Microwave transmission lines: Fundamentals of two wire
transmission lines and coaxial cable. Mode analysis and design
 of rectangular, circular waveguides. Microstrip, strip lines and
      co-planer waveguide (No analysis and design topics)
#Self-study :Different types of waveguides and their application
                        Transmission Line Theory
• In an electronic system, the delivery of power requires the connection of
  two wires between the source and the load.
•    At low frequencies, power is considered to be delivered to the load through
     the wire.
    • In the microwave frequency region, power is considered to be in electric and
      magnetic fields that are guided from place to place by some physical structure.
•    Any physical structure that will guide an electromagnetic wave from one place
     to another place is called a Transmission Line.
               Properties of transmission line
 Has two conductors running parallel
 Can propagate a signal at any frequency (in theory)
 Becomes lossy at high frequency
 Can handle low or moderate amounts of power
 Does not have signal distortion, unless there is loss
 May or may not be immune to interference
 Does not have Ez or Hz components of the fields (TEMz)
                         Types of transmission lines
1.   Two wire line
2.   Coaxial cable
3.   Waveguide
        Rectangular
        Circular
4.   Planar Transmission Lines
        Strip line
        Microstrip line
        Slot line
        Fin line
        Coplanar Waveguide
        Coplanar slot line
                            Two wire transmission lines
• This transmission line consists of a pair of parallel conducting wires separated by a uniform
  distance
• These are used in power systems or telephones lines.
• Alternating electric field between conductors
• Alternating magnetic field surrounding conductors
• Dielectric material inside the conductor
• Disadv: Electric and magnetic fields extend to infinity , influences electronic equipment in the
  vicinity
Coaxial line                                       Coaxial line
 • This consists of an inner and a coaxial outer conducting sheath separated by a dielectric medium .
 • They are used as TV cables, telephones cables and power cables.
 • Electric field is completely contained within both conductors
 • Perfect shielding of magnetic field
 • TEM modes up to certain cutoff frequency
 • Adv: Outer conductor is grounded minimizing radiation losses and field interference.
    Commonly used dielectric
    material
    Polystyrene = 2.5
    Polyethylene = 2.3
    Teflon = 2.1
              Waveguide
• Signal transmission at microwave
  frequencies.
• These are basically hollow conducting tubes
  as they somewhat resemble like coaxial
  cable line but do not have centre conductor
  as present in coaxial cables.
 Has a single hollow metal pipe
 Can propagate a signal only at high frequency:  > c
 The width must be at least one-half of a wavelength
 Has signal distortion, even in the lossless case
 Immune to interference
 Can handle large amounts of power
 Has low loss (compared with a transmission line)
 Has either Ez or Hz component of the fields (TMz or TEz)
                                        Microstrip Lines
              Ground plane reduces excessive field leakage hence reduces radiation losses
 Single layer PCB has high radiation loss and prone to cross talk
Substrate with high dielectric constant minimize field leakage and cross coupling
To reduce interference use multilayer technique i.e. Parallel plate transmission lines
Strip Lines
                     Parallel-plate transmission line
• It has two parallel conducting plates
• separated by a dielectric slab of uniform thickness
Equivalent Circuit of Tx Line
                 Transmission line parameters
• Resistance: This parameter of any transmission line rely on the cross-
  sectional area of the conducting material. As we have already discussed
  that these are distributed parameter networks that means its parameters
  are distributed uniformly along the entire length.
• It is represented by R and its unit is ohms per unit length of the
  conductor.
• It is given by:
• ρ denotes the conductivity of the conducting material
• l denotes the length of the transmission line and
• a denotes the cross-sectional area of the line
• Capacitance: A transmission line is composed of 2 parallel
  conducting wire separated by dielectric material. So it behaves as a
  parallel plate capacitor. Thus it has some capacitance which is also
  distributed uniformly over its length.
• It is measured in farads per unit length of the conductor.
• Inductance: When current flows through a conductor then it
  generates a magnetic field perpendicular to the direction of the
  electric field.
• As the magnetic field varies, electromagnetic flux gets generated in
  the line.
• So, this emf now flows in opposite direction with the current flowing
  through the device which is known as inductance.
• Its value depends on the current flowing through the conductor.
• Inductance is represented by L and its unit is Henry per unit length
  of the conductor.
• Conductance: The two parallel conductors are separated by
  dielectric medium but it is not a perfect insulator.
• Due to which some current also flows through the dielectric. This
  current is called leakage current and it is responsible for leakage
  conductance through the transmission line.
• It is basically present between the conducting wires and is
  represented by G.
• Its unit is mho per unit length of the conductor.
Transmission line parameters
                       Modes of propagation
• According to the direction of oscillation and propagation, there are
  different modes of wave propagation on transmission lines.
• When a time-varying signal starts to flow through a transmission line,
  it aligns the electric and magnetic fields in different directions and
  establishes various modes of wave propagation.
• Depending on the frequency and type of transmission line or
  waveguide used, the mode of propagation varies.
• Electromagnetic waves have both
  electric and magnetic fields that
  are perpendicular to each other
  and travel in the same direction.
• The transverse components of
  electric and magnetic fields are
  determined by their components in
  the z direction.
• When a time-varying signal starts
  to flow through a transmission line,
  it aligns the electric and magnetic
  fields in different directions and
  establishes various modes of wave
  propagation.
Transverse Electric and Magnetic (TEM) Mode
• TEM, also referred to as transmission line mode, is the principal mode of
  wave propagation and exists only in transmission lines made of two
  conductors.
• This mode becomes dominant in wave propagation where the cross-
  sectional area of the transmission line is small compared to the signal
  wavelength.
• That means the electric and magnetic fields are transverse to the direction
  of propagation in this mode.
• The z axis components of electric and magnetic fields are equal to zero.
  Transmission lines support TEM mode with two conductors and have
  uniquely defined voltage, current, and characteristic impedance.
• When the frequency is very small, quasi-TEM modes are used to
  approximate the TEM modes.
• In TEM, Hz=Ez=0
• Transverse Magnetic (TM) Mode
• In this mode, the magnetic field is purely transverse to the direction
  of wave propagation and the electric field does not follow suit. The
  electric field has both transverse and longitudinal components.
• In TM, Hz=0, Ez≠0
• Transverse Electric (TE) Mode
• In this mode, the electric field is transverse to the direction of wave
  propagation and the magnetic field is not. The magnetic field has
  both transverse and longitudinal components.
• In TE, Hz≠0, Ez=0
• TE and TM modes are commonly found in enclosed guiding structures
  and are generally called waveguide modes.
• Both of these modes are dispersive, where the phase velocity is
  dependent on frequency.
• As transmission lines generally operate below this cut-off frequency,
  they support only TEM mode.
• TE and TM modes are limited by a cut-off frequency below which
  there is no wave propagation through it.
• This cut-off frequency causes limited bandwidth in these modes.
• Hybrid Wave Mode
• In this mode, the wave propagates in z direction.
• None of the fields are purely transverse to the direction of propagation in
  this mode.
• Both the magnetic and electric fields have longitudinal components.
• When the longitudinal electric field is dominant, the hybrid wave mode is
  called EH mode.
• When the longitudinal magnetic field is dominant, the hybrid wave mode is
  called HE mode.
• This mode is usually observed in waveguides with inhomogeneous
  dielectric and in optical fibers.
Mode of Wave Propagation   Type of Transmission Line
TEM                        Co-axial line, two-wire line,
                           parallel-plate line, stripline,
                           microstrip line, multi-conductor
                           lines, and coplanar waveguides
TE or TM                   Metal or optical fiber
                           waveguides, cavity resonators
Hybrid wave mode           Optical fibers, open conductor
                           guides
Waveguides
Another mean of transporting EM wave from Source to the Load consist of a
hollow, metal tube through which waves propagate.
• Microwaves propagate through microwave circuits, components and devices,
  which act as a part of Microwave transmission lines, broadly called as
  Waveguides.
• A hollow metallic tube of uniform cross-section for transmitting electromagnetic
  waves by successive reflections from the inner walls of the tube is called as
  a Waveguide.
The tube wall provides distributed inductance, while the empty space between the
tube walls provide distributed capacitance.
Waveguides are practical only for signals of extremely high frequency, where the
wavelength approaches the cross-sectional dimensions of the waveguide.
Below such frequencies, waveguides are useless as electrical transmission lines.
                Transmission Lines                                 Waveguides
Supports TEM wave                               Cannot support TEM wave
                                                Only the frequencies that are greater than cut-off
All frequencies can pass through                frequency can pass through
Two conductor transmission                      One conductor transmission
                                                A wave travels through reflections from the walls
Reflections are less                            of the waveguide
It has a characteristic impedance               It has wave impedance
Propagation of waves is according to "Circuit   Propagation of waves is according to "Field
theory"                                         theory"
Bandwidth is not limited                        Bandwidth is limited
Waves do not disperse                           Waves get dispersed
                   Advantages of Waveguides
• Waveguides are easy to manufacture.
• They can handle very large power in kilowatts .
• Power loss is very negligible in waveguides.
• They offer very low loss low value of alpha−attenuation
• When microwave energy travels through waveguide, it experiences
  lower losses than a coaxial cable.
Types of waveguide
Rectangular Waveguide
• A waveguide which is a hollow metallic tube of a
  rectangular cross-section is known as the rectangular
  waveguide.
• The EM fields can be confined.
• Therefore, the EM waves can be guided by the walls of the
  guide through reflections.
• Rectangular waveguides are usually made in standard
  sizes with breadth “a” (along x-direction) approximately
  twice the height “b” (along y-direction).
• The “a” dimension cannot be less than a one-half
  wavelength.
• This can be seen, as the guide is made up of two-quarter
  wavelength stubs separated by a small distance.
• Any frequency that makes the “a” dimension less than
  one-half wavelength allows no propagation of energy
  down the waveguide.
                               Circular Waveguide
• A circular waveguide is a hollow metal tube with
  a circular cross-section.
• It is basically a tubular, circular conductor.
• This is used only for some special applications.
• For example, it is used in a rotating joint, which
  transmits an electromagnetic wave to the
  feeder of a rotating radar antenna.
• In circular waveguides, the plane of polarization
  is not stable due to geometry.
• The frequency band of the single-mode
  operation of a circular waveguide is narrower
  than the same band of a rectangular waveguide.
Cut Off frequency:
The cutoff frequency of an electromagnetic waveguide is the lowest
frequency for which a mode will propagate in it.
Phase Velocity:
It is the velocity which the electromagnetic waves changes it phase in
the waveguide during propagation.
Group velocity: Group velocity is defined as the rate at which the wave
propagates through waveguide. The group velocity is also can be
defined as the velocity of energy flow in the waveguide system.