Contents Introduction, Microwave Spectrum and Bands Applications of Microwaves. Rectangular Waveguides – TE/TM mode analysis, Expressions for Fields Characteristic Equation and Cut-off Frequencies, Filter Characteristics, Dominant and Degenerate Modes, Sketches of TE and TM mode fields in the cross-section, Mode Characteristics – Phase and Group Velocities, Wavelengths and Impedance Relations; Power Transmission and Power Losses in Rectangular Guide, Impossibility of TEM mode. Related Problems.

Introduction 1/4/2019Dr. P.S.N.Murty2  Microwaves are electromagnetic waves whose frequencies range from about 300 MHz – 300 GHz (1 MHz = 10 6 Hz and 1 GHz = 10 9 Hz) or wavelengths in air ranging from 100 cm – 1 mm.  The word Microwave means very short wave, which is the shortest wavelength region of the radio spectrum and a part of the electromagnetic spectrum.

Properties of Microwaves Following are the main properties of Microwaves.  Microwaves are the waves that radiate electromagnetic energy with shorter wavelength.  Microwaves are not reflected by Ionosphere.  Microwaves travel in a straight line and are reflected by the conducting surfaces.  Microwaves are easily attenuated within shorter distances.  Microwave currents can flow through a thin layer of a cable. 1/4/2019Dr. P.S.N.Murty3

Advantages of Microwaves There are many advantages of Microwaves such as the following − Supports larger bandwidth and hence more information is transmitted. For this reason, microwaves are used for point-to-point communications. More antenna gain is possible. Higher data rates are transmitted as the bandwidth is more. Antenna size gets reduced, as the frequencies are higher. Low power consumption as the signals are of higher frequencies. Effect of fading gets reduced by using line of sight propagation. Provides effective reflection area in the radar systems. Satellite and terrestrial communications with high capacities are possible. Low-cost miniature microwave components can be developed. Effective spectrum usage with wide variety of applications in all available frequency ranges of operation. 1/4/2019Dr. P.S.N.Murty4

Disadvantages of Microwaves There are a few disadvantages of Microwaves such as the following Cost of equipment or installation cost is high. They are hefty and occupy more space. Electromagnetic interference may occur. Variations in dielectric properties with temperatures may occur. Inherent inefficiency of electric power. 1/4/2019Dr. P.S.N.Murty5

Microwave Spectrum and Bands 1/4/2019Dr. P.S.N.Murty6 Electromagnetic Spectrum consists of entire range of electromagnetic radiation. Radiation is the energy that travels and spreads out as it propagates. The types of electromagnetic radiation that makes the electromagnetic spectrum is depicted in the following screenshot

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Applications of Microwaves  Medical: Imaging, selective heating, sterilization etc.  Domestic/industrial: Cooking, traffic & toll management, sensor  Surveillance: Electronic warfare, security system etc.  Radar: Air defense, guided weapon, collision avoidance, weather  Astronomy & Space exploration: Monitor and collect data.  Communication: Satellite, Space, Long distance téléphone, Bluetooth, etc 1/4/2019Dr. P.S.N.Murty8

Different types modes 1/4/2019Dr. P.S.N.Murty9

Transverse Electromagnetic (TEM) (E z = 0; H z = 0) The electric field, E and the magnetic field, H are oriented transverse to the direction of propagation of wave. Exists in plane waves and transmission lines (2 conductors). No cut-off frequency. 1/4/2019Dr. P.S.N.Murty10 y EyEy HzHz x z Direction of Travel

Transverse Electric (TE) The electric field, E is transverse to the direction of propagation of wave and the magnetic field, H has components transverse and in the direction of the wave. Exists in waveguide modes. 1/4/2019Dr. P.S.N.Murty11 y EyEy HyHy HxHx H x z Direction of travel

Transverse Magnetic (TM) The magnetic field, H is transverse to the direction of propagation of wave and the electric field, E has components transverse and in the direction of the wave. Exists in waveguide modes. 1/4/2019Dr. P.S.N.Murty12 y EyEy HzHz x ExEx E z Direction of travel

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Transmission Lines Transmission Line is defined as the path carrying alternating electrical energy form source to load. For example The wire used between TV antenna to TV Receiver. 1/4/2019Dr. P.S.N.Murty14

Types of Transmission Lines There are the following Types of Transmission Lines Balanced two wire Co-Axial Cable Wave Guide Micro Strip Optical Fiber 1/4/2019Dr. P.S.N.Murty15

Balanced two wire 1/4/2019Dr. P.S.N.Murty16

Coaxial line Advantage of coaxial design: little electromagnetic leakage outside the shield and a good choice for carrying weak signals not tolerating interference from the environment or for higher electrical signals not being allowed to radiate or couple into adjacent structures or circuits. Common application: video and CATV distribution, RF and microwave transmission, and computer and instrumentation data connections 1/4/2019Dr. P.S.N.Murty17

Difference between waveguide and transmission line 1/4/2019Dr. P.S.N.Murty18

Waveguides A hollow metallic tube of uniform cross-section for transmitting EM waves by successive reflections from the inner walls of the tube is called a waveguide. 1/4/2019Dr. P.S.N.Murty19

Comparison of WGs with 2-Wire Transmission Lines Similarities : Wave travelling in a WG has a phase velocity and will attenuated as in a transmission line. When the wave reaches the end of the waveguide it is reflected unless the load impedance is adjusted to absorb the wave. Any irregularity in a waveguide produces reflections just like an irregularity in a transmission line. When both incident and reflected waves are present in a WG, a standing wave pattern results as in a transmission line. 1/4/2019Dr. P.S.N.Murty20

Comparison of WGs with 2-Wire Transmission Lines (contd.,) Dissimilarities There is a cut-off value for the frequency of transmission(f) depending upon the dimensions and shape of the WG. Only waves having the frequency greater than cut-off frequency will be propagated. Hence WG acts as high pass filter. WG is a one conductor transmission system. The whole body of WG acts as ground and the waves propagate through multiple reflections from the walls of WG. The system of propagation in WG is in accordance with Field Theory while that in transmission line is in accordance with Circuit Theory and hence return conductor is not required in WG. Further, if one end of the WG is closed with a shorting plate, there will be reflections and hence standing waves. If the other end is closed, then the hollow box so formed can support a signal which can bounce back and forth between two shorting plates resulting in resonance. This is principle of cavity resonators. 1/4/2019Dr. P.S.N.Murty21

TEM mode in Two wire What is comes down to is that the H field is supported by induced currents in the walls and the E field is supported by induced voltages in the walls and in order for the wave to propagate these must reinforce each other, but in a single conductor system they cancel each other. The solution? If you have separate conductors then you can shape them to have the Voltage and Current in the conductors reinforce each other. The conductors will be capacitively and inductively linked, a single conductor can't be. 1/4/2019Dr. P.S.N.Murty22

Rectangular Waveguides  It consists of a hollow rectangular waveguide (rectangular cross section).  That can propagate TM and TE modes but not TEM since only one conductor is present.  The wall of the guides are conductors and therefore reflection from them may take place.  It is a standard convention to have the longest side of the waveguide along x-axis [a (width) > b (length)] 1/4/2019Dr. P.S.N.Murty23

Field components in TM mode Ex component Ey component Hx component Hy component 1/4/2019Dr. P.S.N.Murty24

TM modes in RWG 1/4/2019Dr. P.S.N.Murty25 The order of the mode refers to the field configuration in the guide and is given by ‘m’ and ‘n’ integer subscripts, as TE mn and TM mn. The ‘m’ subscript corresponds to the number of half wave variations of the field in x direction The ‘n’ subscript corresponds to the number of half wave variations of the field in y direction

TM modes in RWG (Contd,.) Depending the values of ‘m’ and ‘n’, we have various modes in TM waves. Various TMmn Modes TM 00 mode : m = 0 and n = 0 If m=0, n= 0, are substituted in Ex, Ey, Hx and Hy, we see that all of them vanish and hence TM 00 mode does not exist. TM 01 mode : m = 0 and n = 1 If m=0, n= 1, are substituted in Ex, Ey, Hx and Hy, we see that all of them vanish and hence TM 01 mode does not exist. 1/4/2019Dr. P.S.N.Murty26

TM modes in RWG (Contd,.) TM10 mode : m = 1 and n = 0 If m=1, n= 0, are substituted in Ex, Ey, Hx and Hy, we see that all of them vanish and hence TM10 mode does not exist. TM11 mode : m = 1 and n = 1 If m=1, n= 1, are substituted in Ex, Ey, Hx and Hy, we see that all four components are exist and hence TM11 mode does exist. All values of m, n greater than 1, then all higher modes can exist. 1/4/2019Dr. P.S.N.Murty27

Cut-off Frequency of a WG or WG as a High Pass Filter We know that Where a is attenuation constant and B is the phase change 1/4/2019Dr. P.S.N.Murty28

Cut-off Frequency of a WG (Contd.,) At lower frequencies ɣ then becomes real and positive and equal to the attenuation constant ‘α’ i.e the completely attenuated and there is no phase change. Hence the wave can not propagate. At higher frequencies ɣ becomes imaginary, there will be the phase change ‘β’and hence the propagation of the wave. At the transmission, ɣ becomes zero and the propagation just starts. The frequency at which ɣ just becomes zero is defined as the cut-off frequency (threshold ferquency) ‘f c’. 1/4/2019Dr. P.S.N.Murty29

Cut-off Frequency of a WG (Contd.,) At f = fc, ɣ = 0; w = w c But The cut off wavelength is given by 1/4/2019Dr. P.S.N.Murty30

Guide Wavelength It is the distance travelled by the wave in order to undergo a phase shift of 2π radians. It is related to propagation constant β as Wavelength in waveguide is different from wavelength in free space. It is related to free space wave length and by 1/4/2019Dr. P.S.N.Murty31

Phase velocity ( ) The phase velocity of a wave is the rate at which the phase of the wave propagates in space. The phase velocity is given by Where w = 2Πf, 1/4/2019Dr. P.S.N.Murty32

Group Velocity ( ) If there is modulation in the carrier, the modulation envelope actually travels at velocity slower than that of carrier alone and slower than speed of light. The velocity of modulation envelope is called the group velocity. 1/4/2019Dr. P.S.N.Murty33

Dominant Mode 1/4/2019Dr. P.S.N.Murty34

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