Q-factor measurement of quasi-optical dielectric resonators under conditions of the whispering gallery mode degeneration removal

An approach that allows one to determine the unloaded quality factor of a quasi-optical dielectric resonator (QDR) under conditions of the resonance line splitting corresponding to twofold degenerative whispering gallery (WG) mode has been proposed. The resonator is represented by an equivalent network as two oscillatory circuits with a certain coupling between them. The approach allows one to determine the Q-factor of a single oscillatory circuit using three measured parameters, namely: 1) ratio between specific amplitudes of the resonator amplitude-frequency response (or its second derivative); 2) resonant frequency; and 3) frequency splitting of the response (or its respective second derivative). The proposed technique is illustrated by the measurements in the millimeter-wave range for sapphire quasi-optical resonators with conducting and high-T/sub c/ superconducting (HTS) film endplates.     

SAW resonator design and fabrication for 2.0, 2.6 and 3.3 GHz

Direct-write electron-beam lithography has been used to fabricate surface-acoustic-wave (SAW) resonators in quartz at 2.05, 2.60, and 3.30 GHz. Typical 2.05-GHz devices show unloaded Q factors of about 2700 and insertion losses of about 9 dB. The best 2.60-GHz devices have unloaded Q of about 2000 with insertion losses less than 11 dB. Preliminary 3.3-GHz devices have shown unloaded Q of about 1600 and insertion losses of 17 dB. These results are for devices tested in chip form in a 50-Omega system. The fabrication of a fundamental-mode resonator with center frequency exceeding 2.6 GHz is claimed to be unmatched in the literature. These results are due in part to improvements in design and electron-beam direct-write capabilities. Design and fabrication of SAW resonators above 2 GHz are described, test results for several wafers including preliminary phase noise measurements for devices at 2 GHz are reported, and problems associated with testing these devices are discussed.     

Thin Film Tl-Based HTS Microwave Devices

Linear microstrip resonators suffer from high peak current density inside the resonators which limit the power handling characteristics. To realise higher power filters for cellular applications it is possible to use two dimensional microstrip resonators (such as disks) to equalise the internal current distribution. We have designed and tested such microstrip resonators, fabricated from TBCCO 2212 thin films deposited by RF sputtering onto 10×10mm and 20×20mm LaAlO₃, substrates. The R_s of such films has been measured at 24 GHz using a sapphire dielectric resonator and shown to be less than 500 scaled to 10 GHz and at 80K. Q values of 3-12 GHz disk resonators have demonstrated considerable improvements when compared to both linear HTS microstrip resonators and comparable copper disk resonators. Additionally, the power handling of such resonators has been shown to be superior to that of conventional linear resonators fabricated from similar material.     

A Novel HTS Shuttle-Shape Resonator for High-Power Application

A novel shuttle-shape microstrip resonator for high-power high-temperature superconductor (HTS) filters is presented. By transmission line theory analysis, it can improve the power handling capability up to 20%, depending on the configuration of the resonator. To confirm this analysis result, two 2-pole HTS filters based on shuttle-shape resonator and rectangle resonator were simulated. Considering the limitation of computer memory, a moderate configuration was chosen for HTS filter design. By computer simulation, a comparison between filters with shuttle-shape and rectangle resonators showed a 10% increase in power handling capability. The HTS shuttle-shape filter was fabricated and tested. It has a center frequency of 2022 MHz with a 2.5% bandwidth. The measured power level was over 34 dBm at 70 K with sufficiently low insertion loss.     

Microwave Q-factor of a dielectric resonator sandwiched between two thin films of superconductor

This analysis provides a comparison between the computed and the measured Q-factors of a microwave resonator consisting of a dielectic resonator sandwiched between two thin films of superconductor using the Bose statistics and the Gorter and Casimir model for a two-fluid model. Such comparisons are helpful not only to design ultrahigh-Q resonators but also in considering the theory of thin films of HTS (high-temperature superconductors).     

High-Q thermoelectric-stabilized sapphire microwave resonators forlow-noise applications

Two low-noise high-Q sapphire-loaded cavity (SLC) resonators, with unloaded Q values of 2×10⁵ and very low densities of spurious modes, have been constructed. They were designed to operate at 0°C with a center frequency of 10.000000 GHz. The cavity was cooled with a thermoelectric (TE) Peltier element, and in practice achieved the required center frequency near 1°C. The resonator has a measured frequency-temperature coefficient of -0.7 MHz/K, and a Q factor which is measured to be proportional to T^-2.5. An upper limit to the SLC residual phase noise of ℒ (100) Hz=-147 dBc/Hz, ℒ (1 kHz)=-155 dBc/Hz, and ℒ (10) kHz=-160 dBc/Hz has been measured. Also, we have created a free-running loop oscillator based on one of the SLC resonators, and measured a phase noise of ℒ(f)~-10-30log [f] dBc/Hz between f=10 /Hz and 25 kHz, using the other as a discriminator     

High Q metal strip SSBW resonators using a SAW design

An experimental study of metal strip surface skimming bulk wave (SSBW) resonators using a surface acoustic wave (SAW) design is presented. Characteristics of SSBW and SAW resonators fabricated with the same photolithographic mask are compared and discussed. High Q low-loss SSBW resonators are achieved using a conventional two-port SAW resonator design and taking special care of the distance L between both interdigital transducers, the metal thickness h/lambda (lambda=acoustic wavelength) and the finger-to-gap ratio. Best overall performance of the SSBW devices in this study is achieved at L=nlambda/2-lambda/4 (compared with L=nlambda/2-lambda/8 for SAW resonators), h /lambda=1.6% (compared with 2% for SAW), and finger-to-gap ratio close to 1. The best device fabricated shows an unloaded Q of 5820 and an insertion loss of 7.8 dB at 766 MHz. The SSBW resonant frequency shows a stronger dependence on the metal thickness than the SAW one. This problem, however, is readily solved by frequency trimming using a CF(4) plasma etching technique. SSBW resonator can be trimmed by 0.2% down in frequency (compared with 0.05% for SAW) without affecting their performance.     

Nonlinear effects in varactor-tuned resonators

This paper describes the effects of RF power level on the performance of varactor-tuned resonator circuits. A variety of topologies are considered, including series and parallel resonators operating in both unbalanced and balanced modes. As these resonators were designed to produce oscillators with minimum phase noise, the initial small signal insertion loss was set to 6 dB and, hence, QL/Q0 = 1/2. To enable accurate analysis and simulation, S parameter and PSPICE models for the varactors were optimized and developed. It is shown that these resonators start to demonstrate nonlinear operation at very low power levels demonstrating saturation and lowering of the resonant frequency. On occasion squegging is observed for modified bias conditions. The nonlinear effects are dependent on the unloaded Q (Q0), the ratio of loaded to unloaded Q (QL/Q0), the bias voltage, and circuit configurations with typical nonlinear effects occurring at -8 dBm in a circuit with a loaded Q of 63 and a varactor bias voltage of 3 V. Analysis, simulation, and measurements that show close correlation are presented.     

High Q-factor distributed bragg reflector resonators with reflectors of arbitrary thickness

The Bragg reflection technique improves the Q-factor of a resonator by reducing conductor and dielectric losses. This is achieved by designing a low-loss inner resonant region (usually free space) surrounded by an outer anti-resonant region made of distributed Bragg reflector layers. In this paper we develop a simple non-Maxwellian model and apply it to design three distinct cylindrical Bragg resonators based on the same set of single-crystal sapphire plates and rings by changing only the dimension of the cavity that supports the structure. To accomplish this, the simple model allows an arbitrary thickness for either the horizontal or the cylindrical dielectric reflectors by relaxing the condition that they must be lambda/4 thick. The model also allows for higher-order field variations in both the resonant and the anti-resonant regions. The resonators were constructed and experimental results were compared with the simple model and the rigorous method of lines analysis. For the fundamental mode, an unloaded Q-factor of 234,000 at 9.7 GHz was obtained. This is larger than that for a whispering gallery mode resonator. The resonator also exhibited a greatly reduced spurious mode density when compared to an overmoded whispering gallery mode resonator.     

Planar HTS structures for high-power applications in communication systems

The use of rotational symmetric modes of superconductive disk (ring) resonators in order to increase the power handling capability of planar filters has been proposed. Several YBCO disk resonators on LaAlO₃ and sapphire substrates have been measured as one- and two ports. The unloaded Q-factor of the resonators has been measured to be greater than 10⁵ up to the oscillating power of 50 kW. Experimental results obtained show that a disk resonator can be used as a building block for low insertion loss, sharp skirt high-power planar filters at low GHz frequency range and temperatures of around 60 K.     

Low temperature limitation on the quality factor of quartzresonators

The quality factor (Q) for different resonators driven at several overtones has been determined between 1.5 and 300 K. These measurements give an improved interpretation of the Q-factor limitation. A significant consequence is a better understanding of the relationship between Q and random frequency fluctuations. The curves of 1/Q=F(T) show the usual features between 20 and 300 K. These include the sodium ion peak at 55 K as well as a peak at 20 K. However, the region of principal interest lies between 1.5 and 20 K. At very low temperatures, a plateau is always observed. If for a given resonator, the 1/Q value of this plateau is subtracted from the experimental values, the residual 1/Q is almost a linear function of T⁴. This variation obeys the Landau-Rumer theory of acoustic wave absorption caused by phonon-phonon interaction in the crystal. Thus the authors conclude that between 6 and 20 K the main limitation in Q is due to the crystal itself, but the plateau is not caused by intrinsic crystal properties. Data for different overtones enable the elimination, at least for the seventh overtone, of damping effects of the crystal supports. Measurements have also been carried out on crystals with crystal surfaces with different roughness characteristics. These roughness characteristics have been measured using optical interferometry. With a well polished, good crystal the authors measured, for the seventh overtone at 3 K a loaded Q of 25 million corresponding to an unloaded Q of 33 million. Better control of surface roughness and crystal quality could lead to a Q of about 100 million in the liquid helium region. This value would be for an 11 MHz, seventh overtone crystal having an diameter of 15 mm     

Dielectric loaded HTS resonators as frequency standards andlow-phase noise oscillators

High-quality, high-temperature superconducting (HTS) thin-films exhibit very low losses at microwave frequencies and, as a result, allow very high Q resonators to be produced. The size of such resonators may be significantly reduced by loading with low-loss single crystal dielectric. The potential for HTS dielectric loaded resonators as practical frequency standards and reference elements for low-phase-noise oscillators is assessed, with emphasis on operation at 60 K, a temperature readily attainable with compact Stirling cycle coolers     

Design and properties of STW asynchronous resonators on quartz

In a surface transverse wave (STW) asynchronous resonator, grating phase shifters are placed between interdigital transducers and reflectors to obtain the incident and reflected waves in phase, and the resonance frequency is located near the center frequency of the reflectors. In this paper, the scattering matrix method is used for design of such resonators with one dominant longitudinal mode. At a frequency of about 509.5 MHz, insertion loss, and loaded and unloaded quality factors of about 6 dB, 5,300 and 11,000, respectively, were obtained. The measured and calculated parameters of this resonator are in good agreement. Design guidelines and comparison of synchronous and asynchronous resonators are presented. Compared to synchronous resonators, low spurious signals' level, location of the resonance frequency near the center frequency of the reflectors, and simple design method make the asynchronous resonators more attractive for manufacture and practical applications.     

Chemical sensor based on surface acoustic wave resonator using Langmuir-Blodgett film

A one-port surface acoustic wave (SAW) resonators incorporating Langmuir-Blodgett (LB) films has been investigated. SAW sensors are one potential applications of SAW devices. Most of the work reported on SAW sensor concerns delay lines. In this paper we characterize the mass loading effects of one-port resonators by depositing successive monolayers of LB films onto the surface. A 90 MHz SAW gas-phase sensor has been fabricated on an ST cut quartz substrate, and one-port resonator configurations have been used as the sensing element. Ultra thin monolayers of arachidic acid and arachidic acid ethyl ester have been deposited using the LB method. The resonant frequencies and the Q values have been measured as sensor response. Experimental results show that the Q values and the resonant frequencies of the one-port SAW resonator vary with film mass loading on the SAW device surface.     

Precise Microwave Characterisation of YBa2Cu3O7−δ Films on Sapphire and Lanthanum Aluminate Substrates

We have precisely measured the surface resistance (R _S) of high quality YBCO thin films, deposited on Lanthanum Aluminate and Silver doped YBCO thin films on Cesium buffered Sapphire substrates using the Hakki-Coleman dielectric resonator at frequency of 10 GHz as a function of temperature from 25 K to 85 K. We have also studied the microwave power dependence of YBCO films on both substrates and the frequency dependence of films on LAO. Precise microwave characterisation of HTS films is needed for selection of best films for mobile phone base station receivers.     

Electromechanical coupling constant extraction of thin-film piezoelectric materials using a bulk acoustic wave resonator

Thin-film piezoelectric materials such as ZnO and AlN have great potential for on-chip devices such as filters, actuators and sensors. The electromechanical coupling constant is an important material parameter which determines the piezoelectric response of these films. This paper presents a technique based on the Butterworth Van-Dyke (BVD) model which, together with a simple one-mask over-moded resonator, can be used to extract the bulk, one-dimensional electromechanical coupling constant K(2) of any piezoelectrically active thin-film. The BVD model is used to explicitly define the series resonance, parallel resonance, and quality factor Q of any given resonating mode. Common methods of defining the series resonance, parallel resonance, and Q are shown to be inaccurate for low coupling, lossy resonators such as the over-moded resonator. Specifically, an electromechanical coupling constant K(2) of (2.6+/-0.1)% was measured for an (002) c-axis textured AlN film with an X-ray diffraction rocking curve of 7.5 degrees using the BVD based extraction technique.     

High, size-dependent quality factor in an array of graphene mechanical resonators

Graphene's unparalleled strength, stiffness, and low mass per unit area make it an ideal material for nanomechanical resonators, but its relatively low quality factor is an important drawback that has been difficult to overcome. Here, we use a simple procedure to fabricate circular mechanical resonators of various diameters from graphene grown by chemical vapor deposition. In addition to highly reproducible resonance frequencies and mode shapes, we observe a striking improvement of the membrane quality factor with increasing size. At room temperature, we observe quality factors as high as 2400 ± 300 for a resonator 22.5 μm in diameter, about an order of magnitude greater than previously observed quality factors for monolayer graphene. Measurements of quality factor as a function of modal frequency reveal little dependence of Q on frequency. These measurements shed light on the mechanisms behind dissipation in monolayer graphene resonators and demonstrate that the quality factor of graphene resonators relative to their thickness is among the highest of any mechanical resonator demonstrated to date.     

Experiments and Model of Intermodulation Distortion in a Rutile Resonator with Y-Ba2-Cu3-O7−δ Endplates

We have derived general equations to calculate intermodulation distortion in resonators with high temperature superconducting (HTS) films which are not restricted to a specific resonator shape and may be used whenever the fields in a resonator generate currents on the surface of one or more HTS films. These equations are applied to rutile-loaded cavities with one or two 10 × 10 mm² Y-Ba₂-Cu₃-O^7?δ endplates and are used to extract parameters characterizing the nonlinearities of these films from intermodulation measurements. Even though the films have similar small-signal performance, we have found large variation in the strength of their nonlinearities.     

Computations of Unloaded Q 0-Factor and Resonant Frequency of the TE011 Mode Hakki–Coleman Dielectric Resonators with Coupling Structures Using ANSOFT HFSS

Microwave characterization of materials using dielectric resonators is based on measurements of the Q-factor of the resonator containing a sample under test and on the loss equation for the test structure. The loss equation contains geometrical factors, which are calculated assuming an ideal metallic cavity of the resonator. In this paper a rigorous analysis of cylindrical parallel plate dielectric resonators has been performed to assess the influence of the presence of coupling holes and cables on the unloaded Q-factor and resonant frequency. Calculations have been done for the TE011 mode resonators with differing cavity to dielectric diameter ratio, conductivity of the cavity material, loss tangent and relative permittivity of the dielectric rod, position of the coupling loops and size of the coupling cables. Results have shown that Qo-factors calculated for real resonators were smaller than Qo-factors for ideal resonators. Also this paper presents a brief history of analysis of dielectric resonators.     

Investigation and Modeling Nonlinear Characteristics of High-Tc Superconducting Resonators

The high-quality resonators and pass-band filters based on high-T _c superconducting (HTS) films are of the most interest for practical applications. The industrial application of the devices is retarded by nonlinearity of the film surface impedance under microwave power of a high level. The phenomenological model of nonlinear characteristics of HTS resonators was developed and applied to different kinds of planar resonators: disk, parallel plate, and micro-strip resonator. A comparison of experimental and modeled characteristics of the resonators revealed the distinctive difference in the model parameters. Some limiting characteristics are discussed.