. Underground pipelines, cables, cultural relics, and other buried objects, as important carriers of modern urban operations, undertake key functions such as energy transmission, information transmission, and cultural heritage protection. However, as buried objects age, complex environmental factors such as soil erosion, geological activity, and temperature and humidity fluctuations can cause them to corrode, shift, or suffer structural damage. Failure to accurately detect and promptly maintain these objects can lead to chain reactions such as pipeline leakage, damage to cultural relics, or underground space collapse, posing a serious threat to urban safety, cultural heritage protection, and public services. Therefore, nondestructive testing and condition assessment of underground objects have become core research areas in modern urban management, archaeological exploration, and disaster prevention.

[0003] Metamaterials are artificially synthesized materials with unique structures and properties that transcend the physical limitations of traditional materials, demonstrating unique control capabilities for electromagnetic waves, particularly the efficient capture and enhancement of evanescent waves. These properties give them significant advantages in the sensing field: high sensitivity, high resolution, and robustness against environmental interference. They offer new technical approaches for detection in complex scenarios. For example, the article "A noncontact feed microwave metal devices deformation and stress sensor based on metamaterial" presents a noncontact feed microwave metal deformation and stress sensor based on a microwave capture metamaterial (MHMA). This sensor is used to detect deformation of metal pipes caused by external forces, pressure, or high temperatures. The article "A wireless passive sensing system for displacement / strain measurement in reinforced concrete members" presents a metamaterial sensor capable of detecting the displacement and deformation of steel bars within simply supported beams. Traditional methods for detecting buried objects are often limited by soil inhomogeneities and signal attenuation at depth. However, metamaterial sensors, by designing specialized metal sensing structures, can accurately sense changes in electromagnetic response caused by minute displacements, material variations, or structural defects. Compared with traditional sensors, its research significance is very important, especially in the detection of underground buried objects, such as underground PVC pipes and steel bars, and has potential application prospects.

[0004] Current traditional electromagnetic sensing technologies suffer from the limitations of a single detection modality and a restricted operating frequency band. These limitations typically manifest in single-parameter detection mechanisms such as resonant peak frequency shift or amplitude response based on scattering parameters, enabling only local characterization of physical properties such as dielectric constant within a single frequency band. For example, the paper "CSRR metamaterial microwave sensor formeasuring dielectric constants of solids and liquids" proposes a CSRR-based metasurface microwave sensor for measuring the dielectric constant of liquids and solids. However, this sensor can only detect the dielectric constant of a material under test (MUT) by varying the frequency within the 1.25-2.50 GHz range. This approach not only results in a lack of detection dimensionality but also limits its adaptability in complex environments due to insufficient frequency coverage. To address this, a dual-band, dual-measurement electromagnetic metamaterial sensor has expanded detection capabilities by integrating multi-band sensing with dual measurement methods. Furthermore, this sensor demonstrates superior sensitivity in dielectric constant detection and has potential applications in the nondestructive detection of buried objects. Summary of the Invention

[0005] The present invention provides a dual-band, dual-measurement metamaterial sensor and its application. Compared with traditional dielectric constant sensors, this sensor can sense dielectric constant in two different ways within a dual-band range and has higher sensitivity. The present invention can effectively solve the technical problem that existing sensors used for underground buried object detection are insufficiently adaptable to the complex environment of underground buried object detection due to their single mode and limited operating frequency band during detection.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is: A sensor for detecting underground buried objects based on metamaterial resonance, the sensor having a three-layer structure, comprising a metal ground layer, a dielectric layer, and a metal patch layer; Two symmetrically arranged C-shaped metal rings are etched on the metal ground layer from the side of the metal ground layer away from the dielectric layer toward the side close to the dielectric layer. The two symmetrically arranged C-shaped metal rings complement each other to form a metal ring with a middle slot.

[0007] The metal patch layer includes two parallel microwave transmission lines, the width of the middle part of the microwave transmission line is greater than the width of the two ends; a metal ring is provided between the two parallel microwave transmission lines, and the two farthest points of the metal ring are respectively tangent to the middle parts of the two microwave transmission lines.

[0008] The microwave transmission lines are microstrip lines, and ports 1 and 2 are provided at the ends of one side of the two parallel microwave transmission lines; ports 3 and 4 are provided at the ends of the other side of the two parallel microwave transmission lines.

[0009] The dielectric constant of the dielectric layer is 6.4-6.6, the thickness is 0.6-0.7 mm, and the material is Rogers 3006.

[0010] The metal ground layer and the metal patch layer are both made of metal copper material, and the thickness thereof is 0.03-0.04 mm.

[0011] The two complementary slotted metal rings of the metal grounding layer and the circular ring of the metal patch layer are circular rings with the same radius, and their centers coincide with each other in the vertical direction.

[0012] The outer radius of the slit metal ring and the circular ring of the metal patch layer is 15.9-16.1 mm, and the inner radius is 13.3-13.5 mm.

[0013] The width of the microstrip line is 2.3~2.5mm; the width of the rectangular strip in the middle is 3.9~4.1mm and the length is 32.0~32.1mm.

[0014] When the sensor is tested, the following steps are specifically adopted: Step 1: Connect port 1 and port 2 of the sensor to the input and output ports of the vector network analyzer respectively; Step 2: Connect ports 3 and 4 of the sensor to a 50Ω load. Step 3: Place the MUT on one side of the metal structure of the metal patch layer ( Figure 3 (a)) shown in the position; Step 4: Observe the transmission curve displayed by the vector network analyzer and detect the dielectric constant of the MUT by observing the changes in amplitude or frequency.

[0015] When the sensor is used to detect underground objects, the following steps are taken: Step 1: The waveguide antenna acts as an excitation source to transmit excitation to the detection area; Step 2: The sensor captures the microwave energy emitted by the waveguide antenna; Step 3: The dielectric properties of the MUT change the electromagnetic field environment around the sensor, causing the sensor's resonance characteristics to shift; Step 4: The sensor's response signal is returned through the feed network; Step 5: The waveguide antenna receives the response signal returned from the sensor, which carries the dielectric properties of the object under test (MUT); Step 6: The waveguide antenna transmits the received response signal back to the vector network analyzer VNA; Step 6: The vector network analyzer (VNA) accurately measures and analyzes the scattering parameters (S 21 parameter); Step 7: The vector network analyzer (VNA) outputs the measured S-parameter data (amplitude, phase, and frequency relationship) to the computer; Step 8: The data processing algorithm receives the measurement data from the vector network analyzer (VNA); based on the pre-established mathematical model between the dielectric constant and the S parameter, the observed S parameter change is inverted into the dielectric constant of the specific MUT.

[0016] Compared with the prior art, the present invention has the following technical effects: The metamaterial sensor provided by the present invention mainly realizes its amplitude sensing through a circular branch line model composed of a metal ring and two parallel microstrip lines. It is a symmetrical structure, and its symmetry is destroyed by loading the object to be measured on a certain half-circular ring branch, so that its characteristic impedance and electrical length are changed. At this time, the resonant peak amplitude of its transmission coefficient changes, thereby achieving the purpose of detecting the dielectric constant through amplitude changes. Its frequency sensing is mainly achieved by etching two complementary slotted metal rings on the metal ground layer to introduce LC resonance. When a branch is loaded with the object to be measured, the change in its dielectric constant will affect the equivalent capacitance of the complementary slotted metal ring, which is caused by As can be seen, its resonant frequency changes accordingly with changes in equivalent capacitance, thereby achieving the purpose of detecting the dielectric constant through frequency changes. In addition, the sensor has high sensitivity, with a detection sensitivity of 2.10dB / epsilon for amplitude changes and 39.8MHz / epsilon for frequency changes. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The present invention will be further described below with reference to the accompanying drawings and examples: Figure 1 Schematic diagram of the overall structure of the sensor in the present invention; Figure 2 (a), (b) and (c) are the top view, bottom view and side view of the metamaterial sensor, respectively; Figure 3 (a), (b), and (c) are the front view, bottom view, and experimental test image of the actual manufacturing model of the metamaterial sensor, respectively; Figure 4 This is the equivalent circuit model diagram of the metamaterial sensor; Figure 5 This is a comparison chart of the electromagnetic simulation and equivalent circuit simulation results; Figure 6is a graph showing the transmission curve of the metamaterial sensor as a function of the thickness of the dielectric layer; Figure 7 It is a graph showing the transmission curve of the metamaterial sensor as the width of the circular ring of the metal patch layer changes; Figure 8 This is the transmission curve corresponding to different dielectric constants of the measured object simulated by the metamaterial sensor; Figure 9 (a) and (b) are the notch amplitude value diagrams corresponding to different dielectric constants of the measured object simulated by the metamaterial sensor and the resonant frequency diagrams corresponding to different dielectric constants; Figure 10 (a) and (b) are the transmission curves corresponding to different dielectric constants of the dielectric plate simulated by the metamaterial sensor and the transmission curves corresponding to different dielectric constants of the dielectric plate actually measured, respectively. DETAILED DESCRIPTION

[0018] A sensor for detecting buried objects based on metamaterial resonance, the sensor having a three-layer structure, comprising a metal ground layer 1, a dielectric layer 2, and a metal patch layer 3; Two symmetrically arranged C-shaped metal rings 4 are etched on the metal ground layer 1, extending from the side of the metal ground layer 1 away from the dielectric layer 2 toward the side closer to the dielectric layer 2. The two symmetrically arranged C-shaped metal rings complement each other to form a metal ring with a central slit. These rings form a complementary split-resonator to achieve the purpose of detecting the dielectric constant by frequency variation.

[0019] The metal patch layer 3 includes two parallel microwave transmission lines 6, each wider in the middle than at its ends. A metal ring 5 is positioned between the two parallel microwave transmission lines, with its two farthest points tangent to the middle of the two microwave transmission lines. This creates a branched-line coupler structure, enabling the detection of dielectric constants using real amplitude variations.

[0020] The microwave transmission lines are microstrip lines, and ports 1 and 2 are provided at the ends of one side of two mutually parallel microwave transmission lines 6 ; ports 3 and 4 are provided at the ends of the other side of the two mutually parallel microwave transmission lines 6 .

[0021] The dielectric constant of the dielectric layer is 6.4-6.6, and the thickness is 0.6-0.7 mm. The range is set because it is difficult to ensure that some physical parameters of the sensor are a certain value during the actual manufacturing process. There will be manufacturing errors, so setting it within a range is more reasonable. The material is Rogers 3006.

[0022] The metal ground layer and the metal patch layer are both made of metal copper material, and the thickness thereof is 0.03-0.04 mm.

[0023] The two complementary slotted metal rings of the metal grounding layer and the circular ring of the metal patch layer are circular rings with the same radius, and their centers coincide with each other in the vertical direction.

[0024] The outer radius of the slit metal ring and the circular ring of the metal patch layer is 15.9-16.1 mm, and the inner radius is 13.3-13.5 mm.

[0025] The width of the microstrip line is 2.3~2.5mm; the width of the rectangular strip in the middle is 3.9~4.1mm and the length is 32.0~32.1mm.

[0026] When the sensor is tested, the following steps are specifically adopted: Step 1: Connect port 1 and port 2 of the sensor to the input and output ports of the vector network analyzer respectively; Step 2: Connect port 3 and port 4 of the sensor to a 50Ω port load; Step 3: Place the MUT on the left branch of the metal structure of the metal patch layer 3 ( Figure 3 (a)) shown in the position; Step 4: Observe the transmission curve displayed by the vector network analyzer and detect the dielectric constant of the MUT by observing the changes in amplitude or frequency.

[0027] When the sensor is used to detect underground objects, the following steps are taken: Step 1: The waveguide antenna acts as an excitation source to transmit excitation to the detection area; Step 2: The sensor captures the microwave energy emitted by the waveguide antenna; Step 3: The dielectric properties of the MUT change the electromagnetic field environment around the sensor, causing the sensor's resonance characteristics to shift; Step 4: The sensor's response signal is returned through the feed network; Step 5: The waveguide antenna receives the response signal returned from the sensor, which carries the dielectric properties of the object under test (MUT); Step 6: The waveguide antenna transmits the received response signal back to the vector network analyzer VNA; Step 6: The vector network analyzer (VNA) accurately measures and analyzes the scattering parameters (S 21 parameter); Step 7: The vector network analyzer (VNA) outputs the measured S-parameter data (amplitude, phase, and frequency relationship) to the computer; Step 8: The data processing algorithm receives the measurement data from the vector network analyzer (VNA); based on the pre-established mathematical model between the dielectric constant and the S parameter, the observed S parameter change is inverted into the dielectric constant of the specific MUT.

[0028] Example: The overall structural diagram of the metamaterial sensor with dual-band dual-measurement mode provided in this embodiment is as follows: Figure 1 As shown: It consists of three layers, which are in the shape of a square, including a metal ground layer with two complementary slotted metal rings etched on it, a Rogers 3006 dielectric layer, and a circular ring and a metal patch layer composed of two parallel microstrip lines tangent to each other above the dielectric layer.

[0029] like Figure 2 (a), (b), and (c) are the top view, bottom view, and side view of the sensor, respectively. Figure 3 (a), (b), and (c) are the front view, top view, and experimental test images of the fabricated model, respectively. The thickness of the metal ground layer and the metal patch layer is ts = 0.035 mm, and the thickness of the Rogers 3006 dielectric layer is h = 0.635 mm. The two complementary slotted metal rings in the metal ground layer and the circular ring in the metal patch layer have the same radius, with an outer radius of R1 = 16.0 mm and an inner radius of R2 = 13.4 mm, respectively. The length of the microstrip line is L1 = 73.2 mm, and the width of the microstrip line is w = 2.4 mm. The center of the microstrip line is a rectangular strip of varying widths, with a width of wl = 4.0 mm and a length of ws = 32.1 mm. The total thickness of the sensor is H = h + 2*ts = 0.705 mm.

[0030] The resonance characteristics of the sensor are analyzed using the equivalent circuit principle. In order to illustrate the interaction between the metal structures of the sensor, Figure 4 The relevant equivalent parameters of the sensor are given. In this model, L1 and L2 represent the equivalent inductance of the two parallel microstrip lines of the metal patch layer. L3 and L4 represent the equivalent inductance of the two semi-circular branches of the circular ring between the microstrip lines. The loading of the MUT will cause the electrical length and characteristic impedance of the L3 branch to change. The electrical length and characteristic impedance affect the amplitude of the transmission curve of the sensor. Therefore, as the dielectric constant of the MUT changes, the amplitude of the transmission curve of the sensor will change accordingly. C1, C2, C3 and C4 represent the equivalent capacitance between the metal patch layer and the metal ground layer. L5 and C5 are the equivalent inductance and capacitance of the C-shaped metal ring on the left side of the CSRR. L6 and C6 are the equivalent inductance and capacitance of the C-shaped metal ring on the right side of the CSRR. Therefore, the sensor has two LC resonance peaks, and its resonant frequency is: . In addition, since the MUT is placed on the left side of the road, where the MUT has a stronger influence on the C-shaped metal ring on the left, by changing the dielectric constant of the MUT, it will be observed that the frequency deviation of the resonance peak formed by the left branch is larger than that of the C-shaped metal ring on the right, and the sensitivity is better. Electromagnetic simulation is performed using CST simulation software. The x, y, and z directions of the sensor are set as open boundaries, and plane waves are set as excitation sources at both ends of the two parallel microstrip lines. The frequency range is set to 0.0-3.0 GHz. Use ADS software to simulate the Figure 4 The results of electromagnetic simulation and equivalent circuit simulation are shown in the figure. Figure 5 As shown in the figure, the black curve represents the CST electromagnetic simulation results, and the red dashed line represents the equivalent circuit model simulation results. The electromagnetic simulation results show three main resonance peaks in the 1.25 to 3.0 GHz range, at frequencies of 1.55 GHz, 2.52 GHz, and 2.74 GHz. Comparing the electromagnetic simulation results with the equivalent circuit simulation results shows near-consistency. Therefore, the equivalent circuit model is reasonable, validating the proposed sensor model.

[0031] In order to obtain the optimal structural parameters, the structural parameters are studied by using a parameter scanning analysis method based on the control variable method. First, the effect of the thickness of the Rogers 3006 dielectric substrate on the sensor is studied. Figure 6 As shown, a step size of 0.1 was used to simulate dielectric substrate thickness variations from 0.4 to 0.7 mm. Observation reveals that variations in dielectric substrate thickness affect the transmission curve of this model. As the substrate thickness increases from 0.4 mm to 0.7 mm, the first resonant peak changes insignificantly (referred to as the amplitude peak), while the frequency and amplitude of the second peak change significantly (referred to as the frequency peak). Its resonant frequency gradually shifts to lower frequencies, decreasing from 2.56 GHz to 2.43 GHz. The amplitude decreases from -30.0 dB (h = 0.4 mm) to 38.6 dB (h = 0.6 mm) before increasing to 32.7 dB (h = 0.7 mm). Since this model only considers the changes in the first two peaks for dielectric constant measurement, the third peak is not described. Considering that the second resonant peak has the deepest notch at 0.6 mm, and based on actual processing, a dielectric plate with h = 0.635 mm was ultimately selected.

[0032] The same method is used to analyze the effect of the ring width of the metamaterial metal patch layer on the sensor. The ring width is changed by changing the size of the inner radius of the ring. Let the ring width be R, and take a step size of 0.2mm to simulate the ring width from 2.4mm to 2.8mm. The simulation results are shown below. Figure 7As shown in the figure, it was observed that as the ring width increased, the resonant frequency of the amplitude peak increased from 1.51 GHz to 1.58 GHz, and the amplitude also gradually increased. The second peak's amplitude notch depth reached a maximum of -27.4 dB at R = 2.6 mm. After comprehensive considerations, R = 2.6 mm was ultimately selected as the ring width for the final sensor.

[0033] The simulation test was conducted by CST software, and the actual sensor was tested by a vector network analyzer. We first simulated the transmission curve of the sensor for five types of buried objects. The simulation results are shown in the figure below. Figure 8 As shown in the figure, it can be observed that the amplitude peak of the simulated transmission curve gradually decreases with the increase of the dielectric constant, from -22.0dB to -43.2dB. The resonant frequency of the frequency peak gradually shifts to lower frequencies with the increase of the dielectric constant, from 2.6GHz to 2.2GHz. Figure 9 (a), Figure 9 (b) shows the notch amplitude value diagram corresponding to different dielectric constants of the object under test simulated by the sensor and the resonance frequency diagram corresponding to different dielectric constants. According to the sensitivity formula It can be seen that Figure 9 The slope of the fitting curve in (a) and (b) is the corresponding sensitivity of the sensor. Therefore, the detection sensitivity of the sensor for amplitude change is 2.10dB / permittivity unit, and the detection sensitivity for frequency change is 39.8MHz / permittivity unit. In order to verify the sensor, we used commonly used dielectric boards as examples to study the actual sensor. We selected three dielectric boards, F4B, FR4 and Rogers 3006, as examples. During the experimental test, the two ports on one side of the sensor were connected to a 50-ohm port load, and the other end was connected to a vector network analyzer. The simulation and measured results are shown in Figure 2. Figure 10 As shown in (a) and (b), the results show that as the dielectric constant of the dielectric plate increases, the amplitude of the simulated amplitude peak gradually decreases, from -23.0 dB to -29.0 dB at 1.54 GHz. The resonant frequency of the frequency peak gradually decreases from 2.48 GHz to 2.32 GHz. The amplitude of the measured amplitude peak decreases from -13.4 dB to -20.5 dB at 1.79 GHz. The resonant frequency of the frequency peak gradually decreases from 2.51 GHz to 2.40 GHz. Comparing the simulated and measured results, it is found that the frequency of the amplitude peak shifts from 1.54 GHz to 1.79 GHz, and the frequency of the frequency peak also shifts slightly. This difference is mainly due to changes in the inherent electrical parameters of the dielectric plate itself and minor deviations in the actual model manufacturing process. However, the overall trends in the amplitude and frequency changes are the same. Therefore, it can be considered that the simulation and measured results of this model are consistent.

Claims

1. A sensor for detecting underground buried objects based on metamaterial resonance, characterized in that: The sensor has a three-layer structure, which is a metal ground layer (1), a dielectric layer (2), and a metal patch layer (3). Two symmetrically arranged C-shaped metal rings (4) are etched on the metal grounding layer (1) and from the side of the metal grounding layer (1) away from the dielectric layer (2) toward the side close to the dielectric layer (2). The two symmetrically arranged C-shaped metal rings complement each other to form a metal ring with an entire middle slot.

2. The sensor according to claim 1, characterized in that The metal patch layer (3) includes two mutually parallel microwave transmission lines (6), the width of the middle portion of the microwave transmission line being greater than the width of the two ends; a metal ring (5) is provided between the two mutually parallel microwave transmission lines, and the two farthest points of the metal ring (5) are respectively tangent to the middle portions of the two microwave transmission lines.

3. The sensor according to claim 2, characterized in that The microwave transmission line is a microstrip line, and a port 1 and a port 2 are respectively provided at the ends of one side of two mutually parallel microwave transmission lines (6); and a port 3 and a port 4 are respectively provided at the ends of the other side of the two mutually parallel microwave transmission lines (6).

4. The sensor according to claim 1, characterized in that The dielectric constant of the dielectric layer is 6.4-6.6, the thickness is 0.6-0.7 mm, and the material is Rogers 3006.

5. The sensor according to claim 1, wherein The metal ground layer and the metal patch layer are both made of metal copper material, and the thickness thereof is 0.03-0.04 mm.

6. The sensor according to claim 1, characterized in that: The two complementary slotted metal rings of the metal grounding layer and the circular ring of the metal patch layer are circular rings with the same radius, and their centers coincide with each other in the vertical direction.

7. The sensor according to claim 1, characterized in that: The outer radius of the slit metal ring and the circular ring of the metal patch layer is 15.9-16.1 mm, and the inner radius is 13.3-13.5 mm.

8. The sensor according to claim 1, wherein The width of the microstrip line is 2.3~2.5mm; the width of the rectangular strip in the middle is 3.9~4.1mm and the length is 32.0~32.1mm.

9. The sensor according to any one of claims 1 to 8, characterized in that When the sensor is tested, the following steps are specifically adopted: Step 1: Connect port 1 and port 2 of the sensor to the input and output ports of the vector network analyzer respectively; Step 2: Connect ports 3 and 4 of the sensor to a 50Ω load. Step 3: Place the object under test MUT at the position shown by the branch on one side of the metal structure of the metal patch layer (3); Step 4: Observe the transmission curve displayed by the vector network analyzer and detect the dielectric constant of the MUT by observing the changes in amplitude or frequency.

10. The sensor according to any one of claims 1 to 8, characterized in that When the sensor is used to detect underground objects, the following steps are taken: Step 1: The waveguide antenna acts as an excitation source to transmit excitation to the detection area; Step 2: The sensor captures the microwave energy emitted by the waveguide antenna; Step 3: The dielectric properties of the MUT change the electromagnetic field environment around the sensor, causing the sensor's resonance characteristics to shift; Step 4: The sensor's response signal is returned through the feed network; Step 5: The waveguide antenna receives the response signal returned from the sensor, which carries the dielectric properties of the object under test (MUT); Step 6: The waveguide antenna transmits the received response signal back to the vector network analyzer VNA; Step 6: The vector network analyzer (VNA) accurately measures and analyzes the scattering parameters (S 21 parameter); Step 7: The vector network analyzer (VNA) outputs the measured S-parameter data, including amplitude, phase, and frequency relationships, to the computer. Step 8: The data processing algorithm receives the measurement data from the vector network analyzer (VNA); based on the pre-established mathematical model between the dielectric constant and the S parameter, the observed S parameter change is inverted into the dielectric constant of the specific MUT.

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