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Waveguide and Cavity Resonators
Assuming z-directed propagation
satisfying
then
From and , we have
and
Solving in terms of and , we have
where
1. TEM waves: , .2. TM waves: , .3. TE waves: , .
TEM waves
, not dispersion.
To support TEM waves, two conductors are necessary.
TM waves
Cutoff frequency occurs when for a given .
For , , propagation mode.
Guided wavelength
Phase velocity
Group velocity
Impedance
, pure real.
For , , evanescent mode.
Impedance
, pure imag.
TE modes
Cutoff frequency occurs when for a given .
For , , propagation mode.
Guided wavelength, Phase velocity, Group velocity same as TM mode.Impedance
Parallel-Plate Waveguide
Assume no variation in the -direction.
TM modes
Wave equation:
B. C.:
Therefore,
Note: when , TM becomes TEM mode.
TE Modes
Wave equation:
B. C.:
Therefore,
Approximation of Attenuation Constant for Low Loss Casesdielectric loss:
conductor loss:
For mode, see Eq. (10.187).
total:
Discontinuities in Rectangular Waveguides
Series Capacitive iris. Pure imaginary series load.
Series Inductive iris. Pure imaginary series load.
Post or screw in a waveguide.
Rectangular CavitiesTM modesAssume
Let
then.
To satisfy boundary condition
then
and
Fundamental mode: .
Dielectric Waveguides
Assume two dimensional TM case.
In the dielectric
In the air
Odd TM modes
In the dielectric
Outside dielectric, plus sign for , minus sign for
must be continuous,
or
also
or
and
Surface impedance
Similarly, for even mode
and
Cutoff frequency occurs at For odd mode
For even mode
Assume two dimensional TE case.
In the dielectric
In the air
Odd TE modes
In the dielectric
Outside dielectric, plus sign for , minus sign for
must be continuous,
also
and
Surface impedance
Similarly, for even mode
and
Cutoff frequency occurs at For odd mode
For even mode
T-junction Magic T
Twist Bend Directional Coupler
Waveguide Components
Waveguide Slot-Line Waveguide Line Section
Waveguide Match Load Coaxial toWaveguide Adapter