# Basic parameters of microwave resonator

September 25, 2019

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The resonant cavity is a resonant element operating at a microwave frequency. It is an arbitrary shaped dielectric region surrounded by a conductive wall (or a magnetically permeable wall) and capable of forming an electromagnetic oscillation therein. It has stored electromagnetic energy and selects a certain frequency signal. The characteristics. Similar to the low-frequency LC tank, it has a wide range of applications in microwave technology. For example, it is used as an energy exchange and frequency selective element in various microwave oscillators and as a frequency selective element in microwave frequency multipliers and amplifiers. The microwave resonant cavity can also directly constitute a microwave wavelength meter. Microwave filters are used for microwave measurement and microwaves. Communication. High-Q resonators are used as echoboxes in radar equipment to detect the performance of radar transmission and reception systems.

The basic parameters of the microwave resonator:

The basic parameters of the LC resonant tank are inductance L, capacitance C and resistance R (or conductance G). For the convenience of measurement and analysis, the resonant frequency Æ’0 (or resonant wavelength Î»0), quality factor Ñ”0, and equivalent conductance G0 are usually used as its basic parameters. The resonator has the following types:

1. Rectangular resonant cavity The rectangular resonant cavity is formed by a rectangular waveguide that is closed at both ends with a conductor plate. As shown in Figure 4-3. Its cavity size is aÃ—bÃ—l. The characteristics of the rectangular cavity are discussed below.

2. Cylindrical Resonator The cylindrical resonator consists of a section of circular waveguide enclosed by conductor plates, as shown in Figure 4-5. Its radius is a and its length is l. Its calculation method is similar to that of the rectangular cavity, and the result in the circular waveguide can be used.

3. Other forms of resonant cavity:

Commonly used microwave resonators, such as axial resonators, microstrip resonators, and reentrant resonators. This kind of resonant cavity, due to working in TEM wave or quasi-TEM wave, has the advantages of wide frequency band, simple oscillation mode and stable field structure. Therefore, they all have wider applications.

Perturbation Theory of Microwave Resonator When there is a slight change in the cavity or cavity filled medium, the basic parameters of the resonator are Æ’0 and Ñ”0, etc., with corresponding minor changes. If this change has little effect on the field distribution and the original parameters, it is called "perturbation." For solving this problem, the perturbation solution is generally approximated based on the known solution before the perturbation, and the wave equation does not have to be solved under new conditions. This solving method is called â€œperturbation methodâ€. .

Resonant cavity excitation and coupling The microwave resonator must be connected to the external circuit as a component of the microwave system to operate, ie it must introduce microwave signals from an external circuit to excite the desired mode of electromagnetic oscillation in the cavity; the oscillation in the cavity must be Through electromagnetic coupling, part of the energy in the cavity can be transferred to the external load. Since most of the microwave components have reciprocity, the excitation and coupling structures and operating characteristics of the resonant cavity are exactly the same, that is, when one element is used for excitation or coupling, its characteristics are the same. The difference between the two is just the opposite direction of wave propagation. The basic requirement for the excitation (or coupling) element of a resonant cavity is that it must ensure that the desired oscillation mode is achievable in the cavity, while avoiding the generation of other interference modes. The establishment of a certain oscillation mode in the resonant cavity is that the excitation component firstly excites the electric field or magnetic field component in a certain local area of â€‹â€‹the cavity in accordance with the desired mode, and then excites the whole cavity from the electric field or the magnetic field. The required oscillations. According to the different types of excitation; generally divided into electrical coupling, magnetic coupling, diffraction coupling and electronic coupling four.

The basic parameters of the microwave resonator:

The basic parameters of the LC resonant tank are inductance L, capacitance C and resistance R (or conductance G). For the convenience of measurement and analysis, the resonant frequency Æ’0 (or resonant wavelength Î»0), quality factor Ñ”0, and equivalent conductance G0 are usually used as its basic parameters. The resonator has the following types:

1. Rectangular resonant cavity The rectangular resonant cavity is formed by a rectangular waveguide that is closed at both ends with a conductor plate. As shown in Figure 4-3. Its cavity size is aÃ—bÃ—l. The characteristics of the rectangular cavity are discussed below.

2. Cylindrical Resonator The cylindrical resonator consists of a section of circular waveguide enclosed by conductor plates, as shown in Figure 4-5. Its radius is a and its length is l. Its calculation method is similar to that of the rectangular cavity, and the result in the circular waveguide can be used.

3. Other forms of resonant cavity:

Commonly used microwave resonators, such as axial resonators, microstrip resonators, and reentrant resonators. This kind of resonant cavity, due to working in TEM wave or quasi-TEM wave, has the advantages of wide frequency band, simple oscillation mode and stable field structure. Therefore, they all have wider applications.

Perturbation Theory of Microwave Resonator When there is a slight change in the cavity or cavity filled medium, the basic parameters of the resonator are Æ’0 and Ñ”0, etc., with corresponding minor changes. If this change has little effect on the field distribution and the original parameters, it is called "perturbation." For solving this problem, the perturbation solution is generally approximated based on the known solution before the perturbation, and the wave equation does not have to be solved under new conditions. This solving method is called â€œperturbation methodâ€. .

Resonant cavity excitation and coupling The microwave resonator must be connected to the external circuit as a component of the microwave system to operate, ie it must introduce microwave signals from an external circuit to excite the desired mode of electromagnetic oscillation in the cavity; the oscillation in the cavity must be Through electromagnetic coupling, part of the energy in the cavity can be transferred to the external load. Since most of the microwave components have reciprocity, the excitation and coupling structures and operating characteristics of the resonant cavity are exactly the same, that is, when one element is used for excitation or coupling, its characteristics are the same. The difference between the two is just the opposite direction of wave propagation. The basic requirement for the excitation (or coupling) element of a resonant cavity is that it must ensure that the desired oscillation mode is achievable in the cavity, while avoiding the generation of other interference modes. The establishment of a certain oscillation mode in the resonant cavity is that the excitation component firstly excites the electric field or magnetic field component in a certain local area of â€‹â€‹the cavity in accordance with the desired mode, and then excites the whole cavity from the electric field or the magnetic field. The required oscillations. According to the different types of excitation; generally divided into electrical coupling, magnetic coupling, diffraction coupling and electronic coupling four.

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