文档介绍：Electromagnetic Field and Wave
电磁场与电磁波
2011.
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Review
1. General Wave Behaviors along Uniform Guiding Structures
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Main topic
1. Rectangular Waveguides
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1. Rectangular Waveguides
Select the rectangular coordinate system and let the broad side be placed along the x-axis, the narrow side along the y-axis, and the propagating direction be along the z-axis.
a
z
y
x
b
,
For TM waves, Hz = 0 , and according to the method of longitudinal fields, the component Ez should first be solved, and from which the other components can be derived.
The z-component of the electric field intensity can be written as
TM waves
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It satisfies the following scalar Helmholtz equation, .
In order to solve the above equation, the method of separation of variables is used. Let
We obtain
where X" denotes the second derivative of X with respect to x, and Y" denotes the second derivative of Y with respect to y.
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The only way the equation can be satisfied is that both terms on the left side are constants.
Now let
where k x and k y are called the separation constants, and they can be found by using the boundary conditions.
Obviously
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where all the constants C1 , C2 , C3 , C4 , and k x , k y , depend on the boundary conditions.
The two equations are second order ordinary differential equations, and the general solutions, are respectively
The z-component of the electric field intensity can be written as
Boundary conditions:
a
z
y
x
b
,
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And all the field components are
where
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