HIGHLY SENSITIVE RESONANCE-BASED PLANAR SENSORS FOR NONDESTRUCTIVE COMPLEX MATERIAL CHARACTERIZATION By Fares Theyab A Alharbi A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Electrical Engineering — Doctor of Philosophy 2022 ABSTRACT Microwave-based sensing methods have accelerated the advances of nondestructive evaluation in a variety of applications, such as material characterization, structural health monitoring, mi- crofluidics identification, agricultural, and biomedical sensing. Resonance-based microwave pla- nar sensors have demonstrated multiple advantages, including simple fabrication, low-cost, real- time measurements, in addition to nondestructive sensing capability. Depending on the sensing application and properties and conditions of the material of interest, customized sensing method- ologies can significantly enhance the performance of the resonance-based planar sensors. This dissertation presents customized, highly sensitive, and nondestructive methods for complex mate- rial characterization problems. Resonance-based planar sensors are highly sensitive to the dielectric properties of the materials in their close vicinity. However, the performance of such sensors deteriorates when the dielectric material is attached to a metallic surface. In the first part of this dissertation, a novel nondestructive sensing methodology is constructed for the measurement and characterization of conductor-backed dielectric materials. It permits the characterization of thin conductor-backed dielectric materials with high sensitivity to the dielectric properties. Moreover, the presented methodology constructs a nondestructive technique for different conductor-backed material measurement applications. Another main challenge of using resonance-based planar sensors in material characterization is the nondiscrimination between the intrinsic electromagnetic properties of composite magneto- dielectric materials. In the second part of this dissertation, a resonance-based sensing method for dielectric and magneto-dielectric material characterization, predicated on the fields-confinement approach, is presented. The method demonstrated high sensitivity to both permeability and per- mittivity of composite magneto-dielectric materials. Differential-based sensing methods have generally been used to enhance the robustness of the measurements by minimizing errors due to the surrounding environmental factors, including the fabrication tolerance and substrate properties of planar resonators. This dissertation takes differ- ential sensing a step further and introduces a novel differential-based sensing method for dielectric and magneto-dielectric material characterization, in the last part of the dissertation. In addition to the enhanced robustness and high sensitivity using the presented differential-based sensing method, it also provides real-time measurements for material characterization and comparison. To my mother Radhyah Alharbi and to the memories of my father Theyab Abdullah Alharbi. iv ACKNOWLEDGMENTS I am grateful to my advisor Professor. Yiming Deng, for his advice, assistance, and support. His encouragement and valuable advice have motivated me to succeed in my graduate studies and to accomplish this dissertation. His great support was not only limited to academics, but also in other aspects of life such as personal and family life. I thank Dr. Deng for his support and solidarity during the time when a member of my family was experiencing serious health challenges. Without his support, this work could not have been accomplished. I are grateful to my committee members Professor. Lalita Udpa, Professor. Satish Udpa, and Professor. Mahmoodul Haq for their time and effort. Their advice and encouragement have motivated me to accomplish this dissertation. I would like to thank all professors who taught and advised me at Michigan State University (MSU) and before I joined MSU. I am thankful to Mr. Brian Wright in the electrical and computer engineering department for his help in the sensors fabrication. I also extend my thanks to Mr. Xenofon Konstantinou and Dr. John Albrecht in the electrical and computer engineering department for their help. I also would like to thank all my friends and colleagues for their encouragement and support for me throughout graduate studies. Thanks go out to my colleagues in the Nondestructive Evaluation Laboratory NDEL. I express my sincere thanks and gratitude reach to my mother, brothers, sisters, my wife, and my three daughters for their support, encouragement, and love. v TABLE OF CONTENTS Chapter 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Organization of the Dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Chapter 2 Microwave-Based Methods for Nondestructive Evaluation and Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1 Material Characterization Using Microwave-Based Sensing Methods . . . . . . . . 5 2.2 Defect Detection as a Special Case of Material Characterization . . . . . . . . . . 11 Chapter 3 Characterization of Conductor-Backed Dielectric Substrates Using a Novel Resonance-Based Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.2 Conductor Backing Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.3 Sensing Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.5 Experimental Validation and Discussion . . . . . . . . . . . . . . . . . . . . . . . 36 3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Chapter 4 Characterization of Magneto-dielectric Material Using A Single Stepped Impedance Resonator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.2 Perturbation Effect of Magneto-dielectric Materials . . . . . . . . . . . . . . . . . 46 4.3 Sensor Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 4.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.5 Experimental Validation and Discussion . . . . . . . . . . . . . . . . . . . . . . . 61 4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 Chapter 5 Differential-based Sensing Method for Magnetodielectric Material Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 5.2 Fields-confinement using DSIR . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5.3 Differential sensing for magneto-dielectric materials using Double SIR . . . . . . . 72 5.4 Experimental Measurements of the DSIR . . . . . . . . . . . . . . . . . . . . . . 77 5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 Chapter 6 Conclusions and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . 85 BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 vi Chapter 1 Introduction 1.1 Motivation The quality of research into nondestructive technologies has been rapidly improving due to advances of their essential roles not only in diagnostic maintenance, but also in prognostic main- tenance, health monitoring, quality assessment, and manufacturing processes. With expanded use of composite materials with engineered properties in many fields such as automotive, aerospace, radio frequency and microwave circuits, there has been a greater demand for high speed, high resolution, simple, and affordable nondestructive evaluation and testing methods. In addition, non- destructive sensing methods need to be compatible with modernized distributed sensing methods, such as structural health monitoring that provides real-time data while using miniaturized and less power-consuming devices. Microwave-based measurement methods provide multiple advantages (e.g, high resolution, high speed, low-power consumption, compact size, and compatibility with wireless networks) that make them suitable for future nondestructive evaluation applications. Due to their nondestructive evaluation capabilities, microwave-based sensing methods are es- sential to a variety of applications, such as material characterization, structural health monitoring, microfluidics identification, food quality control, and biomedical sensing applications [1–9]. Elec- tric permittivity characterization is the key fundamental factor in all aforementioned application. Biomedical sensing applications, such as cancer detection are attainable by determining permittiv- ity of healthy and malignant tissue. The relative permittivity contrasts between malignant tissue and normal breast tissue were found to be 4.7 to 1 [10]. Moreover, dielectric properties of in- vivo cancerous tissue were significantly higher than those estimated by either electrical impedance tomography or by using exvivo measurements [11]. Precise determination and differentiation be- tween the permittivity of healthy and malignant tissue is the essential key factor for cancer de- tection and other biomedical applications, such as determining the glucose level in the blood for 1 diabetes monitoring [12]. Microwave-based methods have been widely employed for extracting electromagnet intrin- sic properties of solid as well as liquid materials. Among microwave-based sensing methods, resonance-based methods using miniaturized planar sensors have become more popular in many nondestructive evaluation applications. They demonstrated multiple advantages including simple fabrication, low cost, and real-time measurements, in addition to their inherent capability of nonde- structive evaluation. However, depending on the sensing application and properties and conditions of the material of interest, customized sensing methodologies can significantly enhance the per- formance of resonance-based planar sensors. This dissertation addresses some of the challenges of using resonance-based planar sensors and presents novel and customized sensing methods for characterizing materials with complex properties and conditions. 1.2 Contributions The main objective of this dissertation is to introduce novel and customized nondestructive resonance-based methods for the measurement and characterization of materials with engineered properties and conditions, such as magneto-dielectric materials and conductor-backed materials using simple yet efficient and low cost planar sensors. In this first part of this dissertation, a novel resonance-based sensing methodology is proposed for the measurement and characterization of conductor-backed materials. The proposed sensing methodology frames a nondestructive method with high sensitivity to the dielectric properties without removing the conductor-backing plane. The sensing methodology is applied for complex permittivity characterization, and it can be further applied for different measurement applications on conductor-backed materials. One of the challenges in using resonance-based planar sensors for material characterization is distinguishing between the intrinsic electromagnetic properties, such as electric and magnetic properties of magneto-dielectric materials. For this purpose, a new sensing method that permits measurement and characterization of magneto-dielectric materials using a single planar sensor is presented. The electric and magnetic fields are confined and intensified on two spatially separated sensing areas. The top plane of the planar sensor is split into two spatially separated sensing 2 areas; each sensing area is highly sensitive to one of the intrinsic electromagnetic properties of the material. It provides large sensing areas for measuring and distinguishing between electric and magnetic properties of magneto-dielectric samples. Furthermore a novel differential-based field localization is is elaborated on further in the last part of the dissertation for dielectric and magneto-dielectric materials sensing and comparison. This dissertation contributes to the state of the art in the following areas: • Introducing a novel nondestructive sensing methodology for the measurement and charac- terization of conductor-backed dielectric materials • Presenting a highly sensitive resonance-based planar sensor for the permittivity characteri- zation of thin conductor-backed dielectric materials • Presenting a highly sensitive resonance-based sensing method, predicated on the fields con- finement approach, for magneto-dielectric material characterization • Facilitating widely spatially separated sensing areas for magneto-dielectric material charac- terization on a single resonance structure • Introducing a novel differential-based sensing method, based on resonance frequency split- ting, for dielectric and magneto-dielectric material characterization • Providing a real-time differential-based comparison between the electromagnetic properties of dielectric and magneto-dielectric materials on a single resonance structure operating on a two-port measurement system. 1.3 Organization of the Dissertation The dissertation is organized as follows. It begins with a brief review, in Chapter 2, about microwave-based nondestructive evaluation methods for material characterization and defects de- tection. Chapter 3 starts with an illustration of the conductor backing effect on material character- ization using planar resonator; it then presents a novel nondestructive sensing methodology for the 3 measurement and characterization of conductor-backed materials with simulation and experimen- tal validation. Afterwards, the fields confinement approach is realized using a single resonance- based planar sensor for magneto-dielectric material characterization in Chapter 4, followed by numerical simulation and experimental validation of the proposed method using materials of dif- ferent electromagnetic properties. Then, Chapter 5 introduces a novel differential-based sensing method is introduced in for dielectric and magneto-dielectric material characterization and com- parison with numerical analysis and experimental validation. Finally, the possibility of expanding on fields-confinement approach for permeability and permittivity differential sensing to dual fre- quency bands on a single resonance structure is proposed in Chapter 6. Chapter 6 also provides concluding remarks and potential directions for future works. 4 Chapter 2 Microwave-Based Methods for Nondestructive Evaluation and Testing The terms nondestructive evaluation and nondestructive testing are usually used interchange- ably in the literature. According to [1], nondestructive evaluation considers intrinsic properties of the material, such as electric and magnetic properties of the material, while nondestructive testing focuses on inspecting the material for abnormalities and defects. Interestingly, the microwave- based measurement methods are proven to be effective tools for both nondestructive evaluation and nondestructive testing. Furthermore, advances in microwave-based sensing methods are also leading to comprehensive structural health monitoring systems [7]. This chapter introduces a brief review about microwave-based methods, and in particular resonance-based planar sensors, for ma- terial characterization and defect detection. 2.1 Material Characterization Using Microwave-Based Sensing Methods Extracting the electromagnetic intrinsic properties of a material using microwave-based sens- ing methods is fundamentally based on analyzing the scattering electromagnetic fields when a wave interacts with the material. Several electromagnetic methods have been employed to extract intrinsic electric and magnetic properties of dielectric materials, such as electric permittivity and magnetic permeability. These methods could be categorized into two main categories: wide-band and narrow-band categories [13]. The use of wide band methods, including free space methods and waveguide methods, per- mit measuring the permittivity and permeability of the material over a wide range of frequency bands. In free space methods, a bi-static or mono-static antennas setup is required to character- ize the material. After scattered waves are measured, electromagnetic analysis methods, such as Nicholson-Ross [14] are applied to extract the permittivity and permeability of the material. In the case of a bi-static, both waves transmitted through and reflected by the material are measured. 5 Mono-static setups are effectively used if the material is only accessible at one side, in which only reflected fields are measured; however, in this case, reflection-only analysis methods are required for material characterization [15]. A main advantage of free space methods is the non-contact pro- cedure in interaction with the material under test [15, 16]. However, expensive experimental setup and heavy computations are involved; in addition, ambient noise in the free space measurements is inevitable. Guidedwave methods, such as a matched rectangular waveguide [17], have been widely used for wide-band material characterization. The sample is inserted into the waveguide, and the scatter- ing dominated mode of the electromagnetic waves reflected by and transmitted through the material are measured to extract the material properties. Coaxial transmission lines are another example of wave guided structures that support transverse electromagnetic (TEM) mode. The characterized sample is placed in the insulation part of the coaxial cable [18]. The precision of guidedwave methods are more accurate compared to free space methods [13]; however, preparing the sam- ple to perfectly fit the waveguide structure is a challenging task [19]. Open-ended waveguides and open-ended coaxial cables [2, 20, 21] also fall in the wide-band category, where the sample is placed on the opening aperture of the open-ended waveguide and only reflection coefficients are measured. However, the reflected waves are highly influenced by the roughness of the material surface, and characterization is also affected by the geometry of the open-ended aperture. Similar to most methods in the wide-band category, the measurement of material properties involves heavy computations. Narrow-band methods, such as resonance cavity methods [22], measures the permittivity and permeability at discrete frequency points. Although using resonance cavities do not provide broad- band information about the sample, these methods more accurate and reliable compared to the wide-band methods [13]; however, the size, the computation cost, and sample perpetration needed for the use of the resonance cavity are some of the difficulties in using resonance cavities [19]. Alternatively, resonance-based methods using resonance-based planar sensors have been in- troduced as effective yet low cost methods for a wide range of applications in material charac- 6 terization [3, 4, 19, 23–36]. Due to the small size of the aforementioned planar sensors compared to the operating wavelength at resonance, quasi-static analysis methods are used to model these resonators [19, 23, 36, 37]. The capability of hosting these resonators on planar transmission lines, such as microstrip lines and coplanar waveguides [23] using inexpensive circuit board technolo- gies, has made them preferable for a variety of applications compared to other microwave-based sensing methods. Moreover, less sample preparation effort is required and less computation is in- volved [19]. Due to these advantages, the implementation of resonance-based planar sensors for nondestructive applications has gained increasing popularity, and considerable efforts have been devoted to improve these methods for material characterization and structural health monitoring. • Resonance-based planar sensors for Material Characterization Planar resonators have been initially utilized in designing miniaturized microwave filters [23]. The resonance behavior of planar resonator depends of the equivalent capacitance and inductance of materials that are in close vicinity of the resonator [23]. That makes them excellent candidates for nondestructive evaluation applications, such as material characterization, and defect detection. R fr (∆ϵE · E 0 + ∆µH 1 · H 0 ) dv = v R 1  (2.1) ∆fr ϵ |E |2 + µ |H |2 v 0 0 0 0 Material characterization using resonance-based planar sensors is based on material perturba- tion method [38]. When a resonance structure is perturbed by a dielectric material, the change on the resonance frequency is presented in (2.1) [38]; where E 0 and H 0 are the electric and mag- netic fields before perturbation, respectively, and E 1 and H 1 are the fields after perturbation. The shift of the resonance frequency ∆fr is attributed to the change of the electric permittivity ∆ϵ and the magnetic permeability ∆µ of the resonance structure when a material perturbs the fields at resonance. ∆fr = f (∆ϵr , ∆µr ) (2.2) Using resonance-based planar sensors for material characterization, the material is loaded to 7 Figure 2.1: Resonance frequency shift due to the increase of the relative permittivity of the loaded material. the resonator either in direct contact or in close vicinity of the resonator. The change in permittivity ∆ϵr , causes a relative change in the resonance frequency ∆ϵr [23]; solving this inverse problem using curve fitting function permits measuring the change in the material permittivity (2.2). For nonmagnetic dielectric materials, the change in the resonance frequency is attributed to the change of the permittivity that the material impose to the resonance structure; Fig. 2.1 illustrates the effect of the increase of the permittivity on the resonance frequency as a result of material perturbation. However when a dielectric material is backed by a conductor, the electric and magnetic fields distribution will be highly affected by the conductor in the vicinity of the resonance-based planar resonator. Chapter 3 shows the effect of the conductor-backing on material characterization using resonance-based planar sensors, and presents a highly sensitive nondestructive sensing methodol- ogy for conductor-backed material measurement and characterization, as briefly illustrated in Fig. 2.2. 8 Figure 2.2: A diagram of the sensing methodology for conductor-backed material using resonance- based planar sensors. Considering (2.1), the change in the resonance frequency due to the material perturbation is de- pendent equally on variations of permittivity and permeability. Magneto-dielectric material, elec- tric permittivity and magnetic permittivity have similar effects on the resonance frequency, which poses challenges in the material characterization. For this purpose, field confinement approach, illustrated in Fig. 2.3, is realized using a stepped impedance resonator to create two spatially sep- arated sensing areas for magneto-dielectric characterization. In this case, the material perturbation effect is local and depends on the field confined in the sensing area. Thus, electric and magnetic properties using material perturbation can then be determined by rewriting to (2.2) to (2.3) in the permittivity sensing area and (2.4) in the permeability sensing area; the details are presented in Chapter 4. 9 Figure 2.3: Fields confinement for magneto-dielectric material characterization on a single reso- nance structure. ∆ϵr = f −1 (∆frn,E ) (2.3) ∆µr = f −1 (∆frn,H ) (2.4) Figure 2.4: Fields confinement for differential-based sensing fo magneto-dielectric material char- acterization on a single resonance structure. The performance of resonance-based measurement methods can be enhanced using differential- based sensing techniques to minimize common sources of errors and compared to a known refer- ence. A differential-based sensing method is introduced in this dissertation not only to enhance measurement efficacy, but also to differentiate between the intrinsic electromagnetic properties of dielectric and magneto-dielectric materials using a single resonance structure. Moreover, the pre- 10 sented differential-based sensing method, illustrated in Fig. 2.4, provides real-time measurements for dielectric and magneto-dielectric material characterization and comparison. 2.2 Defect Detection as a Special Case of Material Characterization Inspecting the integrity of the material and detecting any surface and subsurface anomalies in the material is crucial in many industrial applications. Traditionally, nondestructive testing meth- ods, such as eddy current and flux leakage methods, are developed for inspecting metallic material. On the other hand, microwave-based methods are inherently suitable for inspecting nonmetallic materials for surface and subsurface defects. Although microwave signals are reflected by conduc- tive surfaces, microwave-based sensing methods, including open-ended waveguides, open-ended coaxial cables, and resonance-based sensing methods, are shown to be effective techniques in de- tecting anomalies in metallic surfaces [2]. Compared to the other nondestructive testing methods such as eddy current and flux leakage, the operating wavelengths using microwave-based sensing methods are very small, in the ranges of 10 cm to 1 mm, which allows detecting and differentiating between smaller fatigue surface cracking. The resolution is further enhanced to detect defects that are smaller than the operating wavelength, thus providing higher resolution in detecting and sizing miniature defects. Open-ended waveguide probes operating in the near-field have been used for surface crack detection [39]. In the case of any dielectric insulation, coating, or painting on the metallic surface, the microwave signal propagates through the insulation and gets reflected back by the metallic medium to the waveguide with information about any abnormality in the dielectric coating, as well as the metallic surface. For instance, detecting surface cracks in painted metal surfaces using open-ended waveguide with high resolution is presented [40] . Using the same operational principle, open-ended coaxial cables are employed for metallic and nonmetallic nondestructive testing. Cracks in a metallic surface under film-coating using an open- ended coaxial cable are also shown in [41]. The effect of the geometry of the open-ended coaxial probes on crack detection in metallic surface are presented in [42]. Compared to open-ended waveguide, open-ended coaxial cables support TEM mode and can operate in wide frequency 11 bands including low frequency bands compared to open-ended waveguides which operate over a high cutoff frequency. However, oped-ended waveguide are easier to calibrate [2]. The use of open-ended waveguide and open-ended coaxial cable probes have detected millimeter and sub- millimeter cracks. However, the resolution are very sensitive to the geometry of the waveguide, the orientation of the crack with respect to the opening of waveguides and coaxial probes [43]. Additionally, operating open-ended waveguides and open-ended coaxial cables require the use of RF source, splitters, couplers and mixers which raises the their operational cost. Resonance-based sensing methods have also been employed for material inspection [2]. The unique advantages of resonance-based planar sensors, mentioned in the previous section for ma- terial characterization, are further utilized for defects detection. Detecting abnormality using resonance-based method could be considered as a special case of material characterizing. When the planar sensor is passed by a defect on the material, the resonance structure will be perturbed by a material with different properties. The abrupt change in the inspected material, due to the crack, is reflected as a change in the net capacitance or inductance seen by resonator. As a result, the resonance frequency change, due the abrupt material perturbation in the vicinity of the resonance structure, enables detecting the presence of a crack in the material. Furthermore, by observing the change of the resonance frequency an image of the inspected material can be generated. Resonance-based planar sensors are used for crack detection in metallic as well as nonmetal- lic material in the order of millimeter and sub-millimeter wide cracks [2, 37, 44, 45]. Although, resonance-based methods are sensitive to the air gap between and the planar sensor the inspected material compared to other nearfield sensing methods, such as open-ended waveguide methods. However, the sensing principle in using resonance-based methods is less sensitive to the ampli- tude of the signal which overcomes the error associated with ambient noise that highly affects the signal amplitude. Furthermore less experimental effort and lower operational cost are required using resonance-based planar sensors. These advantages have made planar sensors attractive for nondestructive testing methods in metallic and nonmetallic materials. Using resonance-based planar sensors such as SRR and SIR facilities miniaturizing the sensor 12 to operate at lower frequency with adjustable geometry. This feature enables detecting cracks in the order of fractions of the operating wavelength with high resolution [44]. Since there are different parameters of each sensing method, such as operating wavelength, orientation of the sensor with respect to the concerned crack and prop geometry, resonance-based planar sensors provide wide set of selections that could be customized and optimized for complex inspection applications [2]. Brief illustration about the principle using resonance-based planar sensors for inspecting metallic and nonmetallic materials are presented next. • Resonance-Based Planar Sensors for Dielectric Material Inspection Microwave-based sensors are highly sensitive to surface cracks not only in dielectric materials but also in metallic materials with high resolution. Due to the capability of microwave fields to penetrate nonmetallic materials, most nondestructive applications using microwave sensing meth- ods are focused on dielectric for surface and subsurface crack detection in nonmetallic materials including dielectric substrates and non-conductive composite materials. Defects detection using planar resonator can be considered as a special case of material characterization. In the case of inspecting dielectric materials, placing a dielectric material without cracks, healthy sample, the resonance frequency shifts downwards from the unloaded resonance frequency point, fu to the fh , due to the parallel capacitance effect explained in chapter 3. Labeling fh as a reference of the healthy sample, the presence of a crack in the dielectric material reduces the overall relative per- mittivity of the loaded material; consequently reducing the capacitance of the sample. Therefore, the resonance frequency of the sensor moves from fh upwards towards the unloaded resonance frequency as symbolically illustrated in Fig. 2.5. The resonance frequency variation due to the crack fc moves to higher frequency bands de- pending on the size of the crack. The maximum shift when fcn approach fu indicated that the size of the crack is exceeding the overall sensing footprint of the resonator. 13 Figure 2.5: Crack detection in a dielectric material using resonance-based sensors. H Figure 2.6: Crack detection in metallic materials using electrically excited resonance-based planar sensors. • Resonance-Based Sensors for Metallic Material Inspection While far-field microwave-based methods provide the advantage for inspection in harsh environ- ments, near-field sensors are highly sensitive to surface cracks not only in dielectric materials but also in metallic materials with high resolution. Moreover, microwave-based methods are employed not only for inspecting metallic surfaces, but also for inspecting dielectric materials bodies attached to metallic surfaces, such as dielectric coating, paints, and corrosion. Crack detection in metallic material using resonance planar sensor follow similar principle in detecting defects in dielectric materials. However, the shift of the resonance frequency dependence on the scanning type. For example if capacitive sensing is employed, scanning a sample on a highly concentrated electric field area of the planar resonator, the metallic material increases capacitance due to the parallel plate effect introduced by the material. Therefore high reduction in the resonance frequency occurs when a metallic material is placed from fu to fh as illustrated in Fig. 2.6. 14 H Figure 2.7: Crack detection in metallic materials using magnetically excited resonance-based sen- sors. Cracks in the metallic materials shift the resonance frequency downwards due to the increase of both inductance and capacitance due to induced current in surface of the crack and cavities in the metallic material [37]. On the other hand, when the metallic sample is placed on a highly confined magnetic field, a mutual inductance occurs between the metallic plate and the inductance of the resonator that reduced the inductance of the resonator. Consequently, the resonance frequency of the healthy sample shifts to higher frequency bands as illustrated in Fig. 2.7. 15 Chapter 3 Characterization of Conductor-Backed Dielectric Substrates Using a Novel Resonance-Based Method 3.1 Introduction Nondestructive characterization of dielectric substrates is of significant importance in mi- crowave sensing applications and circuit design. Dielectric substrates are generally backed by copper cladding for many purposes, such as grounding, shielding, and packaging. The presence of a conductor backing a dielectric substrate imposes challenges in extracting intrinsic properties of the material [46]. Conductor-backed materials have been mainly character- ized using broad-band characterization methods such as free space, transmission line, and waveg- uides methods [15, 16, 46–53]. Free space methods permits non-contact procedure for character- izing conductor-backed materials using mono-static antenna system and reflection-only analysis methods [15, 47, 48]. Open-ended waveguide methods provide higher accuracy compared to free space methods [13] in material characterization [46, 49, 50] and thickness measurements [50, 51] of conductor-backed materials. Broad-band methods provide wide-band information about the material at the expense of bulky experimental setup and heavy computation involved in the broad-band analysis methods [19, 26]. Compared to broad-band methods, narrow-band methods, such as resonance-based methods, are more accurate and reliable in material characterization [13, 19]. The material characterization principle using planar transmission lines and resonators is based on material perturbation method [38]. The variation in scattering parameters caused by the pertur- bation, such as frequency variations [3, 4, 19, 24–35, 37, 54] and phase variations [36, 55–57], are analyzed for material characterization, microfluidics identification, defects detection, linear and The content of this chapter has been reproduced with permission from F. T. Alharbi, M. Haq, L. Udpa and Y. Deng, “Characterization of Conductor-Backed Dielectric Substrates Using a Novel Resonance-Based Method,” in IEEE Sensors Journal, vol. 22, no. 3, pp. 2099-2109, 1 Feb.1, 2022, doi: 10.1109/JSEN.2021.3135874. 16 angular displacement, among other measurement applications.In frequency variation based meth- ods, the shift of the resonance frequency and the change on the amplitude of the transmission coefficient due to the material perturbation are the main parameters in material characterization. The conductor backing on a thin dielectric material highly affects these two parameters. The presence of a conductor plane in the close vicinity of a planar resonator is considered in thickness measurements of dielectric material backed by metallic plate [58, 59] and in crack detection in conductive medium [37]. The thickness of a specified dielectric material, mimicking paint coating, is measured using double CSRR in [58]. The relative permittivity and the thickness of dielectric material backed by aluminum block are extracted in [59] using dual-mode resonant. The conductor backing causes a high reduction in the resonance frequency and in the trans- mission coefficient rejection level at the resonance frequency [37, 58, 59]. Moreover, complex permittivity characterization techniques for the dielectric material using planar resonator meth- ods require the removal of any conductor backing. In practice, however, circuit board lamination substrates are generally backed by copper cladding; removing the copper sheet is considered as a destructive procedure. In this chapter, a novel nondestructive resonance-based sensing methodology is presented for conductor-backed dielectric material measurements and characterization without removing the conductor-backing plane. In the sensing methodology, the conductor-backed dielectric substrate is connected to the sensing structure and the conductor is utilized as a new ground plane of the reso- nance structure. The resonator is realized using a CSRR etched out on a finite circular conductive patch hosted to the back side of a microstrip line substrate. The original ground plane of the mi- crostrip line is removed except of the circular patch hosting the CSRR. The effect of the conductor backing in permittivity characterization is mitigated using the proposed method. Moreover, the fre- quency shift and the change of the transmission coefficient amplitude exhibit high sensitivity to the material properties. Full-wave simulation-based analysis of the sensing method for characterizing thin conductor-backed dielectric is presented. The sensor was fabricated using inexpensive circuit board technologies, and the proposed sens- 17 ing method was experimentally validated in characterizing widely used conductor-backed dielec- tric substrates of different dielectric proprieties. The proposed sensor operates in the 2.35 to 4.1 GHz frequency band. The experimental results were in agreement with simulated results, and the extracted material properties were with high accuracy compared to the referenced standard values. In addition, the proposed method was compared to the state of the art permittivity characterization methods. The rest of the chapter is organized as follows. Section 3.2 illustrates the effect of the conductor backing on material characterization using planar resonator. The development of the proposed characterization technique is presented in section 3.3 followed by the results and discussion in section 3.4. For validation of the proposed method, experimental setup and results are presented in section 3.5, in addition to comparison with the state of the art characterization methods. The chapter is concluded in section 3.6. 3.2 Conductor Backing Effect The resonance frequency of the quasi-static resonator is typically determined by its equivalent lumped-element circuit model. For instance, a CSRR hosted to the ground plane of a microstrip line is modeled as a parallel LC resonance unit coupled to the capacitance of the main microstrip line [23, 60]. In [60], the resonance frequency of the CSRR hosted to the ground plane of a microstrip line is given by 1 fr0 = p . (3.1) 2π Lc (C + Cc ) The CSRR is perturbed by placing a dielectric material in the close vicinity of the resonator plane. The effect of the dielectric is modeled by a capacitance Cd in parallel to the capacitance of the CSRR resonator, as in Fig. 3.1. Based on the proportionality of capacitance of the dielectric material to its permittivity, the shift in the resonance frequency is significantly controlled by the permittivity of the loaded material under test (MUT). 1 fr = p . (3.2) 2π Lc (C + Cc + Cd ) 18 L/2 L/2 C Lc Cc Cd Figure 3.1: An equivalent Circuit of a CSRR loaded with dielectric material (no conductor back- ing). Figure 3.2: A top view schematic of a single CSRR. 19 The resonance frequency of the CSSR loaded by a dielectric material is presented in (3.2) [19]. The equivalent circuit model presented in Fig. 3.1 considers the case when the symmetric line of the CSRR is orthogonal with respect to the microstrip line. In this orientation, the CSRR is ex- cited by the electric field through capacitive coupling [23]. According to [61], when the symmetric line of the CSRR is not orthogonal with respect to the microstrip line, as in Fig. 3.2, the CSRR will be excited by both electric and magnetic fields through capacitive and inductive coupling, respectively. Consequently, as demonstrated in [57, 61], there will be a phase difference between the reflection coefficients S11 and S22. Due to the reciprocity of the network, the transmission coefficients S21 and S12 are equal [61]. In [57], it was pointed out that while the phase shift be- tween reflection coefficients S11 and S22 is highly affected by the orientation of the CSRR with respect to the microstrip line, the orientation of the CSRR has little effect on the amplitudes of transmission and reflection coefficients. Since in the current work, the measurements are totally based on the amplitude of the transmis- sion coefficient S21, the equivalent circuit could be represented by only the considering the main capacitive coupling. The general equivalent circuit that considers both capacitive and inductive coupling is presented in [61]. The response of a CSRR hosted to the ground plane of a microstrip line is depicted in Fig. 3.3. However, if there is a conductor backing the dielectric substrate, a change in the response is expected. The electric and magnetic field distribution changes to satisfy the new boundary condition imposed by the conductor [37]. Part of oscillating electric field within the resonator vicinity will be vertically coupled to the conductor. The incident electric field is reflected back by the conductor to resonator and to the main ground plane. Consequently, two capacitance are introduced, a capacitance between the resonator and the conductor plane Ccb , and a capacitance between the conductor and the main ground plane Cbg , as shown in Fig. 3.4. Due to the incident of the electric field and the the circulating magnetic field within the resonator vicinity, a surface current density is induced on surface of the conductor. An inductance is consequently induced on the surface of the conductor Lb . Fig. 3.4 presents a quasi- 20 0 Transmission Coefficient S21(dB) -5 -10 -15 -20 -25 -30 -35 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 Frequency (GHz) Figure 3.3: The response of the unloaded CSRR in Fig. 3.2. static lumped-element circuit model of a CSRR in the presence of a conductor [37]. In Fig. 3.4, Cc and Lc represent the capacitance and inductance of the CSRR, respectively. Due the increase of inductance and capacitance, two main effects are expected on the response, a reduction in the resonance frequency, the resonance frequency shifts to lower frequency bands, and a reduction in the transmission coefficient rejection level at the resonance frequency. For comparison with the proposed method in this work, we include the effect of the conductor backing dielectric material characterization using CSRR. A single CSRR with high sensitivity to dielectric properties is used for comparison. It is hosted to the ground plane of a microstrip line with an outer radius of r = 4.2 mm, a slot width of s = 1.2 mm, and a conducting bridge with a width of g = 1 mm. The schematic and the response of the CSRR are shown in Fig. 3.2 and in Fig. 3.3, respectively. For comparison, the same geometry of CSRR were used in the proposed method presented in the next section. A finite dielectric material larger than the resonator size, a rectangular sample with side lengths of 20 to 40 mm and a width of 1 to 3 mm, is typically placed in contact or in the close vicinity of the resonator for perturbation. To show the effect of the conductor backing on permittivity char- 21 L/2 L/2 C Cbg Ccg Lc Cc Cd Lb Figure 3.4: An equivalent circuit of a CSRR loaded with a conductor-backed dielectric material. acterization using a planar resonator, a finite conductor-backed MUT with free space properties, a surface area of 30 mm2 , and a thickness of 1.5 mm is placed in contact with the resonator plane. In Fig. 3.5, the response of the CSRR loaded with a conductor-backed MUT is compared to the response of the CSRR loaded with a MUT without conductor backing. A reduction in the reso- nance frequency and a reduction in S21 rejection level at the resonance frequency are reflected in the response of the CSRR in the case of conductor-backed MUT, as shown in Fig. 3.5. In addition, due to the extra inductance and capacitance introduced by the conductor, shown in Fig. 3.4, an appearance of a second resonance near to the first resonance frequency band is observed in Fig. 3.5. For further illustration of the effect of the conductor backing on a CSRR when it is loaded with conductor-backed materials of high permittivity, two materials of relative permittivity ϵr = 2 and ϵr = 6 were analyzed with and without conductor backing. To reduce the effect of the finite MUT size, the conductor-backed material occupies the full space underneath the resonance structure with a width of 1.5 mm. The response in Fig. 3.6 shows a reduction in the resonance frequency and a reduction in the 22 0 Transmission Coefficient S21(dB) -5 -10 MUT without conductor backing MUT with conductor backing -15 -20 -25 -30 -35 2 2.5 3 3.5 4 4.5 5 5.5 6 Frequency (GHz) Figure 3.5: The response of the CSRR loaded with dielectric material with and without conductor backing. S21 rejection level at the resonance frequency. In addition, the effect of the conductor backing on permittivity characterization is shown using a CSRR of different geometry and size. A double square CSRR, operating at 4.4 GHz, is similarly loaded with conductor-backed dielectrics with relative permittivity ϵr = 2 and ϵr = 6. The double CSRR has an outer side length of l = 4.5 mm, slots width of s = 0.2 mm, conducting bridge gaps of g = 0.2 mm, and a separation distance between the two rings of d = 0.2 mm, shown in Fig. 3.7a. The response is presented in Fig. 3.7b; it also shows reductions in the resonance frequency and in the S21 rejection level at the resonance frequency. The comparisons between single and double CSRR and the orientation of the CSRR are dis- cussed in [33], and the comparisons between square and circular CSRR are presented in [27]. The reduction in the resonance frequency as well as the reduction in the S21 rejection amplitude due to a conductor in the close vicinity of a planar resonator are also shown in [37, 58, 59]. In Fig. 3.6 and Fig. 3.7b, the reduction in the S21 rejection level is more significant as the permittivity of the MUT, located in the capacitance area between the ground and the conductor 23 0 Transmission Coefficient S21 (dB) -5 -10 Dielectic of 'r=2 -15 CB-Dielectic of 'r=2 -20 Dielectic of 'r=6 CB-Dielectic of 'r=6 -25 -30 -35 -40 1 2 3 4 5 6 Frequency (GHz) Figure 3.6: The response of the CSRR loaded with dielectric materials (Dielectric) and conductor- backed dielectric materials (CB-Dielectric) of different permittivity values. backing planes, increases due to the high dielectric losses. The extraction of the loss tangent of dielectric substrate is achieved by monitoring transmission coefficient amplitude the quality factor changes due to the change of the dielectric loss of the material. However, for materials of high permittivity the transmission coefficients are predominantly affected by the conductor backing. The resonance frequency is also affected by the thickness of the MUT. A higher reduction in the resonance frequency and in the S21 rejection level are expected as the thickness of the MUT decreases [59]. In this study, the thickness of the MUT is fixed to 1.5 mm, a typical thickness of circuit board lamination. 3.3 Sensing Methodology The proposed method for characterizing conductor-backed material integrates the material and the conductor into the resonance structure by employing the conductor as a new ground plane. The ground plane of the transmission line was removed except for a circular conductive patch hosting a CSRR. The circular patch was centered under the main substrate of the transmission line with a radius of r0 = 5.1 mm. Within the circular patch, a CSRR was etched out with an outer radius of 24 (a) 0 Transmission Coefficient S21 (dB) -5 Dielectic of 'r=2 -10 CB-Dielectic of 'r=2 -15 Dielectic of 'r=6 CB-Dielectic of 'r=6 -20 -25 -30 -35 1 2 3 4 5 6 Frequency (GHz) (b) Figure 3.7: Double CSRR(a) A top view of the layout of the sensor (b) The response of a double CSRR loaded with dielectric materials (Dielectric) and conductor-backed dielectric materials (CB- Dielectric) of different permittivity values. 25 r1 = 4.2 mm, a slot width of s = 1.2 mm, and a conducting bridge with a width of g = 1 mm, as illustrated in Fig. 3.9a. The metal part surrounding the CSRR provides a path for the circulating current and connects to the inner metal part of CSRR. A schematic diagram of the proposed sensing methodology is shown in Fig. 3.9b. The resonance frequency of the the CSRR could be controlled by the adjusting the dimensions of the design. For instance, decreasing the radius of the CSRR r1 , from 5 to 3 mm, moves the resonance frequency to higher frequency bands, from 3.55 to 5.6 GHz. However, the normalized sensitivity to the dielectric properties of conductor-backed material at various CSRR radius values is almost negligible as shown in Fig. 3.8a. Increasing the slot width of the CSRR s shifts the resonance frequency to slightly higher bands; however, as shown in Fig. 3.8b the normalized sensitivity to the dielectric properties of the conductor-backed material using CSRR with different slot widths is also negligible. This conclusion is also reflected by changing radius of the circular patch r0 and the conducting bridge g, as illustrated in Fig. 3.8. A desired resonance frequency is attainable by adjusting the design dimensions while consid- ering the constraints of the available manufacturing method. The above parameters were chosen for the sensor to operate around 4.2 GHz. It is worth noting that, while in this work the resonator is realized using a single CSRR for characterizing conductor-backed dielectric materials, resonators of different shapes, orientation, and size, hosted to the finite conductive patch on the backside of the substrate of microstrip line, could be used for characterization and measurement of conductor- backed material by applying the proposed sensing methodology. The Rogers RO4003 substrate is used in the sensor fabrication. It has a thickness of 0.813 mm with a relative permittivity of ϵr = 3.55 and a loss tangent of tan δ = 0.0027. The width of the microstrip transmission line was 1.78 mm for a characteristic impedance of 50 Ω of the sensor. In the development of the sensor design, two configurations of the sensing method for char- acterizing conductor-backed materials are considered, namely perturbation and full integration methods. In perturbation method of the planar resonator, the dielectric side of the conductor-backed 26 10 10 s=0.6mm R1=3.8mm 9 9 s=0.8mm R1=4.0mm s=1mm R1=4.2mm s=1.2mm 8 R1=4.4mm 8 s=1.4mm R1=4.6mm Relative Permitivity 'r Relative Permitivity 'r s=1.6mm 7 7 6 6 5 5 4 4 3 3 2 2 1 1 0.5 0.6 0.7 0.8 0.9 1 0.5 0.6 0.7 0.8 0.9 1 Normalized Resonance Frequency Shift(GHz) frn Normalized Resonance Frequency Shift(GHz) frn (a) (b) 10 10 g=0.4mm R0=4.7mm 9 g=0.6mm 9 R0=4.9mm g=0.8mm R0=5.1mm g=1mm R0=5.3mm 8 g=1.2mm 8 R0=5.5mm Relative Permitivity 'r Relative Permitivity 'r 7 7 6 6 5 5 4 4 3 3 2 2 1 1 0.5 0.6 0.7 0.8 0.9 1 0.5 0.6 0.7 0.8 0.9 1 Normalized Resonance Frequency Shift(GHz) frn Normalized Resonance Frequency Shift(GHz) frn (c) (d) Figure 3.8: The sensitivity of the normalized resonance frequency due to the change of following design parameters (a) CSRR radius r1 (b) CSRR slot width s (c) conducting bridge with a width of g (d) circular patch radius r0 . 27 Resonator on ground plane s 𝑟0 Microstrip line g 𝑟1 Ground plane (a) (b) Figure 3.9: A schematic of the proposed sensing methodology (a) A top view of the layout of sensor (b) A side view of the sensing methodology for conductor-backed material measurements. 28 material is placed in contact with the resonator plane. The MUT surface area is larger than the resonator surface area; however, it does not occupy the full space below the main substrate and the conductor is not connected to the current return path. The MUT has a surface area of 30 mm2 with a thickness of 1.5 mm. The response of this configuration is depicted in Fig. 3.10 and is compared to the response of the CSRR loaded with a conductor-backed material. The effect of the conductor was alleviated and the shape of the response became similar to the response of unloaded CSRR shown in Fig. 3.3. However, this configuration resulted in high losses due to the discontinuity of the ground plane. 0 Transmission Coefficient S21(dB) -5 -10 CSRR -15 Perturbation of proposed senesor -20 -25 -30 2 2.5 3 3.5 4 4.5 5 5.5 6 Frequency (GHz) Figure 3.10: The response of the CSSR compared to the perturbation method of the proposed sensor when loaded with a conductor-backed material. The proposed sensing methodology considers the full integration method of the conductor- backed material with the resonance structure as shown in Fig. 3.9. The conductor side of the conductor-backed material is connected to the current return path of the resonator circuit, and the dielectric side of the MUT is placed in contact with the resonator plane. The conductor-backed sample occupies the full space below the main substrate, as shown in Fig. 3.9b. The equivalent circuit model of the full integration is presented in Fig. 3.12. Compared to the 29 equivalent circuit of the CSRR loaded with conductor-backed dielectric in Fig. 3.4, the capacitance Cbg and inductance Lb are eliminated by the full integration method, as presented in Fig. 3.12. The capacitance introduced between the resonator and the conductor, in Fig. 3.12, Ccg can be modeled in parallel with the capacitance of the dielectric material Cd . The resonance frequency using the full integration of the conductor-backed material with the proposed sensor is presented by (3.3). 1 fr = p (3.3) 2π Lc (C + Cc + Cd + Ccg ) 0 Transmission Coefficient S21(dB) -5 -10 -15 CSRR Perturbation of proposed senesor Full integration of proposed senesor -20 -25 -30 2 2.5 3 3.5 4 4.5 5 5.5 6 Frequency (GHz) Figure 3.11: The response of the CSSR compared to the perturbation method and full integration method of the proposed sensor when loaded with a conductor-backed material. The response of the full integration is depicted in Fig. 3.11. The figure also compares the responses of the full integration and the perturbation methods of the proposed sensor to the re- sponse of the CSRR loaded with conductor-backed material. In the comparison in Fig. 3.11, a conductor-backed material with free space properties is considered to represent unloaded condi- tions while considering the presence of the conductor backing plane at distance of 1.5 from the resonator plane. The full integration of the proposed sensor significantly minimized the losses compared to the 30 perturbation method of the proposed sensor and to the CSRR in the presence a conductor-backed material, as shown in Fig. 3.11. L/2 L/2 C Ccg Lc Cc Cd Figure 3.12: An equivalent circuit model of the proposed full integration method of the proposed sensor with a conductor-backed material. 3.4 Results and Discussion The proposed methods were simulated in full electromagnetic wave mode using ANSYS high- frequency structure simulator HFSS software. Dielectric materials of relative permittivity ranging from ϵr = 2 to ϵr = 10 backed by conductor were simulated, and the results are shown in Fig. 3.13. In the simulation of the full integration method of the proposed sensor, the conductor-backed dielectric materials are of the same surface area as the main substrate of the microstrip line with a thickness of 1.5 mm. The resonance frequency significantly decreases inversely proportional to the permittivity of the dielectric material. In Fig. 3.13, it is noticeable that the effect of the conductor backing is mitigated, and the transmission coefficients at the resonance frequencies are not highly affected by the conductor. Moreover, the S21 for all cases are identical, and there is no appearance of a second resonance near to the first resonance frequency band even for high permittivity cases. In Fig. 3.13, the thickness of the conductor-backed materials is fixed to 1.5 mm. Importantly, 31 0 ' r =1 Transmission Coefficient S21(dB) ' -5 r =2 ' r =3 ' -10 r =4 ' r =5 -15 ' r =6 ' r =7 -20 ' r =8 ' r =9 -25 ' r =10 -30 1.5 2 2.5 3 3.5 4 4.5 Frequency (GHz) Figure 3.13: The response of the proposed full integration method for conductor-backed dielectric materials with different relative permittivity values. 4.5 Simulation Results T=0.5mm 4 Fitted Curve T=0.5mm Simulation Results T=1mm 3.5 Fitted Results T=1mm Simulation Results T=1.5mm -2 (GHz)-2 3 Fitted curve T=1.5mm frn Simulation Results T=2mm 2.5 Fitted curve T=2mm 2 1.5 1 0.5 1 2 3 4 5 6 7 8 9 10 ' Relative Permitivity r −2 . Figure 3.14: The impact of different thickness values of conductor-backed materials on frn 32 the shift of the resonance frequency is also influenced by the thickness of the conductor-backed material. Fig. 3.14 illustrates how the thickness of the conductor-backed material influence the relationship between the change on the resonance frequency and the permittivity of the conductor- backed material. According to [19, 24], and based on the relationship presented in Fig. 3.14, the inverse of the squared normalized resonance frequency is linearly proportional to the change of the relative permittivity of the dielectric material. The thickness of the dielectric material could be extracted from this linear relationship [24]. A general function that considers the permittivity and the thickness of the conductor-backed material is stated in (3.5). The fitted curves plotted in Fig 3.14 are generated using the numerical model presented in (3.5). −2 = (0.9318 + t−0.7114 )(0.135ϵ′ − 0.104) + 0.9318 frn (3.4) d r −2 ∝ C frn (3.5) d fr The normalized resonance frequency is frn = ; where fr0 is unloaded resonance frequency. f r0 10 Simulation Results Ag2=0 m Fitted Curve Ag2=0 m ' 8 Simulation Results Ag2=20 m r Fitted Curve Ag2=20 m Relative Permitivity 6 Simulation Results Ag2=35 m Fitted Curve Ag2=35 m 4 2 0 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 Normalized Resonance Frequency Shift(GHz) frn Figure 3.15: Air gap effect on the resonance frequency; Ag1 = 35µm is considered in all cases. 33 The air gap between the MUT and resonator reduces the coupling between the fields and the material under test and causes a direct impact on the permittivity characterization. The space be- tween the resonator plane and the conductor backing plane is occupied by three layers of materials, two layers of air gap with free space properties and a layer of the dielectric material. The first layer of air gap is a uniform layer around the resonator in the place of the removed copper. The thickness of the first air gap layer equals to the thickness of the copper cladding, Ag1 = 35µm. The second layer of air gap is a nonuniform air gap layer Ag2 on top of the resonator and on top of the first air gap layer due to the expected experimental setup. However it can be modeled as a uniform layer and the thickness of the air gap layer could be determined [25]. Although in practice the air gap is nonuniform, considering the thickness of air gap in the analysis minimizes the error in material characterization. In this work the first air gap is fixed to Ag1 = 35µm, and the second air gap layer is approximately assumed less than the first air gap Ag1 . Three values of the second air gap layer Ag2 were considered to show the air gap influence on the normalized resonance frequency shift. Fig. 3.15 shows the change on the normalized resonance frequency due to the change of the dielectric permittivity of the MUT considering different cases of the second air gap layer. In the analysis, the first layer of air gap, Ag1 = 35µm, is included in all cases. For a conductor-backed material with specified thickness and expected air gap, as shown in Fig. 3.15, the real permittivity can be expressed in terms of the normalized resonance frequency using third order polynomial fitting function (3.6) [19]. The effect of both real part of the relative permittivity and the dielectric loss on the resonance frequency are considered in the analysis. The frequency shift is not highly sensitive to the dielectric loss tangent. However, to account for small variations, the simulated data in Fig. 3.15 were averages of multiple loss tangent conditions, ranging from tanδ=0 to 0.01 with a step of 0.001, for each relative permittivity point. The fitted curves in Fig. 3.15 are generated using third order polynomial functions. The polynomial function of the first case, Ag1 = 35µm and Ag2 = 0µm, is given by 34 ′ 3 + 220.65f 2 − 221.72f + 79.29. ϵr = −77.24frn rn rn (3.6) ′ ωWe ϵr Qd = = ′′ = (tanδ)−1 (3.7) Pd ϵr The sensitivity of relative-based planar resonants Sr for permittivity measures the of change of resonance frequency variation with respect to the change of the material properties (3.8) [32]. The sensitive of the proposed sensor to the permittivity is shown in Fig. 3.18. ∆frn Sr = (3.8) ∆ϵr In a perfect dielectric medium, the quality factor due to dielectric losses, Qd , is stated in (3.7) [13]. In this expression, We is the average electric energy stored in the medium, Pd is the average power dissipated, ω is the resonance frequency. The loss tangent of the dielectric material can be extracted from the inverse of the quality factor. −IL Ql = Qu (1 − 10 20 ) (3.9) The loaded quality factor Ql is given by (3.9) [27, 62]; where IL is the insertion loss in (dB) at the resonance of the loaded case, and Qu is the quality factor under unloaded condition. Qn−1 = E(ϵ′ ) tan δ + C (3.10) r As the loss tangent increases the inverse of the quality factor follows a linear trajectory as Q stated in (3.10); where Qn is the normalized quality factor, Qn = Q l . The slope of the linear u relationship in (3.10) is dependent of the real part of the relative permittivity. The dielectric loss tangent can be extracted using (3.11). Furthermore, the slope of the linear function could be expressed as linear function of the real part of the relative permittivity, as stated in (3.12) for ′ E(ϵr ). 35 Q−1 n −C tan δ = ′ (3.11) E(ϵr ) ′ ′ E(ϵr ) = 2.860ϵr − 0.636 (3.12) A linear fitting tool is used to fit the change of Q−1n due to the change of the dielectric loss tangent from tanδ=0 to 0.01 in a step of 0.001. The corresponding fitted linear curve of each case ′ of ϵr compared to the simulated data are depicted in Fig. 3.16. Although, the quality factor is influenced by other losses, such as conductor losses and the air gap between the resonator and the material, the linear proportionality between the inverse of the quality factor and the loss tangent is still obtained. ′ Table 3.1: Linear coefficients of equation (3.10) for extracted ϵr . ′ ϵr 1 2.2 3 6.15 10.2 E(ϵr ) 2.186 5.272 7.863 17.511 28.048 C 1.048 1.054 1.059 1.0932 1.143 The sensitivity of resonance-based planar sensor S measures the resonance frequency variation due to the change of the material properties (3.13) [32, 63]. The sensitive of the proposed sensor as a function of the permittivity variation is shown in Fig. 3.18. ∆frn S= (3.13) ∆ϵr 3.5 Experimental Validation and Discussion The proposed sensor was fabricated using printed circuit board technologies as shown in Fig. 3.17. For validation of the proposed method, the sensor was tested in the laboratory for char- acterizing conductor-backed dielectric materials. The experiment setup is shown in Fig. 3.19. The samples tested in this study comprise wide range of dielectric properties such, Rogers RT ′ ′ ′ 58850, RO3003, RO3006, and RO3010 with relative permittivity ϵr = 2.2, ϵr = 3, ϵr = 6.15, ′ and ϵr = 10.2, respectively [64, 65]. These substrates are widely used in printed boards design 36 1.45 ' ' ' Simulation results r=1 Simulation results r=5 Simulation results r=9 1.4 Simulation results ' =2 Simulation results ' =6 Simulation results ' =10 r r r ' ' Simulation results =3 Simulation results =7 Corresponding fitted line r r 1.35 ' ' Simulation results r =4 Simulation results r =8 1.3 Normalized Q-1 1.25 n 1.2 1.15 1.1 1.05 1 0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01 Permittivity loss tangent tan Figure 3.16: Dielectric loss tangent as a function of the normalized quality factor and the real part of the relative permittivity. (a) (b) Figure 3.17: Fabricated Sensor (a) Top view, transmission line plane (b) Bottom view, resonator plane. 37 400 350 Sensitivity (MHz) 300 250 200 150 0 2 4 6 8 10 ' r -1 Figure 3.18: Sensitivity of the sensor to the permittivity of conductor-backed materials. technologies for microwave and RF circuits and antenna designs. The tested materials are available with two copper cladding on both sides. One side of the copper cladding is removed while the other copper cladding is the conductor backing side of the dielectric material. The conductor side of conductor-backed material is attached to the SMA con- nector via a conductor tape. In addition, a thin copper sheet with a thickness of 17µm is attached on the top of the conductor side of the MUT and on top of the ground side of SMA connectors. The MUT is easily replaced by removing the thin conductor sheet and the MUT. The scattering parameters of the two port system is measured using a vector network analyzer, as shown in Fig. 3.19. The air gap, as discussed in section.3.4, has two layers, Ag1 and Ag2 . The first air gap layer around the resonator equal to the the thickness of copper cladding Ag1 = 35µm. The second air gap layer, above the resonator plane, is Ag2 = 15µm. The total air gap considered in the simulation is Ag = 50µm, and the results under this condition are depicted in Fig. 3.20. Although 38 Figure 3.19: Experimental setup; the full integration method of the proposed sensor connected to the VNA with a MUT without holders. 0 Transmission Coefficient S21 (dB) -5 Simulated No MUT Measured No MUT -10 Simulated TR5880 Measured TR5880 Simulated RO3003 Measured RO3003 -15 Simulated RO3006 Measured RO3006 -20 -25 -30 1.5 2 2.5 3 3.5 4 4.5 Frequency (GHz) Figure 3.20: A comparison between measured and predicted simulated S21 of different materials (without holders,air gap Ag1 = 35µm and Ag2 = 15µm). 39 it resulted in acceptable results for conductor-backed materials with low permittivity, MUT with high permittivity, such as ϵr = 10.2, were highly affected by the error due the air gap. (a) (b) Figure 3.21: (a) Conductor-backed sample and resonator plane (b) Conductor-backed sample inte- grated with the resonance structure using holders. Alternatively, the second layer of the air gap can be experimentally minimized. To minimize the air gap in the resonance structure, the conductor-backed material and the thin conductor sheet were held at the resonance structure using 3M lightweight holders on the sides. The experimental measurements are compared to the predicted results, with zero air gap in the second layer Ag2 = 0µm while considering the first layer of the air gap with Ag = Ag1 = 35µm, are shown in Fig. 3.22. A good agreement between the simulation predicted and the experimentally measured results were obtained as depicted in Fig. 3.22. The resonance frequencies of the measured compared to the simulated data are presented in Table 3.2. In measuring the reference case, air in Table 3.2, a conductor sheet is placed at a distance equals to the thickness of the dielectric material, 1.5 mm. The SMA connectors were considered in the simulation results presented in Fig. 3.20 and Fig. 3.22 for more practical comparisons with experimental measurements. The complex permittivity parameters of tested samples are extracted based on the measured transmission coefficients depicted in Fig. 3.22. The real part of the relative permittivity is deter- mined using the measured resonance frequency and the numerical fitted model in (3.6). Using the 40 0 Transmission Coefficient S21 (dB) -5 Simulated No MUT Measured No MUT Simulated RT5880 -10 Measured RT5880 Simulated RO3003 Measured RO3003 -15 Simulated RO3006 Measured RO3006 Simulated RO3010 -20 Measured RO3010 -25 -30 1 1.5 2 2.5 3 3.5 4 4.5 Frequency (GHz) Figure 3.22: A comparison between measured and predicted S21 of different materials (with hold- ers, air gap Ag1 = 35µm and Ag2 = 0µm). Table 3.2: Comparison between simulated and measured resonance frequencies data. ′ Resonance fr Normalized Resonance frn Sample (ϵr ) Simulated Measured Simulated Measured Air (1) 4.1080 4.0641 1 1 RT/duroid 5880 (2.2) 3.676 3.624 0.8948 0.8917 RO 3003 (3) 3.446 3.394 0.8315 0.8389 RO 3006 (6.15) 2.822 2.792 0.6865 0.6870 RO 3010 (10.2) 2.358 2.320 0.5740 0.5708 41 quality factor obtained in (3.9) and the resonance frequency, the dielectric loss tangent is calcu- lated using the linear model in (3.11). The coefficients of (3.10) are obtained from the linear fitted curves presented in Fig. 3.16. For the extracted real permittivity values, the coefficients of the linear functions of (3.10) are provided in Table 3.1. The dielectric properties of the characterized conductor-backed materials are tabulated in Table 3.3 and compared to referenced standard values. Table 3.3: Permittivity characterization of conductor-backed material results and comparison with referenced standard values (R=Reference, M=Measured,e=%Error). ′ ′ Sample R ϵr M ϵr (e) R tan δ M tan δ Duroid 5880 2.2 [65] 2.26(2.72) 0.0004 [65] 0.00049 RO 3003 3.0 [64] 3.02(0.67) 0.001 [64] 0.00130 RO 3006 6.15 [64] 6.06(1.46) 0.002 [64] 0.00199 RO 3010 10.2 [64] 10.25(0.49) 0.0022 [64] 0.00353 For comparison with the state of the art permittivity characterization methods using planar resonators, Table 3.4 presents a comparison in determining the real part of the relative permittivity of dielectric material. To compared with the state of the art methods in Table 3.4, the sensitivity was normalized to the operating frequency and calculated as the percentage of the frequency shift exhibited by the sensor from the unloaded resonance frequency fr0 to the resonance frequency fr −fr10 caused by a MUT of a relative permittivity of ϵr = 10; Srn = 0 × 100%. The sensitivity f r0 of the proposed method is 42%. The maximum error in measuring the real part of the relative permittivity was 2.72%. Although dielectric losses reported in Table 3.3 reflect slightly high measurement errors com- pared to standard values, the results are within justifiable tolerance for the measurements of the dielectric losses. The high error in the loss tangent measurement is mainly caused by the unavoid- able air gap in integrating the conductor-backed sample with the resonance structure. For better accuracy in extracting the loss tangent, a test fixture tool is suggested, instead of the lightweight holders, to tighten the sample to the resonance structure. 42 Table 3.4: Comparison with the state of the art methods using planar resonator for dielectric per- mittivity characterizing. ′ Ref Technology fr0 (GHz) Sensitivity Srn % Max E% in ϵr Material Integrated [19] Double CSRR 1.286 37.8% - Dielectric N.A [24] Double CSRR 2.8 35.7% 7.6% Dielectric N.A [26] Single-Compound CSRR fr l =1.26,fr h =3.2 - 4.63% Dielectric N.A 0 0 [26] Single-Compound CSRR fr l =1.816,fr h =4.639 - 6.48% Dual-layer Dielectric N.A 0 0 [27] Double CSRR 2.7 37.03% 3% Dielectric A [33] Single CSRR 10.9 50% - Dielectri N.A [59] Dual-mode LC resonator fr ,l ≈ 1.65,fr ,h ≈ 2.45 - 4.8% Conductor-Backed Dielectric No 0 0 T.W. Single CSRR 4.1 42.65% 2.72% Conductor-Backed Dielectric Yes 3.6 Conclusion This chapter presented a nondestructive resonance-based method for extracting complex per- mittivity of thin conductor-backed material without removing the conductor backing. The proposed method was numerically and experimentally validated. The method was sensitive to the air gap in the resonance structure. Two techniques were considered to alleviate the error associated with air gap by including two layers of air gap in the analysis and by minimizing the air gap experimen- tally using lightweight holders while considering a single layer of air gap. The latter showed good agreement between predicted and measured results. The proposed method framed a nondestruc- tive technique, through integrating the conductor-backed material with the planar resonator for complex permittivity characterization, that could be further applied for different conductor-backed material measurement applications. 43 Chapter 4 Characterization of Magneto-dielectric Material Using A Single Stepped Impedance Resonator 4.1 Introduction Over the last decades, the majority of research effort in material characterization has been de- voted to characterizing dielectric materials and in particular extracting electric permittivity. That is mainly because most of RF and microwave circuits use nonmagnetic dielectric substrates. How- ever, with the emergence of composite magneto-dielectric materials for circuit design miniatur- ization [66, 67], there is an increasing need for characterization methods that have the advantages of planar resonators and the capability of determining the magnetic permeability as well as elec- tric permittivity. Magneto-dielectric materials have also been widely used in radar absorption and electromagnetic signal suppression. The sensing principle used in the resonance-based sensors is predicated on material perturbation theory, briefly explained in the next section. It relates the change in the resonance frequency of the sensor to the change in both intrinsic properties, electric permittivity and magnetic permeability, with equal wights. Attributing the change in resonance frequency to either of the intrinsic properties is not straightforward in characterizing materials that possess high electric permittivity and magnetic permeability [34, 68–70]. An effective method to overcome this challenge using planar resonators is using fields-confinement approach introduced in [34] for magneto-dielectric characterization. The approach intensifies elec- tric and magnetic fields at spatially separated sensing areas over a CSRR [34]. A modified CSRR was proposed to confine electric and magnetic fields at spatially separated sensing areas and lo- calized over a CSRR resonator. The authors of [70] suggested an improvement for the CSSR proposed in [34] to increase the sensing areas and to enhance sensitivity by using dual polarization The content of this chapter has been reproduced with permission from F. T. Alharbi, M. Haq, L. Udpa and Y. Deng, “Magnetodielectric Material Characterization Using Stepped Impedance Resonators”, accepted for publication in IEEE Sensors Journal, 2022. 44 excitation for the CSSR. However, achieving higher sensitivity using CSSR requires operating at higher resonance frequency [33]. Operating at higher frequency using CSSR requires a reduc- tion of the overall size of the CSRR resonator to shift the unloaded resonance frequency to higher frequency bands. Consequently, however, smaller spatially sensing areas could be localized for magneto-dielectric sensing as the over all size of resonator decreases. In this chapter, a new resonance-based method with widely spatially separated sensing areas is presented for dielectric and magneto-dielectric material characterization. The principle of field- confinement in [34] is realized in this work using a single stepped impedance resonator (SSIR). SIRs are semi-lumped resonators that have initially been used for microwave filters [38], permit- tivity characterization [63,71–75], and recently in fluid sensing [76,77] and defects detection [78]. This work introduces SIR for dielectric and magneto-dielectric characterization using the fields- confinement and intensification approach. The resonator splits the top plane of the resonance structure to two spatially separated sensing areas; each sensing area is highly sensitive to one of the intrinsic electromagnetic properties, electric permittivity and magnetic permeability, of the ma- terial. Using SSIR, the electric and magnetic fields are widely separated and highly intensified at the opposite edges of the resonator, which consequently provides larger sensing areas with high sensitivity to the electromagnetic properties. Compared to the available resonance-based planar sensors for magneto-dielectric characteri- zation, the proposed methods provides the following main advantages. The electric and magnetic fields are widely separated and highly intensified at the opposite edges of the resonator. Conse- quently, providing larger sensing areas that permits measuring the permittivity and permeability of large as well as small samples. Equally significant, the proposed method exhibits high sensi- tivity to both intrinsic electromagnetic proprieties. Numerical and experimental validations of the presented method are provided. The rest of the chapter is organized as follows. Section 4.2 introduces the concept of confining electric and magnetic fields and discusses the effect of magneto-dielectric materials on the material perturbation. The development of the proposed sensor is illustrated in 4.3 followed by the results 45 characterizing magneto-dielectric materials in 4.4. For validation of the proposed method, experi- mental step up and experimental results compared with simulation results are presented in section 4.5. The chapter is concluded in section 4.6. 4.2 Perturbation Effect of Magneto-dielectric Materials The resonance frequency of the the structure is directly dependent on the net permittivity and permeability of the resonator structure [38]. Revisiting the material perturbation equation, when the resonance structure is perturbed by a material with high electric permittivity and magnetic permeability, the change of frequency of the structure due to the perturbation as presented in (4.1) [38]. R fr (∆ϵE · E 0 + ∆µH 1 · H 0 ) dv = v R 1  (4.1) ∆fr ϵ |E |2 + µ |H |2 v 0 0 0 0 In magneto-dielectric materials, electric permittivity and magnetic permittivity have equal ef- fect on the resonance frequency which poses challenges in the material characterization. The shift in the resonance frequency due to a perturbation is dependent equally on change of permittivity and permeability stated in (4.1). However, if there is a region in the resonator wherein the intensity of the magnetic field H 0 of the resonator, before the perturbation occurs, is much higher than the electric field E 0 , or the electric field intensity concentration in that area is negligibly small com- pared to the magnetic field, then the shift of resonance frequency ∆fr at this region, due to the material perturbation, is attributed to the change of the magnetic permeability ∆µ [34]. Thus, the change of the permittivity ∆ϵ in this region has negligible effect on the resonance frequency since E 0 is negligibly small. Similarly, in a region wherein the intensity of the electric field before loading E 0 is more domi- nant than the magnetic field, the change in the resonance frequency due to the loading perturbation is correlated to the permittivity change ∆ϵ. In the [34] the authors applied this concept of field confinement and intensification by using special configuration of CSRR to intensify the electric and magnetic fields on spatially separated sensing areas over the CSRR. In this work, the SIR is proposed to confine and intensify electric and magnetic fields at widely spatially separated sensing 46 areas of the resonance structure. The configuration of the proposed method is illustrated in the following section. 4.3 Sensor Design The objective of the design is to intensify and confine the electric and magnetic fields at two spatially separated areas of the resonance structure. Using lumped elements at low frequency reg- imen, electric and magnetic fields are confined and stored at the capacitor and inductors, respec- tively. In microwave regime, however, electric and magnetic fields are stored within the resonator structure and highly overlapped. Thus it is challenging to distinguish which parts of the resonator act like a inductive or capacitive elements. To overcome this difficulty, a semi-lumped elements SIR is proposed. In SIR, inductors are realized by high impedance lines and capacitor are realized by low impedance lines. The SIR is hosted as shunt element to the main transmission line Fig. 4.1. Within the the shunt element(SIR), an inductive element is realized by the thin line L (high impedance line) in series with a capacitive element realized by a rectangular patch S (low impedance line). The thin line L extending from the main transmission line to the patch provides a narrow path of the current which promotes the curling magnetic field around the thin line. Intensifying the current following from the main transmission line to the patch through the thin line results in highly confined magnetic field around the thin line (inductive element) as illustrated in Fig. 4.2b. This confinement of the magnetic field creates the permeability sensing area, area AH . Consequently, the frequency shift and the quality factor variation the sensor exhibit when a magneto-dielectric element is loaded on AH are primarily caused by the change of the magnetic permeability of the sample compared to the unloaded case. 47 Figure 4.1: A diagram of the proposed SIR with a patch width of s =4mm, linked to the main transmission line via a ,n =0.4mm, thin line with a length of m = 8mm. The thin line (high impedance) is connected to a patch with a width of S to enhance the ca- pacitance of the resonator over a wider area at the shunt resonator. Consequently, the electric field is intensified and highly confined at the edges of the rectangular patch. Fig. 4.2a. When a magneto-dielectric sample is placed on sensing area AE of the resonator, the shift of the reso- nance frequency and the transmission loss are affected primarily by the permittivity perturbation. The proposed planar resonator is hosted on the top of microstrip transmission line. The Rogers RO4003 substrate is used for the design. It has a thickness of 0.813 mm with a relative permittivity of ϵr = 3.55 and a loss tangent of tan δ = 0.0027. The width of the microstrip transmission line is 1.8 mm for a characteristic impedance of 50 Ω of the sensor. The dimensions of design play a rule in determining the resonance frequency. For instance, de- creasing the length of the thin line moves the resonance frequency to higher bands, whereas patch side lowers the resonance frequency. A desired resonance frequency is attainable by adjusting the design dimensions. A resonance frequency of 2.308 GHz is chosen in this design; the correspond- ing dimensions are depicted in Fig. 4.1. Proposed SSIR sensor is depicted in Fig. ?? with a patch width of S =4mm and linked to the main transmission line line via a m =0.4mm thin line and length of a m = 8mm. In Fig. 4.2a the electric field intensity at the resonance frequency shown with blue dark spot corresponds to E =0 KV/m while the dark red corresponds E =789 KV/m, which forms (area AE ) permittivity sensing area. Magnetic field intensity in Fig. 4.2b at the resonance frequency 48 (a) (b) Figure 4.2: Confined (a) electric field and (b) magnetic field on the SSIR at resonance, with labels on AE and AH sensing areas. 49 with he dark blue spot corresponds to H =0 A/m and the dark red represented H =82 A/m, which forms (area AH ) permeability sensing area. 1 fr = √ (4.2) 2π Cr Lr If the ratio of the high impedance to the low impedance is high and the length of both lines are electrically short, the overall capacitance of the SIR, Cr , is approximated by the capacitance of the low impedance line [38, 63]. The overall inductance of the SIR, Lr , is also approximated by the inductance of the high impedance line. The SSIR could be modeled with a shunt element to main transmission line as in Fig. 4.3 [63]. The resonance frequency can easily be controlled by the dimensions of the two sections of the SSIR. Decreasing the length of high impedance line decreases the inductance of the line and moves the resonance frequency to higher bands, whereas increasing the patch side increases the capacitance and lowers the resonance frequency. The dimensions of the SSIR were optimized to facilitate two widely spatially separated sens- ing, to operate around 2.4 GHz, and to meet the physical constraints on the resonator size as well as the available fabrication tolerance. The SSIR dimensions are illustrated in Fig. 4.1. The capacitance and inductance of the SIR circuit model are initially calculated using closed form ap- proximation equations of the SIR [38, 63]. Then, the values are optimized using Keysight ADS optimization solver to minimize the error between the S-parameters obtained from the electromag- netic simulation using HFSS compared to the S-parameters calculated using the lossless circuit model simulation in ADS [37, 63]. The extracted values of the equivalent circuit parameters are indicated in Fig. 4.4. 4.4 Results and Discussion The proposed method is simulated using full electromagnetic wave simulations software, high frequency structure simulator (HFSS). The material characterization technique in this work is car- ried out by measuring the material at the two spatially separated sensing. At area AE , the electric field is confined with noticeably no influence of the magnetic field. On the other hand, the mag- 50 L/2 L/2 Lr C Cr Figure 4.3: Equivalent circuit of the sing SIR. 0 Transmission Coefficient (dB) -10 -20 HFSS Simulation Circuit Model Simulation -30 -40 -50 -60 1.8 2 2.2 2.4 2.6 2.8 Frequency (GHz) Figure 4.4: Sensor response of unloaded SSIR using HFSS simulation and circuit analysis with L = 1.78 nH, C = 0.803 pF, Lr = 4.45 nH, and Cr = 1.07 pF. 51 netic field is highly confined at area AH with negligible influence of the electric field on AH . The materials under test (MUT) are simulated and measured on the two indicated sensing areas for different permittivity and permeability conditions. 0 Transmission Coefficients S21 (dB) -5 -10 r'=1 & tan =0 -15 m r'=1& tan m =0.5 -20 r'=2.5 & tan m =0 -25 r'=2.5 & tan =0.5 m -30 -35 -40 1.8 2 2.2 2.4 2.6 2.8 Frequency (GHz) Figure 4.5: The effect of the relative permeability and the magnetic loss tangent variations on the resonance frequency when an MUT is loaded on the permittivity sensing area (AE ) of the SSIR. The real part of electric permittivity is extracted based on the shift that the sensor exhibit when a material is loaded on area AE with respect to the resonance frequency of the unloaded case Fig. 4.6. In AE sensing area, variation of the relative permittivity results in noticeable change. ′ The relative permittivity of low loss dielectric material commonly ranges from ϵr = 1 to 10 and permittivity loss tangent from tanδe = 0 to 0.1. To ensure that the variation of the magnetic permeability on AE has negligible influence to the shift of the resonance frequency, materials of different relative permeability values and different magnetic loss tangent values are measured on the same area, area AE . The results illustrated in Fig. 4.5 confirm that shift in the resonance frequency at area is primarily attributed to the change of the permittivity. Similarly, the real part of the magnetic permeability is extracting by comparing the resonance frequency of the resonance-based sensor when a magneto-dielectric material is loaded on AH to 52 0 Transmission Coefficients S21 (dB) -5 -10 -15 ' r =1 ' -20 r =3 ' r =6 -25 ' =10 r -30 -35 -40 1.6 1.8 2 2.2 2.4 2.6 Frequency (GHz) Figure 4.6: The effect of the relative permittivity variations on the resonance frequency when an MUT is loaded on the permittivity sensing area (AE ) of the SSIR. 0 Transmission Coefficients S21 (dB) -5 -10 -15 =1& tan e=0 r =6& tan e=0.1 -20 r r =10& tan e=0 -25 =10&tan e=0.1 r -30 -35 -40 1.8 2 2.2 2.4 2.6 2.8 Frequency (GHz) Figure 4.7: The effect of the relative permittivity and the dielectric loss tangent on the resonance frequency when an MUT is loaded on the permeability sensing area (AH ) of the SSIR. 53 the unloaded case, Fig. 4.8. The change of the permittivity of the material on the permeability sensing is negligible, as shown in Fig. 4.7. Magneto-dialectic materials typically have magnetic permeability ranging from ′ ′ µr = 1 to µr = 2 and a magnetic loss tangent ranging from tan δm = 0 to tan δm = 0.5 [34]. It is worth mentioning that the variation of permittivity and permeability loss tangents of the magneto- dielectric material has negligible influence on the resonance frequency at the respective sensing area, see Fig. 4.9 and Fig. 4.10. 0 Transmission Coefficients S21 (dB) -5 -10 r'=1 -15 r'=1.3 r'=1.6 -20 r'=2 -25 r'=2.5 -30 -35 -40 1.8 2 2.2 2.4 2.6 2.8 Frequency (GHz) Figure 4.8: Resonance frequency shift as MUT with different magnetic permeability loaded on the permeability sensing area (area AH ). Table 4.1 summaries a comparison with the state of the art planar resonators for magneto- dielectric characterization. The uniqueness of the the proposed sensor compared to the the tech- Table 4.1: Comparison with the resonance-based planar sensors for magneto-dielectric characteri- zation. Reference [34] [70] This Work Technology CSRR CSRR SIR fr (GHz) 2.47 2.36 2.308 Area ϵr (mm × mm) 7.7 × 4.24 8.8 × 5 5×4 Area µr (mm × mm) 1.1 × 3.39 1.12 × 3.4 5×4 54 nologies tabulated in Table 4.1, is that the capability of the SIR to operate around the same fre- quency while achieving confinement of the fields in larger spatially separated sensing areas. Using SIR the size of the MUT in sensing area has to be greater than the confinement limits of the field shown in Fig.2. For instance, the MUT tested for the permittivity at sensing area AE has to be lager than the patch size which is x = 4 and y = 4; x is the horizontal dimension shown in the Fig.2 and y is the vertical dimension. This configuration permits measuring small as well as larger samples. In this study an MUT of x = 5 mm by y = 4 mm is used in both sensing areas. Thus allowing using only one sample for both sensing areas. 0 Transmission Coefficients S21 (dB) -5 -10 tan e =0 -15 tan e=0.02 -20 tan e=0.04 tan e=0.06 -25 tan e=0.08 -30 tan e=0.1 -35 -40 1.8 2 2.2 2.4 2.6 2.8 Frequency (GHz) Figure 4.9: Permittivity loss tangent effect on the transmission coefficient S21 on the permittivity sensing area (area AE ). The effect of the electric and magnetic losses are more noticeable at the resonance frequency. At the resonance frequency of a stopband like resonator for instance, the transmitted power is blocked by the resonator and the S21 is minimal at the resonance frequency. However, due to the losses caused internally by the dielectric, represented in the imaginary part of the permittivity, the transmitted coefficient S21 is does not reach to minimum at the resonance frequency. In other words, insertion loss is minimum if the material has minimal loss tangent. The transmitted power 55 0 Transmission Coefficients S21 (dB) -5 -10 tan m =0 -15 tan m =0.1 -20 tan m =0.2 tan m =0.3 -25 tan m =0.4 -30 tan m =0.5 -35 -40 1.8 2 2.2 2.4 2.6 2.8 Frequency (GHz) Figure 4.10: Permeability loss tangent effect on the transmission coefficient S21 on the permeabil- ity sensing area (area AH ). from the sending port to the receiving port was not blocked by the resonator, nor was it passed to the other port, but it has been dissipated in the the dielectric material as dielectric losses. The effect of the loss tangents could be determine by measuring the quality factor of the sensor after perturbation by the MUT and compared it to the quality factor before the perturbation. For magneto-dielectric materials, the dissipation could be attributed to the loss tangent of the permittivity, denoted tanδe , or to the increased loss due to the magnetic permeability, denoted tanδm , to differentiate between the tow internal material losses. The dissipation due magneto- dielectric material cases higher power dissipation and in fact they are widely as absorbers. The proposed sensor has high sensitivity to the permeability loss tangent on the permeability sensing area AH , Fig. 4.10, compared to negligibly small change in transmission loss when the a magneto-dielectric material is measured on the permittivity sensing area AE Fig. 4.5. On the other hand, loading the MUT at area AE for measuring permittivity loss tangent show a detectable change in the transmission loss Fig. 4.9 while a slightly small change in the transmission loss when the variation of the MUT permittivity loss tangent is tested at area AH Fig. 4.7. 56 10 Simulated data 9 Fitted Curve 8 Relative Permitivity 'r 7 6 5 4 3 2 1 0.9 0.92 0.94 0.96 0.98 1 Normalized Resonance Frequency (GHz) frn Figure 4.11: Simulation results and fitted curve of the resonance frequency shift as function of the real part of the permittivity of the MUT loaded on AE . 2.5 Simulation Results Fitted Curve Relative Permeability r' 2 1.5 1 0.955 0.96 0.965 0.97 0.975 0.98 0.985 0.99 0.995 1 Normalized Resonance Frequency (GHz) frn Figure 4.12: Simulation results and fitted curve of the resonance frequency shift as function of the real part of the permeability of the MUT loaded on AH . 57 ′ 2 − 1201.5f + 616.6 ϵr = 585.9frn rn (4.3) In material characterization using resonance-based methods, curve fitting technique has been widely used to represent the shift of the resonance frequency due to the perturbation effect exhib- ited by sensor loaded when a material is loaded on the sensor [19, 34, 79]. Using th perturbation theorem, the variation of the resonance frequency is a function of the change of the permittivity and permeability as illustrated in section 4.2. However, using the pro- posed method the variation of the resonance frequency when a material is loaded at area AE is primarily a function of the change in the permittivity. Thus the change of the loaded MUT per- mittivity could be quantified as a function of the shift of the resonance frequency when a MUT is loaded at sensing area AE ; a second order polynomial (4.3) quantifies the normalized resonance frequency shift to the real part of the permittivity. ′ 2 − 962.9f + 489.1 µr = 474.8frn rn (4.4) The variation of the resonance frequency of the same sensor when a MUT is loaded at area AH is mainly caused by the change of magnetic permeability of the MUT. The relationship of the real part of the permeability to change in resonance frequency is given by (4.4). frn in (4.3) and (4.4) is the ratio of the resonance frequency when a material is loaded to resonance frequency of the unloaded case. The change of the quality factor is influenced by the electric and magnetic loss tangents as well as the real parts of both the relative permittivity and permeability. Due the confinement of fields in spatially separated areas using the proposed method, the loss could be expressed using (4.5) for permittivity loss tangent and (4.6) for magnetic loss tangent. ′ tan δe = f (ϵr , Q) (4.5) 58 ′ tan δm = f (µr , Q) (4.6) The sensitivity of relative-based planar resonants Sr measures the rate of change of resonance frequency variation with respect to the change of the material properties (4.7) [32]. The sensitive of the SSIR to the permittivity and permeability variation on AE and AH , are shown in Fig. 4.13a and Fig. 4.13b, respectively. ∆frn Sr = (4.7) ∆ϵr + ∆µr 59 50 45 Sr (MHz) 40 35 30 25 0 2 4 6 8 10 ' r -1 (a) 110 100 Sr (MHz) 90 80 70 60 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 ' r -1 (b) Figure 4.13: Sensitivity of the SSIR to the (a) electric permittivity, and (b) magnetic permeability of the loaded MUT. 60 4.5 Experimental Validation and Discussion For validation of the proposed methods, the sensor is fabricated and test in the laboratory as shown in Fig. 4.14 for a variety of dielectric material and magneto-dielectric material. The experimental set up using the network analyzer is presented in Fig. 4.14. Figure 4.14: A picture of the Fabricated SSIR Sensor. The SIR is connected to the microstrip line on the top plane of a Rogers RO4003 substrate, ϵr = 3.38 and tan δ = 0.0027, with a thickness of 0.812 mm; the width of transmission line is 1.82 mm. The fabricated SSIR, presented in Fig. 4.14, resonates at fr = 2.334 GHz compared to f r = 2.308 GHz from EM simulation response. The response of the fabricated SSIR compared to the simulation response is depicted in Fig. 4.15. The samples measured in the experimental setup consist of the following materials, RT58850, ′ ′ ′ ′ RO3003, RO3006, TMM10i, with relative permittivity of ϵr = 2.2, ϵr = 3, ϵr = 6.5, and ϵr = 9.8 respectively, in addition to a composite magnetodielectric (MD) material MR11 (MD-MR11) with ′ ′ a relative permittivity ϵr ≈ 8.3 and a relative permeability µr ≈ 2.5. The rogers substrates are readily available with copper cladding on both sides. The copper claddings were etched out using a copper solvent solution for a smooth sample of the material. 61 Prior to removing the copper cladding, the samples were prepared and cut into identical sizes for all materials. The size of all samples is 5 mm x 4 mm with a thickness of 1.5 mm. The sensitivity of the permittivity variation on the permeability sensing area (area AH ) of the simulated and measured data are compared in Fig. 4.16. Loading the sensor with the dielectric materials RT 58850, Ro3006 and RO3010, that has a permittivity of 2.2 6.15 and 10.2, respectively, resulted in negligible shift of the resonance frequency in the measured results. This observation confirms the effectiveness of the spatially separated sensing areas. 0 -5 Transmission Coefficient (dB) -10 -15 Simulated unloaded single SIR Measured unloaded single SIR -20 -25 -30 -35 -40 1.8 2 2.2 2.4 2.6 2.8 Frequency (GHz) Figure 4.15: Measured and simulated response of the proposed sensor. Using the SSIR, the characterization procedure starts by measuring the response of the sensor when a sample is loaded on AH shown in Fig. 4.14; the sample is placed on the top of the planar resonator over AH and the S-parameters are measured. Loading AH of the SSIR with dielectric ′ materials of high permittivity up to ϵr = 9.8, did not shift resonance frequency fr as shown in ′ Fig. 4.16; however, the response of the MD-MR11 with µr ≈ 2.5 demonstrated a high resonance frequency shift compared to the response of other materials that have high electic permittivity as shown in Fig. 4.17. This observation confirms the effectiveness of the spatially separated sensing areas. 62 0 -5 Transmission Coefficient (dB) -10 Simulated No MUT Simulated TR 5884 -15 Simulated RO 3003 Simulated RO 3006 -20 Simulated TMM10i Measured NoMUT Measured TR 5880 -25 Measured RO 3003 Measured RO 3006 Measured TMM10i -30 -35 -40 1.8 2 2.2 2.4 2.6 2.8 Frequency (GHz) Figure 4.16: Measured results of the permittivity variation effects on the permeability sensing area (area AH ). 0 -5 Transmission Coefficient (dB) -10 Simulated No MUT Simulated TR 5884 -15 Simulated RO 3003 Simulated RO 3006 -20 Simulated MD MR11 Simulated TMM10i Measured NoMUT -25 Measured TR 5880 Measured RO 3003 Measured RO 3006 -30 Measured MD MR11 Measured TMM10i -35 -40 1.8 2 2.2 2.4 2.6 2.8 Frequency (GHz) Figure 4.17: Measured results of the permittivity and permeability variation effects on the perme- ability sensing area (AH ). 63 The materials are then loaded on AE for permittivity measurements; the samples are placed on the top of the planar resonator over AE sensing area shown in Fig 4.14 and S-parameters are measured. The shift of the resonance frequency on the permittivity sensing area AE is proportional to the permittivity of the material as depicted in Fig. 4.18, compared to simulation results in Fig. 4.19. The measurements were repeated five times, and the normalized measurements compared to the simulation results are shown in Fig. 4.20. 0 -5 Transmission Coefficient (dB) -10 Measured NoMUT Measured TR 5880 -15 Measured RO3003 Measured RO3006 -20 Measured MD MR11 Measured TMM10i -25 -30 -35 -40 1.8 2 2.2 2.4 2.6 2.8 Frequency (GHz) Figure 4.18: Experimental measurements of materials with different values of ϵr loaded on (AE ). 64 0 -5 Transmission Coefficient (dB) -10 Simulated No MUT Simulated TR 5884 -15 Simulated RO 3003 Simulated RO 3006 Simulated MD MR11 -20 Simulated TMM10i -25 -30 -35 -40 1.8 2 2.2 2.4 2.6 2.8 Frequency (GHz) Figure 4.19: Simulation results of materials with different values of ϵr loaded on (AE ). 1 Simulation results Normalized Resonance Frequency Average of the measurements 0.98 0.96 0.94 0.92 0.9 2 3 4 5 6 7 8 9 10 Relative permitivity r Figure 4.20: Measured results compared to simulation data using SSIR on AE sensing area of the SSIR. 65 4.6 Conclusion In this chapter, a novel resonance-based method is presented for characterizing magneto-dielectric materials. The confinement of the electric and magnetic fields in the proposed sensor enabled measuring intrinsic properties of the dielectric and magneto-dielectric materials at two spatially separated areas. At the the respective sensing area, the shift of the resonance frequency is caused primarily by the respective intrinsic property while the other intrinsic property has negligible influ- ence. For validation of the proposed method, the sensor is fabricated and measured in the labora- tory. Although the fabrication tolerance and the airgap between the planar sensor and the measured materials affected the measured results, however, the relative shift of the resonance frequency on both sensing area showed acceptable agreement with predicted results from the simulation. The chapter presented promising results for dielectric and magneto-dielectric material characterization by applying fields-confinement approach using a single SIR. In the next chapter, the concept of fields confinement is further extended for differential-based sensing application for material char- acterization and comparison. 66 Chapter 5 Differential-based Sensing Method for Magnetodielectric Material Characterization 5.1 Introduction Using a single resonator for material characterization is considered to be a relative sensing method since the relative frequency shift after loading a material, compared to the unloaded case, on either of the sensing areas are used to measure the corresponding property. A more robust method in material characterization is employing a differential-based sensing procedure which provides reliable results by comparing measurements to a known reference. Differential sensing methods have generally been used to enhance the reliability of the mea- surements by minimizing errors due to the surrounding environmental factors including the fabrica- tion tolerance and substrate properties of the planar resonator. In this chapter, a novel differential- based sensing method is introduced for dielectric and magneto-dielectric material measurements. It provides a differential prop can be used as a sensor and a comparator for dielectric and magneto- dielectric materials. In addition, the introduced method differentiates between the two intrinsic properties of magneto-dielectric materials and provide real time measurements. Differential sensing methods using planar resonators have been reported for a variety of ap- plications including permittivity measurements [32, 63, 80], and microfluidic sensing [30, 81, 82]. Differential sensing could be realized using two sensors hosted to two transmission lines in a four- port system, as in [83]. In the four-port system, the difference between the output of the two two-port systems are considered for comparison. In a direct differential sensing procedure, the two microstrip lines are combined using a splitter and a combiner, as in [72], using a two-port system; in which the differential sensing is based on resonance frequency splitting. The content of this chapter has been reproduced with permission from F. T. Alharbi, M. Haq, L. Udpa and Y. Deng, “Magnetodielectric Material Characterization Using Stepped Impedance Resonators,” accepted for publication in IEEE Sensors Journal, 2022. 67 The two resonators could also be coupled to a single transmission line either physically or in close vicinity, which would reduce error due to the combiner and splitter designs [32]. In this procedure, there are two loading possibilities, either balanced or unbalanced loading. In a balanced loading condition, the resonator exhibits a single resonance, while unbalanced loading produces two resonances. In [63], resonance frequency splitting principle using a two symmetrical stepped impedance resonators SIRs, physically connected to a single transmission line, showed a high sensitivity in differential permittivity measurements of materials inserted within the main substrate. SIRs are semi-lumped resonators that have initially been used for microwave filters [38], permittivity characterization [63, 71–75], and recently in fluid sensing [76, 77] and defects detection [78]. In the previous chapter, the principle of field confinement and intensification is realized using stepped impedance resonators (SIRs) using relative-based sensing methods are presented for di- electric and magneto-dielectric material characterization using a single SIR. This chapter further expands on the fields-confinement approach and introduces permeability and permittivity differen- tial sensing. Four spatially separated sensing areas are established on a single resonance structure using a double-stepped impedance resonator (DSIR). The electric field is intensified within two symmetric sensing areas for permittivity differential measurements, in addition to two symmetric sensing areas that have confined magnetic fields for permeability differential measurements. In comparison to differential-based planar sensors, the presented DSIR enables both differential per- mittivity and differential permeability sensing on a single planar resonator operating on a two-port system. Moreover, materials are loaded on top of the resonator plane and do not require substrate insertion. In a balanced loading, the DSIR exhibits a single resonance; however, when either the permittivity or permeability of the sensing area is different from the corresponding reference, an additional resonance arises. In addition to the real-time differential measurements using a two- port system, the presented DSIR demonstrated high sensitivity to the electromagnetic properties of composite magneto-dielectric materials. The chapter is structured as follows. Section 5.2 introduces the concept of confining electric 68 and magnetic fields using single and double SIR for dielectric and magneto-dielectric materials measurement and characterization. The results of using single and double SIRs for magneto- dielectric characterization are presented in section 5.3. For validation of the proposed methods, experimental setup and experimental results are presented in section 5.4, and the chapter is con- cluded in section 5.5. 5.2 Fields-confinement using DSIR For permittivity and permeability differential measurements on a single resonator, four spatially separated sensing areas are established on a single resonance structure using a DSIR blue as shown in Fig. 5.1. For permittivity differential measurements, the electric field is intensified and localized on two symmetric sensing areas, namely AE1 and AE2 , with negligible magnetic field, as shown in Fig. 5.2a. One of these sensing areas is employed as a permittivity reference while the other is a used as a permittivity sensing area. If the permittivity of the materials that perturb these two sensing areas are the same, the sensor exhibits a balanced response with a single resonance ,fr1 . However, if the permittivity on the sensing area is different than the reference, a resonance frequency splitting occurs with an appearance of an additional lower band resonance notch, fr2 , proportional to the difference of the permittivity between the reference and the measured material. Additionally, on the same resonator, the magnetic field is intensified and mostly confined on two symmetric sensing areas, AH1 and AH2 , with negligible electric field as shown in Fig. 5.2b; these two areas are employed for permeability differential measurement.The electric field intensity at resonance is shown in Fig. 5.2a with the dark blue spots correspond to E =0 KV/m and the dark red corresponds E =184.5 KV/m, and magnetic field intensity is shown in Fig. 5.2b with the dark blue spots correspond to H =0 A/m and the dark red corresponds E =39.8 A/m. In addition to the differential sensing feature that the double SIR offers, it also provides a sensing method to detect materials with high permeability values. For instance, perturbing the permeability sensing areas with a material of unity relative permeability even if it has a high rel- ative permittivity, does not cause a frequency splitting on the response as long as the reference permeability sensing area is unloaded, with µr = 1. However, loading either AH1 or AH2 with 69 Figure 5.1: Diagram of the DSIR. a material of relative magnetic permeability larger than one causes a frequency splitting in the re- sponse, indicating that the measured material possesses magnetic susceptibility. Similarly, permit- tivity sensing areas distinguish between the electric properties of the material with less sensitivity to the magnetic permeability of the magneto-dielectric material. The resonance of the DSIR is determined by the dimensions of the low and high impedance sections that control the capacitance and inductance of the resonator. Additionally in this config- uration, there is a magnetic coupling between the two sides of the DSIR [63]. Since the current is flowing in the opposite direction in the DSIR, the mutual coupling, M , is considered as a neg- ative mutual inductance [84], as shown in the equivalent circuit in Fig. 5.3 [63]. Therefore, the resonance frequency of the DSIR is at a slightly higher band (5.1) compared to the SSIR. In the unloaded and balanced conditions, when Lr1 = Lr2 = Lr and Cr1 = Cr2 = Cr , the reso- nance frequency can be determined using (5.1) [63, 84]. The series inductance Lm modeling the decrease in the inductance of each DSIR branch due to the negative magnetic coupling is obtained using circuit parameters optimization in ADS as explained in previous subsection for the SSIR. Fig. 5.4 presents the unloaded condition of the DSIR response of the HFSS simulation compared to the ADS circuit simulation. 70 (a) (b) Figure 5.2: Confined (a) electric field and (b) magnetic field on the DSIR at resonance frequency, with labels on AE1 AE2 and AH1 AH2 . L/2 L/2 M Lm Lm Lr Lr C Cr Cr Figure 5.3: An equivalent circuit of the DSIR. 71 0 Transmission Coefficient (dB) -10 -20 HFSS Simulation Circuit Model Simulation -30 -40 -50 -60 1.8 2 2.2 2.4 2.6 2.8 Frequency (GHz) Figure 5.4: Sensor response of unloaded DSIR using HFSS simulation and circuit analysis with L = 1.78 nH, C = 0.803 pF, Lr = 4.45 nH, Cr = 1.07 pF, and Lm = −0.28nH. 1 fr = p (5.1) 2π Cr (Lr − Lm ) The equations of finding the two minimum frequencies in an unbalanced loading case are given in [63, 84]. In this study, the additional resonance is used as a measure of the difference in either permittivity or permeability caused by unbalanced material perturbation. 5.3 Differential sensing for magneto-dielectric materials using Double SIR When a material is loaded on the sensing area AE1 with an electric permittivity different than the permittivity of the material on AE2 , an additional resonance appears proportional to the difference of the change in permittivity, fr2 , as in Fig. 5.6. On the same sensing area, AE1 , if the permeability of the dielectric material is different than the permeability of the reference material on AE2 , the DSIR does not exhibit a resonance frequency splitting, as shown in Fig. 5.5. These results ensure that measurements on AE1 and AE2 are only sensitive to the permittivity of the material even if it possesses high magnetic permeability. This feature is very important in magneto-dielectric measurement and characterization since it permits measuring the change in 72 -5 Transmission Coefficients S21 (dB) -10 -15 r'=1 -20 r'=1.5 r'=2 -25 r'=2.5 -30 -35 -40 -45 1.8 2 2.2 2.4 2.6 2.8 Frequency (GHz) Figure 5.5: Materials with ϵr = 1 and different permeability values loaded on AE1 ; the reference AE2 is unloaded. the permittivity while not being affected by the the permeability of the material. The difference between the new fr2 and original fr1 resonance frd = fr2 −fr1 indicates the difference between the permittivity of the materials loaded on area AE1 and AE2 . With ϵr2 = 1 in the reference sensing area AE2 , the permittivity of the MUT loaded on AE1 could be determined based on the ′ linear relationship, in (5.8), that frd showed after material perturbation with respect to ∆ϵr with r2 = 0.992. ′ ′ ∆ϵr = ϵr1 − 1 = 68.16frd − 9.73 (5.2) Permeability differential sensing areas AH1 and AH2 , on the other hand, are highly sensitive to the change in the magnetic permeability and less sensitive to the change in the electric permit- tivity of the MUT. Fig. 5.8 presents the simulated results of loading AH1 with dielectric material with relative permittivity extending up to 10 while the reference sensing area AH2 is unloaded, with µr = 1 and ϵr = 1. 73 0 Transmission Coefficients S21 (dB) -10 ' r =1 -20 ' r =2 ' r =4 ' -30 r =6 ' r =8 ' =10 -40 r -50 1.8 2 2.2 2.4 2.6 2.8 Frequency (GHz) Figure 5.6: Materials with µr = 1 and different permittivity values loaded on AE1 ; the reference AE2 is unloaded. 280 260 frd=fr2-fr1 (MHz) 240 220 EM Simulation Results Linear Fitted Curve 200 180 160 140 1 2 3 4 5 6 7 8 9 ' r Figure 5.7: Difference between fr1 and fr2 after loading material AE1 and AE2 unloaded with ′ ϵr2 = 1. 74 -5 Transmission Coefficients S21 (dB) -10 -15 ' r =1 -20 ' =3 r ' -25 r =6 ' r =10 -30 -35 -40 -45 1.8 2 2.2 2.4 2.6 2.8 Frequency (GHz) Figure 5.8: Materials with µr = 1 and different permittivity values loaded on AH1 ; the reference AH2 is unloaded with µr = 1 and ϵr = 1. -5 Transmission Coefficients S21 (dB) -10 -15 r'=1 r'=1.3 -20 r'=1.6 r'=1.9 -25 r'=2.2 r'=2.5 -30 -35 -40 -45 1.8 2 2.2 2.4 2.6 2.8 Frequency (GHz) Figure 5.9: Materials with ϵr = 1 and different permeability values loaded on AH1 ; the reference AH2 is unloaded. 75 Dielectric materials with high permittivity does not cause an additional resonance since mate- rials on AH1 and AH2 have the same permeability. However, when the permeability of material loaded on AH1 has a small variation compared to the reference, µr = 1 on AH2 , a resonance ′ frequency splitting is reflected in the response, as in Fig. 5.9. Comparing to µr2 = 1 on AH2 , the permeability of the material loaded on AH1 can be obtained by the linear relationship, shown in ′ Fig. 5.10, between fd = fr2 − fr1 and ∆µr in (5.3) with r2 = 0.994. 220 210 frd=fr2-fr1 (MHz) 200 190 EM Simulation Results Linear Fitted Curve 180 170 160 150 0.5 1 1.5 ' r Figure 5.10: Difference between fr1 and fr2 after loading material on AH1 , while AH2 is un- ′ loaded with µr2 = 1. ′ ′ ∆µr = µr1 − 1 = 20frd − 2.8 (5.3) For differential-based sensing methods, the sensitivity is determined based on ∆fr1 and ∆fr2 due to material perturbation on any sensing area, as given by (5.4) [63]. The sensitivity of the DSIR to the permittivity differential measurement and permeability differential measurements are presented in Fig. 5.11. ∆fr1 − ∆fr2 Sd = (5.4) ∆ϵr,1 + ∆ϵr,2 + ∆µr,1 + ∆µr,2 76 5.4 Experimental Measurements of the DSIR Figure 5.12: A picture of the fabricated DSIR. The double SIR are connected at the opposite side of the microstrip line on the same node, Fig .5.12. The planar resonator was patterned using machine etching method on the top of the Rogers RO4003 substrate with a relative permittivity of ϵr = 3.38 and tan δ = 0.0027, and a thickness of 0.812 mm; the width of transmission line is 1.82 mm.The response of fabricated the double SIR resonator is depicted in Fig. 5.13, with a measured resonance fr1 = 2.41 GHz compared to fr1 = 2.38 GHz from the simulated unloaded response. Starting with permeability differential sensing, materials of different permittivity values are loaded on the permeability sensing area AH1 while the permeability reference sensing area AH2 is unloaded, with free space properties. Loading AH1 with materials of high permittivity did not generate a second resonance and is seen by the resonator as a balanced loading, as presented as shown in Fig. 5.14. However when a material of high permeability, such as MD-MR11, is measured on AH1 , a resonance frequency splitting occurred on the response as presented in Fig. 5.15 with comparison responses of the other materials that have high permittivity and unity relative permeability. For permittivity differential sensing the samples are loaded on AE1 , while AE2 and AH2 are 77 160 140 120 Sd (MHz) 100 80 60 40 20 0 2 4 6 8 10 ' r,1 -1 (a) 600 500 Sd (MHz) 400 300 200 100 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 ' r,1 -1 (b) Figure 5.11: Sensitivity of the DSIR to (a) electric permittivity variations on AE1 , and (b) mag- netic permeability variations on AH1 . 78 -5 -10 Transmission Coefficient (dB) -15 -20 Simulated unloaded double SIR Measured unloaded double SIR -25 -30 -35 -40 -45 1.8 2 2.2 2.4 2.6 2.8 Frequency (GHz) Figure 5.13: Simulated and measured response of the unloaded DSIR. -5 -10 Transmission Coefficient (dB) -15 Simulated No MUT -20 Simulated TR 5884 Simulated RO 3003 Simulated RO 3006 -25 Simulated TMM10i Measured NoMUT Measured TR 5880 Measured RO 3003 -30 Measured RO 3006 Measured TMM10i -35 -40 -45 1.8 2 2.2 2.4 2.6 2.8 Frequency (GHz) Figure 5.14: Materials with high electric permittivity measured on the permeability sensing AH1 while AH2 is unloaded with comparison to simulation results. 79 -5 -10 Transmission Coefficient (dB) -15 -20 Simulated No MUT Simulated TR 5884 Simulated RO 3003 -25 Simulated RO 3006 Simulated MD MR11 Simulated TMM10i -30 Measured NoMUT Measured TR 5880 Measured RO 3003 -35 Measured RO 3006 Measured MD MR11 Measured TMM10i -40 -45 1.8 2 2.2 2.4 2.6 2.8 Frequency (GHz) Figure 5.15: Materials with high electric permittivity and magnetic permeability measured on the permeability sensing AH1 while AH2 is unloaded with comparison to simulation results. unloaded. Since all samples have high permittivity, including MD-MR11, resonance frequency splitting is detected in all measurements as illustrated in Fig. 5.16a and compared EM simulation results in Fig. 5.16b. The normalized measurements compared to the normalized simulation re- sults are presented in Fig. 5.17. Table.5.1 summarizes the occurrence of the resonance frequency splitting using DSIR. Due to the magnetic coupling between the two sides of the DSIR, both fr1 and fr2 are affected by material perturbation to any sensing area. To avoid mutual coupling, a series configuration of the resonators separated by transmission line with a length λ/2 could be used [63]. However, series configuration increases the overall size of the resonator [32], and calls for high fabrication precision to achieve same node virtual connection. 80 0 -5 Transmission Coefficient (dB) -10 -15 -20 Measured NoMUT Measured TR 5880 -25 Measured RO 3003 Measured RO 3006 -30 Measured MD MR11 Measured TMM10i -35 -40 -45 1.8 2 2.2 2.4 2.6 2.8 Frequency (GHz) (a) 0 -5 Transmission Coefficient (dB) -10 -15 -20 Simulated No MUT Simulated TR 5884 Simulated RO 3003 -25 Simulated RO 3006 Simualted MD MR11 -30 Simulated TMM10i -35 -40 -45 1.8 2 2.2 2.4 2.6 2.8 Frequency (GHz) (b) Figure 5.16: (a) Materials with high electric permittivity and magnetic permeability measured on the permittivity sensing AE1 while AE2 is unloaded with comparison to (b) the simulation results. 81 0.995 Normalized Resonance Frequency fr1 Simulation results Average of the measurment 0.99 0.985 0.98 0.975 2 3 4 5 6 7 8 9 10 Relative permitivity r (a) 0.93 Normalized Resonance Frequency fr2 Simulation results Average of the measurment 0.92 0.91 0.9 0.89 0.88 0.87 0.86 2 3 4 5 6 7 8 9 10 Relative permitivity r (b) Figure 5.17: Normalized measurements of (a) fr1 (b) fr2 resonance frequencies of the DSIR compared to the simulation results. 82 Table 5.1: Resonance frequency splitting occurrence using DSIR for different materials compared ′ ′ to free space compared ϵr = 1,µr = 1. ′ ′ frequency splitting at AE1 frequency splitting at AH1 Sample (ϵr ,µr ) Simulated Measured Simulated Measured RT/duroid 5880 (2.2,1) Yes Yes NO NO RO 3003 (3,1) Yes Yes NO NO RO 3006 (6.15,1) Yes Yes NO NO TMM10i (9.9,1) Yes Yes NO NO MD-MR11 (≈8.3,≈2.5) Yes Yes Yes Yes The errors between the normalized simulation results and the measurements are due to the fabrication tolerance, shown in the unloaded cases of the fabricated DSIR as shown in Fig. 5.13, and due to the unavoidable air gap between samples and resonators. The offsets caused by the fabrication between the simulated results and experimental measurements are also clearly shown in Fig. 5.14. However, Fig. 5.14 showed that, using DSIR, the sample of high permeability value caused a resonance frequency splitting on the permeability comparison sensing area; meanwhile, other samples of high permittivity did not generate a second resonance, and their responses are identical to the unloaded case of the fabricated DSIR sensor. The measurements errors could be minimized by using a fabrication technology with higher precision and by including the airgap in the numerical analysis. Table 5.2: Comparison with the state of the art magneto-dielectric characterization using resonance-based planar sensors. Ref. Planar Resonator fr0 (GHz) AE area (mmxmm) AH area (mmxmm) Differential [34] CSRR 2.47 7.7 × 4.24 1.1 × 3.39 No [70] CSRR 2.36 8.8 × 5 1.12 × 3.4 No [85] SIW 2.205 5.705 × 2 2.071 × 0.9 No [86] Interdigitated resonator 5.9 4 × 12.8 3 × 12.8 No [83] Two CSRR 2.36 5 × 8.8 1.2 × 3.4 Yes, using tow sensor-four ports system T.W Single SIR 2.33 5×4 5×4 No T.W Double SIR 2.4 5×4 5×4 Yes, using single sensor-two ports system In comparison with planar resonators based on fields-confinement approach for magneto-dielectric characterization, the proposed sensors have the advantages presented in Table 5.2. Due to the wide separation between the electric and magnetic fields, it allows size selection of the sample. There- fore, a single sample of each material could be used for all measurements. 83 Table 5.3: Comparison with various differential-based sensors using planar resonators (D=Dielectric, MD=Magneto-dielectric, N.P.=Number of ports). Ref. Material fr0 (GHz) SM (MHz) Sn % N.P. [32] D 2.1 72 3.4 2 [80] D 2.18 88 4.03 2 [87] D 2.48 114.3 4.61 2 [88] D 2.895 112 3.9 2 [83] MD 2.36 N.A N.A 4 T.W MD 2.38 SM , ϵr =59.38 2.49 2 SM , µr =246.13 10.3 Furthermore, the presented DSIR enables permittivity differential sensing and permeability differential sensing on a single resonance structure. Table 5.3 compares the sensitivity performance of the proposed differential-based sensor (DSIR) to various differential-based sensors using planar resonators. The sensitivity as function of permittivity and permeability variations are shown in Fig 5.11a and Fig. 5.11b, respectively. In Table 5.3, SM is the average sensitivity, while Sn % is the normalized sensitivity to the operating resonance frequency. In addition to the high sensitivity of the DSIR, it provides real time comparison between materials properties using a two-ports measurement system. 5.5 Conclusion In this chapter a novel differential sensing method for dielectric and magneto-dielectric ma- terial characterization and comparison. The method employs both permittivity and permeability differential measurements, based on resonance frequency splitting, operating on a two-ports system using a double-stepped impedance resonator (DSIR) connected to a single transmission line. For materials with unknown properties, permittivity and permeability differential measurement com- pared to free space properties using the presented sensor improves the reliability of characterizing dielectric and magneto-dielectric materials. Furthermore, the DSIR demonstrated high sensitivity to the electromagnetic properties. Since the measurements in the presented sensor are based on the resonance frequency splitting and on the difference between the resonance frequencies, the error between the measured and predicated due to the fabrication tolerance and the airgap values did not highly affect the results. 84 Chapter 6 Conclusions and Future Work This dissertation addressed some of the challenges in using resonance-based planar sensors for material characterization applications. A nondestructive resonance-based sensing methodology was introduced for thin conductor-backed dielectric material characterization with high sensitiv- ity to the properties of the dielectric material. The sensing structure was built by integrating the conductor-backed material with the resonance structure. A resonance-based planar sensor using the the presented sensing methodology was fabricated, and widely used conductor-backed dielectric materials with different material properties were characterized. The presented sensing methodol- ogy could be further utilized by using different resonance-based planar sensors for the different measurement applications of conductor-based materials. For magneto-dielectric material characterization, a novel resonance-based sensing method for intensification and confinement of the electric and magnetic fields on widely spatially separated sensing areas was presented. It enabled measuring the intrinsic electromagnetic properties of di- electric and magneto-dielectric materials with high sensitivity. On the respective sensing area, the shift of the resonance frequency is caused primarily by the respective intrinsic property whereas the other intrinsic property has negligible influence on resonance frequency. Furthermore, a novel differential-based sensing method, employing both permittivity differential sensing and perme- ability differential sensing, was introduced for dielectric and magneto-dielectric material char- acterization and comparison using a single resonance-based sensor. Differential-based sensing methods were shown to be effective techniques in material characterization and comparisons due their capability to overcome common sources of errors, such as environmental factors and fab- rication tolerance. This work advanced differential sensing to differentiate between the intrinsic electromagnetic properties of dielectric and magneto-dielectric materials with real-time measure- ments. For validation of the proposed methods, the sensors were fabricated, and dielectric and 85 Figure 6.1: Fields-confinement approach extended to permittivity and permeability differential sensing on dual frequency bands. magneto-dielectric materials of different properties were characterized. This concept could further be extended to characterize dielectric and magneto-dielectric materials at dual frequency bands by intensifying and confining electric and magnetic fields on spatially separated sensing areas on dual and multiple frequency bands, as suggested in Fig .6.1. Intensifying and confining fields on spatially separated sensing areas were presented for di- electric and magneto-dielectric material characterization using resonance-based planar sensor op- erating on a two-port system. The concept of field confinement and intensification could further be utilized for different applications of complex material characterization and structural health monitoring. 86 BIBLIOGRAPHY [1] R. Zoughi, Microwave non-destructive testing and evaluation principles, vol. 4. Springer Science & Business Media, 2000. [2] K. Brinker, M. Dvorsky, M. T. Al Qaseer, and R. Zoughi, “Review of advances in microwave and millimetre-wave ndt&e: Principles and applications,” Philosophical Transactions of the Royal Society A, vol. 378, no. 2182, p. 20190585, 2020. [3] W. Withayachumnankul, K. Jaruwongrungsee, A. Tuantranont, C. Fumeaux, and D. Abbott, “Metamaterial-based microfluidic sensor for dielectric characterization,” Sensors and Actua- tors A: Physical, vol. 189, pp. 233–237, 2013. [4] A. Ebrahimi, W. Withayachumnankul, S. Al-Sarawi, and D. Abbott, “High-sensitivity metamaterial-inspired sensor for microfluidic dielectric characterization,” IEEE Sensors Journal, vol. 14, no. 5, pp. 1345–1351, 2013. [5] A. Loutfi, S. Coradeschi, G. K. Mani, P. Shankar, and J. B. B. Rayappan, “Electronic noses for food quality: A review,” Journal of Food Engineering, vol. 144, pp. 103–111, 2015. [6] A. M. Hassan and M. El-Shenawee, “Review of electromagnetic techniques for breast cancer detection,” IEEE Reviews in Biomedical Engineering, vol. 4, pp. 103–118, 2011. [7] J. Zhang, G. Y. Tian, A. M. Marindra, A. I. Sunny, and A. B. Zhao, “A review of passive rfid tag antenna-based sensors and systems for structural health monitoring applications,” Sensors, vol. 17, no. 2, p. 265, 2017. [8] V. Mulloni and M. Donelli, “Chipless rfid sensors for the internet of things: Challenges and opportunities,” Sensors, vol. 20, no. 7, p. 2135, 2020. [9] J. Zhang, H. Huang, C. Huang, B. Zhang, Y. Li, K. Wang, D. Su, and G. Y. Tian, “A config- urable dielectric resonator-based passive wireless sensor for crack monitoring,” IEEE Trans- actions on Antennas and Propagation, vol. 67, no. 8, pp. 5746–5749, 2019. [10] N. K. Nikolova, “Microwave imaging for breast cancer,” IEEE microwave magazine, vol. 12, no. 7, pp. 78–94, 2011. [11] A. Swarup, S. Stuchly, and A. Surowiec, “Dielectric properties of mouse mca1 fibrosarcoma at different stages of development,” Bioelectromagnetics, vol. 12, no. 1, pp. 1–8, 1991. [12] M. Hofmann, G. Fischer, R. Weigel, and D. Kissinger, “Microwave-based noninvasive con- centration measurements for biomedical applications,” IEEE Transactions on Microwave Theory and Techniques, vol. 61, no. 5, pp. 2195–2204, 2013. [13] E. J. Rothwell and M. J. Cloud, Electromagnetics. CRC press, 2018. [14] A. Nicolson and G. Ross, “Measurement of the intrinsic properties of materials by time- domain techniques,” IEEE Transactions on instrumentation and measurement, vol. 19, no. 4, pp. 377–382, 1970. 87 [15] R. Fenner, E. Rothwell, and L. Frasch, “A comprehensive analysis of free-space and guided- wave techniques for extracting the permeability and permittivity of materials using reflection- only measurements,” Radio Science, vol. 47, no. 01, pp. 1–13, 2012. [16] E. Kemptner and S. Thurner, “Free space material characterization for microwave frequen- cies,” in 2012 6th European Conference on Antennas and Propagation (EUCAP), pp. 3513– 3515, IEEE, 2012. [17] W. B. Weir, “Automatic measurement of complex dielectric constant and permeability at microwave frequencies,” Proceedings of the IEEE, vol. 62, no. 1, pp. 33–36, 1974. [18] C. A. Jones, J. H. Grosvenor, and C. M. Weil, “RF material characterization using a large- diameter (76.8 mm) coaxial air line,” in 13th Int. Conference on Microwaves, Radar and Wire- less Communications. MIKON-2000. Conference Proceedings (IEEE Cat. No. 00EX428), vol. 2, pp. 417–420, IEEE, 2000. [19] M. S. Boybay and O. M. Ramahi, “Material characterization using complementary split- ring resonators,” IEEE Transactions on instrumentation and Measurement, vol. 61, no. 11, pp. 3039–3046, 2012. [20] S. I. Ganchev, N. Qaddoumi, S. Bakhtiari, and R. Zoughi, “Calibration and measurement of dielectric properties of finite thickness composite sheets with open-ended coaxial sensors,” IEEE Trans. on Instrumentation and Measurement, vol. 44, no. 6, pp. 1023–1029, 1995. [21] M. Kempin, M. T. Ghasr, J. T. Case, and R. Zoughi, “Modified waveguide flange for eval- uation of stratified composites,” IEEE Transactions on Instrumentation and Measurement, vol. 63, no. 6, pp. 1524–1534, 2013. [22] D. C. Dube, M. T. Lanagan, J. Kim, and S. Jang, “Dielectric measurements on substrate materials at microwave frequencies using a cavity perturbation technique,” Journal of applied physics, vol. 63, no. 7, pp. 2466–2468, 1988. [23] J. D. Baena, J. Bonache, F. Martin, R. M. Sillero, F. Falcone, T. Lopetegi, M. A. Laso, J. Garcia-Garcia, I. Gil, M. F. Portillo, et al., “Equivalent-circuit models for split-ring res- onators and complementary split-ring resonators coupled to planar transmission lines,” IEEE transactions on microwave theory and techniques, vol. 53, no. 4, pp. 1451–1461, 2005. [24] C.-S. Lee and C.-L. Yang, “Complementary split-ring resonators for measuring dielectric constants and loss tangents,” IEEE Microwave and Wireless Components Letters, vol. 24, no. 8, pp. 563–565, 2014. [25] C.-L. Yang, C.-S. Lee, K.-W. Chen, and K.-Z. Chen, “Noncontact measurement of complex permittivity and thickness by using planar resonators,” IEEE Transactions on Microwave Theory and Techniques, vol. 64, no. 1, pp. 247–257, 2015. [26] C.-S. Lee and C.-L. Yang, “Single-compound complementary split-ring resonator for simul- taneously measuring the permittivity and thickness of dual-layer dielectric materials,” IEEE Transactions on Microwave Theory and Techniques, vol. 63, no. 6, pp. 2010–2023, 2015. 88 [27] M. A. H. Ansari, A. K. Jha, and M. J. Akhtar, “Design and application of the csrr-based planar sensor for noninvasive measurement of complex permittivity,” IEEE Sensors Journal, vol. 15, no. 12, pp. 7181–7189, 2015. [28] L. Su, J. Naqui, J. Mata-Contreras, and F. Martı́n, “Modeling and applications of metamaterial transmission lines loaded with pairs of coupled complementary split-ring resonators (csrrs),” IEEE Antennas and Wireless Propagation Letters, vol. 15, pp. 154–157, 2015. [29] J. Dong, F. Shen, Y. Dong, Y. Wang, W. Fu, H. Li, D. Ye, B. Zhang, J. Huangfu, S. Qiao, et al., “Noncontact measurement of complex permittivity of electrically small samples at microwave frequencies,” IEEE Transactions on Microwave Theory and Techniques, vol. 64, no. 9, pp. 2883–2893, 2016. [30] P. Vélez, L. Su, K. Grenier, J. Mata-Contreras, D. Dubuc, and F. Martı́n, “Microwave mi- crofluidic sensor based on a microstrip splitter/combiner configuration and split ring res- onators (srrs) for dielectric characterization of liquids,” IEEE Sensors Journal, vol. 17, no. 20, pp. 6589–6598, 2017. [31] E. L. Chuma, Y. Iano, G. Fontgalland, and L. L. B. Roger, “Microwave sensor for liquid dielectric characterization based on metamaterial complementary split ring resonator,” IEEE Sensors Journal, vol. 18, no. 24, pp. 9978–9983, 2018. [32] A. Ebrahimi, J. Scott, and K. Ghorbani, “Differential sensors using microstrip lines loaded with two split-ring resonators,” IEEE Sensors Journal, vol. 18, no. 14, pp. 5786–5793, 2018. [33] S. A. Alotaibi, Y. Cui, and M. M. Tentzeris, “Csrr based sensors for relative permittivity measurement with improved and uniform sensitivity throughout [0.9-10.9] ghz band,” IEEE Sensors Journal, 2019. [34] M. Saadat-Safa, V. Nayyeri, M. Khanjarian, M. Soleimani, and O. M. Ramahi, “A csrr-based sensor for full characterization of magneto-dielectric materials,” IEEE Transactions on Mi- crowave Theory and Techniques, vol. 67, no. 2, pp. 806–814, 2019. [35] A. Ebrahimi, G. Beziuk, J. Scott, and K. Ghorbani, “Microwave differential frequency split- ting sensor using magnetic-lc resonators,” Sensors, vol. 20, no. 4, p. 1066, 2020. [36] L. Su, J. Muñoz-Enano, P. Vélez, M. Gil-Barba, P. Casacuberta, and F. Martin, “Highly sensitive reflective-mode phase-variation permittivity sensor based on a coplanar waveguide terminated with an open complementary split ring resonator (ocsrr),” IEEE Access, vol. 9, pp. 27928–27944, 2021. [37] A. M. Albishi and O. M. Ramahi, “Microwaves-based high sensitivity sensors for crack de- tection in metallic materials,” IEEE Trans. on Microwave Theory and Techniques, vol. 65, no. 5, pp. 1864–1872, 2017. [38] D. M. Pozar, “Microwave engineering,” 2012. [39] F. Mazlumi, S. H. H. Sadeghi, and R. Moini, “Interaction of rectangular open-ended waveg- uides with surface tilted long cracks in metals,” IEEE transactions on instrumentation and measurement, vol. 55, no. 6, pp. 2191–2197, 2006. 89 [40] Y. Gao, M. Ghasr, K. Ying, M. Dvorsky, A. Boots, R. Zoughi, and D. Palmer, “Mil- limeter wave differential probe system for surface crack detection in painted aircraft fuse- lage,” in 2019 IEEE International Instrumentation and Measurement Technology Conference (I2MTC), pp. 1–6, IEEE, 2019. [41] S.-H. Yang, K.-B. Kim, and J.-S. Kang, “Detection of surface crack in film-coated metals using an open-ended coaxial line sensor and dual microwave frequencies,” NDT & E Inter- national, vol. 54, pp. 91–95, 2013. [42] K. M. Donnell, A. McClanahan, and R. Zoughi, “On the crack characteristic signal from an open-ended coaxial probe,” IEEE Transactions on Instrumentation and Measurement, vol. 63, no. 7, pp. 1877–1879, 2014. [43] J. Kerouedan, P. Queffelec, P. Talbot, C. Quendo, S. De Blasi, and A. Le Brun, “Detection of micro-cracks on metal surfaces using near-field microwave dual-behavior resonator filters,” Measurement Science and Technology, vol. 19, no. 10, p. 105701, 2008. [44] A. Albishi and O. Ramahi, “Detection of surface and subsurface cracks in metallic and non- metallic materials using a complementary split-ring resonator,” Sensors, vol. 14, no. 10, pp. 19354–19370, 2014. [45] S. Mukherjee, X. Shi, L. Udpa, S. Udpa, Y. Deng, and P. Chahal, “Design of a split-ring resonator sensor for near-field microwave imaging,” IEEE Sensors Journal, vol. 18, no. 17, pp. 7066–7076, 2018. [46] G. D. Dester, E. J. Rothwell, and M. J. Havrilla, “Two-iris method for the electromagnetic characterization of conductor-backed absorbing materials using an open-ended waveguide probe,” IEEE Trans. on Instrumentation and Measurement, vol. 61, no. 4, pp. 1037–1044, 2011. [47] J. Edwards and R. Zoughi, “Microwave sensitivity maximization of disbond characterization in conductor backed dielectric composites,” Journal of nondestructive evaluation, vol. 12, no. 3, pp. 193–198, 1993. [48] R. Fenner, E. Rothwell, L. Frasch, and J. Frasch, “Characterization of conductor-backed dielectric materials with genetic algorithms and free space methods,” IEEE Microwave and Wireless Components Letters, vol. 26, no. 6, pp. 461–463, 2016. [49] K. Y. You and K. G. Sotirios, “Materials characterization using microwave waveguide sys- tem,” Microwave systems and applications, pp. 341–358, 2017. [50] R. Zoughi, J. R. Gallion, and M. T. Ghasr, “Accurate microwave measurement of coating thickness on carbon composite substrates,” IEEE Trans. on Instrumentation and Measure- ment, vol. 65, no. 4, pp. 951–953, 2016. [51] M. Abou-Khousa and R. Zoughi, “Disbond thickness evaluation employing multiple- frequency near-field microwave measurements,” IEEE Trans. on instrumentation and mea- surement, vol. 56, no. 4, pp. 1107–1113, 2007. 90 [52] M. Havrilla, A. Bogle, M. Hyde, and E. Rothwell, “Em material characterization of conduc- tor backed media using a nde microstrip probe,” Electromagnetic Nondestructive Evaluation (XVI), vol. 38, p. 210, 2013. [53] D. Ghodgaonkar, V. Varadan, and V. K. Varadan, “Free-space measurement of complex per- mittivity and complex permeability of magnetic materials at microwave frequencies,” IEEE Trans. on instrumentation and measurement, vol. 39, no. 2, pp. 387–394, 1990. [54] H. Sun, R. Li, G. Y. Tian, T. Tang, G. Du, and B. Wang, “Determination of complex permit- tivity of thin dielectric samples based on high-q microstrip resonance sensor,” Sensors and Actuators A: Physical, vol. 296, pp. 31–37, 2019. [55] A. Ebrahimi, J. Coromina, J. Muñoz-Enano, P. Vélez, J. Scott, K. Ghorbani, and F. Martı́n, “Highly sensitive phase-variation dielectric constant sensor based on a capacitively-loaded slow-wave transmission line,” IEEE Transactions on Circuits and Systems I: Regular Papers, 2021. [56] L. Su, J. Muñoz-Enano, P. Vélez, P. Casacuberta, M. Gil, and F. Martı́n, “Phase-variation microwave sensor for permittivity measurements based on a high-impedance half-wavelength transmission line,” IEEE Sensors Journal, vol. 21, no. 9, pp. 10647–10656, 2021. [57] A. K. Horestani, Z. Shaterian, and F. Martin, “Rotation sensor based on the cross-polarized excitation of split ring resonators (srrs),” IEEE Sensors Journal, vol. 20, no. 17, pp. 9706– 9714, 2020. [58] M. S. Boybay and O. M. Ramahi, “Non-destructive thickness measurement using quasi-static resonators,” IEEE microwave and wireless components letters, vol. 23, no. 4, pp. 217–219, 2013. [59] A. Ebrahimi, J. Scott, and K. Ghorbani, “Dual-mode resonator for simultaneous permittivity and thickness measurement of dielectrics,” IEEE Sensors Journal, vol. 20, no. 1, pp. 185– 192, 2019. [60] J. Bonache, M. Gil, I. Gil, J. Garcı́a-Garcı́a, and F. Martı́n, “On the electrical characteris- tics of complementary metamaterial resonators,” IEEE Microwave and Wireless Components Letters, vol. 16, no. 10, pp. 543–545, 2006. [61] J. Naqui, M. Durán-Sindreu, and F. Martı́n, “Modeling split-ring resonator (sRR) and comple- mentary split-ring resonator (CSRR) loaded transmission lines exhibiting cross-polarization effects,” IEEE Antennas and Wireless Propagation Letters, vol. 12, pp. 178–181, 2013. [62] K. Chang and L.-H. Hsieh, Microwave ring circuits and related structures, vol. 156. John Wiley & Sons, 2004. [63] J. Naqui, C. Damm, A. Wiens, R. Jakoby, L. Su, J. Mata-Contreras, and F. Martı́n, “Transmis- sion lines loaded with pairs of stepped impedance resonators: Modeling and application to differential permittivity measurements,” IEEE Trans. Microw. Theory Techn., vol. 64, no. 11, pp. 3864–3877, 2016. 91 [64] R. Corporation, “Rogers RO3003 laminates.” https://rogerscorp.com/advanced-connectivity- solutions/ro3000-series-laminates, 2019. [65] R. Corporation, “Rogers RT5880 laminates.” https://rogerscorp.com/advanced-connectivity- solutions/rt-duroid-laminates/rt-duroid-5880-laminates, 2017. [66] N. Altunyurt, M. Swaminathan, P. M. Raj, and V. Nair, “Antenna miniaturization us- ing magneto-dielectric substrates,” in 2009 59th Electronic Compon. and Technol. Conf., pp. 801–808, IEEE, 2009. [67] A. Kabalan, A. Sharaiha, and A.-C. Tarot, “Electrically small wideband monopole antenna partially loaded with low loss magneto-dielectric material,” Magnetism, vol. 2, no. 3, pp. 229– 238, 2022. [68] M. S. KT, M. A. H. Ansari, A. K. Jha, and M. J. Akhtar, “Design of srr-based microwave sensor for characterization of magnetodielectric substrates,” IEEE Microwave and Wireless Components Letters, vol. 27, no. 5, pp. 524–526, 2017. [69] K. M. Shafi, A. K. Jha, and M. J. Akhtar, “Improved planar resonant rf sensor for retrieval of permittivity and permeability of materials,” IEEE Sensors Journal, vol. 17, no. 17, pp. 5479– 5486, 2017. [70] W.-S. Zhao, H.-Y. Gan, L. He, Q. Liu, D.-W. Wang, K. Xu, S. Chen, L. Dong, and G. Wang, “Microwave planar sensors for fully characterizing magneto-dielectric materials,” IEEE Ac- cess, vol. 8, pp. 41985–41999, 2020. [71] J. Naqui, C. Damm, A. Wiens, R. Jakoby, L. Su, and F. Martı́n, “Transmission lines loaded with pairs of magnetically coupled stepped impedance resonators (SIRs): Modeling and ap- plication to microwave sensors,” in 2014 IEEE MTT-S Int. Microw. Symp. (IMS2014), pp. 1–4, IEEE, 2014. [72] L. Su, J. Mata-Contreras, P. Vélez, and F. Martı́n, “Configurations of splitter/combiner mi- crostrip sections loaded with stepped impedance resonators (SIRs) for sensing applications,” Sensors, vol. 16, no. 12, p. 2195, 2016. [73] P. Velez, J. Munoz-Enano, A. Ebrahimi, J. Scott, K. Ghorbani, and F. Martı́n, “Step impedance resonator (SIR) loaded with complementary split ring resonator (CSRR): Model- ing, analysis and applications,” in 2020 IEEE/MTT-S Int. Microw. Symp.(IMS), pp. 675–678, IEEE, 2020. [74] J. Muñoz-Enano, P. Vélez, L. Su, M. Gil, P. Casacuberta, and F. Martı́n, “On the sensitivity of reflective-mode phase-variation sensors based on open-ended stepped-impedance transmis- sion lines: Theoretical analysis and experimental validation,” IEEE Trans. Microw. Theory Techn., vol. 69, no. 1, pp. 308–324, 2020. [75] P. Casacuberta, P. Vélez, J. Muñoz-Enano, L. Su, M. G. Barba, A. Ebrahimi, and F. Martı́n, “Circuit analysis of a coplanar waveguide (CPW) terminated with a step-impedance resonator (SIR) for highly sensitive one-port permittivity sensing,” IEEE Access, vol. 10, pp. 62597– 62612, 2022. 92 [76] P. Vélez, F. Martı́n, R. Fernández-Garcı́a, and I. Gil, “Embroidered textile frequency-splitting sensor based on stepped-impedance resonators,” IEEE Sensors J., 2022. [77] P. Velez, J. Munoz-Enano, A. Ebrahimi, C. Herrojo, F. Paredes, J. Scott, K. Ghorbani, and F. Martin, “Single-frequency amplitude-modulation sensor for dielectric characterization of solids and microfluidics,” IEEE Sensors J., vol. 21, no. 10, pp. 12189–12201, 2021. [78] C. Herrojo, P. Vélez, J. Muñoz-Enano, L. Su, P. Casacuberta, M. G. Barba, and F. Martı́n, “Highly sensitive defect detectors and comparators exploiting port imbalance in rat-race cou- plers loaded with step-impedance open-ended transmission lines,” IEEE Sensors J., vol. 21, no. 23, pp. 26731–26745, 2021. [79] A. M. Albishi, M. S. Boybay, and O. M. Ramahi, “Complementary split-ring resonator for crack detection in metallic surfaces,” IEEE Microwave and Wireless Components Letters, vol. 22, no. 6, pp. 330–332, 2012. [80] A. Ebrahimi, G. Beziuk, J. Scott, and K. Ghorbani, “Microwave differential frequency split- ting sensor using magnetic-LC resonators,” Sensors, vol. 20, no. 4, p. 1066, 2020. [81] A. Ebrahimi, J. Scott, and K. Ghorbani, “Ultrahigh-sensitivity microwave sensor for mi- crofluidic complex permittivity measurement,” IEEE Trans. Microw. Theory Techn., vol. 67, no. 10, pp. 4269–4277, 2019. [82] A. Ebrahimi, F. J. Tovar-Lopez, J. Scott, and K. Ghorbani, “Differential microwave sensor for characterization of glycerol–water solutions,” Sensors and Actuators B: Chemical, vol. 321, p. 128561, 2020. [83] H.-Y. Gan, L.-Q. Li, W.-S. Zhao, D.-W. Wang, and G. Wang, “An improved differential CSRR-based sensor for characterizing the magneto-dielectric materials,” in 2020 IEEE MTT- S Int. Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimiza- tion (NEMO), pp. 1–3, IEEE, 2020. [84] J.-S. G. Hong and M. J. Lancaster, Microstrip filters for RF/microwave applications, vol. 167. John Wiley & Sons, 2004. [85] L.-C. Fan, W.-S. Zhao, H.-Y. Gan, L. He, Q. Liu, L. Dong, and G. Wang, “A high-Q active substrate integrated waveguide based sensor for fully characterizing magneto-dielectric (MD) materials,” Sensors and Actuators A: Physical, vol. 301, p. 111778, 2020. [86] L. Ali, C. Wang, F.-Y. Meng, K. K. Adhikari, and Z.-Q. Gao, “Interdigitated planar mi- crowave sensor for characterizing single/multilayers magnetodielectric material,” IEEE Mi- crow. Wireless Compon. Lett., 2022. [87] Q. Liu, H. Deng, P. Meng, and H. Sun, “High sensitivity sensor loaded with octagonal spi- ral resonators for retrieval of solid material permittivity,” IEEE Sensors J., vol. 21, no. 18, pp. 20010–20017, 2021. [88] P. Mohammadi, A. Mohammadi, and A. Kara, “T-junction loaded with interdigital capacitor for differential measurement of permittivity,” IEEE Trans. Instrum. Meas., vol. 71, pp. 1–8, 2022. 93