A Permittivity Measurement Sensor Based on Ridge Substrate-Integrated Waveguide

Abstract

In this paper, a novel ridge substrate-integrated waveguide (RSIW) sensor is proposed, and the RSIW is optimized and simulated using full-wave simulation. A RSIW-based system was developed for measuring the permittivity of substances, and a neural network algorithm was utilized to reconstruct the permittivity in real time. The system was employed to measure the permittivity of mixed solutions of ethanol and deionized water, and the results were consistent with those obtained using a Keysight commercial probe. The relative errors of the real part and loss tangent were found to be less than 3% and 5%, respectively. These results indicate that the RSIW measuring apparatus is capable of accurate real-time measurement of the permittivity of materials. The simplicity of the manufacturing process, the reduced quantity of measurement samples, and the ease with which they can be prepared all contribute to the potential for microwave energy and microwave wastewater detection application.

1. Introduction

The accelerated advancement of science and technology, in conjunction with the rapidity of change, has resulted in uninterrupted advancement in microwave technology, which has become a significant field of study [1,2]. The advancement of microwave technology is not confined to a single field of study; rather, it has permeated numerous disciplines, including medicine, materials science, chemistry, and others [3,4,5,6]. Concurrently, microwave energy has emerged as a prominent source of efficient and clean energy in industrial production. The utilization of microwave energy is inextricably linked to the dielectric properties of materials. From the perspective of electromagnetism, the complex permittivity of a substance represents a significant parameter that characterizes the absorption and reflection capacity of a substance to microwaves [7]. The complex permittivity of different media varies considerably. The study of the complex permittivity of the medium allows for the analysis of the interaction between electromagnetic waves and the surrounding material environment, as well as the potential effects of the medium on microwave energy. By accurately grasping the complex permittivity of the material, it is possible to provide a foundation for the application of microwave energy [8]. In practical applications, the accurate, real-time measurement of permittivity is of great significance for the rational use of microwave energy.

The design of microwave sensors is a crucial element in the attainment of accurate permittivity measurements, as the reliability of the resulting data is significantly influenced by the performance of the sensor. A growing body of research has examined microwave sensor designs, such as coaxial probes, waveguides, and dielectric resonators, with the aim of accurately characterizing material properties in terms of complex permittivity [9,10]. As a commonly used transmission line, rectangular waveguides are widely used in permittivity measurement. Ridge waveguides are also frequently employed as measurement sensors [11,12]. In comparison to conventional waveguides, ridge waveguides concentrate electromagnetic field energy between the metal ridges and the material to be measured is situated within this region, which provides high measurement accuracy and is commonly utilized for measuring the complex permittivities of materials in the centimetere and millimetere-wave frequency bands [13,14].

However, they are mostly costly, since their structure design entails a complicated measurement setup and a complex design construction. The development of planar measurement devices has significantly advanced the technology of permittivity measurement. These instruments offer an optimal foundation for the development of compact and cost-effective sensors with high precision, as well as improved sensitivity for permittivity measurements [15,16,17]. Scholars have proposed a substrate-integrated waveguide structure, which integrates the waveguide into a plane. Substrate-integrated waveguide (SIW) technology is very attractive since it combines the best features of both waveguide and planar technologies [18]. The structure reduces the volume and is easy to connect with the planar circuit. The upper and lower rows of metal vias with a certain spacing are used to replace the metal sidewalls of the rectangular waveguide to form a substrate-integrated waveguide. Its electromagnetic wave propagation characteristics are similar to those of a rectangular waveguide, and it has the advantages of low loss and high performance [19].

In recent years, SIW has been presented and used to design many active and passive devices [20]. SIW structures have been put forth as a means of designing a variety of planar microwave permittivity measurement apparatuses [21,22]. Similar to the ridge waveguide, the ridge substrate-integrated waveguide is obtained by adding a partial-height metal rib located in the middle of the broad wall of the substrate-integrated waveguide. In fact, RSIW structures are completely shielded and can be fabricated by adopting the standard printed circuit board (PCB) manufacturing process. They are regarded as a promising option thanks to the low-cost mass production of microwave circuits [23,24,25]. The implementation of the ridge waveguide in an SIW structure allows for the advantageous combination of high sensitivity in measurement devices and miniaturization of the structure.

In order to obtain accurate permittivity measurements, it is often necessary to conduct real-time measurements. The Nicolson–Ross–Weir (NRW) method is the most widely employed method thanks to its theoretical simplicity and ease of implementation in algorithms [26]. It is also possible to use modern optimization algorithms to reconstruct the permittivity of a material in real time [27]. Artificial neural networks (ANNs) represent one of the most rapidly evolving fields of computer science, with a vast array of potential applications [28]. It is evident that ANN computational modules are now being applied to microwave techniques; this development renders them a valuable tool [29,30]. In permittivity measurement, it is possible to obtain the scattering parameters of a given medium from microwave measurements. However, the relationship between the permittivity and the scattering parameters is complex. Neural networks are capable of learning complex nonlinear mapping relationships through training, making them particularly well-suited to high-dimensional data and prediction tasks. ANNs can be trained in a test system to learn the behavior of the effective permittivity of a material under microwave irradiation. This process enables the discovery of potential patterns from large datasets, which can be used to predict or solve various problems [31,32,33]. ANNs can provide fast and accurate results in material permittivity measurements, and consequently, based on the ANN, real-time measurement can be realized.

This paper proposes an RSIW sensor that combines a ridge waveguide and an SIW structure for the accurate measurement of the complex permittivity of materials at 2.45 GHz. The sensor is attached to a vector network analyzer to form a measurement system. During the measurement process, the material under investigation is positioned within the measurement area of the sensor, and the S-parameters are then measured by the vector network analyzer. The resulting S-parameters are then imported into an artificial neural network, which is employed to determine the permittivity of the material under investigation in real time. The proposed method has several major advantages, namely the simplicity of the measurement process, the ease of processing and fabrication of the measurement apparatus, and the small number of samples required.

2. Materials and Methods

2.1. Ridge Substrate-Integrated Waveguide Measurement System

The configuration of the ridge substrate-integrated waveguide-based system used for measuring permittivity is illustrated in Figure 1. The system is composed primarily of a ridge substrate-integrated waveguide, a vector network analyzer, two coaxial cables, and a personal computer. During the measurement process, the sample to be analyzed is placed into the measurement hole, and the S-parameters of the sample are then measured by the vector network analyzer. The S-parameters obtained from the experimental measurements are fed into an artificial neural network that has been trained using a computer. The complex permittivity of the specimen is then calculated using the trained neural network. This measurement system allows for the real-time measurement of liquid and solid powder samples.

The schematic of the core measurement structure RSIW proposed in this paper is shown in Figure 2. The diameter of the metal vias, d, the distance s between adjacent metal vias, the width w between the top and bottom rows of metal vias, the diameter D of the measurement hole, the diameter d₁ of the ridge vias, the distance s₁ between the measurement hole and the neighboring ridge vias on both sides, and the spacing of the ridge vias, s₂, are the parameters affecting the measurement performance of the RSIW. Furthermore, the prerequisites for SIW equivalence with conventional rectangular waveguides are as follows [34]:

$${\displaystyle \frac{s}{d}}<2,{\displaystyle \frac{d}{w}}<0.2$$

(1)

Subsequent to satisfying Equation (1), the loss of SIW is minimized and the propagation characteristics are shown to be similar to those of rectangular waveguide. On the basis of this similarity, an empirical equation can be derived between the geometrical dimensions of the SIW with the same propagation characteristics and the effective width w_eff of the rectangular waveguide. Utilizing this formula, preliminary dimensions for the SIW design can be obtained. Commonly used empirical formulas are as follows [18]:

$$w_{eff}=w-1.08{\displaystyle \frac{d^2}{s}}+0.1{\displaystyle \frac{d^2}{w}}$$

(2)

An alternative formulation of this concept is as follows:

$$w={\displaystyle \frac{2w_{eff}}{\pi }}{\cot }^{-1}\left({\displaystyle \frac{\pi s}{4w_{eff}}}\ln {\displaystyle \frac{s}{2d}}\right)$$

(3)

As demonstrated in Equations (1) and (2), the initial dimensions of the SIW can be obtained, a row of ridge via is added to the centere of the broad wall of the SIW to form the RSIW [35,36], and a measurement hole is provided in the geometrical centere of the measurement structure to hold the material to be measured. The parameters of the measurement sensor were optimized using full-wave simulation software, and it is important to note that the complex permittivity of a material is represented by the real part and the loss tangent, meaning that the S-parameter is affected by both parameters. The reconstruction of the complex permittivity is achieved by utilizing the scattering parameters, with the objective of optimizing the avoidance of the multi-value problem in the correspondence between the S-parameters and the complex permittivity when the complex permittivities are varied. This enhances the accuracy of the reconstruction. The final dimensions of the RSIW are determined after adjusting various parameters through a comprehensive analysis and optimization of the factors affecting the performance of the RSIW. The optimized dimensions of the sensor permit the S-parameters to have an essentially monotonic relationship with the real part of the permittivity and the loss tangent of the different samples, respectively. The dimensions of the measurement sensor that have been optimized are shown in

Table 1. Structure dimension table of the RSIW.

Parameter	Value (mm)
$\mathrm{d}$	1
$\mathrm{s}$	1.8
$\mathrm{w}$	51.26
${\mathrm{s}}_1$	3.5
${\mathrm{s}}_2$	1.8
$\mathrm{D}$	5
${\mathrm{d}}_1$	1
$h_1$	3
$h_2$	1

. The fabricated RSIW sensor is illustrated in Figure 3, and the permittivity of the dielectric substrate is represented by ε_r’= 2.65 and tanδ = 0.0015.

2.2. Simulation Parameter Setting and Result Analysis

Complex permittivity is considered a crucial parameter for evaluating the capacity of a medium to absorb and reflect microwaves. This representation is typically denoted by a real part (ε′) and an imaginary part (ε″), as illustrated below:

$$\epsilon ={\epsilon }^{\prime }-j{\epsilon }^{″}$$

(4)

The loss tangent (tanδ) is a parameter for calculating the ratio of the imaginary part to the real part of the complex permittivity and its formula is as follows:

$$tan\delta ={\displaystyle \frac{{\epsilon }^{″}}{{\epsilon }^{\prime }}}$$

(5)

The permittivity of a material is generally challenging to measure directly with conventional instruments; however, a measurement system consisting of a ridge substrate-integrated waveguide and a vector network analyzer can provide the S-parameter. There is a mathematical relationship between the permittivity and the S-parameter, and by measuring the S-parameter, the permittivity of a substance can be calculated. Given the complexity of the relationship between the two, this paper proposes a neural network algorithm for obtaining the permittivity through the S-parameter. The training process of the neural network necessitates a substantial number of S-parameters and corresponding permittivities as sample data. However, the reconstruction of permittivities from S-parameters using artificial neural networks may encounter the issue of multiple values, which can potentially compromise the accuracy of permittivity reconstruction. Consequently, the employment of the S-parameter for the reconstruction of permittivity in the design of RSIW serves to reduce the complexity of the neural network, while concomitantly enhancing the accuracy of the reconstruction, on the condition that there is a single-valued correspondence between the S-parameter and permittivity over a substantial range of permittivity variations.

As demonstrated in Figure 4, the simulation results indicate that the scattering parameter undergoes substantial changes in response to the variation of permittivity when the real part ranges from 1 to 80 and the loss tangent ranges from 0 to 1, respectively. Furthermore, a monotonic relationship exists between the scattering parameter and the complex permittivity in most regions. These findings provide a foundation for the precise calculation of the permittivity using scattering parameters. Moreover, the |S₁₁|, |S₂₁|, and φ_S11 can be used to calculate the permittivity of the material under investigation. This approach not only circumvents the issue of multiple values that may arise when using a single parameter to calculate the complex permittivity, but also enhances the accuracy of the calculation.

2.3. Artificial Neural Network Design

An artificial neural network can be defined as a series of mathematical models inspired by neurology and biology. These models are used to simulate the structure and function of the human brain nervous system. They do this by connecting a large number of artificial neuron nodes to form a whole. The relationship between the change in permittivity and the sensor response is complex. The models approximate and fit various complex functions by adjusting the interconnection relationship between the internal artificial neurons. This enables them to process information [30].

The neural network designed in this paper is composed of three parts: an input layer, three hidden layers, and an output layer. The model is shown in Figure 5. The input layer is the S-parameters, the hidden layer takes the output of the previous layer as the input of this layer, and after a nonlinear transformation, this is the output of the layer. To balance network complexity and reconstruction accuracy, S-parameters (|S₁₁|, |S₂₁| and φ_S11) were chosen as input features [37]. The permittivity (ε′, tanδ) is the output of the neural network. The number of neurons in each of the three hidden layers is 64, 32, and 16, respectively. The ReLU (rectified linear unit) activation function was employed to circumvent the local optimal solution and ensure convergence on the global optimal solution.

The output value of the first layer ${\mathrm{a}}^{\mathrm{i}}$ ($\mathrm{i}$ = 1, 2, 3, 4) is as follows:

$${\mathrm{a}}^{\mathrm{i}}=\mathrm{f}\left({\sum }_{\mathrm{j}-1}^{\mathrm{m}}{\mathsf{\omega }}^{\mathrm{i}-1}{\mathrm{a}}^{\mathrm{i}-1}+{\mathrm{b}}^{\mathrm{i}-1}\right)$$

(6)

Here, m is the number of neurons in the (i − 1) layer, ${\mathsf{\omega }}^{\mathrm{i}-1}$ is the weight of the ($i-1$) layer, ${\mathrm{a}}_{\mathrm{j}}^{\mathrm{i}-1}$ is the output value of the j neuron in the (i − 1) layer, ${\mathrm{b}}^{\mathrm{i}-1}$ is the bias of the ($i-1$) layer, f(x) is the activation function, and the input layer ${\mathrm{a}}^0$ is as follows:

$${\mathrm{a}}^0={[\left|{\mathrm{S}}_{11}\right|,{\mathrm{\phi }}_{\mathrm{s}11},|{\mathrm{S}}_{21}\left|\right]}^{\mathrm{T}}$$

(7)

The output layer ${\mathrm{a}}^4$ is as follows:

$${\mathrm{a}}^4=[{\mathsf{\epsilon }}^{\prime },\tan \mathsf{\delta }{]}^{\mathrm{T}}$$

(8)

In practice, the material to be measured must be placed into the RSIW measurement hole, whereupon both ends of the RSIW are to be connected to a vector network analyzer (VNA) with coaxial cables in order to measure the S-parameters of the material. Thereafter, the S-parameter values are to be entered into a trained neural network in order to obtain the permittivity.

In order to verify the predictive efficacy of the trained neural network, a total of 80 sample data items differing from those in the training set were selected and sent to the trained neural network for analysis. The prediction results are displayed in Figure 6. In Figure 6, the horizontal coordinate is the true permittivity and the vertical coordinate is the predicted value. The true value of the complex permittivity is to be selected from the full-wave simulation software, following which the corresponding S-parameters are to be calculated. When the relationship between the predicted value and the true value is closer to this curve, the accuracy of the prediction result of the neural network is higher. The mean square errors of the predicted real part and loss tangent of the permittivity are 0.67% and 3.7%, respectively, thereby substantiating the credibility of the neural network model.

3. Results

As illustrated in Figure 7, the measurement system was constructed and the measurement device was tested to verify the accuracy of its measurement. In the measurement process, the core apparatus employed was the RSIW, which was connected at both ports to a vector network analyzer via coaxial cables. In order to ascertain the precision of the measurements, a two-port calibration method, known as SOLT (Short-Open-Load-Through), was employed [38]. During the experiment, the S-parameters of the material to be measured can be obtained by putting the material into the measurement hole. The sample fills the cylindrical measuring hole with a diameter of 5 mm, a height of 3 mm, and a volume of approximately 0.06 mL. The S-parameters and permittivity of the liquid under investigation can be obtained by inputting the S-parameters into a reconstruction program based on a neural network algorithm. In this case, the test liquid used in the experiment was an ethanol-water mixture solution, and ten sets of mixture solutions with different concentrations were obtained by mixing ethanol and deionized water. In order to eliminate random error and increase the reliability of the experiment, each sample was measured on three separate occasions. Then, the mean of the three values was calculated. The results obtained from the measurements were then compared with those obtained using the Keysight N1501A dielectric probe kit [39]. As demonstrated in Figure 8, the values of the permittivity of the ethanol-water mixtures measured by the RSIW structure are essentially equivalent to those measured by the Keysight commercial probe, with the relative error of the real part and the loss tangent not exceeding 3% and 5%, respectively. The results indicate that the RSIW measurement sensor can be utilized to measure the permittivity with a high accuracy. The presence of minor inaccuracies may be attributable to a number of factors, including errors in measuring instruments, variations in dimensional specifications during the machining process, and errors occurring during the reconstruction process.

As illustrated in

Table 2. Performance comparison with recently reported works.

Work	Maximum Relative Errors of ε′	Measurement Speed	Sample Volume	Machining Complexity	Measurement Method
[11]	6.626%	Rapidly	8.5 mL	Medium	Non-resonant
[14]	9.8%	Real-time	5 mL	Medium	Non-resonant
[40]	11%	Real-time	1.8 mL	Low	Resonant
[41]	3.96%	Real-time	<0.1 mL	Low	Resonant
This work	3%	Real-time	<0.1 mL	Low	Non-resonant

, a comparison is made between the proposed design and the results obtained from recently reported works. It is evident that the proposed sensor is not only accurate in measurement, but also capable of real-time measurement. The utilization of a planar structure renders the proposed RSIW sensor susceptible to a straightforward manufacturing process. Furthermore, the sensor’s design minimizes the necessity for sample volume, a feature that enhances its performance.

4. Conclusions

In this paper, a permittivity measurement sensor based on the RSIW structure was proposed and employed to form a permittivity measurement system at 2.45 GHz. The S-parameters measured by VNA were then used to reconstruct the permittivity of materials using artificial neural networks. The system was utilized to ascertain the real part and loss tangent of the complex permittivity of ethanol, deionized water solutions, and their mixtures at room temperature. The measurements were in excellent agreement with those produced by Keysight commercial probes, thus validating the accuracy of the system’s measurements. The method is distinguished by its straightforward sensor processing and fabrication, the uncomplicated construction of the measurement system, the minimal number of samples required, and a rapid and precise measurement process that provides data on the permittivity of substances for practical microwave energy applications. In addition, the use of microwave permittivity measurement technology makes it possible to carry out real-time online monitoring of wastewater. This can help to automate control and optimize the operation of wastewater treatment facilities.