Lijuan Su

Miniature Microwave Notch Filters and Comparators Based on Transmission Lines Loaded with Stepped Impedance Resonators (SIRs)

In this paper, different configurations of transmission lines loaded with stepped impedance resonators (SIRs) are reviewed. This includes microstrip lines loaded with pairs of SIRs, and coplanar waveguides (CPW) loaded with multi-section SIRs. Due to the high electric coupling between the line and the resonant elements, the structures are electrically small, i.e., dimensions are small as compared to the wavelength at the fundamental resonance. The circuit models describing these structures are discussed and validated, and the potential applications as notch filters and comparators are highlighted.

Modeling Metamaterial Transmission Lines Loaded With Pairs of Coupled Split-Ring Resonators

A lumped-element equivalent circuit model of the unit cell of metamaterial transmission lines loaded with pairs of coupled split-ring resonators (SRRs) is presented. It is assumed that the dominant coupling mechanism between the SRRs forming the pair is magnetic, and that the distance between SRRs of adjacent cells is high enough to neglect such additional inter-resonator coupling. SRRs are oriented with their symmetry plane orthogonal to the line axis. Under these conditions, the line-to-SRR coupling is also magnetic, the electric coupling being negligible. The presented model accounts for the rupture of symmetry that can be caused, for instance, by asymmetric dielectric loading of the SRRs. Thus, the analysis is carried out on a general model where the SRRs of the pair have different inductance and capacitance. Then, different cases are studied, in particular a line with identical SRRs, and a line with different SRRs, but with the same resonance frequency. It is shown that coupling between SRRs tends to far or split the resonance frequencies of the loaded lines (transmission zeros), except for the symmetric case, where only one resonance (different to the one of uncoupled SRRs) appears. The model is validated by comparing circuit simulations using extracted parameters with electromagnetic simulations and experimental data.

Modeling and Applications of Metamaterial Transmission Lines Loaded With Pairs of Coupled Complementary Split-Ring Resonators (CSRRs)

This letter is focused on the modeling, analysis, and applications of microstrip lines loaded with pairs of electrically coupled complementary split-ring resonators (CSRRs). Typically, these epsilon-negative (ENG) metamaterial transmission lines are implemented by loading the line with a single CSRR (etched beneath the conductor strip) in the unit cell. This provides a stopband in the vicinity of the CSRR resonance. However, by loading the line with a pair of CSRRs per unit cell, it is possible to either implement a dual-band ENG transmission line (useful, for instance, as a dual-band notch filter), provided the CSRRs are tuned at different frequencies, or to design microwave sensors and comparators based on symmetry disruption (in this case by using identical CSRRs and by truncating symmetry by different means, e.g., asymmetric dielectric loading). The design of these CSRR-based structures requires an accurate circuit model able to describe the line, the resonators, and the different coupling mechanisms (i.e., line-to-resonator and inter-resonator coupling). Thus, a lumped element equivalent circuit is proposed and analyzed in detail. The model is validated by comparison to electromagnetic simulations and measurements. A proof-of-concept of a differential sensor for dielectric characterization is proposed. Finally, the similarities of these structures with coplanar waveguide transmission lines loaded with pairs of SRRs are pointed out.

Transmission lines loaded with pairs of magnetically coupled stepped impedance resonators (SIRs): Modeling and application to microwave sensors

This paper is focused on the analysis and modeling of transmission lines loaded with pairs of shunt-connected stepped impedance resonators (SIRs), and their application to differential sensors for dielectric characterization, and for diagnosis and quality control of material samples by comparison to a reference. It is demonstrated that by placing the SIR junctions in the same position of the line, the SIRs are magnetically coupled. Such coupling has significant influence on the sensitivity of the sensor, determined by the split in frequency caused by an asymmetric dielectric loading of the SIRs. The circuit model of the structure, including magnetic coupling between SIRs, is proposed and validated through electromagnetic simulations and measurements. Finally, the principle of sensing is experimentally validated by a proof-of-concept demonstrator.

Splitter/Combiner Microstrip Sections Loaded With Pairs of Complementary Split Ring Resonators (CSRRs): Modeling and Optimization for Differential Sensing Applications

This paper focuses on the analysis of splitter/ combiner microstrip sections where each branch is loaded with a complementary split ring resonator (CSRR). The distance between CSRRs is high, and hence, their coupling can be neglected. If the structure exhibits perfect symmetry with regard to the axial plane, a single transmission zero (notch) at the fundamental resonance of the CSRR, arises. Conversely, two notches (i.e., frequency splitting) appear if symmetry is disrupted, and their positions are determined not only by the characteristics of the CSRRs but also by the length of the splitter/combiner sections. A model that includes lumped elements (accounting for the CSRR-loaded line sections) and distributed components (corresponding to the transmission lines) is proposed and used to infer the position of the transmission zeros. Frequency splitting is useful for the implementation of differential sensors and comparators based on symmetry disruption. Using the model, the length of the splitter/combiner sections necessary to optimize the sensitivity of the structures as sensing elements is determined. Parameter extraction and comparison with electromagnetic simulations and measurements in several symmetric and asymmetric structures is used to validate the model. Finally, a prototype device sensor/comparator based on the proposed CSRR-loaded splitter/combiner microstrip sections is presented.

Transmission Lines Loaded With Pairs of Stepped Impedance Resonators: Modeling and Application to Differential Permittivity Measurements

Differential techniques are widely used in communication and sensor systems, as these techniques have been shown to improve the performance. This paper shows how differential sensing of permittivity can be conducted in a simple way. For that purpose, a microstrip line loaded with a pair of stepped-impedance resonators is used in two different resonator connections: parallel and cascade. Each resonator is individually perturbed dielectrically so that: 1) when the two individual permittivities are identical, the structure exhibits a single resonance frequency and 2) when the permittivities are different, resonance frequency splitting occurs, giving rise to two resonances (all these resonances are seen in the form of transmission zeroes). The two sensing approaches are successfully validated through electromagnetic simulations and experiments. By virtue of a differential measurement, robustness against changing ambient factors that may produce sensor miscalibration is expected.

Microwave Microfluidic Sensor Based on a Microstrip Splitter/Combiner Configuration and Split Ring Resonators (SRRs) for Dielectric Characterization of Liquids

A microwave microfluidic sensor for dielectric characterization of liquids in real time is presented in this paper. The sensor is implemented in microstrip technology and consists of a symmetric splitter/combiner configuration loaded with a pair of identical split ring resonators (SRRs) and microfluidic channels placed on top of them (gap region). The sensor works in differential mode and sensing is based on frequency splitting. Thus, if the structure is unloaded or if it is symmetrically loaded with regard to the axial plane, only one transmission zero (notch) in the frequency response appears. However, if the axial symmetry is disrupted (e.g., by the presence of different liquids in the channels), two transmission zeros arise, and the difference in magnitude (notch depth) and frequency between such transmission zeros is indicative of the difference in the dielectric properties (complex dielectric constant). A circuit schematic, including transmission line sections to describe the distributed components, lumped elements to account for the SRRs and their coupling to the lines and lumped elements to model the liquid properties, is presented and validated. After proper calibration, the functionality of the proposed sensor is demonstrated by measuring the complex permittivity in solutions of deionized water and ethanol as a function of the ethanol content.

Configurations of Splitter/Combiner Microstrip Sections Loaded with Stepped Impedance Resonators (SIRs) for Sensing Applications

In this paper, several configurations of splitter/combiner microstrip sections loaded with stepped impedance resonators (SIRs) are analyzed. Such structures are useful as sensors and comparators, and the main aim of the paper is to show that the proposed configurations are useful for the optimization of sensitivity and discrimination. Specifically, for comparison purposes, i.e., to determine anomalies, abnormalities or defects of a sample under test (SUT) in comparison to a reference sample, it is shown that up to three samples can be simultaneously tested. Simple models of the proposed structures are presented, and these models are validated through electromagnetic simulation and experiment. Finally, the principle of operation is validated through a proof-of-concept demonstrator.

Cascaded splitter/combiner microstrip sections loaded with complementary split ring resonators (CSRRs): Modeling, analysis and applications

This paper is focused on the study of splitter/combiner microstrip sections where each branch is loaded with a complementary split ring resonator (CSRR). If the structure is symmetric with regard to the axial plane, only one transmission zero (notch) in the transmission coefficient arises. Conversely, two notches appear if symmetry is disrupted. A model that combines lumped elements (describing the CSRR-loaded line sections) and distributed components (accounting for the transmission lines) is proposed and used to obtain the position of the transmission zeros. The model is validated through parameter extraction and comparison to electromagnetic simulations and measurements, where up to three cascaded splitter/combiner sections (symmetric and asymmetric) are considered. Finally, the three-section symmetric structure is asymmetrically loaded to demonstrate the possibility of using the proposed device as a microwave sensor/detector able to identify defects or abnormalities between a sample under test (SUT) and a reference sample. With this technique, as many samples as splitter/combiner sections can be sensed simultaneously.

Transmission line metamaterials based on pairs of coupled split ring resonators (SRRs) and complementary split ring resonators (CSRR): A comparison to the light of the lumped element equivalent circuits

This paper analyzes and compares two types of transmission line metamaterials: (i) coplanar waveguide (CPW) transmission lines loaded with pairs of magnetically coupled split ring resonators (SRRs), and (ii) microstrip lines loaded with pairs of electrically coupled complementary split ring resonators (CSRRs). Both structures are described by lumped element equivalent circuit models rather different. However, both structures exhibit very similar phenomenology, and there is a mapping between the elements of both models that gives identical results for the analytical expressions providing the resonance frequencies (transmission zeros) that these lines exhibit. It is shown that these artificial lines are useful as dual-notched filters and as differential sensors and comparators.