BASIC CONCEPTS OF TRANSMISSION LINES & WAVEGUIDES ForC 18 DECE unit 1, SBTET

Electromagnetic Spectrum, Microwave Properties, Microwave Bands Designation, Types of transmission lines, Define the line parameters, TE mode, Tm mode & TEM mode, Waveguide structure, Waveguides Bends, Waveguides Twists, Waveguide Junctions, Circulators, Directional coupler, Advantages of Waveguides.

1. MICROWAVE COMMUNICATIONS AND
TELEVISION
DECE, II YEAR-IV SEMESTER
Nenavath Ravi Kumar
Associate Professor
ECE Dept-MIST

2. UNIT-1
BASIC CONCEPTS OF
TRANSMISSION LINES
&
WAVEGUIDES

3. FIRST, SOME DEFINITIONS:

In radio frequency engineering , a transmission
line is a specialized cable or other structure designed to
conduct alternating current of radio frequency, that is,
currents with a frequency high enough that their nature
must be taken into account.

A waveguide is a structure that guides waves, such
as electromagnetic waves or sound, with minimal loss of
energy by restricting the transmission of energy to one
direction. Without the physical constraint of a
waveguide, wave amplitudes decrease according to
the inverse square law as they expand into three
dimensional space.

4. FIRST, SOME DEFINITIONS:


Transmission Line – A two conductor structure that can
support a TEM wave.

Waveguide – A one conductor structure that cannot support
a TEM wave.

Q: What is a TEM wave?

A: An electromagnetic wave wherein both the electric and
magnetic fields are perpendicular to the direction of wave
propagation.

5. ELECTROMAGNETIC SPECTRUM

6. MICROWAVE PROPERTIES
Microwaves frequency range 1 GHz – 300 GHz

Microwave is an electromagnetic radiation of
short wavelength.

 Reflected by conducting surfaces

Microwave currents flow through a thin outer
layer of an ordinary cable.

They are not reflected by ionosphere

7. MICROWAVE BANDS DESIGNATION
Band Frequency
(GHz)
Wavelength(cm)
L 1 to 2 30.0 to 15.0
S 2 to 4 15 to 7.5
C 4 to 8 7.5 to 3.8
X 8 to 12 3.8 to 2.5
Ku 12 to 18 2.5 to 1.7
K 18 to 27 1.7 to 1.1
Ka 27 to 40 1.1 to 0.75
Millimeter 40-300 0.75-0.1

8. TYPES OF TRANSMISSION LINES
Parallel Transmission line

Twisted pair transmission line

Coaxial cable

Wave guides

Fiber optic cables

9. CHARACTERISTIC IMPEDANCE, IMPEDANCE MATCHING


If a uniform lossless transmission line is
considered, for a wave travelling in one direction,
the ratio of the amplitudes of voltage and current
along that line, which has no reflections, is called
as Characteristic impedance.
To achieve maximum power transfer to the load,
impedance matching has to be done. To achieve
this impedance matching, the following conditions
are to be met.
The resistance of the load should be equal to that
of the source.

10. REFLECTION CO-EFFICIENT, VOLTAGE STANDING WAVE RATIO


The parameter that expresses the amount of
reflected energy due to impedance mismatch in a
transmission line is called as Reflection coefficient.
It can be defined as "the ratio of reflected voltage to
the incident voltage at the load terminals".

The standing wave is formed when the incident wave
gets reflected. The standing wave which is formed,
contains some voltage. The magnitude of standing
waves can be measured in terms of standing wave
ratios.
The ratio of maximum voltage to the minimum voltage
in a standing wave can be defined as Voltage Standing
Wave Ratio

11. TRANSMISSION LINES – BASIC THEORIES
Introduction
At high frequencies, the wavelength is much smaller than the circuit size,
resulting in different phases at different locations in the circuit.
Quasi-static circuit theory cannot be applied. We need to use transmission line theory.

A transmission line is a two-port network connecting a
generator circuit at the sending end to a load at the receiving
end.
Unlike in circuit theory, the length of a transmission line
is of utmost importance in transmission line analysis.

12. DEFINE THE LINE PARAMETERS
The parameters of a transmission line are:

Resistance (R) is defined as the loop resistance per unit
length of the wire. Its unit is ohm/Km.

Inductance (L) is defined as the loop inductance per unit
length of the wire. Its unit is Henry/Km.

Capacitance (C) is defined as the loop capacitance per unit
length of the wire. Its unit is Farad/Km.

 Conductance (G) is defined as the loop conductance per unit
length of the wire. Its unit is mho/Km.

13. AC STEADY-STATE ANALYSIS:
DISTRIBUTED PARAMETER REPRESENTATION

14. R’ = resistance per unit length, (Ω/m) L’
= inductance per unit length, (H/m)
G’ = conductance per unit length, (S/m)
C’ = capacitance per unit length, (F/m)
z = increment of length, (m)
We use the following distributed parameters to
characterize the circuit properties of a transmission line.
These parameters are related to the physical properties of
the material filling the space between the two wires.
where µ, ,  = permittivity, permeability, conductivity
of the surrounding medium.
L'C'  
C' 
G'


(See Text Book No.3,
pp. 432-433)

15. For the coaxial and two-wire transmission lines, the
distributed parameters are related to the physical
properties and geometrical dimensions as follows:
Surface
resistivity of
the conductors
(See Text Book
No.3, pp. 445-
447)

16. DEFINE CHARACTERISTIC IMPEDANCE
Characteristic impedance is the impedance
measured at the sending end of the line. It is
given by.

Z0 = Г(Z/Y), where
Z = R + jωL is the series impedance
Y = G +jωC is the shunt admittance

17. EQUATIONS AND SOLUTIONS
Consider a short section Δz of a transmission line
(dropping the primes on R’, L’, G’, C’ hereafter) :
Using KVL and KCL circuit theorems, we can derive the
following differential equations for this section of
transmission line.
Generator Load

18. dz
For sinusoidal varying voltages and currents, we can use
phasor forms.
vz,t   ReV ze
jt 
iz,t   ReI ze
jt 
V(z) and I(z) are called phasors of
v(z,t) and i(z,t). In terms of phasors, the
coupled equations can be written as:

dV (z)
 (R  jL)I (z)
dz

dI (z)
 (G  jC)V (z)

19. After decoupling,
I  z 
2
2
  V  z 
2
d
2
I (z)
 
2
2
d V (z)
dz
dz
    j   R  jLG  jC 
 is the complex propagation constant whose real part  is
the attenuation constant (Np/m) and whose imaginary
part  is the phase constant (rad/m). Generally, these
quantities are functions of .

20. 0 0

V (z)  V

(z)  V

(z)
0 0
I (z)  I

(z)  I

(z)
 V

e
 z
 V

e
 z
 I

e
 z
I

e
 z
Forward
travelling
wave.
Backward
travelling
wave.
0 0 0 0 V

,V

, I

, I

= wave amplitudes in the forward and
backward directions at z = 0. (They
are complex numbers in general.)
SOLUTIONS TO TRANSMISSION LINE EQUATION

21. 0 0
V

V

From the solutions to the transmission line equations, it
can be shown (using the coupled transmission line
equations) that:
R  jL
 I

I

0
 
0

This ratio is called characteristic impedance Z
0.
TRANSMISSION LINE PARAMETERS

22. Z
0 and  are the two most important parameters of
a transmission line. They depend on the
distributed parameters (RLGC) of the line itself
and  but not the length of the line.
R  jL
G  jC  G  jC
Z 
R  jL



0
R  jLG  jC     j 

23. For lossless transmission lines, R = G = 0.
  0
   LC   

u  phase velocity 


1 1

LC 
p
  complex propagation constant

 j  j   j2f   j
2
 jk
PARAMETERS FOR LOSSLESS TRANSMISSION LINES

24. f LC
1



2

1
f  f  f

u
p
  wavelength along the transmission line

C
L
R  jL
G  jC
Z
0  characteristic impedance



26. WAVEGUIDES

Waveguides are basically a device ("a guide") for
transporting electromagnetic energy from one region
to another. Typically, waveguides are hollow metal
tubes (often rectangular or circular in cross section).

The waveguide acts as a high pass filter in that most of the
energy above a certain frequency (the cutoff frequency) will
pass through the waveguide.

Greater than 300 MHz, with 8 GHz and above being
more common.

Waveguides are wideband devices, and can carry (or
transmit) either power or communication signals.

27. TE MODE, TM MODE & TEM MODE
Transverse Electric wave:
In this mode of wave propagation, the electric field
component is totally transverse to the direction of
wave propagation whereas magnetic field is not
totally transverse to the direction of wave
propagation. It is abbreviated as TE mode.

Transverse Magnetic wave:
In this mode of wave propagation, the magnetic field
component is totally transverse to the direction of wave
propagation while the electric field is not totally
transverse to the direction of wave propagation. It is
abbreviated as TM mode.

28. TE MODE, TM MODE & TEM MODE
Transverse electromagnetic wave:
In this mode of wave propagation, both the field
components i.e., electric and magnetic field are totally
transverse to the direction of wave propagation. It is
abbreviated as TEM mode.


It is to be noted here that, TEM mode is not supported in
waveguides. As for the TEM mode, there is a need for
the presence of two conductors and we already know
that a waveguide is a single hollow conductor.

29. WAVEGUIDE STRUCTURE
Metallic waveguide:
*Hallow metal
waveguide
 *Coaxial Cable
 *Micro strip
Dielectric Waveguide
* optical Fiber
* Integrated
Waveguide

30. WAVEGUIDE PARAMETERS
Guide Wavelength
It is defined as the distance
travelled by the wave in
order to undergo a phase
shift of 2π radians.
It is related to phase
constant by the relation
λ
g = 2π / β
Wave Impedance
It is defined as ratio of
strength of electric field in
one transverse direction to
the strength of magnetic
field along other transverse
direction.

31. WAVEGUIDE PARAMETERS
Phase Velocity
The phase velocity is
defined as the velocity with
which the wave changes
phase in terms of the guide
wavelength
Vp = λg * f
Group Velocity
velocity of  The group
a wave is defined as the
rate at which the wave
through
the
propagates
waveguide.
 Vg = dω / dβ
The product of phase and group velocities is equal to
square of the velocity of light. i.e. v
p * v
g = c
2

32. WAVEGUIDES BENDS
The below figure gradual
bend is known as an E bend
because it distorts the E
fields. The E bend must
have a radius greater than
two wavelengths to prevent
reflections.
Another common bend is
the gradual H bend shown
in the below part of the
figure. It is called an H
bend because the H fields
are distorted when a
waveguide is bent in this
manner

33. WAVEGUIDES TWISTS
Sometimes the electromagnetic fields must be rotated
so that they are in the proper phase to match the phase
of the load. This may be accomplished by twisting the
waveguide as shown in the figure. The twist must be
gradual and greater than two wavelengths (2·λ).




It is only used in short sections where no other
reasonable solution is available.

34. WAVEGUIDE JUNCTIONS
H-type T-junction
An H-type T-junction is illustrated in the beside figure. It is called an H-
type T-junction because the long axis of the “B” arm is parallel to the plane
of the magnetic lines of force in the waveguide. The E-field is fed into arm
A and in-phase outputs are obtained from the B and C arms. The reverse is
also true.


35. WAVEGUIDE JUNCTIONS
E-type T-junction
This junction is called an E- type T junction because the junction arm
extends from the main waveguide in the same direction as the E-field in the
waveguide. The outputs will be 180° out of phase with each other.

36. WAVEGUIDE JUNCTIONS
Magic-T-Hybrid Junction
A simplified version of the magic-T-hybrid junction is shown in the
figure. The magic-T junction can be described as a dual
electromagnetic plane type of T-junction. It is a combination of the
H-type and E-type T.junction. Therefore the most common
applications of this type of junction are for example as the mixer
section for microwave radar receivers or as a part of a
measurement system.

37. CIRCULATORS
A circulator is a multi port junction in which the wave can
travel from one port to next immediate port in one
direction only.
Commonly used circulators are three-port or four-port
devices although more number of ports is possible.

38. DIRECTIONAL COUPLER
The basic directional coupler is a four port waveguide junction. It
consists of a primary waveguide 1-2 and a secondary waveguide 3-4.
when all points are terminated in their characteristics impedances,
there is free transmission of power, without reflection, between
port 1 & port 2.
The degree of coupling between port 1 & port 4 and between port 2
& port 3 depends on the structure of the coupler.

39. ADVANTAGES OF WAVEGUIDES

Following are few advantages of Waveguides.
Waveguides are easy to manufacture.
They can handle very large power [Math
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Power loss is very negligible in waveguides.
They offer very low loss [Math Processing
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When microwave energy travels through
waveguide, it experiences lower losses than a
coaxial cable.

40. CONTACT FOR
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