Modulation of dielectric properties in low-loss polypropylene-based composites at GHz frequencies: theory and experiment.

Polymer composites with high dielectric constant and low loss tangent are highly regarded as substrates for modern high-speed electronics. In this work, we analyze the high-frequency dielectric properties of two types of composites based on polypropylene infused with high-dielectric-constant microparticles. Two types of fillers are used: commercial ceramics or titanium oxide (TiO2) with different concentrations. The key observation is that adding the fillers causes an increase of dielectric constants by around 100% (for highest loading) up to 4.2 and 3.4, for micro-ceramics and TiO2 based composites, respectively. Interestingly, for the TiO2 composite, the loss tangent depends on the filler loading volume, whereas the other composite has a slightly increasing tendency, however, being at the level ~ 10-3. To explain the experimental results, a theoretical model determined by microwave reflection and transmission through a representative volume element is proposed, which allows the investigation of the impact of volume ratio, grain shape, aggregation, and size on the loss tangent and permittivity evolution. This approach could be used for modeling other low dielectric loss materials with inclusions.

High Q Dielectric Titanium Tellurite Thick Films on Alumina Substrates for High Frequency Telecommunications.

The vital role of high-quality-factor (Q) high-frequency (f) dielectric resonators in the growing microwave telecommunication, satellite broadcasting and intelligent transport systems has long motivated the search for new, small size, and lightweight integrated components and packages, prepared by low cost and sustainable processes. One approach is replacing the currently used bulk ceramic dielectrics by thick films of low-sintering-temperature dielectrics fabricated by affordable processes. Here we demonstrate the fabrication of high-Q TiTe3O8 thick films directly on low loss Al2O3 substrates by electrophoretic deposition using sacrificial carbon layer. Nineteen-micrometre-thick TiTe3O8 films on Al2O3 sintered at 700 °C are found to have a relative permittivity εr of 32 and Q × f > 21,000 GHz. Being thus able to measure and provide for the first time the microwave dielectric properties of these films, our results suggest that TiTe3O8 films on Al2O3 substrates are suitable for microlayer microstrip array applications.

Precision Multi-Mode Dielectric Characterization of a Crystalline Perovskite Enables Determination of the Temperature-Dependent Phase Transitions.

Simple perovskite crystals undergo structural phase transitions on cooling to low temperatures, which significantly change the material properties of the crystal. In this work, we rigorously characterize the temperature evolution of permittivity of a perovskite crystal as it undergoes phase transitions. In particular, we have undertaken precision measurements of a single crystal of Strontium Titanate from 294.6 to 5.6 K, by measuring the frequency of multiple microwave transverse electric (TE) and magnetic resonant modes simultaneously. The multi-mode microwave measurement technique of resonant frequency used in this work allows high precision determination of any induced anisotropy of the permittivity as the crystal undergoes structural phase transitions. Compared with previous results, we unequivocally show that the permittivity has an isotropic value of 316.3±2.2 at room temperature, consistent with its well-known cubic structure, and determine the onset of dielectric anisotropy as the crystal is cooled to lower temperatures. We show that the crystal exhibits uniaxial anisotropy in the permittivity below 105 K when the structure becomes tetragonal, and exhibits biaxial anisotropy in the permittivity below 51 K when the structure becomes orthorhombic.

Microwave Measurements of Electromagnetic Properties of Materials.

A review of measurement methods of the basic electromagnetic parameters of materials at microwave frequencies is presented. Materials under study include dielectrics, semiconductors, conductors, superconductors, and ferrites. Measurement methods of the complex permittivity, the complex permeability tensor, and the complex conductivity and related parameters, such as resistivity, the sheet resistance, and the ferromagnetic linewidth are considered. For dielectrics and ferrites, the knowledge of their complex permittivity and the complex permeability at microwave frequencies is of practical interest. Microwave measurements allow contactless measurements of their resistivity, conductivity, and sheet resistance. These days contactless conductivity measurements have become more and more important, due to the progress in materials technology and the development of new materials intended for the electronic industry such as graphene, GaN, and SiC. Some of these materials, such as GaN and SiC are not measurable with the four-point probe technique, even if they are conducting. Measurement fixtures that are described in this paper include sections of transmission lines, resonance cavities, and dielectric resonators.

Rigorous broadband study of the intrinsic ferromagnetic linewidth of monocrystalline garnet spheres.

This work demonstrates the first application of direct broadband (1 GHz-30 GHz) quality (Q) factor measurements of the uniform precession mode in magnetised garnet spheres for the accurate determination of the room-temperature intrinsic ferromagnetic linewidth (ΔH). The spheres were enclosed in a subwavelength cavity, so that the measured Q-factor depended mainly on their magnetic losses and the conduction losses of the cavity walls. The contribution of the latter is assessed by means of the recently proposed magnetic plasmon resonance model and has been found to be negligible. A total of 10 samples made from commercially available pure yttrium iron garnet (YIG) and gallium-substituted YIG have been measured, differing in diameter and/or saturation magnetisation Ms. The dependence of the intrinsic ΔH on the internal magnetic field is found to have near-perfect linear dependence, which cannot be said about the typically studied extrinsic ΔH even at high frequencies. It is found that the difference between the two linewidths, which becomes significant at low frequencies, can be attributed to a geometric effect. Due to its fundamental nature, this work is applicable not only to magnetic material characterization, but also to the study of the origins of losses in magnetic materials.

Ferromagnetic Resonance Revised - Electrodynamic Approach.

Resonance in a ferromagnetic sphere, known in the body of literature as the mode of uniform precession, has recently been proven to be magnetic plasmon resonance (MPR). This finding has prompted research which is presented in this paper on the relation between the Q-factor at the MPR and the ferromagnetic resonance (FMR) linewidth ΔH, which is a parameter of magnetized gyromagnetic materials. It is proven in this paper that ΔH can be unequivocally determined from the Q-factor measured at the MPR, if all losses in the resonance system are properly accounted for. It can be undertaken through a rigorous but simple electrodynamic study involving the transcendental equation, as proposed in this paper. The present study also reveals that electric losses have a substantially reduced impact on ΔH due to the large magnetic to electric energy storage ratio at the MPR. Theoretical results are supported by measurements of the Q-factors on a monocrystalline yttrium iron garnet (YIG) sphere.

Electrodynamic study of YIG filters and resonators.

Numerical solutions of coupled Maxwell and Landau-Lifshitz-Gilbert equations for a magnetized yttrium iron garnet (YIG) sphere acting as a one-stage filter are presented. The filter is analysed using finite-difference time-domain technique. Contrary to the state of the art, the study shows that the maximum electromagnetic power transmission through the YIG filter occurs at the frequency of the magnetic plasmon resonance with the effective permeability of the gyromagnetic medium µr ≈ -2, and not at a ferromagnetic resonance frequency. Such a new understanding of the YIG filter operation, makes it one of the most commonly used single-negative plasmonic metamaterials. The frequency of maximum transmission is also found to weakly depend on the size of the YIG sphere. An analytic electromagnetic analysis of resonances in a YIG sphere is performed for circularly polarized electromagnetic fields. The YIG sphere is situated in a free space and in a large spherical cavity. The study demonstrates that both volume resonances and magnetic plasmon resonances can be solutions of the same transcendental equations.

Invited article: Dielectric material characterization techniques and designs of high-Q resonators for applications from micro to millimeter-waves frequencies applicable at room and cryogenic temperatures.

Dielectric resonators are key elements in many applications in micro to millimeter wave circuits, including ultra-narrow band filters and frequency-determining components for precision frequency synthesis. Distributed-layered and bulk low-loss crystalline and polycrystalline dielectric structures have become very important for building these devices. Proper design requires careful electromagnetic characterization of low-loss material properties. This includes exact simulation with precision numerical software and precise measurements of resonant modes. For example, we have developed the Whispering Gallery mode technique for microwave applications, which has now become the standard for characterizing low-loss structures. This paper will give some of the most common characterization techniques used in the micro to millimeter wave regime at room and cryogenic temperatures for designing high-Q dielectric loaded cavities.

Microwave conductivity of very thin graphene and metal films.

The surface resistance of Ag, Au and A1 thin conducting films deposited on low loss dielectric substrates at microwave frequencies using TE011 mode single post-dielectric resonator (10-13.22 GHz) was measured to calculate their conductivity in relation to layers thickness. This method enabling measurements near metal-insulator percolation transition was also applied for epitaxial graphene deposited on semi-insulating SiC. Moreover, effective microwave conductivity has been determined for intentionally made aluminum island structure where the DC conductivity is equal to zero. Special attention was paid to films thickness measurements which is critical for accuracy of sheet resistance calculation. Conductivity of thin metal layers and very thin graphene was compared.

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.

Complex permittivity measurements of ferroelectrics employing composite dielectric resonator technique.

Composite cylindrical TE(0n1) mode dielectric resonator has been used for the complex permittivity measurements of ferroelectrics at frequency about 8.8 GHz. Rigorous equations have been derived that allowed us to find a relationship between measured resonance frequency and Q-factor and the complex permittivity. It has been shown that the choice of appropriate diameter of a sample together with rigorous complex angular frequency analysis allows precise measurements of various ferroelectric. Proposed technique can be used for materials having both real and imaginary part of permittivity as large as a few thousand. Variable temperature measurements were performed on a PbMg(1/3)Nb(2/3)O3 (PMN) ceramic sample, and the measured complex permittivity have shown good agreement with the results of measurements obtained on the same sample at lower frequencies (0.1-1.8 GHz).

Room temperature measurement of the anisotropic loss tangent of sapphire using the whispering gallery mode technique.

The anisotropic loss tangent has been determined in monocrystalline sapphire for components parallel and perpendicular to the crystal axis, using the whispering gallery (WG) mode method. The Q-factors of quasi-TE and quasi-TM modes were measured precisely in four cylindrical sapphire resonators at room temperature, from which was determined a maximum attainable Q-factor of (2.1 +/- 0.2) x 10(5) at 9 GHz in a quasi-TM mode. Sapphire dielectric material from three different manufacturers was compared over the 270-345 K temperature range and the 5-16 GHz frequency range.

High Q-factor microwave Fabry-Perot resonator with distributed Bragg reflectors.

A Fabry-Perot resonator operating at 39 GHz, with two pairs of quarter-wavelength single-crystal quartz Bragg reflectors has been realized. For the length of 98.26 mm, its Q-factor is about 560,000, which is 4.3 times better than for the same resonator without Bragg reflectors. Rigorous finite-difference frequency-domain analysis has been applied to the problem and is compared with simplified semi-analytical solutions. Good agreement between theoretical and experimental resonant frequency and Q-factors has been obtained. Thermal compensation of the resonant frequency of the Fabry-Perot has been proposed employing rods and cylinders made of metals with different thermal expansion coefficients.

Spherical Bragg reflector resonators.

In this paper we introduce the concept of the spherical Bragg reflector (SBR) resonator. The resonator is made from multiple layers of spherical dielectric, loaded within a spherical cavity. The resonator is designed to concentrate the energy within the central region of the resonator and away from the cavity walls to minimize conductor losses. A set of simultaneous equations is derived, which allows the accurate calculation of the dimensions of the layers as well as the frequency. The solution is confirmed using finite-element analysis. A Teflon-free space resonator was constructed to prove the concept. The Teflon SBR was designed at 13.86 GHz and exhibited a Q-factor of 22,000, which agreed well with the design values. This represents a factor of 3.5 enhancement over a resonator limited by the loss-tangent of Teflon. Similarly, SBR resonators constructed with low-loss materials could achieve Q-factors of the order of 300,000.

Whispering-gallery mode technique applied to the measurement of the dielectric properties of Langasite between 4 K and 300 K.

We report new measurements of dielectric properties of Lanthanum gallium silicate (Langasite or LGS) conducted with the whispering-gallery mode technique at microwave frequencies and between 4.2 K and 300 K. The real part of the permittivity tensor of LGS presents two components having temperature coefficients of opposite sign. This unique property enables the design of a temperature compensated resonator that may be useful in building stable microwave oscillators or filters. We report also the first measurements of the two independent components of the imaginary part of the permittivity tensor. It appears LGS is a relatively high-loss dielectric material compared with sapphire or quartz.

The microwave characterization of single crystal lithium and calcium fluoride at cryogenic temperatures.

The whispering-gallery mode method is used for very accurate permittivity and dielectric loss measurements of single crystal lithium fluoride (LiF) and calcium fluoride (CaF2) over the temperature range of 4.5 K to 300 K. The absolute uncertainty in the real part of permittivity was estimated to be less than 0.1%, and it was limited principally by uncertainty in dimensions of the samples. Dielectric losses were measured with uncertainties of about 10% limited by the accuracy of Q-factor measurements. The measured materials exhibited dielectric losses between 2-4 x 10(-7) near 5 K. The relative permittivity was evaluated as 6.502 (4.9 K) to 6.844 (296 K) at 17.5 GHz for CaF2 and 8.534 (4.6 K) to 9.063 (300 K) at 13.5 GHz for LiF.

High Q-factor Bragg-reflection sapphire-loaded cavity TE01delta mode resonators.

An innovative method of enhancing the quality factor of TE01delta cavity resonators with a dielectric tube made of monolithic sapphire is presented. Very high Q-factor is achieved by employing a Bragg reflection technique. A TE01delta mode in a copper cavity was measured to have a Q-factor of 1 x 10(5) at 8.78 GHz and 290 K. This is only 30% less than the limit due to the loss tangent of the dielectric material. The technique confines electromagnetic energy in the sapphire dielectric and in the vacuum well away from the cavity walls, thus reducing the surface losses in the copper shield. The technique offers some significant advantages over other methods. One advantage is the very low spurious mode density, which can improve filter and resonator design capabilities. Another is the small compact design, with a single sapphire piece, as compared to previously published Bragg reflection techniques. Finite element simulations and experimental data for this method were compared and found to be in very good agreement. The cavity dimensions were optimized to achieve maximum quality factor.