prepared by: ronnie asuncion. hollow conductive tube usually rectangular in cross section but...
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Prepared by: Ronnie Asuncion
Hollow conductive tube Usually rectangular in cross section but
sometimes circular or elliptical Electromagnetic (EM) waves propagate within
its interior Serves as a boundary that confines EM energy The walls of it reflect EM energy Dielectric within it is usually dehydrated air or
inert gas EM energy propagate down in a zigzag pattern
Generally restricted to frequencies above 1 GHz
Rectangular and circular waveguides
Parallel-wire transmission lines and coaxial cables cannot effectively propagate EM energy above 20 GHz
Parallel-wire transmission lines cannot be used to propagate signals with high powers
Parallel-wire transmission lines are impractical for many UHF and microwave applications
Most common form of waveguide For an EM wave to exist in the waveguide
it must satisfy Maxwell's equation Note: A limiting factor of Maxwell’s
equation is that a transverse electromagnetic (TEM) wave cannot have a tangential component of the electric field at the walls of the waveguide
EM wave cannot travel straight down a waveguide without reflecting off the sides
The TEM wave must propagate in a zigzag manner to successfully propagate through the waveguide with the electric field maximum at the center of the guide and zero at the surface of the walls
In parallel-wire transmission lines, wave velocity is independent of frequency, and for air or vacuum dielectrics, the velocity is equal to the velocity in free space
In waveguides the velocity varies with frequency
Group and phase velocities have the same value in free space and in parallel-wire transmission lines
The velocities are not the same in waveguide if measured at the same frequency
At some frequencies they will be nearly equal and at other frequencies they can be considerably different
The phase velocity is always equal; to greater than the group velocity
The product of the two velocities is equal to the square of the free space propagation speed
Vg Vph = c^2 where: Vph = phase velocity (meters/second) Vg = group velocity (meters/second)
c = free space propagation speed = 300,000,000 (meters/second)
The velocity of group waves The velocity at which information signals
of any kind are propagated The velocity at which energy is
propagated Can be measured by determining the time
it takes for a pulse to propagate a given length of waveguide
The apparent velocity of a particular phase of the wave
The velocity with which a wave changes phase in a direction parallel to a conducting surface, such as the walls of a waveguide
Determined by increasing the wavelength of a particular frequency wave, then substituting it into the formula:
Vph = f λ where: Vph = phase velocity (meters/second) f = frequency (hertz) λ = wavelength (meters/second)
may exceed the velocity of light Phase velocity in waveguide is greater
than its velocity in free space Wavelength for a given frequency will be
greater in the waveguide than in free space
Free space wavelength, guide wavelength, phase velocity and free space velocity of electromagnetic wave relationship:
λg = λo (Vph / c) where: λg = guide wavelength (meter/cycle) λo = guide wavelength (meter/cycle) Vph = phase velocity (meters/second) c = free space velocity (meter)
Cutoff Frequency - minimum frequency of operation - an absolute limiting frequency
Cutoff Wavelength - maximum wavelength that can be propagated down the waveguide -smallest free-space wavelength that is just unable to propagate in the waveguide
The relationship between the guide wavelength at a particular frequency is:
λg = (c) / [(f^2)-(fc^2)]^(1/2) where: λg = guide wavelength
(meter/cycle) fc = cutoff frequency (hertz) f = frequency of operation (hertz) Determined by the cross-sectional dimension of
the waveguide
fc = c/2a = c/λcWhere: fc = cutoff frequency a = cross-sectional length (meter) λ = cutoff wavelength (meter/cycle)
Electromagnetic waves travel down a waveguide in different configurations called propagation modes
There are two propagation modes: - TEm,n for transverse-electric waves - TMm,n for transverse-magnetic waves TE1,0 is the dominant mode for rectangular
waveguide At frequencies above the fc, higer order TE
modes are possible
It is undesirable to operate a waveguide at frequency at which higher modes can propagate
Next higher mode possible occurs when the free space λ is equal to a
A rectangular waveguide is normally operated within the frequency range between fc and 2fc
Zo = 377/{1-(fc/f)^2} = 377(λg/ λo)Where: Zo - characteristic impedance (ohms) fc - cutoff frequency f - frequency of operation
Reactive stubs Capacitive and inductive irises
Used in radar and microwave applications The behavior of electromagnetic waves in
circular waveguides is the same as it is rectangular waveguides
Are easier to manufacture than rectangular waveguides
Disadvantage is that the plane of polarization may rotate while the signal is propagating down it.
Cutoff wavelength, λo λo = 2πr/kr
where: λo = Cutoff wavelength (meters/cycle) r = internal radius of the waveguide kr = solution of Bessel function equation TE1,1 is the dominant mode for circular
waveguides the cutoff wavelength for this mode is:
λo = 1.7dd = waveguide diameter
Consist of spiral wound ribbons of brass or copper
Short pieces of the guide are used in microwave systems when several transmitters and receivers are interconnected to a complex combining or separating unit
Used extensively in microwave test equipment
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