Channels of transmission

are the transmission lines Can be either

i. Hard mediumOn Electrical conductor

On Optical fibers

or

ii. Soft medium

Such as open space.

Modes of transmissionmodes of propagation of energy.

• Sound waves:

Longitudinal propagation

• Electro-magnetic waves:

Transverse Propagation

Electromagnetic propagation

Optical waves are electromagnetic waves.

Radio waves are electromagnetic waves.

When current flows in a conductor, it follows electromagnetic propagation.

Properties of EM waves and Optical waves are same.

Reflection Refraction Diffraction Polarization Interference Absorption Doppler effect.

(to be revised by the students)

Frequency-wavelength relationship

• The wavelength-frequency product of a transmitted wave is constant for a given media.

c = velocity of light = 3 x108 meter/sf = frequency of wave in Hz. = wavelength of the wave in meters.

r = relative permittivity of the media (for air it is unity).Generally constant, can vary with temperature, moisture content, oxygen, ionization, impurity in insulating material etc.

f =c/r

For air: as media

• The spectra of frequencies with air as channel extends from 3x10 Hz to 3x 1012

Hz. Lowest is the voice frequency while highest is optical.

• For convenience, we split this frequency spectra in several ranges in terms of powers (n) in 3x10n Hz

The wavelength is 1011-n mm• When n=1, 3 Hz wavelength is 1010 mm• When n=6, 3 MHz wavelength is 105 mm• When n=9, 3 GHz wavelength is 102 mm

Spectra: for every n the range is n:10n

n abb application

01 ELF Power frequencies & their Harmonics

02 VF Voice frequencies, Audio Signals

03 VLF Sonar: Marine navigation, ultrasound

04 LF Sonar: Marine navigation, ultrasound

05 MF Medium wave AM Broadcasting

06 HF Short wave AM broadcasting

07 VHF FM, TV, public service

08 UHF TV, Cellular, WLAN

09 SHF Satellite, TV, radar, LMDS

10 EHF mm waves, radar, LMDs

11.... optical sub-mm, visible light, medical instrumentation

Optical spectra

Range of n

application

11 14 Infra red

14 15 Partial: visible light followed by Ultraviolet

15 16 Ultra violet

16 18 Soft x-rays

18 19 Hard x-rays

19 21 Gamma Rays.

Characteristic Impedance

• Input impedance of an infinite length transmission line (TL) is termed as Characteristic impedance Zo.

• It is the ratio of electric field intensity (E) volt per meter to magnetic field intensity (H) ampere per meter of TL.

• In infinite length TL, power inputted is fully absorbed in it, load connected to the sinking end is irrelevant. Mullett, ”Basic Telecommunication: physical layer”, p.295; Thomson Learning.

Balanced Transmission line

• Here the signal current circulates is one pair of wires running simultaneously. One wire carries forward current while the other, return current.

• The properties of transmission line depends whether or not these pair of wires

twisted and /or

shielded.

Unbalanced transmission line

• Only one wire conducts the signal.

The return path is through shield or, ground.

• Coaxial cable, instrument probes are the examples.

The equivalent electric circuit of a section

no. of sections per meter is frequency dependent.

R L

C G

unbalanced section of transmission line

values of inductance and capacitance per unit length.

R/2 L/2

C GR/2 L/2

balanced section of transmission line

values of inductance and capacitance per unit length.

Z0

R sL

G sC

When several such sections are connected in cascade, Zo in both case is as below. Should R and G 0, Zo = L/C

Zo Zo

sections/length increases with frequency.

ABCD parameters are preferred for Calculations of the sections.

The characteristic impedance is resistive at radio frequencies.

Kennedy and Davis, ”Electronic Communication Systems”, 4/e,McGraw Hills, pp185-193

More on Zo…

• We take two sections of TL for our review.

• For infinite sections, the impedance seen at 1-2 would be the same as seen at 1’-2’ etc.

• It is equivalent to taking one section and loading it with Zo..

S1 S2

1

2

1’

2’Infinite sections

Zo ZoZo

More on Zo…

• This implies that: Impedance measured at the input of a TL now of finite length with the output terminated in Zo will be Zo itself.

• For maximum power to be transferred, connect conjugate terminating impedance Zo

*.

• Note that Zo = [ZocZsc] also.

For one section or equivalent one section,

zo = [zseries arm / Yshunt arm].

conjugate

Free space impedance

•The free space impedance, also known as characteristic impedance of vacuum/air, depends on ratio of permeability of air and permittivity of air.

Zo = [o/o] = 120 = 377 ohm

It varies depending on the values of o & o at any instance. ?? Can the impedance in any other media also be written as Zx= [x /x] ?

Components of Characteristic impedance

decides the characteristic of the channel

Characteristic impedance for the loss less media is Zo = [L/C] . It is resistive at radio frequencies.

L and C are defined per unit length of the media.

L and C decide the characteristic of the channel. It is band-limited: can be base band or pass band.

Recall that frequency of resonance of a loss less LC filter is fo = 1/2LC and its critical resistance: Rc = [L/C].

• As you will learn in electro-magnetics and antenna,

Any system of conductors will RF energy if the conductor separation nears half the wavelength of the operating frequency.

Such transmission line acts as antenna.

Essentials for propagation

A time varying electric signal is applied to a conductor. This makes a current to flow in the conductor. It creates an electric field.

This current is parallel to the electric field.

This current carrying conductor surrounds a magnetic field.

This magnetic field is perpendicular to electric field.

Thus the time varying electric field and time varying magnetic field are mutually perpendicular.

Polarization

• Polarization refers to physical orientation of the radiated waves in space.

• A vertical antenna will have vertical Electric field.

• The propagation of em wave takes place in the direction perpendicular to the electric field helically.

010

2030

40

-1

-0.5

0

0.5

1-1

-0.5

0

0.5

1

time

Helix propagation of E.M.Waves

magnetic field

ele

ctr

ic f

ield

For vertical Antenna, propagation is perpendicular to the electric field.

Speed of signaling is media dependantVelocity ‘c’ of EM wave in a media is c = 1/( ) velocity of EM wave in free space = 3x108 M/s, o =1.257x10-6 H/M, o= 8.854x10-12 F/M

cvac= 1/ (1.257x10-6 H/M x 8.854x10-12 F/M)= (0.08985) 109 M/ (FM) 3 x 108 M/s as FM =1/ f = s

The velocity of signal in open space is at the rate of the velocity of light in vacuum or, air.

Velocity of signal in a media…

Thus velocity of an EM wave

i.e. electrical and optical signal,

in a loss-less media,

is decided by

the permeability and permittivity

of the media.

Velocity factor• The velocity factor VF = c/cvac

• Since c = 1/( ) and cvac=1/(oo) Denoting r as relative permeability and r as the relative permittivity

• As the relative permeability of the vacuum/air is the same as that of any dielectric material, velocity factor depends only on relative permittivity and thus can be written as

• You may relate the above velocity factor with coefficient of refraction in optics.

VF = {(o/)(o/)} = 1/ rr

VF =1/r

The Zo can also be calculated by physical dimensions of the channel.

• Zo = {120/(ek)} log (D/d) : coaxial cable

= (138/k) log (D/d) : : coaxial cable

• Zo = (2x138/k) log (2s/d) : parallel wires

120/e = 377/e = 138 as e is natural base.

k is the relative dielectric constant of the insulation.

d

s

Parallel wire d diameters distance

dD

Coaxial Cabled diameter of coreD diameter of insulation

Example: A piece of RG-59B/U coaxial cable has a 75 ohm

characteristic impedance and nominal capacitance of 69 pF/m. What is its inductance pr meter? If the diameter of the inner conductor is 0.584 mm and the dielectric constant of the insulation is 2.23, what is the outer diameter.

• Soln: Given Zo = 75 , C = 69 pF/M, k = 2.23 (relative)

(a) Since Zo= L/C, Hence L = 0.388 H/m.

(b) Zo = [138/k] log (D/d)

log (D/d)=Zo/ [138/k] = 0.81

D=3.77 mm.

Propagation of EM waves near the earth surface

Properties of EM Waves.

• Reflection

• Refraction

• Absorption

• Diffraction

• Interference,

• Doppler effect.

Terrestrial Propagation

Terrestrial Propagation is not hurdle free.

The hurdling factors can be

a. curvature of earth,

b. Hills & high buildings,

c. Changes in atmospheric conditions,

d. Certain layers that are formed in the sky above the earth as a result of pollution, ionization, solar radiations etc and are ambience dependent.

e. Rivers and water ponds conduct em waves.

Reflection, absorption and refraction

When an EM Wave hits a surface having change in physical properties, the wave can take a series of recourse in different proportions.

It can refract through the media due to change in the velocity.

It can be absorbed by the media. It is reflected back.

Absorption Part energy is always absorbed by the media. The

absorption factor depends on

frequency dependent behavior of the media temperature, Whether day ?humidity, contents of oxygen etc.

See next slides

Average Atmospheric attenuation due to water vapors and oxygen vrs frequency in GHz range.

A. Sea Level at 20C at 760 mm atmospheric pressure and Humidity 7.5 g/M3

B. 4 kM Elevation: at 0 C and humidity 1g/M3.

Oxygen water

Absorption

Attenuation Charactristics

Absorption characteristics:

• The experimental investigations showed that in sub millimeter and millimeter wavelength range, the attenuation characteristic of transmission is highly dependant on the presence of oxygen and water vapors.

• In the following slide, we see the effect of objects in routine partitions such as wood and concrete.

Absorption in wood and concreteIn wood, absorption is instant

In concrete absorption depends on thicknessof the concrete block.

Skin depth is the distance where the wave intensity reduces to 37 %

Reflectiona) The two mirrors in a barber shop, one in the front and

other at the back of the dressing chair,

b) An object kept at an angle results in multiple reflections in them. They get blur/echoed after each reflection.

• Why??

a. The mirrors are uneven surfaced and polished,

b. They absorb part of the optical energy

c. Multiple reflections

Refraction here is negligible.

Reflection..This we treat as property of the mirror.We can “see” this property of EM waves in mirror at ‘vision’ frequencies. Similar property is held by other media in other frequency range that we can not “see”.

• Earth is a good reflecting media for e.m. waves including light. It also partly absorbs the em wave energy.

• It does not refract them.

Multiple hop sky wave propagation: frequency range 3-30 MHz.

multiple reflections in the forward direction, called hopping, are due to reflection of em waves between earth and F ionospheric layers.

Ionospheric layers

Earth

Reflections…Reflected waves add to reception.

• In a given frequency range, the ionospheric layers reflect the em waves.

• Depending on the angle () of transmitting antenna of the polarized wave and extending maximum useable reflecting frequency (MUF), this media refracts the e.m.wave through ionospheric layers. The wave thus “escapes” through the layers. (Next slide)

• Critical frequency fc = (MUF) cos ()

• The range of operating reflecting frequency (<f c ), is 3 MHz to 30 MHz.

Sky wave Propagation

Antenna at different angles

> fc

Line of Sight (LOS) propagation

LOS communication• When frequency range is above 300 MHz, e

m Waves do not get absorbed and are not sufficiently refracted to be reflected by ionosperic layers as shown in next slide.

• At 10’s of GHz and above; such as in upper W and optical range, get absorbed by water vapors and presence of oxygen.

• Fiber optic cables are must for unattenuated “surface communication” while W links work in ambience.

• There is no optical link for satellites yet.Ziemer+Tranter,”Principles of communication” 5/e,Wiley p 10-11.

Overall effect of skywave reflection

Total internal reflection

Refraction

Attenuation Charactristics

Interference

• Multipath reception are due to multiple reflections of the same signal.

• It creates echo effect in the receiver.• It is called interference.• The multipath reception can be from

objects on earth, reflection from ionosphere, LOS reception, surface wave transmission etc.

• Signal from unknown source, called noise may also be found at the receiver.

Realistic link behavior

Multiple reception

multiple reflection create interference

Satellite communication

• The technique to refract the EM wave though the ionospheric layers is called trans-ionospheric propagation, basic for satellite communications.

• It depends on angle of antenna and frequency of operation.

• Beyond 300 MHz, the ionospheric layers refracts the em waves but does not reflect.

The ionospheric layers

• At about 70 KM to 350 KM above the earth there exists several D, E, F1 & F2 layers created by ionization of ultraviolet, , and rays emitted by the solar system.

• These layers have varied properties that depend on position of the Solar planets with respect to earth, presence of clouds and industrial wastes, and whether it is day or, night.

Effect of sudden atmospheric changes

D layer

• Lowest layer is D. It is 10 kM thick at about 70 kM above the earth.

• It disappears at night.

• It reflects VLF and LF waves (3-300 kHz) and

partially absorbs the MF and HF waves (0.3-30 MHz)

E-Layer and sporadic E-layer• It exists at 100 kM above earth and has

thickness of about 25 kM.

• During the day sun creates ionization in this layer that disappears at night.

• It reflects HF waves (3-30 MHz) during day.

• It partially helps surface wave propagation in MF range (0.3-3 MHz) .

• The sporadic E-layer exists during the night also and its cause is still not known. It is found to contribute to long distance propagation.

F- layers: F1 and F2

• F1 layer exists at about 180 kM in day time. Its thickness is 20 kM.

• F2 layer exists at about 250 to 400 kM. Its height rises with atmospheric temperature. It’s thickness at times can be about 200 kM.

• At night, F1 & F2 layers merge.• It is the topmost layer and with reduced degree,

remains ionized during the night.• It reflects HF (3-30 MHz) waves which in turn

yield better reception.

Ionospheric Layers

Frequency range for different propagation layers

D-Layer E- Layer F-Layer Trans-ionosphere

VLF:

3-30kHz

LF :

30-300kHz

MF:

0.3-3 MHz

HF:

3-30 MHz

VHF:

30-300MHz

Surface wave propagation• This mode of propagation of the EM wave is over the

surface of the earth.• The polarization of antenna is vertical.

Else, earth being a good conductor, the electrical component will be short circuited.

• As the wave propagates over the surface, due to induction and absorption of induced em Wave by earth, jungle, hills, buildings etc. the wave “lies down and dies”. It reduces amplitude.

• Diffraction tilts the wave.• Increasing the transmitting and receiving antenna

heights, the process can be slowed.

Propagation through surface wavesfrequency range 0.3 to 3 MHz

Surface wave propagation

The electric field strength and voltage developed are

= 120ht I/ d volt/meter• V= 120ht hr I/ d voltWhere:

ht and hr : effective heights of transmitting and receiving antennas

d: distance from transmitting antennaI: Antenna current,: wavelength.

Diffraction

• In optics, we saw that when a parallel wave incident on any sharp object, it creates diffraction and causes change in the shape of the wave-front.

• Due to reflection of this diffracted light from an object, we see objects in a room.

• Such effect are eminent in em waves.

Differaction of EM wave

Doppler Effect

• If there is a relative motion between the source (or, reflected source) and the receiver, there is a change seen in the frequency of reception.

• If it moves object moves towards the receiver, it increases and vice versa.

• Fdopple= f[1 + vr/c]

velocity of object toward receiver/velocity of light

Ex. A radar emitting 10.5 GHz, finds that the reception frequency is increased by 1172.5 Hz.

Calculate the speed and the direction of the reflecting surface, which in this case is an automobile.

Soln:

• Let the speed of the automobile be vr mtrs /sec.

• Since the frequency is found increased, the automobile is coming towards the radar.

• Doppler frequency is 1172.5 Hz.

• Hence vr = 33.5 mtr/sec.