Mô tả:
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TRANSMISSION LINES
AND WAVEGUIDES
Outline
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1. General Solutions for TEM, TE, and TM Waves
2. Parallel Plate Waveguide
3. Rectangular Waveguide
4. Circular Waveguide
5. Coaxial Line
6. Surface Waves on a Grounded Dielectric Sheet
7. Stripline
8. Microstrip Line
9. The Transverse Resonant Technique
10. Wave Velocities and Dispersion
Transmission Line
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General two – conductor Tx.
Closed waveguide
General Solutions for TEM, TE and TM Waves
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Assume time harmonic fields with e-jt dependence and
wave propagation along the z-axis.
The electric and magnetic field :
Transverse components Longitudinal
fields components
Maxwell Equation
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Four Transverse Field Components
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Cut-off wave number
Wave number:
Permittivity of material
TEM Wave
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Transverse electromagnetic (TEM) waves are characterized by:
Cut-off wave
number :
kc = 0
Helmholtz Wave Equation for Ex
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For
dependent,
Laplace’s Equation
TEM Wave (Cont.)
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Electric field can be expressed as the gradient of a Scalar potential
also satisfies Laplace ‘s equation
The voltage and current
Wave Impedance
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Procedure for Analyzing a TEM Line
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1.Solve Laplace’s equation, for (x, y). The solution will contain several
unknown constants
2. Find these constants by applying the boundary conditions for the known
voltages on the conductors.
3. Compute 𝑒 and 𝐸 from (3.13) and (3.1a). Compute ℎ and 𝐻from (3.18) and
(3.1b).
4. Compute V from (3.15) and I from (3.16).
5. The propagation constant is given by (3.8), and the characteristic
impedance is given
by Z0 = V/I .
TE Wave
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Transverse electric (TE) waves are characterized by:
Cut-off wave number:
Propagation constant:
Helmholtz Wave Equation for Hz
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TE wave impedance:
TM Wave
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Transverse magnetic (TM) waves are characterized by:
Cut-off wave number:
Propagation constant:
Helmholtz Wave Equation for Ez
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TE wave impedance:
Procedure for Analyzing a TE & TM Line
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1. Solve the reduced Helmholtz equation, (3.21) or (3.25), for hz or ez .
The solution will contain several unknown constants and the unknown
cutoff wave number, kc.
2. Use (3.19) or (3.23) to find the transverse fields from hz or ez .
3. Apply the boundary conditions to the appropriate field components to
find the unknown constants and kc.
4. The propagation constant is given by (3.6) and the wave impedance
by (3.22) or (3.26).
Attenuation Due to Dielectric Loss
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Outline
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1. General Solutions for TEM, TE, and TM Waves
2. Parallel Plate Waveguide
3. Rectangular Waveguide
4. Circular Waveguide
5. Coaxial Line
6. Surface Waves on a Grounded Dielectric Sheet
7. Stripline
8. Microstrip Line
9. The Transverse Resonant Technique
10. Wave Velocities and Dispersion
Parallel Plate Waveguide
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Parallel plate waveguide is
the simplest type of
waveguide that can support
TE, TM and TEM
TEM Mode
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TEM mode solution can be obtained by solving Laplace’s equation:
The boundary condition for
:
There is no variation in x, the solution is:
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