Waveguides are used to guide electromagnetic power, whereas cavity resonators confine the power.
The modes of wave propagation in the waveguide can be classified into two types: transverse electric mode or transverse magnetic mode.
Cavity resonators are source-free, and in the ideal case, are examples of a lossless system. However, the losses in the dielectric medium filled inside the cavity and the losses caused by the boundary walls damp out electromagnetic oscillations and make the cavity resonator non-ideal.
Waveguides and cavity resonators play an essential role in microwave applications
In microwave engineering applications, engineers have to learn to work with electromagnetic energy. In certain cases, the electromagnetic energy needs to be guided from one location to another, and there are even applications where the energy is confined in a space.
In these scenarios, engineers use waveguides to guide electromagnetic power and cavity resonators to confine the power. In waveguides and cavity resonators, the desired functionality can be achieved by setting material boundaries.
Waveguides and Cavity Resonators
Waveguides and cavity resonators play an essential role in microwave applications—they are used in microwave devices as well as for physical measurements. Waveguides and cavity resonators are theoretically based on Maxwell’s equations of the electromagnetic field.
Electromagnetic energy poses a problem: when transmitted through free space, it scatters. Waveguides are a proven solution to this issue, as they have definite boundaries made of material structures that connect two locations in a circuit. Waveguides are made using wire, co-axial cables, parallel plates, or optical fibers to carry electromagnetic power from one point to another.
A two-wire transmission line is the simplest waveguide system. As a waveguide, they can be formulated using distributed circuit elements such as capacitance and inductance. However, there are contrary theories to this, where a waveguide is viewed as a single conductor transmission line. In the single conductor concept, the waveguide is analyzed using electromagnetic field theory, and the two-wire transmission analysis is taken from the circuit point of view.
Rectangular waveguides are the preferred waveguide shape. In a rectangular waveguide, the electric and magnetic fields in the x and y directions are expressed in terms of the electric and magnetic components in z directions, denoted by Ez and Hz. With the two independent wave equations for Ez and Hz, the modes of wave propagation in the waveguide can be classified into two types:
1) Transverse electric mode (TE mode): (Ez=0 and Hz≠0). In this mode, the electric field is entirely transverse and an axial component of the magnetic field exists.
2) Transverse magnetic mode (TM mode): (Hz=0 and Ez≠0). In this mode, the magnetic field is in a plane perpendicular to the direction of wave propagation. The component of the electric field is in the direction of wave propagation in TM mode.
Various forms of TE and TM modes are possible in the waveguide, but their characteristics are limited by the waveguide’s dimension and frequency. The various forms of TE and TM modes are distinguished by subscripts m and n, which only take integer values. The cut-off frequency of the waveguide propagation increases with the increase in m and n values. TE10 is the dominant mode in rectangular waveguides.
In microwave engineering applications, lumped circuit elements fail at high frequencies. For frequency applications in and above the range of 300 MHz to 3GHz, cavity resonators are used.
Cavity resonators can be considered short-circuited transmission lines and are realized using a metallic box with any arbitrary shape with short-circuited boundaries. Short-circuiting the waveguide of any shape, for example, rectangular, cylindrical, or circular, is one method of constructing a cavity resonator with a high-quality factor. In cavity resonators, the boundary walls are made of high-conducting metals and, thus, the electromagnetic energy is confined to the cavity.
Cavity Oscillators in a Resonant State
When equal to one of the resonant frequencies, the signal frequency in the cavity resonator leads to oscillation mode or a resonant state of the cavity oscillator. In this resonant state, the electromagnetic fields are confined in the cavity and the maximum magnetic energy stored is equal to the maximum electric energy. The conversion of the electric field to the magnetic field and vice versa occurs periodically inside the cavity, forming electromagnetic oscillations similar to an LC circuit or tank circuit. The cavity resonator doesn’t require any input energy to sustain these electromagnetic oscillations.
The cavity resonators are source-free, and in the ideal case, they are a lossless system. However, the losses in the dielectric medium filled inside the cavity and the losses caused by the boundary walls damp out the electromagnetic oscillations, with respect to time, and make the cavity resonator non-ideal.
As an example, let’s consider a rectangular cavity resonator; it is a section of rectangular waveguide enclosed with conducting plates at its two ends. The electromagnetic waves traveling in the opposite direction (simultaneously in z-direction) form standing waves in the z-direction inside the cavity resonator. The fields in the rectangular cavity resonator are standing waves in x, y, and z directions. In the cavity resonator, different modes of wave propagation are possible.
In advanced telecommunication circuits, waveguides and cavity resonators are widely used in the microwave band of frequencies to make filters, amplifiers, and oscillators. The waveguides and cavity resonators can be made into shapes—such as rectangles, circles, and cylinders—that are suitable in amplifying and oscillating circuits. At high frequencies, waveguides are used to transmit electromagnetic power and signals. Similarly, the application of cavity resonators in tuned circuits is found extensively in high-frequency microwave circuits. Waveguides and cavity resonators are integral parts of microwave circuits, and proper design of these useful tools can improve the performance of the entire system utilizing them.
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