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In this paper, low cost, small size and wideband microwave notch filter with good peak attenuation based on complementary circular spiral resonator (CCSR) is realized analytically, calculated numerically and verified experimentally. Fundamental frequency of the proposed filter is 2.47 GHz with notch depth − 13.89 dB and unloaded Q factor 49.4. The...

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## Citations

... When designing a high-sensitivity sensor, these three parameters are to be considered while staying within the fabrication and measurement limits. Interactive methods such as parameter sweeping are used in practice to realize the tuning of parameters [25,26]. In [25], the parametric sweep method was used to study the effects of resonator dimensions on the resonance frequency and notch depth of a filter by varying one parameter while holding the others constant. ...

... Interactive methods such as parameter sweeping are used in practice to realize the tuning of parameters [25,26]. In [25], the parametric sweep method was used to study the effects of resonator dimensions on the resonance frequency and notch depth of a filter by varying one parameter while holding the others constant. In [26], four geometric parameters were utilized to tune the resonant frequency of the CSRR, utilizing the parametric sweep technique. ...

This paper presents the design, optimization, and calibration of multivariable resonators for microwave dielectric sensors. An optimization technique for the circular complementary split ring resonator (CC-SRR) and square complementary split ring resonator (SC-SRR) is presented to achieve the required transmission response in a precise manner. The optimized resonators are manufactured using a standard photolithographic technique and measured for fabrication tolerance. The fabricated sensor is presented for the high-resolution characterization of dielectric substrates and oil samples. A three-dimensional dielectric container is attached to the sensor and acts as a pool for the sample under test (SUT). In the presented technique, the dielectric substrates and oil samples can interact directly with the electromagnetic (EM) field emitted from the resonator. For the sake of sensor calibration, a relation between the relative permittivity of the dielectric samples and the resonant frequency of the sensor is established in the form of an inverse regression model. Comparisons with state-of-the-art sensors indicate the superiority of the presented design in terms of oil characterization reliability. The significant technical contributions of this work include the employment of the rigorous optimization of geometry parameters of the sensor, leading to its superior performance, and the development and application of the inverse-model-based calibration procedure.

... In this context, one of the most attractive types of resonators is complementary split-ring resonators (CSRRs), which are artificial engineered structures [14] featuring planar design, inexpensive fabrication suitable for mass production, and versatility of potential applications. Various aspects of CSRRs, including equivalent circuit modeling [15], electrical characterization [16], and miniaturization [17], have been broadly investigated in the literature thus far. The crucial parameter of microwave sensors is sensitivity [18], depending on the resonant frequency of the resonator, and the EM properties of the MUT. ...

... In practice, parameter tuning is realized using interactive methods such as parameter sweeping. For example, in [17], the CSRR is optimized using two geometric parameters by changing one parameter individually, keeping the other parameter constant. In [23], four geometric parameters are used to optimize the resonant frequency of the CSRR, again, using the parametric sweep method. ...

... The CSRR has been optimized for four resonant frequencies, by taking into account the relevant performance figures as well as fabrication constraints. The surrogate identified using the preoptimized data allows us to redesign the CSRR parameters over a broad range of operating frequencies (5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) and at minimum computational expenses. The specific sensor design optimized for 15 GHz has been experimentally validated. ...

Design optimization of multivariable resonators is a challenging topic in the area of microwave sensors for industrial applications. This article proposes a novel methodology for rapid redesign and parameter tuning of complementary split-ring resonators (CSRRs). Our approach involves inverse surrogate models established using preoptimized resonator data as well as analytical correction techniques to enable rapid adjustment of geometry parameters and CSRR optimization over broad ranges of operating frequencies. The tuning process is arranged to precisely allocate the operating frequency while maximizing the quality factor of the circuit. The procedure is generic and characterized by an extremely low computational cost of up to two electromagnetic (EM) analyses of the circuit at hand (not counting the inverse model setup). The presented technique is demonstrated using a circular CSRR coupled to a microstrip transmission line (MTL) and optimized to operate between 5 and 20 GHz. The design optimized for 15 GHz is fabricated and experimentally validated using a vector network analyzer. The sensor works in the transmission mode and senses the shift in resonance frequency determined by the properties of the material under test (MUT). Furthermore, an inverse regression model is developed that allows for directly finding the unknown permittivity of the MUT based on the measured resonant frequencies of the sensor. The obtained results corroborate the design utility of the proposed optimization method, as well as the practical usefulness of the specific CSRR structure developed with the aid thereof.

... And Eq. (38) is not applicable for every component; homologous fitting formula can be presented for diverse types of components. There are some recent works on this topic [102][103][104][105], and Yao [57] pointed that the methods modified via the average stress are unsatisfactory due to the inapplicability of average stress on describing the arbitrary notch geometry. Therefore, more systematic researches should be established. ...

Under external loadings, notched components always show varying degrees of stress concentration. Accordingly, different kinds of approaches have been presented to characterize notch fatigue behaviours under complex loading histories. Among them, the considering of the stress gradient effect is a popular perspective, together with the fatigue damage zone and critical distance concepts. This work systematically reviews recent advances on notch fatigue analysis considering the stress gradient effect. Specifically, four approaches are summarized and explored, namely the local stress/strain-based approaches, critical distance-based approaches, critical plane-based approaches, and weighting control parameters-based approaches. This review aims to provide a systematic review and comparison on these methods, therefore to offer a reference for subsequent research on notch fatigue.

... Metamaterials are classified into two broad groups in which one is the split ring resonators (SRRs), introduced by Pendry et al., [3] and other is the complementary SRR (CSRR), introduced by Falcone et al. [4]. They have been used in the miniaturization of oscillators [5,6], microwave filters [7,8], microwave sensors [9][10][11][12], and communication antennas [13][14][15][16]. ...

Metamaterial-based microwave sensor having novel and compact structure of the resonators and the slotted microstrip transmission line is proposed for highly precise measurement of dielectric properties of the materials under test (MUTs). The proposed sensor is designed and simulated on Rogers’ substrate RO4003C by using the ANSYS HFSS software. A single and accumulative notch depth of -44.29 dB in the transmission coefficient (S21) is achieved at the resonant frequency of 5.15 GHz. The negative constitutive parameters (permittivity and permeability) are extracted from the S-parameters which are the basic property of metamaterials or left handed materials (LHMs). The proposed sensor is fabricated and measured through the PNA-X (N5247A). The sensitivity analysis is performed by placing various standard dielectric materials onto the sensor and measuring the shift in the resonant frequencies of the MUTs. A parabolic equation of the proposed sensor is formulated to approximate the resonant frequency and the relative permittivity of the MUTs. A very strong agreement among the simulated, measured, and calculated results is found which reveals that the proposed sensor is a highly precise sensor for the characterization of dielectric properties of the MUTs. Error analysis is performed to determine the accuracy of the proposed sensor. A very small percentage of error (0.81%) and a very low standard deviation are obtained which indicate high accuracy of the proposed sensor.

... The size of the CMSSR resonator is 6 mm × 6 mm, and the width of resonator lines is 0.5 mm. The effect of geometrical dimensions on the bandwidth and unloaded Q factor is already discussed in Reference [45]. According to [45], the maximum value of the Q factor is achieved using a 0.5 mm wide resonator. ...

... The effect of geometrical dimensions on the bandwidth and unloaded Q factor is already discussed in Reference [45]. According to [45], the maximum value of the Q factor is achieved using a 0.5 mm wide resonator. The substrate and pool material are selected due to low cost, and the thickness is chosen due to easy availability. ...

This paper investigates the effect of complementary metaresonator for evaluation of vegetable oils in C and X bands. Tremendously increasing technology demands the exploration of complementary metaresonators for high performance in the related bands. This research probes the complementary mirror-symmetric S resonator (CMSSR) that can operate in two bands with compact size and high sensitivity features. The prime motivation behind the proposed technique is to utilize the dual notch resonance to estimate the dielectric constant of the oil under test (OUT). The proposed sensor is designed on a compact 30×25 mm2 and 1.6 mm thick FR-4 substrate. A 50 Ω microstrip transmission line is printed on one side, while a unit cell of CMSSR is etched on the other side of the substrate to achieve dual notch resonance. A Teflon container is attached to CMSSR in the ground plane to act as a pool for the OUT. According to the simulated transmission spectrum, the proposed design manifested dual notch resonance precisely at 7.21 GHz (C band) and 8.97 GHz (X band). A prototype of complementary metaresonator sensor is fabricated and tested using CEYEAR AV3672D vector network analyzer. The comparison of measured and simulated data shows that the difference between the first resonance frequency is 0.01 GHz and the second is 0.04 GHz. Furthermore, a mathematical model is developed for the complementary metaresonator sensor to evaluate dielectric constant of the OUT in terms of the relevant, resonant frequency.

... The first notch has a resonance at 5.37 GHz with a notch depth of -76.21 dB, while the second notch has a resonance at 7.95 GHz with a notch depth of -20.14 dB. using the following relation [37]: ...

In this work, a compact, inexpensive, and efficient dual band microwave sensor is proposed. The sensor is based on two Complementary Symmetric Split-Ring Resonators (CSSRRs) and possesses a high Q factor and wide sensing range. These CSSRRs are coupled electrically with two inductive patches to the Microstrip Transmission Line (MTL). This combination provides two dual bands, first at 5.35 GHz with a notch depth of -55.20 dB and second at 7.99 GHz with a notch depth of -22.54 dB. The sensor works in transmission mode and senses shift in frequency. Some commonly available dielectric substrates with relative permittivity ranges between 1 and 12 are considered Material Under Test (MUT), and detailed sensitivity analysis is being performed for each band. The dual band sensor is fabricated on a low-cost, widely available FR4 substrate and measured by CEYEAR AV3672D vector network analyzer. Additionally, the least square curve fitting method is used to develop a mathematical model for the measured results. An excellent agreement is observed between simulated, measured, and formulated results.

... Thus, a narrower band and a sharper dip of the cut-off frequency of the bandwidth lead to higher Q-factor value. Figure 17 demonstrates the measurement of the quality factor obtained from the scattering parameter S21 based on the bandpass [36,85,86] and bandstop responses [16,76,[88][89][90][91]. ...

Recent developments in the field of microwave planar sensors have led to a renewed interest in industrial, chemical, biological and medical applications that are capable of performing real-time and non-invasive measurement of material properties. Among the plausible advantages of microwave planar sensors is that they have a compact size, a low cost and the ease of fabrication and integration compared to prevailing sensors. However, some of their main drawbacks can be considered that restrict their usage and limit the range of applications such as their sensitivity and selectivity. The development of high-sensitivity microwave planar sensors is required for highly accurate complex permittivity measurements to monitor the small variations among different material samples. Therefore, the purpose of this paper is to review recent research on the development of microwave planar sensors and further challenges of their sensitivity and selectivity. Furthermore, the techniques of the complex permittivity extraction (real and imaginary parts) are discussed based on the different approaches of mathematical models. The outcomes of this review may facilitate improvements of and an alternative solution for the enhancement of microwave planar sensors’ normalized sensitivity for material characterization, especially in biochemical and beverage industry applications.

... The equivalent lumped element circuit model of the coupled structure is shown in Figure 1d, the resonance frequency of the equivalent circuit can be calculated using the following relation [61]: The 3D model of the proposed sensor is simulated in ANSYS HFSS software with the simulation conditions given in ref. [58]. The proposed sensor shows a resonance at 15.17 GHz with notch depth of -39.84 dB as shown in Figure 2. The unloaded quality factor of the proposed sensor is 505 which can be calculated by the following relation [62]: The 3D model of the proposed sensor is simulated in ANSYS HFSS software with the simulation conditions given in ref. [58]. The proposed sensor shows a resonance at 15.17 GHz with notch depth of -39.84 dB as shown in Figure 2. The unloaded quality factor of the proposed sensor is 505 which can be calculated by the following relation [62]: ...

... The proposed sensor shows a resonance at 15.17 GHz with notch depth of -39.84 dB as shown in Figure 2. The unloaded quality factor of the proposed sensor is 505 which can be calculated by the following relation [62]: The 3D model of the proposed sensor is simulated in ANSYS HFSS software with the simulation conditions given in ref. [58]. The proposed sensor shows a resonance at 15.17 GHz with notch depth of -39.84 dB as shown in Figure 2. The unloaded quality factor of the proposed sensor is 505 which can be calculated by the following relation [62]: ...

In this paper, an extremely sensitive microwave sensor is designed based on a complementary symmetric S shaped resonator (CSSSR) to evaluate dielectric characteristics of low-permittivity material. CSSSR is an artificial structure with strong and enhanced electromagnetic fields, which provides high sensitivity and a new degree of freedom in sensing. Electromagnetic simulation elucidates the effect of real relative permittivity, real relative permeability, dielectric and magnetic loss tangents of the material under test (MUT) on the resonance frequency and notch depth of the sensor. Experiments are performed at room temperature using low-permittivity materials to verify the concept. The proposed design provides differential sensitivity between 102% to 95% as the relative permittivity of MUT varies from 2.1 to 3. The percentage error between simulated and measured results is less than 0.5%. The transcendental equation has been established by measuring the change in the resonance frequency of the fabricated sensor due to interaction with the MUT.

... The curve that relates the differential output to the differential input is termed as a transfer function of the sensor and its slope is the sensitivity of the sensor. Mathematically it can be expressed as [37]: where ɛ rd = ɛ r2 -ɛ r1 is the differential input of the sensor and f d = f u -f l is the differential output of the sensor. In our case the differential input is the difference between the relative permittivity of MUT and air while the differential output is the difference of resonance frequencies of the sensor due to interaction with air and MUT. ...

In this paper, three dual notch microwave sensors are presented based on a microstrip transmission line and complementary metamaterial resonators. The main aim of this paper is to compare the constitutive parameters and sensitivity of all three dual notch sensors which are based on complementary symmetric split ring resonator (CS-SRR), complementary asymmetric split ring resonator (CAS-SRR) and complementary bisymmetric split ring resonator (CBS-SRR). The main motivation beyond the presented work is to use dual notches to estimate the relative permittivity of material under test (MUT). Electromagnetic simulation elucidates the origin of dual mode resonance of all the three resonators. Sensitivity analysis is performed on each sensor by using fifteen MUTs with relative permittivity ranges from 1.006 to 16.5 and constant dimensions 10 mm x 10 mm x 1 mm. To verify the concept, a sensor is fabricated and its response is measured using a vector network analyzer (AV3672). Using curve fitting technique the shift in the resonance frequencies of the fabricated sensor due to interaction with MUT is presented as a function of permittivity. Simulated, measured and formulated results are in good agreement with each other.

Low permittivity materials are widely used in many electronic systems. However, dielectric measurement on low permittivity material is challenging. To address this difficulty, a dual-band resonant sensor is developed. The proposed sensor is an improved design from the complementary square spiral resonator (CSSR). By adding a square patch on top of the resonant cell, the local field is significantly increased. Therefore, the interaction between field and material is strengthened, resulting in enhancement in measurement sensitivity. Owing to the increased sensitivity, low permittivity samples down to 1.19 can be measured with an accuracy of better than 3%. Such results demonstrate that this sensor is promising for low permittivity characterization. Moreover, this sensor is also capable of measuring samples with permittivity in the range of 2-10, with an accuracy of 5%. Furthermore, two resonances are created, enabling dual-band operation. The unloaded resonances take place at 2.00 GHz and 5.41 GHz. Particularly, the measurement can be conducted simultaneously in the two operation bands. Measured results demonstrate that the accuracy and sensitivity are satisfactorily high and comparatively superior to the designs in the literature for low permittivity measurement.