1. RESONATORS AND WAVEGUIDES
BY: P. Vijaya & Niraja

2. Microwaves
Microwaves are the electromagnetic waves with wavelengths ranging from as long as a few centimeter to as short as one millimeter and with frequencies ranging from 1GHz to 1000 GHz.
Microwaves include the entire SHF band (3 to 30 GHz).

3. Electromagnetic Waves Frequency Bands
Frequency Range
Uses
VLF
3-30KHz
Used for long distance Communication. LF
30-300KHz
Used For Marine Communication. MF
KHz
Used for Radio broadcasting. HF
3-30MHz
For long distance Communication
VHF
30-300MHz
FM Radio, Television broadcasting.
UHF
MHz
For short distance communication.
SHF
3-30GHz
Satellite/Space communication.
EHF
30-300GHz
Radar, Space communication.

4. Advantage of Microwaves
1. Larger Bandwidth
2. Better Directive Properties
3. Lower Power Requirement
4. Fading effect

5. Frequency-Wavelength
A definite relationship exists between the frequency (f) and the corresponding wavelength (λ) of electromagnetic waves .The product of these two i.e. (f) and (λ) gives the velocity of propagation of electro-magnetic waves and it is equal to the velocity of light .
This is expressed as c = f * λ
c= velocity of light. (approx. 3* 108 m/sec ).

6. Applications Of Microwaves
1.Communication :
Microwaves is used in broadcasting and Telecom. transmission, due to their short wavelength, highly directional antennas are smaller . Mobile phone networks, like GSM, use the low microwave/UHF frequencies around 1.8 and 1.9GHz .

7. Microwaves are used in television signal to transmit a signal from a remote location to a television station from a specially equipped van.
Microwave are used for comm. from one point to another via satellite.
Satellite TV either operates in the C band for the traditional large dish fixed satellite service or Ku band for direct –broadcast satellite.

8. 2. Remote Sensing :
The most important application of remote sensing is RADAR, that uses a transmitter to illuminate an object and a receiver to detect its position and velocity.
Another class of remote sensing is radio astronomy .It is a sub-class of astronomy that studies celestial objects at radio frequencies.

9. 3.Heating Application
Baking :
The heating property of microwaves are used for baking, cooking using microwave oven. In microwave oven ,the food is heated directly by microwave radiations without heating the container. The cooking time very small as compare to conventional heating

10. Concentrating :
Permits concentration of heat sensitive solution and slurries at relatively low temperatures. Also applicable to highly corrosive or viscous solutions
Drying :
microwaves are used for drying the solids. Drying is uniform throughout the product moisture present in the product is evaporated out .Drying is at relatively low temp.

11. Enzyme Inactivation :
The enzyme inactivation can be achieved by rapid and uniform heating which can control and terminate enzyme reactions.
Precooking :
Microwaves are ideal for precooking the food items because there is no overcooking of the surface and cooking losses are negligible i.e is nutrients in the food are not lost.

12. Parameters Of Microwaves System
Frequency Characteristics : Microwaves are very short frequency radio waves that have many of the characteristics of light waves they travel in line of sight paths and can be reflected and focused .
By focusing these ultra high radio waves into a narrow beam, their energies are concentrated and relatively low transmitting power is required for reliable transmission over long distance .

13. System Capacity :
Microwaves communication systems are used to carry telephony, television and data signals.
Majority of the system carry multi- channel telephone signals (base band ). Individual telephone channels , 4KHz wide are multiplexed together in a multiplexer equipment to get the base band. At microwave due to high bandwidth capacity is more.

14. Microwave Frequency Bands
As already mentioned ,microwave is an electromagnetic wave ranging from approximately 1GHz in frequency, but older usage includes lower frequencies . Most common applications are within the range1 to 40GHz.

15. Letter Designation Frequency Range L band 1 to 2 GHz S band 2 to 4 GHz
C band
4 to 8 GHz
X band
8 to 12 GHz
Ku band
12 to 18 GHz
K band
18 to 26.5 GHz
Ka band
26.5 to 40 GHz
Millimeter (mm)
40 to 300 GHz
Sub –Millimeter
300 to above (GHz)

16. Classification of Microwaves on the basis of Frequency bands :
1. L-band: L-band (20-cm radar long band) is a portion of the microwave band of the electromagnetic spectrum ranging roughly from 0.39 to 1.55 GHz. It is used by some communication satellite and by terrestrial.
2. S-band: S-band or 10 cm. radar short band, is the part of microwave band of the electromagnetic spectrum ranging roughly from 1.55 to 5.2 GHz. It is used by weather radar and some communication satellites

17. 3. C-band: C-band (“ Compromise” band) is a portion of electromagnetic spectrum in the microwave range of frequencies ranging from 4 to 6 GHz. 4. X-band: The X-band (3 cm radar spot band) of the microwave band of the electromagnetic spectrum roughly ranges from 5.2 to 10.9 GHz. It is used by some communication satellite and X-band radar. 5. Ku-band: The Ku-band (Kurz-under band) is a portion of electromagnetic spectrum in the microwave range of frequency range 11 to 18 GHz. It’s primarily used for satellite communication.

18. 6. K-band: It is a portion of the EM wave spectrum in the microwave range of frequency range between 12 to 40 GHz. The K comes from Kurz. K-band between 18 to 26.5GHz is absorbed easily by water vapour. 7. Ka-band: The Ka-band ( Kurz-above band is a portion of the K-band) of the microwave band of the electromagnetic spectrum. Ka-band roughly ranges from 18 to 40 GHz.

19. Rectangular Waveguides

20. Waveguide to coax adapter
Waveguide component
Waveguide to coax adapter
Rectangular waveguide
Waveguide bends
E-tee

21. Dr. Sandra Cruz-Pol
More waveguides
Electromagnetics, waveguides

22. Uses To reduce attenuation loss High frequencies High power
Dr. Sandra Cruz-Pol
Uses
To reduce attenuation loss
High frequencies
High power
Can operate only above certain frequencies
Acts as a High-pass filter
Normally circular or rectangular
We will assume lossless rectangular
Electromagnetics, waveguides

23. Dr. Sandra Cruz-Pol
Rectangular WG
Need to find the fields components of the em wave inside the waveguide
Ez Hz Ex Hx Ey Hy
We’ll find that waveguides don’t support TEM waves
Electromagnetics, waveguides

24. Rectangular Waveguides: Fields inside
Dr. Sandra Cruz-Pol
Rectangular Waveguides: Fields inside
Using phases & assuming waveguide filled with
lossless dielectric material and
walls of perfect conductor, the wave inside should obey.
Electromagnetics, waveguides

25. Then applying on the z-component

26. Fields inside the waveguide
Dr. Sandra Cruz-Pol
Fields inside the waveguide
Electromagnetics, waveguides

27. Dr. Sandra Cruz-Pol
Substituting
Electromagnetics, waveguides

28. Dr. Sandra Cruz-Pol
Other components
From Faraday and Ampere Laws we can find the remaining four components:
*So once we know Ez and Hz, we can find all the other fields.
Electromagnetics, waveguides

29. Modes of propagation From these equations we can conclude:
Dr. Sandra Cruz-Pol
Modes of propagation
From these equations we can conclude:
TEM (Ez=Hz=0) can’t propagate.
TE (Ez=0) transverse electric
In TE mode, the electric lines of flux are perpendicular to the axis of the waveguide
TM (Hz=0) transverse magnetic, Ez exists
In TM mode, the magnetic lines of flux are perpendicular to the axis of the waveguide.
HE hybrid modes in which all components exists
Electromagnetics, waveguides

30. TM Mode Boundary conditions: From these, we conclude:
Dr. Sandra Cruz-Pol
TM Mode
Boundary conditions:
From these, we conclude:
X(x) is in the form of sin kxx, where kx=mp/a, m=1,2,3,…
Y(y) is in the form of sin kyy, where ky=np/b, n=1,2,3,…
So the solution for Ez(x,y,z) is
Electromagnetics, waveguides

31. Dr. Sandra Cruz-Pol
TM Mode
Substituting
Electromagnetics, waveguides

32. TMmn Other components are Dr. Sandra Cruz-Pol
Electromagnetics, waveguides

33. Dr. Sandra Cruz-Pol
TM modes
The m and n represent the mode of propagation and indicates the number of variations of the field in the x and y directions
Note that for the TM mode, if n or m is zero, all fields are zero.
See applet by Paul Falstad
Electromagnetics, waveguides

34. TM Cutoff The cutoff frequency occurs when Evanescent: Propagation:
Dr. Sandra Cruz-Pol
TM Cutoff
The cutoff frequency occurs when
Evanescent:
Means no propagation, everything is attenuated
Propagation:
This is the case we are interested since is when the wave is allowed to travel through the guide.
Electromagnetics, waveguides

35. Dr. Sandra Cruz-Pol
Cutoff
attenuation
Propagation
of mode mn
fc,mn
The cutoff frequency is the frequency below which attenuation occurs and above which propagation takes place. (High Pass)
The phase constant becomes
Electromagnetics, waveguides

36. Phase velocity and impedance
Dr. Sandra Cruz-Pol
Phase velocity and impedance
The phase velocity is defined as
And the intrinsic impedance of the mode is
Electromagnetics, waveguides

37. Summary of TM modes Wave in the dielectric medium Inside the waveguide
Dr. Sandra Cruz-Pol
Summary of TM modes
Wave in the dielectric medium
Inside the waveguide
Electromagnetics, waveguides

38. Related example of how fields look:
Dr. Sandra Cruz-Pol
Related example of how fields look:
Parallel plate waveguide - TM modes
m = 1
m = 2
m = 3 x z a Ez
a x
Electromagnetics, waveguides

39. TE Mode Boundary conditions: From these, we conclude:
Dr. Sandra Cruz-Pol
TE Mode
Boundary conditions:
From these, we conclude:
X(x) is in the form of cos kxx, where kx=mp/a, m=0,1,2,3,…
Y(y) is in the form of cos kyy, where ky=np/b, n=0,1,2,3,…
So the solution for Ez(x,y,z) is
Electromagnetics, waveguides

40. Dr. Sandra Cruz-Pol
Substituting
Note that n and m cannot be both zero because the fields will all be zero.
Electromagnetics, waveguides

41. TEmn Other components are Dr. Sandra Cruz-Pol
Electromagnetics, waveguides

42. Cutoff The cutoff frequency is the same expression as for the TM mode
Dr. Sandra Cruz-Pol
Cutoff
attenuation
Propagation
of mode mn
fc,mn
The cutoff frequency is the same expression as for the TM mode
But the lowest attainable frequencies are lowest because here n or m can be zero.
Electromagnetics, waveguides

43. Dr. Sandra Cruz-Pol
Dominant Mode
The dominant mode is the mode with lowest cutoff frequency.
It’s always TE10
The order of the next modes change depending on the dimensions of the guide.
Electromagnetics, waveguides

44. Waveguides Pipe through which waves propagate
Can have various cross sections
Rectangular
Circular
Elliptical
Can be rigid or flexible
Waveguides have very low loss

46. Modes Waves can propagate in various ways
Time taken to move down the guide varies with the mode
Each mode has a cutoff frequency below which it won’t propagate
Mode with lowest cutoff frequency is dominant mode

48. Mode Designations TE: transverse electric
Electric field is at right angles to direction of travel
TM: transverse magnetic
Magnetic field is at right angles to direction of travel
TEM: transverse electromagnetic
Waves in free space are TEM

49. Rectangular Waveguides
Dominant mode is TE10
1 half cycle along long dimension (a)
No half cycles along short dimension (b)
Cutoff for a = c/2
Modes with next higher cutoff frequency are TE01 and TE20
Both have cutoff frequency twice that for TE10

51. Cutoff Frequency
For TE10 mode in rectangular waveguide with a = 2 b

52. Usable Frequency Range
Single mode propagation is highly desirable to reduce dispersion
This occurs between cutoff frequency for TE10 mode and twice that frequency
It’s not good to use guide at the extremes of this range

53. Example Waveguide RG-52/U Internal dimensions 22.9 by 10.2 mm
Cutoff at 6.56 GHz
Use from GHz

54. Group Velocity Waves propagate at speed of light c in guide
Waves don’t travel straight down guide
Speed at which signal moves down guide is the group velocity and is always less than c

56. Phase Velocity Not a real velocity (>c)
Apparent velocity of wave along wall
Used for calculating wavelength in guide
For impedance matching etc.

58. Characteristic Impedance
Z0 varies with frequency

59. Guide Wavelength
Longer than free-space wavelength at same frequency

60. Summary of TE modes Wave in the dielectric medium Inside the waveguide
Dr. Sandra Cruz-Pol
Summary of TE modes
Wave in the dielectric medium
Inside the waveguide
Electromagnetics, waveguides

61. Variation of wave impedance
Dr. Sandra Cruz-Pol
Variation of wave impedance
Wave impedance varies with frequency and mode h
hTE h’
hTM
fc,mn
Electromagnetics, waveguides

62. Group velocity, vg Is the velocity at which the energy travels.
Dr. Sandra Cruz-Pol
Group velocity, vg
Is the velocity at which the energy travels.
It is always less than u’
Electromagnetics, waveguides

63. Dr. Sandra Cruz-Pol
Group Velocity
As frequency is increased, the group velocity increases.  
Electromagnetics, waveguides

64. Dr. Sandra Cruz-Pol
Power transmission
The average Poynting vector for the waveguide fields is
where h = hTE or hTM depending on the mode
[W/m2]
[W]
Electromagnetics, waveguides

65. Attenuation in Lossy waveguide
Dr. Sandra Cruz-Pol
Attenuation in Lossy waveguide
When dielectric inside guide is lossy, and walls are not perfect conductors, power is lost as it travels along guide.
The loss power is
Where a=ac+ad are the attenuation due to ohmic (conduction) and dielectric losses
Usually ac >> ad
Electromagnetics, waveguides

66. Attenuation for TE10 Dielectric attenuation, Np/m
Dr. Sandra Cruz-Pol
Attenuation for TE10
Dielectric attenuation, Np/m
Conductor attenuation, Np/m
Dielectric conductivity!
Electromagnetics, waveguides