Magneto-Dielectric Composites Characterization Using Resonant Sensor and Neural Network Modeling

This article presents a novel way to estimate magnetodielectric composites’ complex permittivity (<inline-formula> <tex-math notation="LaTeX">$\varepsilon $ </tex-math></inline-formula>) and permeability (<inline-formula> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula>). A methodology based on artificial neural network (ANN) modeling is proposed to determine <inline-formula> <tex-math notation="LaTeX">$\varepsilon $ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> from <inline-formula> <tex-math notation="LaTeX">$S$ </tex-math></inline-formula>-parameter measurements around 2.45 GHz, obtained using a new microstrip split ring resonator (SRR)-based resonant sensor.

This letter proposes a novel SRR sensor, and a parameter extraction procedure based on artificial neural networks (ANNs) to determine ε and µ parameters simultaneously from an MD sample.The sensor excites two sensing areas to concentrate electric and magnetic fields for a single measurement on the sample, eliminating the need to relocate the sampleunder-test (SUT) and reducing associated errors.The ANN method processes the sensor output, considering the intrinsic correlation between ε and µ, thus avoiding inaccuracies from separate extraction procedures.
The proposed sensor and parameter extraction methodology are evaluated by determining ε and µ parameters for MD composite materials with varying concentrations of Fe 3 O 4 nanoparticles.The results validate the usability of the proposed approach for characterizing new materials.

II. MAGNETO-DIELECTRIC SAMPLE PREPARATION AND ITS MAGNETIC CHARACTERIZATION
The MD composite samples used in this work are fabricated based on PDMS-silicon (DecorRom, ASKU0055) mixed with Fe 3 O 4 20-30 nm nanoparticles (98% purity) from SkySpring Nanomaterials, Inc. [15], adapting procedures suggested in [16] and follow standard compounding techniques from pharmacy industry such as geometric dilution and levigation.The proposed weight ratio for silicone and nanoparticles is 5%, 10%, 15%, 25%, 40%, and 50% of the Fe 3 O 4 nanoparticles.
A U.S. Solid USS-DBS8 Digital Analytical Balance Scale with a resolution of 0.1 mg is used to control the weights of silicone and nanoparticles before mixing; then, they are thoroughly mixed and introduced into a vacuum chamber at −1 atm to avoid the possibility of forming air bubbles.The mixture is then spread into a Delrin mold previously machined using a CNC, configured for the sample dimensions of 10.5 mm length, 6 mm width, and 1 mm height.Each sample is weighted after being removed from the mold, and the actual composite proportions are calculated.Fig. 1 shows the fabrication process.

A. Magnetic Characterization
Magnetic measurements are performed using a MicroSense VSM(EZ9HF VSM), varying the excitation of the H -field up   to 1 T at room temperature.The responses are shown in Fig. 2, and as observed, the saturation magnetization increases proportionally with the nanoparticle concentration for all the evaluated composites.By the other hand, it is observed no significant variation on the coercivity neither the magnetic susceptibility of the samples when varying the nanoparticles concentration, confirming the retention of composite's superparamagnetic characteristics, a highly desirable condition for low-loss microwave materials [16], [17], [18], [19], [20].
Once the MvsH-behavior of the composites is evaluated, the estimation of their ε and µ parameters is carried out to complete the E-H material characterization.A resonant sensor having the capability of simultaneously sensing ε and µ at microwave frequencies is designed and used, as explained hereafter.

III. PLANAR SENSOR FOR SIMULTANEOUSLY MEASURING PERMITTIVITY AND PERMEABILITY
Planar microwave sensors play a crucial role in researching the EM properties of materials, providing a controlled environment and a fast non-destructive way to study how materials interact with EM fields at microwave frequencies.In particular, the resonant method for the characterization of materials using microwave sensors is based on the field perturbation theory: the used sensing circuit is configured such that the electric-E (magnetic-H ) field is confined to specific regions; loading of a sample in such regions causes the material ε (µ) to interact with the circuit E (H ) field, leading the sensor resonant parameters, resonant frequency f r and quality factor Q, to vary.The sample ε (µ) value is then estimated from the evaluation of the change in f r and Q [21].Processes of the technique to determine SUT permittivity and permeability values by ANN modeling. of proximity coupling.Each feeding line is composed of two main sections: a 50 segment, and a narrower section bent 90 • terminated with a small patch.The length of the narrow section is adjusted in simulations for the SRRs to be critically coupled [21], so the resonant parameters can be clearly extracted.Both SRR sections are electrically separated by a gap on the ground-plane in order to isolate them.The circuit was designed using a Rogers 1 RO4003C dielectric substrate having ε r = 3.55, tanδ = 0.0021, and height h = 0.813 mm.[22]; SonnetSoftware 1 was employed to configure and tune the circuit.

A. Design of the Planar Micro Resonant Sensor
As shown in Fig. 3(a), the SUT is placed over the two portions of the SRRs, configured as the SUT-ε and SUT-µ sensing areas, and are defined by a high-intensity region of the E-field produced by the first SRR, and the concentration of the H -field on the second SRR, respectively.
By employing Ansys-HFSS simulator, the sensing circuit and SUT are analyzed; ε r and µ r of the SUT are configured to vary from 1 to 10, and from 1 to 2, respectively, in steps of 0. Using MATLAB, 1 an ANN model was implemented as shown in Fig. 4. It is composed of an input layer with 8 neurons (resonant parameters for the pair ε-µ of the SUT), 10 hidden layers, and an output layer with two neurons (SUT ε and µ).The training inputs are 2000 datasets obtained from the reflection coefficient responses as a function of the frequency from each sensor full-wave simulation.This dataset was divided into three subsets, taking 70% of data for training, 15% for validation, and 15% for testing.Classes for the trained model are established by ε r , µ r , and by the electric and magnetic loss tangents (tanδε, and tanδµ), respectively.
Under this data segmentation, the model provides a testing performance (error between the input values and the actual output values) of 0.003 in 31 epochs.Finally, the most 1 Registered trademark.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.Once the error on the ANN model is minimized, the trained model is used with the experimental data as input, obtaining ε r , µ r , tanδε, and tanδµ for each MD sample fabricated.

V. EXPERIMENTAL VALIDATION
To validate experimentally the applicability of the proposed method to characterize the MD composites, the designed sensor is fabricated by PCB milling technique.Then, two-port S-parameters measurements are performed from 2 to 3 GHz using an Agilent 8753ES-series vector network analyzer (VNA).The equipment was previously calibrated using a short-open-load-thru (SOLT) calibration procedure, establishing a reference impedance of 50 .Fig. 3(d) and (e) show the fabricated sensor and the implemented setup.
To minimize potential variations in the PDMS-Fe 3 O 4 mixture, three samples (n = 3) were fabricated for each concentration.Subsequently, S-parameter measurements were conducted for each set, involving five consecutive frequency sweeps (m = 5).The data used to determine ε and µ were derived from the averaged results of these sweeps and the average of the sample sets corresponding to the Fe 3 O 4 concentration.
Fig. 5(a) and (b) show the return loss responses of the sensor for ε and µ estimation, respectively.When each prepared composite having different Fe 3 O 4 concentrations is placed as SUT; measurements of the empty sensor serve as the reference data, as stated in the resonant measurement technique [21].
Subsequently, the results shown in Fig. 5 serve as input data for the proposed ANN model.This, in turn, yields the values of εr , µr , tanδε, and tanδµ for the manufactured MD composites.The resulting data for each concentration of Fe 3 O 4 is shown in Fig. 6 Due to various mechanisms of electric and magnetic losses, such as hysteresis loss, dielectric loss, and residual loss, ε r and µ r of the MD materials are complex-valued [24], i.e., ε r = ε ′ r (1 − j tan δ ε ) and µ r = µ ′ r 1 − j tan δ µ , where ε ′ r and µ ′ r are the real parts of the ε and µ.Losses in resonant sensors are quantified by the quality factor (Q), Usually determined as Q = f r / f 3dB , where f r is the resonant frequency and f 3dB is the 3-dB bandwidth.It is important to note that this method to determine Q is applicable to resonators with a single resonant point with a simple R-L-C or G-L-C equivalent circuit [25].However, when the SUT is placed in the sensor, multiple resonant points appear, superposing and affecting the 3-dB values of the particular resonance, leading to inaccuracies in Q calculation, especially for low Q responses, as observed when the Fe 3 O 4 concentration increases, as shown in Fig. 5.
Therefore, to accurately determine the Q factor of the evaluated MD composites, it is necessary to consider the intrinsic relationship between ε r , µ r , tanδε, and tanδµ, as provided by the proposed ANN model.Thus, Q factor can be calculated from the intrinsic properties of the material as Qε = ε r /tanδε and Qµ = µ r /tanδµ.The results obtained using this expression are shown in Fig. 7.
Compared to previous studies, the proposed method enables the systematic extraction of ε r , µ r , tanδε, and tanδµ from an ANN model.This model considers the intrinsic relationship between ε and µ, allowing for the quantification of losses in MD composites.This approach helps to avoid underestimation issues that arise when using the single-point resonant method to obtain the Q factor in low resonant sensor responses.A summary of the findings is presented in Table I.

VI. CONCLUSION
An innovative machine learning-based method was introduced to determine complex ε and µ, demonstrating its effectiveness in assessing the fabrication process of MD composites.The studied MD material exhibited low magnetic hysteresis and a high electric and magnetic Q-factor, supporting its suitability for microwave component development.Notably, the integration of SRRs and ANN modeling for characterizing MD material fabrication is a pioneering effort, suggesting the potential extension of this technique to other nanoparticle-composite formulations.Thus, this approach could guide manufacturing processes to align high-frequency properties more effectively with the resulting material characterization.

Fig. 3 (
Fig. 3(a) shows the designed circuit, which comprises two sections composed of a square-shaped SRR each, etched on the ground plane (top view); such resonators are configured to act as the sensing elements, and they are fed by open-terminated transmission lines (bottom view) by means

Fig. 4 .
Fig. 4. Processes of the technique to determine SUT permittivity and permeability values by ANN modeling.

1 .
Reflection responses |S 11 | and |S 22 | are obtained, and the resonant parameters f r (resonant frequency), | | f r (magnitude of reflection at f r ), BW (3-dB bandwidth), and the power loss for µ and ε sensors are extracted from each curve.Losses obtained from the ε section were calculated as Loss ε = 1 − |S 11 | 2 while those obtained for the µ were obtained as Loss µ = 1 − |S 22 | 2 [23].Then, these parameters extracted from EM simulations are used as training, validation, and testing data, as explained hereafter.IV.ANN FOR THE MAGNETO-DIELECTRIC COMPOSITES CHARACTERIZATION As |S 11 | and |S 22 | responses of the sensor contain information on the ε and µ of the MD composites sample, their characteristic resonant parameters f r , | | f r , BW, and Losses of each corresponding pair ε-µ can be used as training parameters to implement an ANN model.

Fig. 5 .
Fig. 5. Measured reflection curves of the sensor loaded with the different Fe 3 O 4 concentration SUTs for calculation of (a) ε and (b) µ.

Fig. 7 .
Fig. 7. Comparison of the Q factor obtained from a single point resonant (Q = f r / f 3dB ) and calculated using intrinsic parameters from the proposed ANN modeling for (a) ε sensor and (b) µ sensor (n = 3, m = 5).
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