1. Prepared by: Ronnie Asuncion
WAVEGUIDES
Prepared by: Ronnie Asuncion

2. What is waveguide? 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

3. Rectangular and circular waveguides
What is waveguide?
Generally restricted to frequencies above 1 GHz
Rectangular and circular waveguides

4. Why use waveguide?
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

5. Rectangular Waveguide
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

6. Rectangular Waveguide
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

7. Phase and Group Velocities
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

8. 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)

9. Group Velocity 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

10. Phase Velocity 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)

11. Phase Velocity 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

12. Phase Velocity
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)

13. Cutoff Frequency and Cutoff Wavelength
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

14. Cutoff Frequency and Cutoff Wavelength
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

15. Cutoff Frequency and Cutoff Wavelength
fc = c/2a = c/λc Where: fc = cutoff frequency a = cross-sectional length (meter) λ = cutoff wavelength (meter/cycle)

16. Modes of Propagation
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

17. Modes of Propagation
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

18. Characteristic Impedance
Zo = 377/{1-(fc/f)^2} = 377(λg/ λo) Where: Zo - characteristic impedance (ohms) fc - cutoff frequency f - frequency of operation

19. Impedance Matching
Reactive stubs
Capacitive and inductive irises

20. Circular Waveguide 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.

21. Circular Waveguide 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 = 1.7d
d = waveguide diameter

22. Flexible Waveguide 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

23. Flexible Waveguide