Parallel Plate Resonator Research Articles

The complementary derivatives method: a second-order accurate interpolation scheme for non-uniform grid in FDTD simulation

Non-uniform grid in finite-difference time-domain methods, which is typically used to resolve fine structures, can reduce the computational domain and therefore lead to a reduction of the computational cost. However, for high-accuracy problems, such as partially-filled parallel plate waveguide and resonators, using different grid size increases the truncation error at the boundary of domains having different grid size. To address this problem, in this work, we introduce the complementary derivatives method (CDM). Theoretical discussion and numerical results will be presented to show that the CDM can maintain second-order accuracy throughout the computational domain.

RF characterization and modeling of various wire bond transitions

This paper presents radio-frequency (RF) characterization and modeling of various wire bond transitions between chips and packages. Test modules composed of Si chips and alumina packages are fabricated in conductor-backed (CB) structures, and they are characterized at frequencies up to 20 GHz. It is shown that the parallel plate resonance of the CB coplanar waveguide (CPW) persists in wire bonding transitions, and narrower-ground CPW-CPW transitions show better characteristics than wider-ground CPW-CPW transitions. The results of three-dimensional full-wave electromagnetic simulation on the test modules reproduce the measured results with a reasonable accuracy. Simple equivalent circuit modeling can reproduce the measured results of the narrower ground CPW transition with no resonance structures. Finally, the effects of bond wire length and impedance mismatch on RF performance are investigated.

Hexagonal zero mode TEM coil: A single‐channel coil design for imaging multiple small animals

A novel hexagonal coil design for simultaneous imaging of multiple small animals is presented. The design is based on a coaxial cavity and utilizes the magnetic field formed between two coaxial conductors with hexagonal cross-sections. An analytical solution describing the B(1) field between conductors of the hexagonal coil was found from the Biot-Savart law. Both experimental results and analytical calculations showed a variation in the B(1) field within the imaging region of less than 10%. Numerical calculations predicted approximately 35% improvement in B(1) field homogeneity with the hexagonal coil design compared to a cylindrical coaxial cavity design. The experimentally-measured signal-to-noise ratio (SNR) of the hexagonal coil loaded with six 50-mM phantoms was only 4-5% lower than that of a single parallel plate resonator loaded with one phantom. In vivo spin-echo (SE) images of six 7-day-old rat pups acquired simultaneously demonstrated sufficient SNR for microimaging. The construction scheme of the coil, simple methods for tuning and matching, and an anesthesia device and animal holder designed for the coil are described. The hexagonal coil design utilizes a single receiver and allows for simultaneous imaging of six small animals with no significant compromise in SNR.

An Efficient Volume Integral-Equation Approach for Characterization of Lossy Dielectric Materials

An efficient volume integral-equation approach for characterizing lossy dielectric materials in the Courtney holder type of measurement environment is proposed. Utilizing the parallel-plate dyadic Green's functions and the volume equivalence theorem, an effective electric-field integral equation is developed for azimuthally invariant mode analysis of a parallel-plate dielectric resonator. Volumetric cylindrical pulse basis functions and a point-matching moment-method procedure are used to formulate an eigenvalue problem. A novel singularity treatment, which uses a Bessel function identity, is presented. In an iterative permittivity searching process, perturbation of the eigenmatrix equation involves solely recomputing a diagonal matrix, which is a function of permittivity only. Therefore, the efficiency of the searching process is greatly increased. Two numerical examples are provided to illustrate the applicability and validity of the proposed approach to the evaluation of dielectric constant, loss tangent, and surface resistance of the parallel plates.

Error in surface resistance originating from the dielectric loss of the parallel-plate dielectric resonator using the two-resonators method

An error in surface resistance ( R s) originating from the dielectric loss (tan δ) of the parallel plate dielectric resonator using the two-resonators method is investigated. In the two-resonators method, the error in R s( ΔR s) due to the difference in tan δ( Δtan δ) between the TE 011 and TE 01 n mode rods is examined, considering the actual scattering of values of tan δ among sapphire rods. Taking this scattering into account, the projected value of ΔR s cannot be disregarded for general R s values (about 0.1 mΩ) of HTS films. As a comparative simulation, the case of a single resonator was also considered where the tan δ is neglected in the estimate of R s. Due to the uncertainty and complexity in the two-resonators method, this method is not so superior to the single-rod resonator measurement by neglecting tan δ at higher resonance frequency.

Microwave radiation force and torque on a disk resonator excited by a circularly polarized plane wave

A numerical simulation method [S. Makarov and S. Kulkarni, Appl. Phys. Lett. 84, 1600 (2004)] is used in order to determine the radiation force and radiation torque on a parallel-plate disk resonator, whose size is comparable to wavelength. The method is based on the MOM solution of the electric-field integral equation, accurate calculation of the near field, and removal of the self-interaction terms responsible for the pinch effect. The local force/torque distribution at the normal incidence of a circularly polarized plane wave is found. It is observed that, at the resonance, the individual disks are subject to unexpectedly large local force densities, despite the fact that the net radiation force on the resonator remains very small. On the other hand, the total axial torque on the disk resonator also increases at the resonance.

Surface resistance measurements of HTS films placed inside a cavity with a puck resonator

Possibilities of dielectric puck resonators for measuring of the surface resistance of arbitrary shaped pieces of high temperature superconducting (HTS) films, placed inside a copper shielding cavity are discussed. Effect of additional microwave losses, caused by the field perturbation, on the results of the surface resistance measurements is analysed. The problem is investigated experimentally by comparing the results obtained by puck and parallel plate resonator techniques for an YBCO film.

Nonlinear microwave response of anMgB2 thin film

MgB2 is atwo-gap superconductor and as a result may manifest unusual physical properties. The performanceof MgB2 films at microwave frequencies has so far been rather poor compared to that of Nballoys and this may result from intrinsic behaviour related to the double-gapstructure or extrinsic properties due to non-optimized thin films. Here we give adetailed report on the microwave magnetic field dependent surface impedance of anMgB2 thin film, using a parallel plate resonator, as a function of temperature. We discuss whetherthe framework used to analyse nonlinear behaviour for other superconductors, both low and highTc, but single-gap,has any validity for MgB2 and whether the films are limited by intrinsic or extrinsic behaviour. The key resultis the observation of junction-type switching effects at high microwave power.

Microwave radiation force on a parallel-plate resonator

A simulation method is proposed and tested in order to determine the radiation force on metal targets whose size is comparable to wavelength. The method is based on the method of moments solution of the electric-field integral equation, accurate calculation of the near field, and removal of the self-interaction terms responsible for the pinch effect. The method is used to determine the local force distribution for a parallel-plate metal resonator. It is observed that, at the resonance, the individual metal plates may experience large force densities, despite the fact that the net radiation force on the resonator still remains very small. A potential use of this observation is discussed, which is directed toward possible excitation of acoustic vibrations.

Surface resistance measurements of HTS films placed inside a cavity with a puck resonator

Possibilities of dielectric puck resonators for measuring of the surface resistance of arbitrary shaped pieces of high temperature superconducting (HTS) films, placed inside a copper shielding cavity are discussed. Effect of additional microwave losses, caused by the field perturbation, on the results of the surface resistance measurements is analysed. The problem is investigated experimentally by comparing the results obtained by puck and parallel plate resonator techniques for an YBCO film.

Microwave performance of high-density bulk MgB2

We have performed microwave measurements on superconducting hot-isostatically pressed (HIPed) bulk MgB2 using a parallel-plate resonator technique. The high density and strength of the HIPed material allowed preparation of samples with mirror-like surfaces for microwave measurements. The microwave effective surface resistance Rs decreased by about 40% at 20 K when the root-mean-square surface roughness was reduced from 220 to 110 nm through surface polishing and ion milling. The Rs was independent of surface microwave magnetic field at least up to 4 Oe and below 30 K. We attribute this behavior, and the overall low Rs (∼0.8 mΩ at 10 GHz and 20 K), to the high density of our samples and the absence of weak links between grains.

Sputter deposition conditions and penetration depth in NbN thin films

NbN films have been reactively sputter deposited from a 15.24 cm Nb target using a variety of deposition conditions. Film penetration depth has been measured using Taber's parallel plate resonator technique. These measurements have been compared with penetration depth measurements obtained from SQUID measurements. Penetration depth results have also been correlated with film superconducting transition temperature, resistivity, resistance ratio, and x-ray diffraction patterns. The films have been deposited over a variety of substrates and buffer layers including oxidized Si, sapphire, and a variety of metal and metal nitride seed layers.

Orientation and direct current field dependent dielectric properties of bulk single crystal SrTiO3 at microwave frequencies

The dielectric properties of bulk single crystal SrTiO3 (STO) are studied in the temperature range 30–300 K, under dc field 0–10 kV/cm at 1.0 kHz and in the frequency range 0.3–2.0 GHz. Two sets of circular disk shaped parallel plate resonators have been fabricated and tested experimentally. In the first set thin YBa2Cu3O7 films have been epitaxially grown on both surfaces of [100] STO disks. In the second set, three crystal orientations of SrTiO3 [100], [110], and [111] have been used to make parallel-plate resonators with evaporated Cu/Ti electrodes. No peculiarities in field dependent dielectric permittivity are detected for STO with smaller densities of impurities. For samples with larger impurity densities double loop hysteresis is observed in the dc field dependent permittivity. For all orientations the losses are minimum at temperatures about 50–55 K. The losses at microwave frequencies increase with the applied dc field regardless of the orientation of the STO crystal. At relatively high dc fields (depending on the temperature) the losses start decreasing slightly.

Double loop hysteresis in direct current dependent dielectric permittivity of SrTiO3

Experimental double loop hysteresis in dc field dependent dielectric permittivity in bulk single crystal SrTiO3 is reported. Small signal measurements of the permittivity are performed in the frequency range 0.5–1.5 GHz at temperatures below 77 K using electrically thin circular parallel-plate resonators. The dielectric permittivity is extracted form the measured resonant frequency. The double loop hysteresis may be caused by field induced local paraelectric/ferroelectric phase transitions, and/or switching (polarization reversal) in local opposing ferroelectric domains associated with symmetry breaking impurities/structural defects.

Low temperature dependence of the penetration depth in YBCO thin films revisited by mm wave transmission and surface impedance measurements

We report results obtained with two different experimental set-ups in state-of-the-art YBCO thin films as similar as possible, prepared by pulsed laser deposition on LaAlO3 substrates: a surface impedance measurement on 4000 A thick films using a parallel plate resonator (10 GHz), and a far infrared transmission (100-400 GHz) measurement which requires thinner (1000 A) samples. The former measurement yields the temperature variation of the penetration depth λ(T) and the real part of the conductivity, provided the absolute value of λ(T) is known. The latter yields the imaginary part of the conductivity, hence the absolute value of the penetration depth, as well as its temperature dependence at the measuring frequency. Combining these two experiments, we establish a quasi-linear temperature variation of λ(T), with a 2 A K-1 low temperature slope, and a fairly large zero temperature value λ(T = 0)=(1800±200) A . The scattering rate of the quasi-particles calculated from a two-fluids model shows that the films compare to good quality single crystals, where twice a larger slope has been found. This surprising behavior is described in detail, including an in-depth structural analysis of the samples in order to evaluate their similarities. We find that the 10 GHz data obtained in the thickest films can be fitted to the dirty d-wave mode in the unitarity limit, with an extrapolated slope of 3 A K-1, but yield a scattering rate that is difficult to reconcile with the high T c (92 K) of the films.

Non-linear microwave response of HTS thin films: a comparison of intermodulation and conventional measurements

The non-linear microwave response of HTS thin films is a crucial issue for applications of the cuprates in future communications technologies. We report comparisons of nonlinear characterisation measurements made by two different techniques. The first involves two-tone intermodulation measurements, for which the HTS thin films are incorporated into a high Q resonant structure and two spectrally pure tones are injected within the resonator bandwidth. The second consists of a conventional high power steady-state parallel-plate resonator measurement of the non-linear response of Z/sub s/(H/sub rf/). Two very different HTS thin film samples are examined and simple physical models, involving grain boundary effects or film heating, are used to relate the intermodulation and power dependent impedance results to properties of the HTS thin film.

Intermodulation Measurements on High Temperature Superconducting Thin Films

A high temperature superconducting GdBa2Cu3O7−δ thin film was characterized using a parallel plate resonator at 5.5 GHz and a dielectric puck resonator at 10 GHz, to observe the dependence of surface resistance on microwave power at the fundamental frequency, and the production of intermodulation products using a two-tone measurement setup, respectively. The electromagnetic field pattern of the dielectric puck-HTS thin film mode was modeled using the commercial software package MAFIA. The intermodulation product was compared with a simple RSJ model.

Mode chart of electrically thin parallel-plate circular resonators

Modes in electrically thin circular parallel-plate resonators are discussed in detail. It is shown that the widely used mode indices (found from the field solutions) do not indicate the radial numbers of the field maximums in a straightforward manner. The diameter of the disc, not the radius, accommodates integer numbers of the field maximums (antinodes). These diametrical numbers are expressed in terms of radial mode indices. Emphasis is placed on the first axially symmetric mode TM020, which was incorrectly regarded as TM010 in the past. Some applications of the mode chart, including interpretation of experimental observations, are also discussed. Comparison is made with microstrip and annular resonators.

Microwave electrodynamics of the antiferromagnetic superconductor GdBa 2Cu 3O 7−δ

The temperature dependence of the microwave surface impedance and conductivity are used to study the pairing symmetry and properties of cuprate superconductors. However, the superconducting properties can be hidden by the effects of paramagnetism and antiferromagnetic long-range order in the cuprates. To address this issue we have investigated the microwave electrodynamics of GdBa 2Cu 3O 7−δ, a rare-earth cuprate superconductor which shows long-range ordered antiferromagnetism below T N = 2.2K, the Neel temperature of the Gd ion subsystem. We measured the temperature dependence of the surface resistance and surface reactance of c-axis oriented epitaxial thin films at 10.4, 14.7 and 17.9 GHz with the parallel plate resonator technique down to 1.4 K. Both the resistance and the reactance data show an unusual upturn at low temperature and the resistance presents a strong peak around T N mainly due to change in magnetic permeability.

Microwave electrodynamics of electron-doped cuprate superconductors

We report microwave cavity perturbation measurements of the temperature dependence of the penetration depth, lambda(T), and conductivity, sigma(T) of Pr(2-x)Ce(x)CuO(4-delta) (PCCO) crystals, as well as parallel-plate resonator measurements of lambda(T) in PCCO thin films. Penetration depth measurements are also presented for a Nd(2-x)Ce(x)CuO(4-delta) (NCCO) crystal. We find that Deltalambda(T) has a power-law behavior for T<T(c)/3, and conclude that the electron-doped cuprate superconductors have nodes in the superconducting gap. Furthermore, using the surface impedance, we have derived the real part of the conductivity, sigma(1)(T), below T(c) and found a behavior similar to that observed in hole-doped cuprates.