Lecture #1
INTRODUCTION TO TRANSMISSION LINES
Objective: To appreciate the following items
Transmission Line?
General Application of Transmission Lines
Radio Spectrum
Timeline for Transmission lines
Classification of Transmission Lines
Conductor based current supporting transmission
lines
Single Conductor Overhead Transmission
Lines
Coaxial Transmission Line
Telephone Transmission lines
Single Conductor Line
Two Conductors Line
Planar Transmission lines
Waveguides
1
What is a transmission line?
In general it is an one dimensional electromagnetic
wave propagating medium. In particular it is
system of conductors used to transmit the electrical
power or electrical signal from one location to
another.
Electrical Power Transmission Line
In communication engineering, we are interested in
the transmission of low power electrical signals -
Sinusoidal signal, un-modulated or modulated
Digital signal.
On the transmission line, the electric energy/ signal
does not travel with the drift velocity of electrons in the
conductor, which is only in mm/s range. It travels with
a velocity of light through the EM field in the open
space in the case of the overhead line or through the
dielectric medium between two concentric conductors.
2
General Application of Transmission Lines
Long Distance Carrier of Electric Signals.
( Telephonic signals, Internet, modulated carrier signals)
Short Distance Carrier of Electric Signals -
Interconnects.
( On-chip communications, on board communications etc.)
Development of Passive Microwave and mm-wave
components and circuits.
(Antenna, Resonant Circuits, Filters Couplers, Power
Divider, Matching Network etc.)
Development of Models for Waveguides and Other
Wave Supporting Structures.
( Simple Waveguides, Planar Transmission Lines,
Multilayer Waveguides & Planar Transmission Lines,
Ionospheric Wave Propagations, Wave Propagation in
Multilayer Dielectric Slabs etc.)
3
Spectrum
Microwave Waves
Microwave Wave: 300 MHz- 30 GHz (100cm-1.00 cm)
MM-wave: 30GHz-300GHz (10mm-1mm)
Tera-Hz Wave (Sub-millimeter wave) :
300 GHz-3000GHz ().3 THz-3THz), (0.1mm – 1.0mm)
4
Microwave Frequency Bands
Bands L S C X Ku K Ka Q
1 2 4 8 12 18 26.5 33
GHz - - - - - - – -
2 4 8 12 18 26.5 40 50
Bands U V E W F D G Y
40 50 60 75 90 110 140 220
GHz - - - - - - - -
60 75 90 110 140 170 220 325
5
Timeline for Transmission lines
---------------------------------------
1837 : Cooke and Wheatstone patented Telegraph.
1844 (May) : Samuel F.B. Morse demonstrated
publically by sending a message from Supreme
Court, Washington, DC to Baltimore -
"What hath God wrought?"
1855: Kelvin developed RC circuit model for the
submarine cable.
He ignored the inductive effect due to the current in
cable. This theory provided a parabolic equation
PDE showing diffusion of voltage/current in the
telegraph cable rather a wave propagation.
1864: Maxwell's Equations and prediction for
existence of EM-Wave. Light is a EM-wave.
1866 (27 July): Transatlantic communications
through ocean laid telegraph line.
1876 : Alexander Graham Bell invented the
telephone and established conversation between , 2
miles separated Boston and Cambridge port by the
overhead line. Elisha Gray filed a patent
application 3 hours after Bell.
6
1881: For 3/4 mile underground cable used for
telephone.
1881: Alexander Graham Bell invented Twisted
pair cables for telephone
1884 (4th Sept.) : Opening of telephone service
between Boston and New York, 235 miles
1887: Heinrich Hertz demonstrates existence of
electromagnetic waves.
1887: Oliver Heaviside derived transmission line
equations and PDE for the wave equations on it
from the RLCG model of the telegraph cable. It is
applicable to telephone line also.
1893: Early waveguide. J. J. Thomson in 1893
Proposed waveguide. In 1894 it was experimentally
tested by Oliver Lodge. In 1897 Lord
Rayleigh developed its first mathematical analysis.
1893: An early form of broadcasting was started in
Budapest over 220 miles of telephone wires serving
6000 subscribers who could listen at regular
schedules to music, news, stock market prices,
poetry readings and lectures.
7
1896 (Nov): J.C Bose demonstration at Town Hall
of Kolkata microwave ignited gunpowder. He also
operated a bell at a distance using millimetre range
wavelength microwaves.
1896: Marconi got patent for the wireless telegraph.
1906: Conversation by underground cable, 90
miles-New York to Philadelphia.
1907: First installation in Canada (Edmonton,
Alta.). Invention of small dial and two-wire system
eliminating ground at subscriber’s station.
1909: Marconi and Karl Ferdinand Braun got the
Nobel Prize in Physics for their work in the
development of wireless telegraphy.
1910: Peter Debye in Holland, developed theory
for optical waveguides. He was ahead of his time.
1911: Using loading coils with overhead telephone
line link established for 2,100 miles -- New York to
Denver.
1915: On January 25 opening of First Trans-
continental telephone line, New York to San
Francisco, 3600 miles. On October 21 first
transmission of speech across the Atlantic by
radiotelephone, Arlington, Va., to Paris.
8
1921: Conversation by deep sea cable, 115 miles--
Key West, Fla., to Havana, Cuba.
First conversation between Havana, Cuba, and
Catalina Island by submarine cable, overhead and
underground lines and radio telephone-distance
5,500 miles.
1935 (April 25): First around-the-world telephone
conversation by wire and radio.
1936 - Invention of coaxial cable is announced at a
joint meeting of the American Physical Society and
the IRE (April 30).
1936 - George C. Southworth and Wilmer L.
Barrow demonstrated experimentally wave
propagation in waveguide and obtained several
modes.
9
Classification of Transmission Lines
_____________________________
Conductor based current supporting
transmission lines:
Single conductor with the earth return
path.
Coaxial transmission line.
Two wire transmission line.
Planar transmission lines.
EM-wave supporting hollow metallic
waveguides.
Dielectric based waveguides:
Planar dielectric waveguides.
Optical fiber lines.
Free space as a transmission line.
Axon nerve lines.
10
Conductor based current supporting
transmission lines
-------------------------------------------------
Single Conductor Overhead Transmission
Line.
Coaxial Transmission Line
---------------------------------------------------
At low frequency these structures supports
the TEM mode with cut-off frequency at
fc=0.
At higher frequencies coaxial cable can
support non-TEM higher order modes such
as TE, TM, HE and EH.
Coaxial cable normally has characteristic
impedance 50Ω and 75Ω. 50Ω is more
common for RF and microwave
applications.
The outer shield avoids EMC and EMI.
11
Single Conductor Overhead
Transmission Lines
----------------------------------------------
The overhead single conductor line was used by Steinheil
in Munich around 1838, and was applied by Wheatstone
and Cooke in their telegraph from Paddington to Slough
around 1840. Vail and Cornell introduced it in 1844 for the
U.S. commercial line from Washington, D.C. to Baltimore.
The original insulated copper wire was replaced by iron
wire for strength, with little increase in resistance. A
ground return was used.
Single Conductor Telegraph Line
Single Conductor Telegraph Line
12
Coaxial Transmission Line
----------------------------------------
TEM mode field in a coaxial cable
Coaxial cable provides excellent immunity to induced
“noise” from external sources. It is used in DC and low-
frequency AC circuits. It commonly used at RF,
microwaves and mm-waves.
13
For a line length less than λ/4 of the signal on the line;
the line is taken as electrically short. When length is a
significant part of the wavelength or several electrically
long.
The propagation delay can be ignored for a electrically
short line; whereas as it is accounted for the electrically
long line. The electrically short line supports the
electrical oscillation ( AC circuit); whereas the
electrically long line supports the wave propagation.
In case of the electrically short line, the terminating
load impedance dominates circuit behavior. The source
effectively sees nothing but the load’s impedance,
barring any resistive losses in the transmission line.
In case of the electrically long line, the characteristic
impedance of the transmission line dominates circuit
behavior. For instance an infinitely long line length
provides only the line's characteristic impedance as the
load to the source.
A finite length of line also transform the terminated
load presented to the source.
14
Transatlantic telegraph cable route
Ship used in laying the transatlantic telegraph cable
Transatlantic telegraph original cable
There is no outer shield for this submarine cable. It is
provided by the salty sea water.
15
Some Coaxial Cables and Connectors
A male N-type connector
A male F-type connector used with
common RG-6 cable
Several Coaxial Cables Semi-Rigid coax installed in an Agilent
N9344C 20GHz spectrum analyser
Semi-Rigid coax assembly
Air filled rigid coax assembly
16
Coaxial Cables feeding mobile tower.
17
Coaxial Cables in Antenna & Transmitter
Omni-directional Base-station antennas
for mobile communication
75Ω Coaxial feed to Dipole
antenna
18
Transmission line called a cage line, used for high
power, medium wave and long wave low feeder line to
antenna. It is like a rectangular coaxial cable.
Rigid Coaxial Cable Network at Output of MW Transmitter
19
Single conductor Telephone transmission line
Early arrangement of telephone circuit
Single conductor early telephone
20
Two conductor Telephone transmission line
Balanced line in twin lead
format. Used with Yagi
antennae.
Balanced line in twisted pair format.
Twisted pair cables were invented
by Alexander Graham Bell in 1881
21
Two Conductor Transmission Circuit for
Digital Applications
---------------------------------------------
22
Two Conductor Transmission Lines in
SW Transmitter
---------------------------------------------------
A reflective array antenna for radar consisting of numerous dipoles fed in-phase.
Note Two wire Line feed to antenna elements
23
Planar Transmission Lines
Microstrip Lines
Coplanar Waveguide (CPW)
Slot Lines
Coplanar Strip (CPS)
Fin Lines etc.
24
Microstrip Lines
25
26
27
28
On Chip Planar Lines
29
Hollow metallic waveguides
Waveguides
Waveguide Excitation
(a) Electric field coupling (b) Magnetic field coupling
30
Waveguide TE and TM Modes
TE10 mode is the dominant mode of a rectangular
waveguide with a>b
31
Field of TE10 Mode
Side View (TE10)
End View (TE10)
____ Electric field lines
_ _ _ Magnetic field lines
Top View (TE10)
TM modes, m=0 and n=0 are not possible, thus,
TM11is the lowest possible TM mode
Field of TM11Mode
End View (TM11) Side View (TM11)
____ Electric field lines
_ _ _ Magnetic field lines
32
Cut-off Wavelengths of Circular
Waveguides
TE (Transverse Electric) Mode
The lower cutoff frequency (or wavelength) for a particular TE mode in circular
waveguide is determined by the following
q
equation: , where p'mn is
u
e
m n p'm1 p'm2 p'm3
c
y
0 .
3.832 7.016 10.174
F
o
1 r 1.841 5.331 8.536
r
e
2 c 3.054 6.706 9.970
t
a
n TM (Transverse Magnetic) Mode
g
u
The lower cutoff frequency (or wavelength) for a particular TM mode in
l
circular waveguide is determined by the following
a
r
w
equation:
a (m), where pmn is
v
m e
g pm1 pm2 pm3
u
i
0 d
e
2.405 5.520 8.654
t
1h 3.832 7.016 10.174
i
s
2i 5.135 8.417 11.6
s
33
Waveguide Components
34
Waveguide Components
35
Waveguide System
Parabolic Antenna Feed Connected Waveguide
1.3 MW Klystrons and waveguide system. In the blue
frame on the left: 1.3 MW, CW salt-water load. Bottom,
from left to right: circulator with its 300 kW CW coaxial
load, waveguide, klystron K2.
36
J.C. Bose Microwave Experiment
(1894)
Bose's 60 GHz microwave apparatus at the Bose
Institute, Kolkata, India. His receiver (left)used
a galena crystal detector inside a horn antenna and
galvanometer to detect microwaves. Bose invented the
crystal radio detector, horn antenna, and other apparatus
used at microwave frequencies.
37
Comparison of Patch Antenna with Short Surface
Mounted Horn with Standard Horn ( German Patent )
38
