Transmission lines loaded with electrically small resonators : modeling, analysis and applications to microwave sensors

Microwave sensing for material characterization is a promising and developing technology which has been successfully used in recent decades for various applications in industry, chemistry, engineering, medicine and biomedical area, etc. Electrical characteristics of materials depend on their dielectric properties, whose main parameter is the complex permittivity. It describes the material behavior when it is subjected to an external electromagnetic field. Different materials present different permittivities which are also variable in function of the frequency of the applied electromagnetic field. Therefore, when a microwave structure is loaded with a material under test (MUT), it can be possible to characterize this material. This thesis focuses on the modeling, analysis and applications of planar transmission lines loaded with electrically small resonators as microwave sensors for material characterization. Planar transmission lines loaded with electrically small resonators as sensors for material characterization have the advantages of easy to fabricate, low manufacturing cost, compactness in size and simple sample preparation, thus it is the method utilized in this thesis to design different structures. The electrically small resonators used throughout the thesis are split ring resonators (SRRs), complementary split ring resonators (CSRRs), stepped impedance resonators (SIRs) and the complementary counterpart – slot-SIRs. These resonators are subwavelength particles, typically one tenth of the guided wavelength or less at their fundamental resonant frequency, in contrast to the conventional transmission line resonators. Therefore, high level of miniaturization is expected by using these particles. In addition, they have strong response to electromagnetic fields and their properties are substantially affected by MUTs. In this thesis, the sensing techniques are based on frequency splitting and frequency variation. For frequency splitting strategy, structures could be used as comparators and microwave sensors. The principle is, for structures of transmission lines loaded with two identical resonators, transmission zero splits to two if one of the resonators is loaded with a MUT which is different from the loaded reference material in the other resonator. Otherwise, only one transmission zero exists. Besides, a step with materials possessing known dielectric properties to calibrate the structure is needed before characterizing the MUTs. Through different output results by loading MUTs, with the relation to variable causing the changes, the dielectric permittivities of MUTs could be obtained. As for frequency variation strategy, an accurate circuit model including not only the loss of the substrate, but also the losses of the resonator (conductive loss from conductive strip and loss from substrate), is proposed, and analytical expressions to obtain the dielectric constant and loss tangent of MUTs are provided. Several common transmission lines loaded with those electrically small resonators have been studied in this thesis. Their lumped element equivalent circuit models have been proposed and analyzed, through which analytical expressions to predict transmission zeros are deduced as well. Among all the proposed structures serving as sensing purpose, it is noticeable that the mutual coupling between the loaded resonators forming the pair has the effect of degrading the sensitivity. Topologies to prevent those inter-resonator couplings are introduced, i.e., microstrip section with each line loaded with a CSRR or a SIR, in a splitter/combiner configuration, and a microstrip line loaded with two SIRs, in cascade configuration. For the splitter/combiner configuration, each resonator individually coupled to a line, if perturbing the resonators by extra dielectrics, the new emerging transmission zeros positons are influenced by an interfering phenomenon of two resonator-loaded lines (affected by the electric length of the microstrip section). In order to obtain enhanced sensitivity for small perturbations, the short circuit to ground caused by resonating the shunt circuit branch (where the resonator locates) has to be translated to the input/output, which provide a condition to get optimum electric length of these lines, to obtain improved sensitivity. As for the cascade configuration, two SIRs separate from each other through a transmission line with a certain electric length (long enough to avoid inter-resonator coupling). From the equivalent circuit model, the positions of two transmission zeros do not change even if the line in-between the two SIRs is different when two resonators are perturbed. But if the electric length of the transmission line in-between the SIRs is set to be pi, the circuit model could be simplified to the same as the structure with two SIRs directly in contact with the line in the same junction, without mutual inter-resonant coupling, thus improving the sensitivity. In order to demonstrate applications as comparators and sensors, proof-of-concept prototypes have been fabricated and experiments have been performed, validating the structures and application purposes. The results from the measurements are in good agreement with lumped equivalent circuit model simulations and EM simulation results.