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«SYAZANA BASYIRAH BINTI MOHAMMAD ZAKI UNIVERSITI SAINS MALAYSIA 2015 DESIGN OF 10 GHz NEGATIVE RESISTANCE DIELECTRIC RESONATOR OSCILLATOR by SYAZANA ...»

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2.3.2 Theory of Dielectric Resonator Resonators are an important component in microwave circuits. They play a major role in frequency definition in oscillators where they store energy at the resonant frequency in the electric and magnetic fields. The important characteristics of the microwave resonators are the resonant frequency, quality factor (Q), which defines the bandwidth of the resonance and the input impedance of the resonator (Ugurlu, 2011). There are several kinds of resonant circuits which include lumped element resonant circuits, transmission line distributed resonant circuits, and cavity resonators.

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frequency source. It is made of the material with high dielectric constant, high Q factor, and low temperature coefficient (Bing et al., 2009). The dielectric constant,  r varies from 20 to 80. DRs have been widely used to make temperature compensated stable oscillators. But for most applications they also need to have low noise characteristics as close as a few hundreds of Hz off the carrier. During the past several years, a variety of microwave components which employ DRs have been developed due to the availability of low-cost, temperature-stable, high permittivity materials. Since the sizes of DRs are small depends on the material and the frequency and can be as small as a few centimeters and they are the most preferable resonator in high frequency applications(Ugurlu, 2011).

The DR functions as a resonator due to internal reflection of the electromagnetic waves at the high dielectric constant material or air boundary. The interface between the air and the high dielectric constant material can be explained as a hypothetical magnetic wall (covered by a perfect magnetic conductor (PMC)), on which the normal component of the electric field and the tangential component of the magnetic field will vanish at the boundary. Hence, most of the energy will be internally reflected. The reflection coefficient increases as the ratio of the dielectric constant of the DR to air increases.

As in a conventional metal cavity, an infinite number of modes can exist in a DR. The most commonly utilized mode in a cylindrical DR is called the TE01∂ mode. Some call it a “magnetic dipole mode” because of this mode appears as a magnetic dipole, instead of using the term TE01∂. This particular mode for a given diameter or length ratio has the lowest resonant frequency and therefore is designated the fundamental mode.

The most important properties for a DR in microwave circuit applications are dielectric

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frequency. The unloaded quality factor, Qu depends on both dielectric and environmental losses.

The Q factor is a measure of the energy stored in the field inside the resonator as compared to the energy lost or dissipated per cycle.

The next issue is to couple the DR to the microwave circuit. The simplest way is to place it on top of a microstrip substrate. The lateral distance between the DR and the microstrip conductor determines the amount of coupling between the resonator and the microstrip line. The entire device is usually enclosed in a metal shielded box which is used to prevent radiation losses and to shield the circuit from stray external fields (Pan, 1991).

2.3.2.1 Electric and Magnetic Field Patterns There are many field patterns or mode present in a DR depending on the shape of the DR. Cylindrical shape which operates at TE01∂mode is the most popular shape of the DR that has been used recently in the industry until now (Hunter, 2001). There are four different basic modes which present in a dielectric waveguide; Transverse Electric (TE), Transverse Magnetic (TM), Electric Hybrid (EH) and Magnetic Hybrid (HE) modes.

2.3.2.2 Resonant Frequency The resonant frequency of the DR is primarily determined by its dimensions and its surroundings. Therefore, the frequency fluctuates very little producing a more stable frequency source with a corresponding improvement in phase noise.Although the geometrical form of a DR is extremely simple, an exact solution of the Maxwell equations is considerably more difficult than for the hollow metallic cavity. For this reason, the exact resonant frequency of a certain amount of mode, such as TE01∂, can only be computed by rigorous numerical procedures.

Currently, practical DRs cover a frequency range of 1 to 100 GHz. The lower frequency limit is 24

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