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.

Bulk acoustic wave filters synthesis and optimization for multi-standard communication terminals.

This article presents a design methodology for bulk acoustic wave (BAW) filters. First, an overview of BAW physical principles, BAW filter synthesis, and the modified Butterworth-van Dyke model are addressed. Next, design and optimization methodology is presented and applied to a mixed ladder-lattice BAW bandpass filter for the Universal Mobile Telecommunications System (UMTS) TX-band at 1.95 GHz and to ladder and lattice BAW bandpass filters for the DCS1800 TX-band at 1.75 GHz. In each case, BAW filters are based on AlN resonators. UMTS filter is designed with conventional molybdenum electrodes whereas DCS filters electrodes are made with innovative iridium.

Microwave study of tunable planar capacitors using mn-doped Ba0.6Sr0.4Tio3 ceramics.

This paper deals with the microwave study of coplanar tunable capacitors using Mn-doped Ba(0.6)Sr(0.4)TiO(3) ceramics. These ceramics are developed to improve performance at microwave frequencies (i.e., compromise between tuning capabilities and insertion losses). Interdigitated capacitors were first fabricated on thick Mn-doped BST ceramics. The capacitors showed reduced tuning factor because of a parasitic capacitance between the contact pads. The use of Mn-doped BST/ SiO(2) bilayers led to a significant enhancement of the capacitor performance (57% of agility under 200 V at 1 GHz).

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.

Designs of a microwave TE011 mode cavity for a space borne H-maser.

Method of Lines and Finite Element Analysis investigations have been performed to optimize parameters in a TE011 mode cavity resonator suitable for a spaceborne hydrogen maser. We report on designs that were explored to find a global maximum in the important design parameters for the microwave cavity used in a hydrogen maser. The criteria sought in this exercise were both the minimization of the total volume of the cavity and the maximization of the product of the z-component of the magnetic energy filling factor and the cavity TE011 mode Q-factor (Q.eta). Different configurations were studied. They were a sapphire tube in a copper cylinder, a sapphire tube in a copper cylinder with Bragg reflectors, and spherical copper cavities both empty and sapphire-lined on the inside cavity surface. At 320 K, the simulations resulted in an optimum product Q.eta = 4.9 x 10(4), with an inner cavity radius of 80 mm and unity aspect ratio. This represents a 54% improvement over an earlier design. The expected increase in the product Q . eta) with the inclusion of Bragg reflectors to the sapphire tube was not achieved. Moreover, the z-component of the magnetic energy filling factor was greatly reduced due to an increase in the radial magnetic field. The sapphire-lined spherical cavity showed no better performance than an equivalent-sized empty copper spherical cavity. For the empty cavity the simulations resulted in the product Q.eta = 4.4 x 10(4). The empty spherical cavity resonator is not suitable for the spaceborne hydrogen maser as the total volume in this case is 33% larger than that of the optimized sapphire tube resonator.

Distributed bragg reflector resonators with cylindrical symmetry and extremely high Q-factors.

A simple non-Maxwellian method is presented that allows the approximate solution of all the dimensions of a multilayered dielectric TE0qp mode cylindrical resonant cavity that constitutes a distributed Bragg reflection (DBR) resonator. The analysis considers an arbitrary number of alternating dielectric and free-space layers of cylindrical geometry enclosed by a metal cylinder. The layers may be arranged along the axial direction, the radial direction, or both. Given only the aspect ratio of the cavity, the desired frequency and the dielectric constants of the material layers, the relevant dimensions are determined from only a set of simultaneous equations, and iterative techniques are not required. The formulas were verified using rigorous method of lines (MoL) calculations and previously published experimental work. We show that the simple approximation gives dimensions close to the values of the optimum Bragg reflection condition determined by the rigorous analysis. The resulting solution is more compact with a higher Q-factor when compared to other reported cylindrical DBR structures. This is because it properly takes into account the effect of the aspect ratio on the Bragg antiresonance condition along the z-axis of the resonator. Previous analyses assumed the propagation in the z-direction was independent of the aspect ratio, and the layers of the Bragg reflector were a quarter of a wavelength thick along the z-direction. When the aspect ratio is properly taken into account, we show that the thickness of the Bragg reflectors are equivalent to the thickness of plane wave Bragg reflectors (or quarter wavelength plates). Thus it turns out that the sizes of the reflectors are related to the free-space propagation constant rather than the propagation constant in the z-direction.

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.

Simple design rules for optimal design of dielectric temperature-compensated sapphire resonators.

It has been shown that the use of two dielectric crystals with opposite temperature coefficient of permittivity allows the realization of a resonator with a zero temperature coefficient of frequency. By using sapphire and rutile materials, which have low-loss tangents, some compensated resonators with very high Q-factors have been realized. In this work we develop rules that greatly simplify the design of a dielectric-compensated resonator. We show that the optimum design for compensation at a specific temperature may be determined by simply selecting the aspect ratio of the sapphire resonator.

Cryogenic dual-mode resonator for a fly-wheel oscillator for a caesium frequency standard.

A dual-mode, sapphire-loaded cavity (SLC) resonator has been designed and optimized with the aid of finite element software. The resonance frequency was designed to be near the frequency of a Cs atomic frequency standard. Experimental tests are shown to agree very well with calculations. The difference frequency of two differently polarized modes is shown to be a highly sensitive temperature sensor in the 50 to 80 K temperature range. We show that an oscillator based on this resonator has the potential to operate with fractional frequency instability below 10(-14) for measurement times of 1 to 100 seconds. This is sufficient to operate an atomic clock at the quantum projection noise limit.

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.