Pair Of Coupled Resonators Research Articles

Validating an algebraic approach to characterizing resonator networks

Resonator networks are ubiquitous in natural and engineered systems, such as solid-state materials, electrical circuits, quantum processors, and even neural tissue. To understand and manipulate these networks it is essential to characterize their building blocks, which include the mechanical analogs of mass, elasticity, damping, and coupling of each resonator element. While these mechanical parameters are typically obtained from response spectra using least-squares fitting, this approach requires a priori knowledge of all parameters and is susceptible to large error due to convergence to local minima. Here we validate an alternative algebraic means to characterize resonator networks with no or minimal a priori knowledge. Our approach recasts the equations of motion of the network into a linear homogeneous algebraic equation and solves the equation with a set of discrete measured network response vectors. For validation, we employ our approach on noisy simulated data from a single resonator and a coupled resonator pair, and we characterize the accuracy of the recovered parameters using high-dimension factorial simulations. Generally, we find that the error is inversely proportional to the signal-to-noise ratio, that measurements at two frequencies are sufficient to recover all parameters, and that sampling near the resonant peaks is optimal. Our simple, powerful tool will enable future efforts to ascertain network properties and control resonator networks in diverse physical domains.

Design of In-Line Filters With Strongly Coupled Resonator Triplet

This paper presents a complete design procedure for in-line evanescent mode filters using an innovative pseudoelliptic structure, namely, the strongly coupled resonator triplet (SCRT). The SCRT can be seen as the combination of a strongly coupled resonator pair (SCRP) and a third resonator next to the pair. Compared to the SCRP, which at the passband frequencies generates a pole and a transmission zero, the new SCRT is capable of generating an additional passband pole, thus leading to the design of more compact in-line filters. Similar to the SCRP, the basic structure for filter design purposes is obtained by embedding the SCRT between two outer resonators. The coupling mechanisms and functional properties of this basic structure are explained. A suitable circuit model for the SCRT is introduced, thus allowing the synthesis of a low-pass prototype as well as the evaluation of the coupling coefficients and resonating frequencies to assign to the physical filtering structure. The proposed design procedure is validated by means of several examples, one of which including the detailed dimensions and experimental results of a manufactured prototype.

Circularly polarised integrated filtering antenna with polarisation reconfigurability

A new design of circularly polarized (CP) integrated filtering antennas with reconfigurable polarization is proposed in this paper. Two phase-reconfigurable coupled λ/2-resonator pairs have been used to feed the antenna and generate the 2nd-order filtering response and the circular polarization simultaneously. By switching the PIN diodes inserted in the feeding network, a phase difference of +90° or - 90° can be realized at the outputs of the feeding network. This renders the antenna’s capability of switching its polarization from right hand circular polarization (RHCP) to left hand circular polarization (LHCP) or vice versa. The use of the coupled-resonator pairs significantly improves the frequency selectivity and out-of-band rejection of the CP antenna. To the best of the authors’ knowledge, this is the first report of a multifunctional antenna which has integrated filtering performance, circular polarization and polarization reconfigurability. To verify the design concept, a reconfigurable CP antenna operating at 2.45 GHz is implemented. The simulated and measured results agree well with each other and show that the antenna has an impedance bandwidth of 4.5 %, an average in-band gain of 6.0 dBic (LHCP)/6.1 dBic (RHCP), out-of-band rejections of greater than 10.8 dB, and 3-dB AR bandwidth of 9.4 %/10.5 %.

Design of compact filtering rat‐race hybrid with λ /2‐resonators

A novel compact filtering rat-race hybrid coupler with improved upper stopband is presented in this letter. Four coupled-resonator pairs are utilized to replace the λ/4- and 3λ/4-transmission lines in the conventional hybrid. Each coupled-resonator pair exhibits a bandpass filtering response and acts as a K-inverter. Eight resistors are placed at the center of the λ/2-resonators to suppress the 2nd-harmonic. For verification, a filtering rat-race hybrid is implemented with a center frequency of 1.27 GHz and 20-dB rejection band of 2.73 f0. Good in-phase and out-of-phase characteristics are obtained. The proposed device has a simple circuit topology, compact size and good performance.

MICROSTRIP DUAL-BAND BANDPASS FILTER USING U-SHAPED RESONATORS

Coupled resonators are widely used in the design of filters with dual-passband responses. In this paper, we present a dual-band bandpass filter using only couplings between adjacent resonators without cross-couplings. The dual-band bandpass filter with centre frequencies of 1747MHz and 1879MHz respectively is designed and fabricated using microstrip U-shaped resonators. Using the coupled resonator pair as a dual-band cluster, a miniaturised structure is achieved as compared to the conventional topology. The measured responses agree closely with the simulations.

LTCC Multilayered Helical Filters With a Mixed Electric and Magnetic Coupling Structure

In this paper, compact multilayered helical resonators and various coupled resonator pairs with a mixed electric and magnetic coupling structure were developed. A multilayer structure is suitable for miniaturization and enhances mutual coupling. A pair of transmission zeros (TZs) can be created using mixed coupling between two coupled helical resonators, achieving superior frequency selectivity. An equivalent circuit model was proposed to analyze the creation of TZs. The planar helical structure provides design flexibility in control of TZs. Eight coupled resonator pairs were proposed for synthesizing various filter responses. An experimental second-order helical filter was fabricated using low-temperature cofired ceramic technology. The measurement results of this second-order filter showed the center frequency to be 0.976 GHz, with two TZs located at 0.8 and 1.4 GHz. The insertion loss was lower than 1.96 dB, and the return loss was 25 dB at $f_{0}$ . The size of this filter was only $5.7~\textrm {mm} \times 3.4$ mm ( $0.051~\lambda _{g}\times 0.031~\lambda _{g}$ ), which is highly compact compared with filters from other published studies. In addition, the proposed coupled pairs have potential in the construction of high-order filters with superior frequency selectivity by cascading multiple coupled helical pairs.

A spatial filter bank model of the Veselago–Pendry superlens

We present a canonical filter bank model that emulates the transmission of both propagating and evanescent electromagnetic fields through a Veselago–Pendry Superlens. The model consists of an array of coupled resonator pairs; each pair transmits one term of the spatial Fourier series of the object field. In addition to emulating the steady-state transfer function of the superlens, the model also approximates its dynamic response. Closed-form expressions for the values of the circuit elements are derived in terms of the geometry and the constitutive parameters of the lens at the frequency of operation in the steady state. Losses can be included by adding dissipative elements to the equivalent circuit. The concept of the Veselago–Pendry superlens as a filter in k-space provides physical insight into the resonant nature of image transmission and may suggest new ways to realize such a device.

DESIGN OF MINIATURIZED BANDPASS FILTERS USING QUASI-LUMPED MULTILAYER RESONATORS

A novel design procedure for a compact multilayer bandpass filter is proposed and examined. The filter is realized using quasi-lumped multilayer resonators. Based on the orientation of these coupled-resonator pairs, a second-order bandpass filter is realized with transmission zeros. In order to achieve a low external quality factor, i.e., a wider filter bandwidth, different types of feeder realization are considered. The design methodology with all relevant steps is presented and the equivalent-circuit of the resonator is also derived and verified. The filter design is simulated using a 3D electromagnetic model and validated by measurements on the fabricated filter. The simulation and experimental results are in good agreement.

A Novel Miniaturized Bandpass Filter Using Interdigital-Coupled Spiral-Shaped Resonators

In this paper, we present a novel miniaturized bandpass filter with high-selectivity performance and compact topology. For circuit size reduction, a spiral-shaped resonator with three branches is developed and examined. By suitably combining the resonators as the interdigital form, a special coupling scheme, which simultaneously provides electric and magnetic couplings, can be obtained readily. To investigate the new coupling scheme, the equivalent-circuit model of the proposed filter is derived and the lumped parameters are extracted. It is found that two transmission zeros can be realized close to the passband edges, resulting in high skirt selectivity. Meanwhile, the interdigital combination of the coupled-resonator pair makes the filter structure more compact. To verify the presented concept, an experimental filter operating at 1 GHz is demonstrated. The active area of the filter is only 11.6mm x 11.6 mm (0.061λg x 0.061λg), where λg is the guided wavelength at the operating frequency.

Compact interlocked-coupled filter using folded stepped-impedance resonators

A microstrip interlocked-coupled bandpass filter is proposed with a markedly compact structure. The low-impedance open-end line of the quarter-wavelength Stepped-Impedance Resonator (SIR) is replaced by two open-end high-impedance lines, which not only facilitate the coupling mechanism but also provide the strong electric coupling between resonators. With the proper utilization of folded SIRs, the occupied area of coupled-resonator pair can be reduced. By applying the proposed coupled-resonator pair, the passband filter with the compact size can be realized. Good agreement between measured and simulated results is observed. The proposed filter is desirable for compact and high-performance microwave circuit applications.

STOPBAND-EXTENDED BALANCED FILTERS USING BOTH λ/4 AND λ/2 SIRS WITH COMMON-MODE SUPPRESSION AND IMPROVED PASSBAND SELECTIVITY

Benefltting from the simultaneous utilization of quarter- wave (‚/4) and half-wave (‚/2) microstrip resonators, a via-free balanced bandpass fllter (BPF) with direct-coupled scheme is presented in this study. In the beginning, a single-ended fllter with transmission zeros (TZs) is newly proposed and the mechanism of creating two TZs around the passband without necessitating cross couplings is adopted. The TZs can be made structure-inherent based on the coexisted out-of-phase couplings among a coupled-resonator pair. On the foundation of the presented single-ended fllter, a balanced fllter featuring extended difierential-mode (DM) stopband, good common- mode (CM) suppression, and improved passband selectivity has been designed and implemented. The DM stopband extension is achieved by misaligning the higher-order harmonic frequencies of each resonator in the DM bisected circuit while the CM suppression is accomplished by both harmonic misalignment and careful designed coupled structure in the CM bisected circuit. Eventually, a demonstrated balanced fllter centering at 1.5GHz possesses DM stopband extended up to 8f d 0 , where f d 0 denotes the DM operation frequency, and its CM rejection ratio (CMRR) within DM passband better than 51.9dB is attained. For measurement convenience, the DM characterizations have been accomplished by 2-port network analyzer with simple rat-race baluns and are found relatively accurate within the i15dB bandwidth of the utilized baluns.

Band-Rejected Ultrawideband Planar Monopole Antenna With High Frequency Selectivity and Controllable Bandwidth Using Inductively Coupled Resonator Pairs

A novel band-rejected ultrawideband (UWB) planar monopole antenna is investigated. By utilizing the resonance nature of folded strips and a new inductive coupling scheme, the antenna demonstrates bandstop-filter-like response with high frequency selectivity and controllable bandwidth at the rejection band. The design methodology is introduced. The simulated and measured results including impedance matching, radiation patterns, and gain responses are investigated. An antenna equivalent circuit model with improved accuracy is discussed as well. When compared with our previous work, the new design demonstrates substantial improvements in many aspects. The argument will be discussed and verified carefully throughout the communication.

Dual-band bandpass filter using coupled resonator pairs

This letter proposes and fabricates a novel dual-band bandpass filter topology. The proposed topology facilitates the split resonating frequencies of coupled resonator pairs in realizing the dual-band response and introduces transmission zeros for improving the stopband attenuation. The semi-lumped prototype enables the integration of the filter in a multilayer circuit for miniaturized implementation. Finally, a design example fabricated with low temperature co-fired ceramic (LTCC) technology is presented for validating the filter configuration.

An improved resonance equation for AT-cut quartz crystals

A modified version of the conventional resonance equation for AT-cut quartz resonators is shown to correctly predict the optimum dimensional ratios for single resonators and to give improved accuracy when designing coupled resonator pairs. The equation is based on the simple waveguide cavity analogy first proposed by Mortley.