Dielectric Resonator
1.Introduction
A dielectric is an electrical insulator that can be polarized by an applied electric field. When a dielectric is placed in an electric field, electric charges do not flow through the material, as in a conductor, but only slightly shift from their average equilibrium positions causing dielectric polarization. Because of dielectric polarization, positive charges are displaced toward the field and negative charges shift in the opposite direction. This creates an internal electric field which reduces the overall field within the dielectric itself. [1] If a dielectric is composed of weakly bonded molecules, those molecules not only become polarized, but also reorient so that their symmetry axis aligns to the field.
High quality resonating elements are key to the function of most microwave circuits and systems. They are fundamental to the operation of filters and oscillators, and the performance of these circuits is primarily limited by the resonator quality factor. At microwave frequencies, the quality factor (Q) of metal transmission line resonant circuits proportional to its volume. As a result, wave guide structures are often employed to increase Q at the expense of size, weight and cost. Dielectric losses improving constantly, whereas metal losses, with the exception of superconductors, have remained substantially the same. These resonators can be made to perform the same functions as waveguide filters but are, in contrast, very small, stable and lightweight. The popularization of low-loss dielectric resonators roughly coincides with the miniaturization of many of the other associated elements of most microwave circuits. When taken together, these technologies permit the realization of small, reliable, lightweight and stable microwave systems. A dielectric resonator (also dielectric resonator oscillator, DRO) is an electronic component that exhibits resonance for a narrow range of frequencies, generally in the microwave band. The resonance is similar to that of a circular hollow metallic waveguide, except that the boundary is defined by large change in permittivity rather than by a conductor. Dielectric resonators generally consist of a "puck" of ceramic that has a large dielectric constant and a low dissipation factor. The resonance frequency is determined by the overall physical dimensions of the puck and the dielectric constant of the material.
2.The Early Years
In the late 19th century, Lord Rayleigh demonstrated that an infinitely long cylindrical rod made up of dielectric material could serve as a waveguide.[1] Additional theoretical [2] and experimental [3] work done in Germany in early 20th century, offered further insight into the behavior of electromagnetic waves in dielectric rod waveguides. Since a dielectric resonator can be thought of as a truncated dielectric rod waveguide, this research was essential for scientific understanding of electromagnetic phenomena in dielectric resonators. In 1939 Robert D. Richtmyer published a study in which he showed that dielectric structures can act just as metallic cavity resonators. He appropriately named these structures dielectric resonators. Richtmyer also demonstrated that, if exposed to free space, dielectric resonators must radiate because of the boundary conditions at the dielectric-to-air interface. These results were later used in development of DRA (Dielectric Resonator Antenna). Due to World War II, lack of advanced materials and adequate manufacturing techniques, dielectric resonators fell in relative obscurity for another two decades after Richtmyer's study was published. However, in the 1960s, as high-frequency electronics and modern communications industry started to take off, dielectric resonators gained in significance. They offered a size-reducing design alternative to bulky waveguide filters and lower-cost alternatives for electronic oscillator,[5] frequency selective limiter [6] and slow-wave [7] circuits. In addition to cost and size, other advantages that dielectric resonators have over conventional metal cavity resonators are lower weight, material availability, and ease of manufacturing. There is a vast availability of different dielectric resonators on the market today with unloaded Q factor on the order of 10000s.
From a historical perspective, guided electromagnetic wave propagation in dielectric media received wide spread attention in the early days of microwaves. Surprisingly, substantial effort in this area predates 1920 and includes such famous scientists as Lord Rayleigh, Sommerfeld, Bose and Debye. The term “dielectric resonator” first appeared in 1939 when Richtmyer of Stanford University showed that unmetalized dielectric objects (toroid) can function as microwave resonators. However, his theoretical work failed to generate significant interest, and practically nothing happened in this area for more than 25 years. In 1953, a paper by Schlicke reported on super high dielectric constant materials (-1,000 or more) and their applications as capacitors at relatively low radio frequencies (RF). In the early 1960s, researches from Columbia University, Okaya and Barashh, rediscovered dielectric resonators during their work on high dielectric materials (single-crystal TiO2 rutile), paramagnetic resonance, and masers. Their papers provided the first analysis of modes and resonator design. Nevertheless, the dielectric resonator was still far from practical applications. High dielectric constant materials, such as rutile, exhibited poor temperature stability, causing correspondingly large resonant frequency changes. For this reason, in spite of the high-Q and small size, dielectric resonators were not considered for use in microwave devices.
In the mid-1960s, Cohn and his coworkers at Rentec Corporation performed the first extensive theoretical and experimental evaluation of the dielectric resonator. Rutile ceramics were used for experiments that had an isotropic dielectric constant in the order of 100. Again, poor temperature stability prevented development of practical components.
A real breakthrough in ceramic technology occurred in early 1970s when the first temperature-stable, low-loss, barium tetratitanate ceramics were developed by Raytheon. Later, a modified barium tetratitanate with improved performance was reported by Bell Labs. These positive results led to actual implementations of dielectric resonators as microwave components. The materials, however, were in scare supply and not commercially available.
The next major breakthrough came from Japan, when Murata Mfg. Co produced (Zr-Sn)TiO4 ceramics. They offered adjustable compositions so that the temperature coefficient could be varied between commercially available at reasonable prices. Afterward, the theoretical work and use of dielectric resonators expanded rapidly.
3.Dielectric Resonator
Dielectric Materials of the wave guiding properties of dielectric materials is not a new idea. Despite this fact, dielectric resonator filters have only been recently developed due to the previously poor characteristics of ceramic materials. Now with the advanced development of improved dielectric materials and the rapid expansion of cellular and satellite communications, dielectric resonator filters have been the source of much research.
A dielectric resonator is the basic unit of a ceramic filter. It is described as a shaped piece
of high dielectric constant material, commonly known as a puck. The puck is usually supported by a structure made of low dielectric constant material and is surrounded by a conducting enclosure.
At the resonant frequency most of the electromagnetic energy is stored within the dielectric resonator. The support is used to ensure that there is no contact between the puck and the enclosure. The enclosure acts as a shield to prevent radiation and due to the puck’s remoteness the resonant frequency is controlled by its cross sectional area and permittivity constant .The most important characteristics of a dielectric resonator include: its field patterns, Q factor, resonant frequency and spurious free bandwidth [1]. These factors are dependent on the dielectric material used, the resonator’s shape and the resonant mode used.
Dielectric Resonator Oscillators (DRO) are used widely in today's electronic warfare, missile, radar and communication systems. They find use both in military and commercial applications. The DROs are characterized by low phase noise, compact size, frequency stability with temperature, ease of integration with other hybrid MIC circuitries, simple construction and the ability to withstand harsh environments. These characteristics make DROs a natural choice both for fundamental oscillators and as the sources for oscillators that are phase-locked to reference frequencies such as crystal oscillators.
Microwave dielectric ceramics as the key basic materials to modern communication technology, after years of continuous research and development, using the latest technology to produce microwave ceramics have achieved a variety of dielectric constant, quality factor Q of the new media ceramic materials, and as a dielectric material application microwave frequencies of modern circuits, and modern electronic communications in the filters, resonators, dielectric substrates, such as microwave dielectric waveguide circuit components materials. Comparing with microwave dielectric resonator made of ceramic materials and metal cavity resonator, obviously, dielectric resonator features with a light weight, small volume, temperature coefficient of stability, cheap, and so on. They have been widely used in satellite broadcast reception systems, filters, base stations, radar detectors, wireless mobile communications, telecommunications computer systems, military facilities, microwave, modern medicine and many other areas. Taking advantage of microwave dielectric ceramic materials for dielectric resonators and filters, with a relatively high dielectric constant, can make the device smaller, space-saving design of the circuit; high quality factor Q value and low dielectric loss, in order to ensure a good selection frequency characteristics and low insertion loss of the device; the temperature coefficient is small, in order to ensure the thermal stability of the device. Dielectric constant, quality factor Q, the temperature coefficient, these three parameters to evaluate the important microwave dielectric ceramic material specifications and production.
3.1Field Pattern
There are many field patterns or modes present in a dielectric resonator dependent on the shape of the dielectric resonator. Despite this, the most commonly used puck that is widely accepted in industry is the cylindrical shaped dielectric resonator operating in the TE01d mode [1]. Cohn first described this mode in 1968. He used a simple model that approximated the fields inside the dielectric by assuming a Perfect Magnetic Conductor (PMC) covered all surfaces except the end-caps. This allowed energy to leak out from the flat surfaces and thus the problem was reduced to a simpler waveguide problem.
The mathematical analysis is quite complex and the theory is detailed in Reference. From this theory there are three basic modes present in a dielectric waveguide: Transverse Electric (TE); Transverse Magnetic ™; and Hybrid (HE) modes. TE and TM modes do not contain electric and magnetic fields in the axial direction respectively. Hybrid modes contain properties of both electric and magnetic fields that can propagate in all directions.
As mentioned previously the majority of applications use TE01d (in single mode applications) and also HE11d (for dual mode operation), as they are the two lowest modes to resonate when a DR is placed within conducting boundaries. When designing, modes are chosen to best suit the application.
The dimensions of the DR and the exterior boundary conditions imposed, e.g. tuning elements, shields and supports, determine which mode has the lowest resonant frequency or is fundamental. These fundamental modes are desirable as most of their E field is confined within the DR, indicating a high Q characteristic. Q factor will be described later in this report.
3.2Resonant Frequency
At the resonant frequency of a DR, the magnetic field energy equals the electric field energy and electromagnetic waves can be transmitted with minimal loss. Only at a resonant frequency can electromagnetic fields be sustained. The resonant frequencies of the dominant mode and the spurious modes of a DR are important in the design of a DR filter. Spurious modes within the pass band can degrade a filter’s response. Therefore the calculation of these parameters is required to achieve a desired response in a microwave filter.
The resonant frequency and field patterns of a DR can be determined approximately by simple models such as Cohn’s, as well as the Itoh and Rudokah’s models [3]. These models have limitations with regards to the accuracy of resonant frequency. The more sophisticated techniques are required in the design of DR cavities and filters and take into account the influence of the surrounding environment. Some more rigorous techniques have been developed to calculate a solution by excessive approximations converging to an exact solution. Therefore field distribution and resonant frequency can be calculated to a desired accuracy. These rigorous techniques are mode matching, finite element/finite difference and method of moments.
3.3Quality Factor
The Quality factor (Q) is another important design parameter to consider in the design of DR filters. Q is determined by losses in a structure and in filter terms is a measure of bandwidth (as resonator bandwidth is inversely proportional to Q). It is also a major factor in insertion loss and the selectivity of a filter. In general, the Q factor relates to a resonant circuit’s capacity for electromagnetic storage with its energy dissipated as heat.
Q factor is a parameter often used to assess the performance of a dielectric resonator. It is
determined by the equation below:
Q= (time average energy stored at resonant frequency / energy dissipated in one period at this frequency)
From the determination of the Q factor, resonator bandwidth and loaded resonant frequency can also be calculated.
In a resonant cavity acting as a load in a microwave circuit, several Q factors are defined. These Q factors are loaded Q (QE), unloaded Q (QU) and overall Q (QL). The loaded and unloaded Q accounts for external and internal losses respectively. The overall Q factor accounts for both internal and external losses.
3.4Theory of Operation
The dielectric element functions as a resonator because of the internal reflections of the electromagnetic waves at the high dielectric constant material/air boundary. This results in confinement of energy within and in the vicinity of the dielectric material, which, therefore, forms a resonant structure.
Although dielectric resonators display many similarities to resonant metal cavities, there is one important difference between the two: while the electric and magnetic fields are zero outside the walls of the metal cavity (i.e. open circuit boundary conditions are fully satisfied), these fields are not zero outside the dielectric walls of the resonator (i.e. open circuit boundary conditions are approximately satisfied). Even so, electric and magnetic fields decay from their maximum values considerably when they are away from the resonator walls. Most of the energy is stored in the resonator at a given resonant frequency for a sufficiently high dielectric constant . Dielectric resonators can exhibit extremely high Q factor that is comparable to a metal walled cavity.
There are three types of resonant modes that can be excited in dielectric resonators: transverse electric (TE), transverse magnetic ™ or hybrid electromagnetic (HEM) modes. Theoretically, there are an infinite number of modes in each of the three groups, and desired mode is usually selected based on the application requirements. Generally, TE01n mode is used in most non-radiating applications, but other modes can have certain advantages for specific applications.
Approximate resonant frequency of TE01n mode for an isolated cylindrical dielectric resonator can be calculated as:
Where a is the radius of the cylindrical resonator and L is its length. Both a and L are in millimeters. Resonant frequency fGHz is in gigahertz. This formula is accurate to about 2% in the range:
However, since a dielectric resonator is usually enclosed in a conducting cavity for most applications, the real resonant frequencies are different from the one calculated above. As conducting walls of the enclosing cavity approach the resonator, change in boundary conditions and field containment start to affect resonant frequencies. The size and type of the material encapsulating the cavity can drastically impact the performance of the resonant circuit. This phenomenon can be explained using cavity perturbation theory. If a resonator is enclosed in a metallic cavity, resonant frequencies change in following fashion:
- If the stored energy of the displaced field is mostly electric, its resonant frequency will decrease;
- If the stored energy of the displaced field is mostly magnetic, its resonant frequency will increase. This happens to be the case for TE01n mode.
Most common problem exhibited by dielectric resonator circuits is their sensitivity to temperature variation and mechanical vibrations. Even though recent improvements in materials science and manufacturing mitigated some of these issues, compensating techniques still may be required to stabilize the circuit performance over temperature and frequency.
As in a conventional metal wall cavity, an infinite number of modes can exit in a dielectric resonator. To a first approximation, a dielectric resonator can be explained as a hypothetical magnetic wall cavity, which is the dual case of a metal (electric) wall cavity. The magnetic wall concept 9on which the normal component of the electric field and tangential of a magnetic field vanish at the boundary) is well known and widely used in theoretical tool in electromagnetic field theory. In a very crude approximation, the air/high-dielectric constant material interface can be modeled as such a magnetic wall (open circuit). Hence, the field distribution and resonant frequencies can be calculated analytically.
To prove this model, and take into consideration that, in actuality, some of the electromagnetic field leaks out of the resonator and eventually decays exponentially in its vicinity (this leaking field portion is described by a mode subscript δ), the magnetic wall model was gradually modified. At first, two lateral magnetic wall waveguide below cutoff was introduced.
This gave calculated frequency accuracy for the TE01 mode of about 6%. The magnetic wall waveguide below cutoff with a dielectric resonator inside. The circular wall was also removed (dielectric waveguide model), and the accuracy of calculations of resonant frequency was improved to 1-2%. In an actual resonator configuration, usually some sort of metal-wall cavity or housing is necessary to prevent radiation of the electromagnetic field and resulting degradation of resonator Q. Taking this into consideration, the model of the dielectric resonator assembly was modified, and electromagnetic field distribution in the structure were obtained through the mode matching method.
In advanced models, additional factors, such as dielectric supports, tuning plate and micro strip substrate, can also be taken into account. The resonant frequency of dielectric resonators in these configurations can be calculated using mode-matching methods with accuracy much better than 1%. Recently available electromagnetic simulation programs (3-D) enable additional improvement of calculations of relatively complex structures. The resonator housing, tuning and coupling elements can be precisely modeled, and very accurate results can be obtained. An additional feature of these programs is that electromagnetic field distribution, dissipated power, etc. can be visualized and plotted easily.
The most commonly used mode in a dielectric resonator is the TE10 (in cylindrical resonator) or the TE11 (in rectangular resonator). The TE01 mode for certain diameter/length (D/L) ratios has the lowest resonant frequency and, therefore, is classified as fundamental mode. In general, mode nomenclature in a dielectric resonator is not as well defined as for a metal cavity (TE and TM modes).
Many mode designations exit and this matter is quit confusing as is true for the dielectric waveguide. The mode designation proposed by Kobayashi is the most promising and should be adopted as a standard (this was addressed by the MTT Society Standards Committee and, presently two designations, including Kobayashi’s, are recommended).
The TE01 mode is the most popular and is used in single-mode filters and oscillators. HE11 (hybrid mode) is used in high-performance dual-mode filters, directional filters and oscillators. The TM mode is being used in cavity combines and filters, as well as low-frequency filters.
3.5Coupling to Microwave-Transmission Lines
An advantage of dielectric resonators is the ease with which these devices couple to common transmission lines, such as waveguide and micro strip. A typical dielectric resonator in the TE01 mode can be transversely inserted into a rectangular waveguide. It couples strongly to the magnetic field and act as a simple band stop filter. Coupling in the magnetic field in the waveguide. Coupling to a magnetic field in the waveguide can be adjusted by either rotating the resonator or moving a resonator towards the side of waveguide. In micro strip line applications, a dielectric TE01 resonator couples magnetically and forms a band stop filter. The coupling can be easily adjusted by either moving the resonator away (or toward center) from the micro strip or by lifting the resonator on a special support above the micro strip.
The resonant frequency of a dielectric resonator in this very special case can be calculated using an equation. The resonant frequency in this topology can be adjusted to higher frequency with a metal screw or plate located above the resonator and perturbing the magnetic field or down in frequency by lifting the resonator (moving it away from the ground plane). A typical range is in order of 10%. Extra care must be taken, however, not to degrade the Q or temperature performance of the resonator by the closely positioned metal plate.
One of the advantage of dielectric resonators over the corresponding metal wall cavities is the ease of dielectric shaping. Typically, dielectric resonators have a disc form, however this shape can be easily modified to include notches or flats or tuning, additional shaping for a conventional mounting, holes at various location to control spurious modes, multilayer resonators, multiple resonators (for tenability), etc.
An interesting modification of the dielectric resonator is the so called double resonator. In this configuration, two halves of the ceramic disc or plate acts as one resonator. A much wider linear tuning range can be obtained in this configuration without degradation of the Q.