Abstract
MATLAB is a powerful visual computing software suitable for many professional disciplines and various task platforms. It has a variety of library functions, toolboxes and simulation application modules. MATLAB can be used to conduct scientific discussions and deal with various engineering design and practical problems. Therefore, when we solve electromagnetic field numerical solution problems, we can use MATLAB’s powerful development environment and interactive tools to solve practical electromagnetic field problems, and draw the field distribution diagram of electromagnetic waves transmitted in various modes in metal waveguide devices.
On a cross-section perpendicular to the purpose of electromagnetic wave transmission, electromagnetic waves with different forms have various modes of field distribution structures. Each field distribution is a form. In devices such as rectangular and circular waveguides, It can transmit different forms of electromagnetic waves. I used MATLAB to study it. Because MATLAB has powerful visual computing software suitable for many disciplines, it has a large number of different library functions, toolboxes and simulation application modules. You can use MALTAB’s numerical solution toolbox for partial differential equations and assembled programs to solve practical problems and plot different modes of electromagnetic waves.
Therefore, when solving electromagnetic field numerical and graphical problems, we can use the design and simulation and engineering and scientific drawing functions of MATLAB control system to study the field distribution of guided wave transmission in different modes in metal waveguide devices. In this way, the graphics are simple and clear, which can enhance our understanding and practical application of metal waveguide devices.
Keywords: MATLAB; metal waveguide; electromagnetic waves; electromagnetic field distribution diagram
Table of contents
Abstract II
Introduction 1
1Classification of guided wave modes 3
1.1 Transverse electromagnetic waves (TEM waves) 3
1.2 Transverse electric wave (TE wave) 3
1.3 Transverse magnetic waves (TM waves) 3
2 Wave mode analysis in metal waveguide devices 4
2.1 TM waves and TE waves in metal rectangular waveguide 4
2.2 TE mode and TM mode in circular waveguide 5
3 Realization of MATLAB under different wave modes of metal waveguide 8
3.1 MATLAB program is used for field distribution in different modes of metal rectangular waveguide cross-section perpendicular to the propagation direction 8
3.2 MATLAB program is used for field distribution in different modes of metal circular waveguide 9
Summary 11
Reference 12
Acknowledgments 14
Introduction
At present, high-frequency electromagnetic waves are widely used in many fields, such as communication technology, television, network communications, etc. Therefore, studying high-frequency electromagnetic waves has far-sighted significance for our lives and the future, such as studying high-frequency electromagnetic wave energy. transmission effect. Compared with the transmission of electromagnetic wave energy with low frequency, the transmission of high-frequency electromagnetic wave energy has different characteristics. We know that all energy is conveyed in the field. In the case of low frequency, because the relationship between the field and circuit parameters is relatively simple and clear, the role of the field can be expressed in circuit equations using circuit parameters to solve practical problems. In a field with high frequency, the fluctuation of the field changes greatly, and the parameters in the circuit cannot be applied. Moreover, the current and electromagnetic field on the circuit have corresponding fluctuation properties. At the same time, the voltage has no accurate meaning, so we cannot use the circuit in the field. Parameters express circuit equations to solve practical problems. At this time, we should change our approach to study. We can indirectly study the interaction between the field and the charge current on the circuit, and deal with the electromagnetic field, so that we can deal with the transmission effect of electromagnetic energy.
Double-wire transmission is commonly used in low-frequency power systems. When the frequency becomes higher, the surrounding environment will interfere with the transmission of electromagnetic wave energy, and at the same time, the electromagnetic wave transmission will suffer serious losses. In order to solve this problem, we can allow electromagnetic waves to transmit in the medium between two conductors, then we can replace the two-wire transmission line with a coaxial transmission line composed of a hollow conductor tube and a core wire. When the frequency becomes higher, the heat loss in the inner conductors and the medium will be very serious. At this time, we can use hollow metal tubes with generally circular and rectangular cross-sectional shapes to replace the coaxial transmission lines. This device is called metal Waveguide devices, metal waveguide devices are usually distinguished by cross-sectional shape, generally using metal circular waveguides and metal rectangular waveguides. Waveguide transmission is generally suitable for the microwave range
A metal waveguide with a fixed shape is a non-finite-length straight waveguide. Usually its cross-sectional shape, size and length, the internal structure of the waveguide wall and the distribution of media in the waveguide are all fixed along its axis. As the most basic microwave transmission device, regular metal waveguides are widely used in the fields of communication technology and microwave technology. It is of great far-sighted practical significance to study and regulate the electromagnetic field structure distribution of metal waveguides to find out the common characteristics of their guided wave transmission.
MATLAB is an interactive system that can perform matrix operations, draw functions and data, implement algorithms, create user interfaces, connect programs in other programming languages, etc. It is mainly used in engineering calculations, electromagnetic field theory, communication signal processing, and images. processing, signal detection and other fields. It is simple to operate, quick and easy to use. Therefore, when we solve electromagnetic field numerical solution problems, we can use MATLAB’s powerful development environment and interactive tools to solve practical electromagnetic field problems, and can draw various modes of metal waveguide devices. Field distribution diagram of transmitted electromagnetic waves.
Therefore, when solving electromagnetic field numerical and graphical problems, we can use the design and simulation and engineering and scientific drawing functions of MATLAB control system to study the field distribution of guided wave transmission in different modes in metal waveguide devices. In this way, the graphics are simple and clear, which can enhance our understanding and practical application of metal waveguide devices.
1 Classification of guided wave modes
The Hertzian electric vector and the Hertzian magnetic vector can be derived by using Maxwell’s equations, and the vector Helmholtz equation for these two non-scalar quantities can be constructed. By solving this equation, the Hertzian vector can be obtained and the various electromagnetic fields in the waveguide device can be determined. Component expression. Through the relationship between the various field components in the guided wave device, it can be seen that the transverse field component of the guided wave is only related to the longitudinal field component, so the guided wave modes can be classified according to whether there is a longitudinal field component in the guided wave.
1.1 Transverse electromagnetic waves (TEM waves)
There is no longitudinal field component of the electromagnetic field during the transmission process of this transmission form, that is. To make it not 0, it can be known from the expression of the transverse field component that there is. Finally, the expression of TEM wave can be obtained as
This equation proves that TEM waves can be transmitted only in a waveguide device that can establish a non-moving field.
1.2 Transverse Radio Wave (TE Wave)
Transverse electric waves satisfy that all field component expressions can be derived from the longitudinal magnetic field components.
1.3 Transverse magnetic wave (TM wave)
Transverse magnetic waves satisfy that all field component expressions can be derived from the longitudinal electric field components.
2 Wave mode analysis in metal waveguide devices
Waveguide transmission is suitable for the microwave range. The device that guides microwave transmission is the waveguide device. According to its material composition, it can be divided into dielectric waveguide devices and metal waveguide devices. Among them, the metal waveguide device can be divided into metal rectangular waveguide and metal rectangular waveguide according to its cross-sectional shape of circular and rectangular. Metal waveguide is the most fundamental microwave transmission system and is widely used in communication technology and microwave technology. Study the electromagnetic field structure distribution of fixed-shaped metal waveguides, thereby solving the practical effect of metal waveguide characteristics that has a very far-sighted effect.
2.1 TM wave and TE wave in metal rectangular waveguide
TEM waves cannot be transmitted in metal waveguides because they do not meet the boundary conditions of metal waveguides. If there are TEM waves during the transmission process of the metal waveguide, the magnetic field lines emitted by the magnetic field should be distributed inside the cross-section of the metal waveguide system and be a closed curve connected end to end. According to the Maxwell equations we have learned, we know that the line integral of the closed curve magnetic field should be equal to the axial curve of the intersection of the closed curve. This axial current can be a conduction current or a displacement current. Longitudinal conduction current cannot exist in hollow core waveguides. According to the definition of TEM, there is no longitudinal electric field in TEM waves, so longitudinal displacement current cannot exist. Therefore, we can conclude that it is impossible to have closed magnetic field lines in the waveguide cross section, so we can know that there will be no TEM waves in the waveguide device.
Figure 1.1 Rectangular waveguide
The figure above shows the cross-section of a metal rectangular waveguide, with the wide side ruler being a and the narrow side ruler being b. When transmitting TM in a waveguide, . Solve it first and then determine,,,. Any component u of can be solved by the separation of variables method:
u(x,y)==
Now apply boundary conditions to determine the fixed parameters,
Boundary conditions: x=0, a
y=0,b
The field components of the TM wave in the rectangular waveguide can be obtained
Following the method of solving the TM wave, we can obtain the field component expression of the TE wave in the rectangular waveguide.
2.2 TE mode and TM mode in circular waveguide
Metal circular waveguide is shown in the figure. The longitudinal field component Helmholtz equation of the field has the form in cylindrical coordinates:
Let the separation variable solution of the equation be
To find its solution, the linear combination is
The biggest feature of the TM module is that its expression
Use boundary conditions to determine, at r=a, that is, the requirement
Similarly, the field component expression of TE wave in metal circular waveguide can be obtained as
3 Implementation of MATLAB under different wave modes of metal waveguide
3.1 MATLAB program is used for field distribution in different modes of metal rectangular waveguide sections perpendicular to the propagation direction
Use MATLAB to calculate the propagation mode of a metal circular waveguide. Assume that the rectangular cross-section is 3cmX1.5cm and the medium in the waveguide is air (vacuum). The field distribution of several TE mode and TM mode components in the rectangular waveguide in the cross section perpendicular to the waveguide is shown in the figure.
This program is used to display the field distribution in different modes of a metal rectangular waveguide cross-section perpendicular to the propagation direction.
Clear
epslion_0=8.85e-12; % fill in the blank with the dielectric constant
Mur_0=4.0*pi*1.0e-7; %Fill in the blank magnetic permeability coefficient
epslion_r=1.0; % relative dielectric constant of filling medium
Mur_r=1.0; % relative magnetic permeability coefficient of filling medium
Epslion=epslion_0*epslion_r; % fill in the blank with the dielectric constant
Mur=mur_0*mur_r; % magnetic permeability coefficient of filling medium
a=0.03; % metal waveguide x-direction size (variable)
b=0.015; % metal waveguide y-direction size (variable)
E0=1.0; % field amplitude
H0=1.0; % field amplitude
disp('please choose the incident wave: TM=-1 or TE=1');
wavetype=input('wavetype is:');
disp('please input the number of the modes');
m=input(the modes number of x axis is:’); %Transmission mode
n=input(the modes number of y axis is:’); %Transmission mode
3.2 MATLAB program is used for field distribution in different modes of metal circular waveguides
Use MATLAB to calculate the propagation mode of the circular waveguide, assuming that the radius of the circular waveguide is a=3cm and there is air (vacuum) in the waveguide. The field distribution of several TE modes and components in the waveguide in the cross section perpendicular to the waveguide is shown in the figure.
This program is used to display the field distribution in different modes of metallic circular waveguides.
Clear
epsilon_0=8.85e-12; %Dielectric constant in vacuum
mur_0=4.0*pi*1.0e-7; % Magnetic permeability coefficient in vacuum
epslion_r=1.0; %Fill in the blanks relative permittivity of the medium
mur_r=1.0; %Fill in the blank relative magnetic permeability coefficient of the medium
epslion_0*epslion*_r; % Fill in the blanks for the dielectric constant of the medium
mur=mur_0*epslion_r; %Fill in the blanks the magnetic permeability coefficient of the medium
a=0.03; % waveguide radius (variable)
delta=0.0001; %The maximum error when solving transcendental equations using the dichotomy method
NN=0; %temporary variable
MM=0; %temporary variable
Z=0; % displays the field value of the z=0 plane
%Select the mode type of transmission
disp(please choose the incident wave:TM=-1 or TM=1’);
wavetype=input(wavetype is :’);
disp(please input the number of the modes:M and N’);
m=input(M is associated with the number
of varitations in phi direction:’);
%transmission mode
n=input(N is associated with the number
of variations in direction:’);
%transmission mode
Jmo=0; %Temporary variable that stores the Bessel function value
Jumo=0; %Temporary variable that stores the derivative value of the Bessel function
Summary
On the cross-section perpendicular to the direction of electromagnetic wave transmission, different modes of electromagnetic waves have different modes of field distribution. Each field distribution is a mode, which can convey various forms of electromagnetic waves in different metal waveguide systems. , I use MATLAB to study, because MATLAB has powerful visual computing software suitable for many disciplines, and has a large number of different library functions, toolboxes and simulation modules. You can use MALTAB’s numerical solution toolbox for partial differential equations and programmed programs to solve unknown quantities and draw different modes of electromagnetic waves.
First of all, I first understood the relationship between the longitudinal field component and the transverse field component of the electromagnetic field in the waveguide device. We have a clear understanding of the classification of guided wave waveforms, and deduced the field component formulas of TM waves and TE waves in rectangular waveguides, as well as the field component formulas of TE modes and TM modes in metal circular waveguides. Then I became familiar with the drawing and simulation of the MATLAB program. I used the MATLAB program to write the field distribution of the rectangular waveguide in different modes perpendicular to the propagation direction, and the field distribution of the metal circular waveguide perpendicular to the propagation direction in different modes, realizing the different modes of the metal waveguide. Application of MATLAB in mode.
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