Our communication elements: - Wave Propagation in Parallel - Plane Waveguide, Analysis of Waveguide – General Approach, Rectangular wave, Modal Propagation in Rectangular Waveguide, Surface Currents on the Waveguide Walls, Field Visualisation, Attenuation in Waveguide.
Wave Propagation in Parallel-Plane Waveguide:-
There are two endless parallel planar waves, which operate on completely different plates from a similar distance, which are used to guide electromagnetic waves. It is one of the simplest woven structures and is often studied to understand the basic principles of wave spread.
Basic Principle:
When an electromagnetic wave is introduced in a parallel plate structure, the operating boundaries force the tangent electrical area to be zero on the surfaces. This area position shapes the area distribution between the plates and allows only a few modes to propagate.
Spreading mode
- Transverse Electric (TE) mode: The electric field is transverse in the direction of perfectly scattered (EZ = 0).
- Transverse magnetic (TM) mode: The magnetic field is completely transverse (Hz = 0).
- TEM mode: Both electric and magnetic areas are purely transverse; the only thing that exists is when the wave is filled with a homogeneous dielectric.
Cut-off Frequency:
Only a specific cut-off rate can propagate waves with frequencies:
Where:
- m = mode number
- d = plate separation
- c = speed of light
- εr = relative permittivity of the medium
Application:
- Parallel plan waves are used:
- Microwave oven lab experts
- Antenna lining system
- Educational performance for the wave application
Analysis of Waveguide – General Approach:-
There are wave structures, such as direct electromagnetic waves, with minimal damage from one point to another. They are widely used in microwaves, radars, and communication systems. The general approach to waveguide analysis involves determining how waves spread in a given geometry and satisfying the equations and boundary conditions in Maxwell.
1. Define geometry and content
The first step is to specify the medium that fills the cross-sectional mould (rectangular, circular, parallel plate) and the medium that fills the gaming (air, dhank). Physical dimensions play an important role in determining which modes can propagate.
2. Use the equations of Maxwell
Begin with the curl equations of Maxwell for time-homogeneous regions:
These equations are used to achieve wave equations for electric and magnetic field components.
3. Select mode type
Based on the field configuration, it can be promoted as a wave:
- Tea (transverse electric) – ez = 0
- TM (transverse magnetic) – Hz = 0
- TEM (transverse electromagnetic) – EZ and OF are both zero (rare in closed waves).
4. Use the border conditions
Walls that operate completely as walls require that the electric field tangent to the boundary is zero. This area leads to a different solution for distribution.
5. Determine the cutting frequency and spread constantly
Solving the wave detection with border conditions leads to cutting frequency and spreading constant β for each mode, which defines how the phase changes with a loom.
Rectangular wave: -
A rectangular waveguide is a hollow metal structure with a rectangular cross-section, designed to direct electromagnetic waves, especially in microwaves and millimetre wave frequencies. It is one of the most common wave types used in radar, satellite and communication systems due to its simple geometry and low disadvantages.
Structure and principle:
A rectangular wave is usually made by a good conductor such as copper or aluminium. The interior is hollow and can be filled with wind or dying material. The wave is limited inside the operating walls, which forces the tangent component in the electric field to be zero on the boundaries.
Spreading mode:
In a rectangular woven guide, waves may not be present in a hollow waveguide, mainly in TE (transverse electric) or TM (transverse magnetic) mode-TEM mode.
- TE mode is the main mode, which has the lowest cut-off frequency and the most effective spread.
- High-Norwegian Mode (TEₘₙ, TMₘₙ) reproduction frequencies are only above the cutting values.
There is a cutting frequency for the tea mode:
Where 𝑎 and 𝑏 are the width and height of the wavy.
Advantage:
- Low descending on high frequencies
- High power capacity
- Immunity for external intervention
Application:
- Microwave communication link
- Radar system
- Satellite bottom station
- RF transmission of high power
Modal Propagation in Rectangular Waveguide: -
A rectangular wave is a hollow metal structure with a rectangular cross-section, which is widely used to direct microwave and millimetre wave signals. Model proliferation refers to the way electromagnetic waves move within the wavy in the specific field configurations, called modes.
Types of mode:
In a hollow rectangular wave, only transverse electric (TE10) and transverse magnetic (TM) modes can exist:
- TE-MODS: There is no longitudinal component in the electric field (EZ = 0); the magnetic field consists of both transverse and longitudinal components.
- TM mode: There is no longitudinal component in the magnetic field (Hz = 0); there are both transverse and longitudinal components in the electric field.
The transverse electromagnetic (TEM) mode cannot propagate in a hollow wave, as it requires two conductors.
Cut-off Frequency:
Each mode has a cut-off frequency, below which it cannot propagate:
Where:
- m,n = mode indices
- a = width of waveguide
- b= height of waveguide
- c = speed of light
TE10 mode is the main mode in rectangular waves because it has the lowest cut-off frequency and minimum damage.
Propagation Characteristics:
Over the cut-off, waves spread less than the speed of light with a phase constant β and the speed of the group. Field pattern mode depends on M and N; high mode cross sections have several field variations.
Application
It is necessary to understand model spread:
- Design microwave oven coupling
- Antenna lining system
- Radar and satellite communication
Surface Currents on the Waveguide Walls: -
In a wave, electromagnetic waves are limited in operating walls and lead energy from one point to another. While the fields are mainly present inside the hollow structure, the interaction between the fields and the metal walls induces the flows on the surface, which plays an important role in wave spread and energy transfer.
Formation of surface flows
When an electromagnetic wave spreads through a wave, the tangent component in the electrical field in the operating area should be zero (correct management view). This area position forces the motion of electrons to move into the metal, which creates surface currents floating along interior walls.
These streams:
- Fly parallel to magnetic field lines on the surface.
- The strongest is where the magnetic field is maximum in the area.
- Distribution varies depending on dissemination mode (TE or TM).
Role in power transfer:
Surface currents produce a magnetic field, which, combined with the electric field inside the wave, maintains the marketing wave. They also carry the power of the guide as the poke vector stream in the inner area.
Damage due to surface flows:
In an ideal conductor, no force is lost. However, real leaders have completed conductivity, causing OMMIK damage. These disadvantages:
- Change the part of the signal force to heat.
- Increase with frequency due to hay effects, where streams are limited to a very thin surface layer.
Practical idea:
To reduce losses:
- Use excessive conductive materials (copper, silver coating).
- Maintain smooth interior surfaces to reduce resolution.
Field visualisation: -
Field visualisation is the process of representing and interpreting the distribution of electric and magnetic fields in space so that engineers and researchers can understand how electromagnetic waves behave in a given structure. When it comes to waveguides, antennas or transmission lines, the field visualisation helps explain how energy propagates, interacts with boundaries and is distributed in a medium.
Regionalization purposes
Electromagnetic fields are vector volumes that vary in space and time. Without visualisation, their complex patterns can be difficult to understand. Field provides visualisation:
- The spontaneous understanding of modes in waves or resonance.
- Insight into energy, money, and leakage.
- Guidance for design adaptation to reduce losses and improve efficiency.
Used technology:
Field visualisation can be done analytically or numerically:
- Analytical solutions provide mathematical manifestations for field components in simple geometric (e.g., TE₁₀ mode in rectangular waves).
- Numerical methods such as the finite element method (five) or finite inter-domain (FDT) are used for complex structures.
The results usually appear as follows:
- The vector field plot shows the direction and amount of E- and H-fields.
- Contour map for the intensity of the region.
- 3D animation to portray time on other behaviour.
Application:
- Waveguide mode analysis to identify the main and higher-order modes.
- Antenna radiation pattern design.
- Electromagnetic Compatibility (EMC) studies.
- Microwave and optical device optimisation.
Attenuation in Waveguide: -
A wavy degree refers to the gradual reduction in the strength of the umbrella signal when electromagnetic waves move along its length. Although waves are designed to guide energy effectively, damage due to physical properties and inevitable.
Causes of Attenuation:
Leader:
The inner walls of the wave consist of the operation of the material. When the waves spread, the surface flows on these walls. Due to the final conductivity of metals, these currents cause OMM damage and convert parts of the signal energy into heat. The effect of the skin boundaries flows to a thin layer, increases the resistance to high frequencies and leads to high damage.
Candidate losses
If the cavity is filled with a dielectric material (in addition to wind or vacuum), the final loss of the material causes thermal energy waste, which occurs in the form of heat in the dielectric medium.
Radiation loss
Deficiencies, bending or wave of wave can disappear to remove some energy, contributing to the damping.
Attenuation Constant:
The signal determines the speed of α (in length per unit length per unit). It depends on wave mode, frequency, the conductivity of walls and the geometry of the structure. For a rectangular wave in major tea mode, the loss of conductor is usually the primary contributor.
Minimising Attenuation:
- Use high operating metals such as copper or silver for covering walls.
- Maintain smooth interior surfaces to reduce resolution.
- Avoid unnecessary turns or dissatisfaction.
- Work with frequencies directly above the cutting frequency to balance size and loss.
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