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