1

2

UNIT 1 - Antenna Basics & Thin Wire antennas Introduction, Basic antenna parameters: patterns, , Beam Area, Beam Efficiency, Directivity, Gain, resolution, antenna aperture, Relation between effective aperture and directivity, Natural current distributions, Effective height, Radiation Resistance, efficiency. Fields from oscillating dipole, field zones,, Antenna theorems, Radiation-Basic Maxwell’s equations, retarded potential-Helmholtz theorem, Radiation from small electric dipole, half wave dipole and quarter wave monopole, Current distribution ,field components. Power radiated, Radiation Resistance, Beamwidth, Directivity, effective area, effective height. Far fields and patterns of thin linear center fed antennas of different lengths. Loop Antennas: Small loop-comparison of far fields of small loop and short dipole, D and Rr of small and large loops(Quantitative treatment)

Antenna Basics Introduction:

Generally in any communication system , at transmitter end information is modulated and amplified. In case of wireless communication links this amplified signal from the transmitter (note up to here it is a guided wave) is to be launched to free space. At the receiving free space signal is to be guided to receiver for demodulation and extraction of original information. The transitional structure between a guided wave and free-space wave (or vice-versa) is called “ANTENNA”. At transmitter side the guided to free space wave transition is achieved by means of transmitting antenna. At receiver end the conversion of free space to guided wave is done by receiving antenna.

The guiding device may take the form of parallel wire transmission line or a coaxial cable or a waveguide, and it is used to transport electromagnetic energy from the transmitting source to the antenna, or from the antenna to the receiver. The radio waves from the transmitting antenna reach the receiving antenna following different modes of propagation depending upon several factors and these aspects are dealt in wave propagation. The antennas can be classified on their electrical size or by type.

Classification of antennas by size: 1. Electrically small - physical length of antenna L <<λ : primarily used at low frequencies where the wavelength is long 2. Resonant antennas- physical length of antenna L=λ / 2: most efficient; examples are slots, dipoles, patches 3. Electrically large- physical length of antenna L>λ : can be composed of many individual resonant antennas; good for radar applications (high gain, narrow beam, low side lobes)

is the wave length of EM wave.

Classification of antennas by physical structure 1.Wire antennas 2. Aperture antennas 3.microstrip antennas 4.reflectors 5. Lenses 6. Array antennas Wire Antennas :

, Helix Dipole Circular loop Rectangular loop

Aperture Antennas:

3

Pyramidal horn , Conical horn dish ,

Microstrip Antenna Yagi-Uda antenna

Array antennas Array antennas

Terminology and basic antenna parameters. Isotropic Radiator or Isotropic antenna An isotropic radiator is defined as a hypothetical lossless antenna having equal radiation in all directions. Although it is ideal and not physically realizable, it is often taken as a reference for expressing the directive properties of actual antennas. Directional Radiator A directional antenna is one having the property of radiating or receiving electromagnetic waves more effectively in some directions than in others. Omni-directional antenna: Antenna having uniform radiation in one plane and directional pattern in other plane.

4

Radiation pattern and lobes The performance of the antenna is usually described in terms of its principal E-plane and H-plane patterns. For linearly polarized antennas, the E-plane pattern is defined as “the plane containing the electric field vector and the direction of maximum radiation”, and the H-plane pattern is defined as “the plane containing the magnetic field vector and the direction of maximum radiation”. When the antenna has both EΘ and EΦ components a simple way is to deal with Power Pattern P(Θ,Φ) that is power radiated in watts as a function of the coordinates Θ and Φ at a specific distance r from antenna.

. Typical 3D pattern Different parts o f radiation pattern are referred to as lobes Major lobe or main lobe: It is also called main beam and is defined as the radiation lobe containing the direction of maximum radiation. Minor lobe: is any lobe except a major lobe. Side lobe: is a lobe adjacent to the main lobe that occupies the hemisphere in direction of the main lobe. Back lobe: Normally refers to a minor lobe that occupies the hemispheres in a direction opposite to that of the main lobe. Minor lobes usually represent radiation in undesired directions and they should be minimized. Side lobes are normally the largest of the minor lobes. The level of minor lobes is usually expressed as a ratio of the power density in the lobe in question to that of the major lobe. This ratio is often termed side lobe ratio or side lobe level. Front to back ratio: It is the ratio of power radiated in desired direction to power radiated in opposite direction. Radiation Intensity: Radiation intensity is a quantity, which does not depend upon the distance from the radiator and is denoted by a letter U. It helps in defining various antennas terms. Radiation intensity is defined as the radiated power per unit solid angle. The radiation intensity can be calculated as

d

dP

dd

ddrSrU rad

)sin(

)sin().ReRe

22S

Where d = element of solid angle = ddsin

The radiation intensity, U is also equals r2 times the magnitude of the time average Poynting vector .

Symbolically avesrU 2.

The radiation intensity can be also expressed as 2

max ),(FU),(U

Where 2

max ),(FandU are respectively the maximum radiation and the power pattern normalized to a

5

maximum value of unity. The total radiated power is obtained by integrating the radiation intensity over all

angles around the antenna. dFUdUdsPP averad

2

max ),(),(.

Example: The radiation power density of an antenna is given by

radiatedpower totalFind elsewhere. zero

and 20 ; 2/0for / cos2),( SrWU

watts22

2 cos2 d

2

2sin 4

d cos sin22d d sin cos 2),(

/2

0

2/

0

2/

0

2

0

2/

0

2

0

2/

0

xdUPrad

Directive Gain or Directivity : is defined as the ratio of the radiation intensity U in a certain direction of the antenna to that of an isotropic radiator Ui radiating the same amount of power. It is a function of direction. Directive gain will be high with narrow beam-width. It is expressed mathematically as

averageradi U

U

P

U

U

UD

),(),(4outputpower radiation same having antennasboth

),(),(

Generally directivity refers to maximum directive gain and is denoted by D.

Power Gain The Power Gain G is defined as the ratio of the radiation intensity U of the test antenna to that of an isotropic

radiator Ui with same power input.

inputP

U4πinputpower same having antennasboth

,

iU

UG

The directive gain and power gain are identical except that power takes into account the antenna losses.

It may be written as DG where is the efficiency of antenna.

Effective Isotropic ally radiated power:EIRP is product of input power to the transmitting antenna and its gain. EIRP (dBi) is given for a reference of the isotropic antenna, but ERP (dBd) for a half-wave dipole. Beam Area or Beam Solid Angle (ΩA): The Beam Solid Angle is the solid angle through which all the power of the antenna would flow if its radiation intensity were constant and equal to maximum value UMAX for all

angles within A .The power radiated is given by AMAXrad UP

Let the radiation intensity of an antenna be of the form ),(),( 0 FBU

The maximum value of U is then given by MAXMAX FBU 0 ,where 0B is a constant.

The total radiated power is then given by

2

0 0

0 sin),(),( ddFBdUP

Therefore, directivity, D, is given as

2

0 0

sin),(

),(4

4

),(),(

ddF

F

P

UD

Maximum directivity is given by

MAX

MAX

F

ddFddF

FD

2

0

2

0 0

0

]sin),([

4

sin),(

4

orA

D

4

0 where the Beam Solid Angle.is MAX

AF

ddF

2

0 0

sin),(0

Maximum directivity =Arad

P

U

iU

UD

4

4/maxmax

max

Beam area HpHPA .

There is an approximate relation for D given by Dapprox= HPHP

4

where θ HP and ΦHP are half power beam widths.

6

A

4 2nor

),(FmaxDi

U

2nor

),(FmaxU

iU

),(U),(D

2

nor),(F is normalized to a maximum value of 1, the maximum value of directivity is Dmax.

Beam Efficiency: Ratio of beam area of main lobe and total beam area. If the total beam area ΩA is divided into components ΩM due to main lobe and Ωm due to minor lobes that is ΩA= ΩM + Ωm

Beam efficiency is expressed as εM. = ΩM/ ΩA. It also can be expressed as

4

2

2

,

,

dF

dFmainbeam

M

Resolution of antenna is defined as ability of antenna to distinguish between transmitters on two adjacent geostationary satellites. It is equal to half of beam width between first nulls that is (FNBW/2). But

(FNBW/2) ≈HPBW and 2/2/ FNBWFNBWHpHPA

The number of radio transmitters an

antenna can resolve N=(4π)/ ΩAΦ

.

that is numerically equal to D, directivity of antenna.

Radiation resistance: Rr : It is defined as the virtual or fictious resistance , that dissipates the same amount of power as radiated by the antenna when carries the same peak current as in antenna wire. Power radiated by antenna= ½ Im2Rr

Antenna efficiency: The efficiency of an antenna is defined as the ratio of the total radiated power to the total

input power supplied to the antenna and is given by l

Prad

Prad

P

powerinputTotal

powerRadiated

. If the peak current

through antenna is Im then Prad=rR2

mI2

1. The total input power is sum of radiated power and power loss in

antenna. Then l

RrRrR

where Rr is the radiation resistance and Rl represents the Ohmic loss resistance of

the antenna. Effective Aperture Ae : In the transmitting mode of antennas, the time varying current and charges radiate electromagnetic waves, which carry energy. The receiving antenna extracts energy from an incident electromagnetic wave and delivers it to a load. The concept of effective area is best understood by considering a receiving antenna . over effective area it extracts electromagnetic energy from an incident em wave. So the Effective Area Ae characterizes the antenna’s ability to absorb the incident power density and deliver it to the load. It is defined as ratio of power in terminating or load impedance to power density of incident wave .

aveS

loadP

eA or aveSrR

VeA

4

2

max where Pload = Power received in Watts.

Save= the incident power density in Watts/m2 . Ae= Effective area in m2 . Of the received power some power is delivered to load .Some power received will be dissipated as heat in antenna gven by I2Rloss where Rloss is loss resistance of antenna. The loss aperture Aloss is given by ratio of power dissipated as heat to incident power density. The remaining of incident power is dissipated in radiation resistance or scattered. Accordingly scattering aperture As is defined as ratio of reradiated power to incident power density. Ratio of scattering aperture to effective aperture is called scattering ratio. Or β=As/Ae

Physical aperture Ap The physical aperture is related to the actual physical size (or cross-section) of the antenna and is denoted by Ap. The physical aperture may be defined as “ the cross-section perpendicular to the direction of propagation of incident electromagnetic wave with antenna set for maximum response”.

ep AA (if no losses)

Relation between maximum effective aperture and Directivity: Consider an antenna with effective aperture Ae. The antenna radiates all the power over beam area ΩA. Let the field be of uniform value Ea. Prad=Ea2Ae/Z0 Consider a receiving point at a distance r and field there is uniform of value Er.

emAD2

4

7

Power radiated is also equal to Prad=Er2r2 ΩA/Z0 andEr=(EaAe)/(rλ). So Prad=(EaAe)2r2 ΩA/(Z0r2 λ2). Equating the two ( Ea2Ae/Z0)=(Ea2Ae2r2 ΩA)/(Z0r2 λ2) λ2=AeΩA or 4π λ2=4π AeΩAor( 4π/ΩA) =(4π/ λ2) Ae or D=( 4π Ae / λ2)

Considering the maximum value for D and Ae we get emAD2

4

Effective Length or Effective height he ( applicable to wire antennas only) In electrically small antennas whose length is less than λ/50 the current is assumed uniform throughout and effective length will be same as physical length L. when the antenna length is more than this the current distribution has to be taken into consideration. Whenever the physical length is between λ/50 to λ/10 the current is assumed to have triangular distribution and effective length will be 0.5 times physical length that is he=L/2. For antennas of greater length sinusoidal current distribution is assumed and he=(2/π) L or 0.64L The term effective length of an antenna represents the effectiveness of an antenna as radiator or as collector of electromagnetic wave energy. For a receiving antenna, the effective length is the ratio of the induced voltage at the terminal of the receiving antenna under open-circuit condition to the incident electric field intensity E. that

is E

Vhe . The effective length can also be written as

377maxeArR

2eh

.

For transmitting antenna, the effective length is that length of an equivalent linear antenna that has the same current I (as the terminal of the actual antenna) uniform at all the point along its length and that radiates the same field intensity E as the actual antenna. I = current at the terminals of the actual antenna, I(z) = current at any point z of the antenna he = effective length, l = physical length.Hence for transmitting antenna the

effective length is L

mI

avIL

dzzI

mIeh

0)(

1

Fields from oscillating dipole: Consider a dipole with two equal and opposite type charges oscillating up and down in harmonic motion with instantaneous separation d( maximum separation d 0). Consider a single electric field line. At time t=t0 the

charges are at maximum separation and undergo maximum acceleration dv/dt. When they reverse direction current will beI=0. After T/8 period later charges are moving towards each other. At T/4 they cross mid point the line detaches and new one of opposite sign is formed. At this time equivalent current I is maximum and charge acceleration is zero. As time progresses to half a period fields continue to move out.

Antenna Field Regions or Field zones: The space surrounding an antenna is usually sub-divided mainly into two regions near field or Fresnnel zone and far field or Fraunhofer zone. The

boundary between the two is taken to be at a radius m )/2( 2 LR , where is

the wavelength and L is the maximum dimension of the antenna. Antenna theorems : Reciprocity theorem: The reciprocity theorem for antenna is stated as follows“ If an e.m.f. is applied to the terminals of an antenna no.1 and the current measured at the terminals of antenna no.2, then an equal current both in amplitude and phase will be obtained at the terminals of antenna no.1, if the same e.m.f. is applied to the terminals of antennas no.2.” or If a current I1, at

the terminals of antenna no.1 induces an emf E21 at the open terminals of antenna no.2 and a current I2 at the

8

terminals of antenna no.2 induces an emf E12 at the open terminals of antenna no.1, then E12 = E21 provided

I1 = I2.

Consider two antennas 1 and 2 located in free space separated by distance r. A transmitter of frequency f and zero impedance be connected to the terminals of antenna no.2, which is generating a current I2 and inducing

an emf E12 at the open terminals of antenna no.1. Now the same transmitter

is transferred to antenna no. 1, which is generating a current I1 and inducing

an emf E21 at the open terminals of

antenna no.2. According to the statement of reciprocity theorem I1= I2 provided E12 = E21.

antenna 2 (source) antenna 1( source) Equality of directional pattern : directional pattern of a receiving antenna is identical with its directional pattern as a transmitting antenna. Keep antenna at center of large sphere and connect to voltage source V. A small dipole is moved along the surface of sphere and current I is measured at different locations. Now the voltage V is applied to dipole and moved along the surface of the sphere considered earlier. Measure the current in test antenna for different locations of dipole. Now for every location of dipole the ratio of V/I will be same in both cases ( reciprocity theorem). Hence the equality of directional properties Equality of transmitting and receiving antenna impedance: impedance of isolated antenna when used for receiving is same as when used for transmitting. consider two antennas A1 and A2. When antenna 1 is transmitting Self impedance of antenna 1=Z1=V1/I1=Z11.

When antenna 2 is transmitting with current I2 and

antenna 1 is receiving with load impedance ZL

Induced voltage in antenna 1 = Open circuit voltage=Voc=Z12I2 and Short circuit current Isc=

(Z12I2/Z11).

Transfer impedance or ZTh= (Voc/Isc)=Z11 that is the

self impedance of antenna 1 .so while receiving the impedance is same as that while transmitting Equality of effective length: The effective length of an antenna for receiving is equal to its effective length as a transmitting antenna. The term “effective length” is used to indicate the effectiveness of the antenna as a radiator or collector or e m energy. The effective length is used with wire antennas only Examples 1.Determine the power density at a distance of 50km from an isotropic antenna radiating 1.2Kw Power 2.An antenna has intensity given by U(θ,Ф)=Umsinθsin2Ф for 0≤θ≤π; 0≤Ф≤π. Calculate the exact and approximate directivities. 3.What is the maximum effective aperture of a microwave antenna with directivity 900. 4. An antenna has normalized field pattern given by En=sinθsinФ for 0≤θ≤π; 0≤Ф≤π and zero elsewhere. Calculate the exact and approximate directivities 5.To produce power density of 1mW/m2 in a given direction at distance of 2km an antenna radiates 180W.An isotropic antenna has to radiate 2400 W to produce same power density at that distance. Find directive gain of

9

practical antenna in dB. 6. Calculate the radiation efficiency of an antenna if input power is 2k W., maximum directivity is 22dB and radiated power density at a distance of 10km in direction of maximum directivity is 0.2 mW/m2

7.Calculate the radiated and dissipiated power by antenna if input power is 1.5kW and radiation efficiency is 95%. 8.A magnetic field strength of 5 μA/m is required at a point on θ=π/2, 2km away from antenna in free space. Neglecting ohmic loss how much power must the antenna transmit it it’s a Hertzian dipole of length λ/25. 9.Calculate the radiation efficiency of an antenna if the input power is 2 kW, maximum directivity 22dB and the radiated power density at a distance of 10km in the direction of maximum directivity is 0.2mW/m2 Examples from Krauss exercise

Basic Maxwell's Equations: Maxwell's Equations mathematically describe the propagation of electromagnetic waves. Maxwell's four equations can be presented as in the table. In differential form: In integral form:

D

(Gauss’s Law)

tBE

(Faraday’s Law)

0B

(Gauss’s Law)

JtDH

(Ampere’s Law)

V dvS dsD

(Gauss’s Law)

C S dsBdtddlE

(Faraday’s Law)

S 0dsB

(Gauss’s Law)

S dsJC S dsDdtddlH

(Ampere’s Law)

10

E : electric field intensity (V/m),

B : magnetic flux density (tesla; T);

H : magnetic field intensity (A/m),

D: electric displacement, electric flux density (C/m2);

J : electric current density (A/m2); : electric charge density (C/m3)

Constitutive relations: ED and HB

, is permittivity of the medium Farads/meter,

is the permeability of the medium Henrys/meter.A linear medium is one where the permittivity, , and

permeability, , are independent of field strengths. For vacuum or free space o = 8.854 x 10-12 F/m. o = 4

X 10-7 Henrys/m. In an isotropic medium, the permittivity is independent of orientation and is described

accurately by the scalar relation D =E. But Isotropic does not necessarily mean homogeneous.

In an inhomogeneous medium, permittivity can be a function of position and (r) can have different values depending upon spatial location in the material. Electromagnetic Wave Polarization: The polarization of an uniform plane wave refers to the time varying behavior of the electric field intensity vector at some fixed point in space. The polarization of an antenna is the polarization of the wave radiated in a given direction by the antenna when transmitting. It refers to the physical orientation of the radiated waves in space. Principle of radiation The fundamental source of electromagnetic radiation is accelerated charge. When charge accelerates, it gives off electromagnetic radiation. Steady, time-invariant current does not radiate (because the charge constituting this current is moving at a constant velocity), while time-varying current does radiate(because it constitutes accelerated charge). If a charge is not moving, current is not created and there is no radiation. If a charge is moving with a uniform velocity: (i)There is no radiation if the wire is straight and infinite in extent. (ii)There is radiation if the wire is curved, bent, discontinuous, terminated, or truncated. If charge is accelerating, there is radiation even if the wire is straight Radiation By Currents and Charges: When variable currents carry charges from one locality to another, causing a changing charge density, the resulting time dependent fields propagate outward at the finite velocity of light. An observer at some distance from the varying charge distribution would sense temporally varying electric and magnetic fields varying inversely as square of distance of observation point. The relation between B and A

is AB

.In case of time varying fields the modified relation is t

AVE

.

XAB since and t

JXBor

E

tD

JH

)t

AV(

tJA

.Substituting the vector identity A)A(A 2

2

2

2 )()(t

A

t

VJAA

or)

t

VA(J

t

AA

2

22

Since we are free to choose the divergence of A

, let t

VA

and J

t

AA

2

22

is the non-

homogeneous vector wave or Helmholtz equation for vector potential . A

The corresponding non-homogeneous scalar wave equation for scalar potential V is given as

v

2

22

t

VV . If A

is known B

(or H

), and E

can be found. The solutions are,

''

4),(

Vdv

r

JtrA

and '

'4

1),(

V

v dvr

trV

Retarded Potential: If r is the distance between source and the observation point the vector magnetic potential and the electric scalar potential at distance r from the source at time t depend on the value of the charge density and the electric current density at an earlier time (t - r/u) where u is the velocity of wave propagation. It is necessary to

11

introduce the concept of retardation or the effect reaching a distant point P from a given element at an instant t, due to a current value, which was flowing at an earlier time. While dealing with antennas the finite time of

propagation is of great importance. For this reason the vector magnetic potential A

and the scalar electric potential V are called retarded potentials .

retarded vector potential

'V'dv

r

)c/rt(J

4)t,r(A

retarded scalar potential

''

)/(

4

1),(

V

v dvr

crttrV

Helmhotz theorem statement: Helmholtz’s theorem states that “A vector field is completely defined only when both its curl and divergence are known”

Thin linear wire antennas Radiation from small electric dipole Any Linear antenna may be considered as large number of very short conductors connected in series end to end and hence it is important to consider the radiation properties of such short conductors. A very short current element terminated at both ends in two small spheres is called Hertzian dipole or small electric dipole. The conductor is so short that current may be assumed to be constant. In such antenna the current vanishes at the ends of the wire where charges must be accumulated. Consider an electric dipole of length l along the z-axis centered on the coordinate origin.

Let the instantaneous current in a short wire be a sinusoidal function of time expressed as

)cos(or tIeII mtj

m

Im is the maximum or peak current. I is the current at any instant. f2 , is the angular frequency.

Using the concept of retarded current the instantaneous current is given by

)cos(][ )/(

c

rm

crtjm torIeII

.Where r : the distance traveled, c : the velocity of propagation, [I ] :

retarded current.

12

The general expression for magnetic vector potential is given by

'V'dv

r

)c/rt(J

4)t,r(A

The magnetic vector potential A

is acting along z direction so will have only A Z the z-component . Since the

current element is excited by the current )tcos(II m

dlds'dv and dsJI ( ds is the cross-section area and dl is the length).

The equations for the retarded vector magnetic potential can be written as.

dl

rtosIA m

z

4

)(c r

rtm

I

zA

4

)cos(or

To find the components of vector potential A in spherical co-ordinate system knowing Az

13

14

15

Thus finally the non –zero components are HΦ, E r and E θ and the field components expressions are

21

4

)()sin(

rrj

rtjemI

H

31

24

)()sin(

3

124

)()sin(

and , 3

122

)()cos(

rjrrj

rtjelmI

orrjrr

jrtj

elmIE

rjr

rtjelmI

rE

In the above equation,

represents the intrinsic impedance of the medium (= 120 Ohms, in free

space). Thus, we conclude that here out of six components of electromagnetic field only three components

16

namely

HandEEr

,, exist.

The term in the above expressions varying inversely as distance (1/r) represents radiation field or far field. This field is of great significance at large distance. The term varying inversely as square of the distance represent near field or induction field. Induction field will be predominant at points close to the current element, where r is small. It represents the energy stored in the magnetic field surrounding the current element or conductor. This energy alternatively stored in the field and returned to the source (current element) during each half cycle. The induction field is of little importance as far as radiation is concerned. The term varying inversely as a cube of distance (1/r3), denotes electrostatic field due to its similarity with components of an electrostatic dipole. (It is important near the current element). The space surrounding an antenna can be divided into three regions Case I : Far field region. Considering those terms varying as (1/r) and neglect terms with (1/r2)and (1/r3).

cr

rtjelmIjE

4

)()sin(

and

r

rtjelmIjH

4

)()sin(

The electric field and the magnetic field lie on the spherical surface and for a small area would appear as a plane wave-traveling in the outward direction.

The ratio of E and H represents the intrinsic impedance. At point P( r, , ) in free space

120oo

H

E

Case II: Near field region: at distances r <</2, field components of significance are those terms that vary with (1/r2) . They are

and 24

)()sin(

, 22

)()cos(

r

rtjelmIE

r

rtjelmI

rE

24

)()sin(

r

rtjemI

H

The electric filed has components Er and Ewhich are both in time phase quadrature with magnetic field.

For E and H components, the near field pattern are the same as the far field patterns as both are proportional

to “sin ”. However near-field pattern for Er is proportional to “cos ”.

Case III: Quasi-stationary field region : At very low frequencies that is as approaches zero

2 4

)sin( and, 3 4

)sin( , 3 2

)cos(

r

lmIHr

lmIEr

lmIrE

The electric fields are identical to electrostatic fields of two point charges Q separated by a distance l. The relation for magnetic field may be recognized as Biot-Savart law for the magnetic field of a short element current.

17

Radiation Resistance and effective aperture of a short dipole: If a surface integral of the average Poynting

vector is taken over any surface enclosing an antenna, the total power radiated is ds)*HERe(21

radP

In the far field the non zero components are Eand H. Thus the radial component of the Power radiated by the antenna into far field zone is given by

1

c

1 noting

0

d 3sin 2 22 2

22

4

112

0 0

d d 2r 222216 2

3sin 22 24

120

1

2

0 0

d d sin 2r 222216

2sin 22212

0 0

d d sin 2r

2

4

)sin(1

radP

Ecomponent field electric thegconsiderin ds 2

2

12

2

1Re

21

c

mI

rc

mI

rc

mI

cr

lm

I

HdsE

xHEradP

This is the average power or rate at which energy is streaming out of a sphere surrounding the short dipole.

Therefore, it must be equal to the power, rm RI2

21 , delivered to the dipole, if no losses are assumed. Equating

Prad to rm RI2

21 and simplifying

Radiation resistance is .2

8002280

rR

*For linear antennas use e in place of to find the approximate value of Rr.

Effective aperture of short dipole: From the relation emAD2

4

Noting that the directivity of short dipole is 1.5 we get

4

2DemA 0.1193 λ2

HPBW of ideal/short dipole is 900

Example: l

18

Radiation Pattern of a thin wire antenna In the previous section, we have assumed constant current distribution on the short electric dipole. But it has been found numerically and confirmed experimentally that the current on thin wire antennas is approximately sinusoidal. We will use such approximation to analyze the radiation fields of a linear thin wire half wave antenna. Thus,

consider the linear wire antenna of length l (or L) shown in fig. The sinusoidal current distribution is expressed as

2/2/)(sin)( lzlzlIzI m

From this current, we can calculate the radiation pattern, Since it is a z-directed line source. By regarding the antenna as made up of a series of infinitesimal dipoles of length dz. The field of the entire antenna may then be obtained by integrating the fields from all of the dipoles making up the antenna.

The far field components dE and dH at a distance “s “from the infinitesimal dipole dz are

2/

2/

)sin(60l

ls

dzIretardedjE

2/

2/2

)sin(l

ls

dzIretardedjH

Introducing the value of Iretarded

dzl sj

ezls

dz

l

sjezl

stje

mjI

H2/

0

))(sin(1

0

2/

))(sin(1

2

sin

At large distance the effect between s and r can be neglected as in its effect on the amplitude although its effect

on the phase must be considered. From fig.s r z cos Substituting and also s=r for for the amplitude factor,

Thus the magnetic field in -direction follows as

sin

)2/cos()2/coscos(

2

ll

r

jIretardedH

.

Multiplying Hby 120gives E as

sin

)2/cos()2/coscos(60 ll

r

IjretardedE

The time average power density 2sin

)2/cos()2/coscos(152

2

ll

r

I

rmP

and

sin

)2/cos()2/coscos( llF

The factor F() Represents the relative pattern radiation as a

function of . Plots of F()2 for linear antennas of of various electrical lengths are shown in fig. Power radiated ,Radiation resistance and effective aperture of Half Wavelength Dipole

dzl zj

ezl

dz

l

zjezl

r

rtje

mjI

H2/

0

)(cos))(sin(

0

2/

)cos())(sin(

2

)(sin

19

20

Effective height: since L= λ/2 ; he= (2/π)L= 0.64L= 0.32λ

21

22

20

Quarterwave monopole The length of dipole can be reduced by half by employing image theory and building a quarter wave monopole. A monopole antenna is a dipole that has been divided into half at its center feed point and fed against a ground plane. This will have identical field patterns in the upper half plane. The normalized power density is zero for 90 ≤Θ≤ 1800 The directivity is doubled. D=1.64x2=3.28 ZA mono=VA mono/IA mono= ½(VA dipole)/I A dipole = ½ (ZA dipole) =1/2(73.2+j 42.5). =36.6+j21.25.so for λ/4 monopole Radiation

resistance is 36.6 . A monopole fed against a perfect ground plane radiates one half total power of similar dipole in free space. So the beam solid angle of monopole is one half of similar dipole in space. Hence directivity is doubled and Dquarter wave monopole = 2x D half wave dipole =2x1.64=3.28=5.16dB.

23

Loop antennas A closed loop current whose maximum dimension is less than about a tenth of a wavelength is called a small loop antenna. Small loop is interpreted as meaning a loop antenna that is electrically small or small compared to the wavelength. The pattern for a small loop is independent of its shape and it is similar to that of an ideal electric dipole. This can be accomplished by dealing only with far-field region. We assume that the current has constant amplitude and zero phase around the loop. Each side of the square loop is a short uniform electric current segment that is modeled as an ideal dipole. The two side parallel to the axis have a total vector potential that is x-directed and y-directed and is given by (see fig.) The radiation fileds of small loops are independent of shape of loop and depend on area . Circular loop of radius a give same radiation pattern as a square loop of side d when π a2=d2

Figure Relation of square loop antenna to coordinates Length of dipole L=d and area S = d2

yRe

Re

xRe

Re

r4

uIlaaA

3

)3Rt(j

1

)1Rt(j

2

)2Rt(j

4

)4Rt(j

By comparing the parallel path length, we find from geometrical consideration that

)cos()sin(rR2

l1 , )sin()sin(rR

2

l2

)cos()sin(rR2l

3 , )sin()sin(rR2

l4

Substituting and for far field amplitudes calculations taking R1= R 2 =R 3 =R 4 =r and simplifying total vector

potential can be written as

sinSjA

r4

Ie )rt(j

, where S is the area of the loop.

The far-field components are given by E= - jωA and evaluating we get

r

SISE

rIe rtj

sin120sin

2

2

4

2 )(

, and

24

2

r

S sinsin

)(

ISH

rIe rtj

In general case for circular loop of any radius a located with its center at origin

Where J1() is Bessel function of first order and argument (β a sinθ). The directivity is given by D=(Um)/(U0) or

C

dyyJ

CJCD

2

0

2

max

2

1 sin2 where Cλ=βa and y is any function

The relation is

x

yJxJ

2

0

2

0

2

1 dy x

1d sinsin

.

For small loops Cλ < λ/3 ; D=(3/2) Sin2θ and Dmax=3/2

For large loops D=

max

2

1 sin2 CJC and for Cλ≥ 1.854 .J1(CλSinθ) =0.582 and D=0.68Cλ

sin

2H ,sin

60E ;sin a

r 2

a 111 aJ

r

IaaJ

r

IaAjaJ

IjA

24

The poyinting vector is

sin15

sin42

1120Re

2

1

2

12

2

0

2

1

2

02

2

aJr

aI

aJaIxrx

xZHSr

Power radiated=

0

2

1

2

0

2

2

0 0

2 d sinsin30d d sin aJaIrSr

For small arguments J1 (x)≈x/2 and

4

sinsin

2222

1

aaJ .

Therefore the power radiated

, 10d sin4

300

2

0

4423

4

2

0

2

Iaa

I

22

0

401 SI

Where S=π a2 is area of circular loop. The Radiation resistance of a small loop The radiation resistance is found by calculating the power radiated using small loop radiation, which is given

by 2aS and a is radius of loop .thus c=2πa is circumference. Rearranging we get Rr=

2420 S 2

2

2

2

424

r

2

022

03120032020R and ;

2)(10

SSSR

ISIP

r

2

2

4320

S =

4

42

4320

a =

4

44

2 1620

a = 4197

C , where )/2(

aC The radiation resistance of a loop antenna can be increased

significantly by using multiple turns. The radiation resistance of N turn loop increases by factor N2 and is

given by 2NSr )(200.31R 2

comparison of far fields of small loop and short dipole

s.no Parameter Short dipole Small loop

1 Far Zone Electric field

L

r

IjE

sin][60

2

2

sin120

S

r

IE

2 Far Zone magnetic field

L

rI

jH2sin][

2r

sin

SIH

3 Radiation resistance 2280

2420 S

S is area of loop =π a2 or d2 where a radius of circular loop and d is side of square loop.

The fields of electric dipole and of loop are in time-phase quadrature. Illustrative examples 1.A linear antenna has current distribution Iz=Io cosβz along its length from z=-λ/4 to z=λ/4. Determine its effective length. 2.A half wave dipole is center fed with a current of 2mA rms. Calculate the field at a distance of 10km. Find the gain of this dipole with respect to isotropic radiator. 3.Find the maximum effective aperture and directivity of half wave dipole

25

4,An electric field strength of 10μV/m is to be measured at an observation point θ=π/2, 500 km from a half wave dipole antenna operating at 50 MHz. Find length of dipole, current that must be fed to antenna, average power radiated by antenna and aperture of dipole. Find the effective aperture of half wave dipole. A lossless half wave dipole antenna with Z=73+j42.5 with directional gain 2.2 dB is excited by 10V 50Ω generator. Find electric field intensity at a distance of 10km in a plane perpendicular to the antenna. What should be length of a half wave dipole operating at 100 MHZ. What is the power radiated if it is fed with current of amplitude 20A. An antenna fed with 15 A radiates 5 kW. Find its radiation resistance.

26

UNIT-II: UHF, VHF and MW antennas -I

Arrays with parasitic elements- Yagi-uda array Folded dipoles and their characteristics Helical antenna - geometry, modes, Practical design considerations for mono-filar helical antenna in axial and normal mode Horn antennas, types, Fermat’s principle, Optimum horns, Design considerations for pyramidal horns

Several antennas can be arranged in space and interconnected to produce a directional radiation pattern. Such a configuration of multiple radiating elements is referred to as an array antenna, or simply, an array. Many small antennas can be used in an array to obtain a level of performance similar to that of a single large antenna. The arrays may have all elements active, requiring a direct connection to each element by a feed network. In

case if only a few elements are fed directly, then the array is referred to as a parasitic array. The elements that are not

directly driven called parasitic elements receive their excitation by near-field coupling from the driven elements.

Dipole antenna with parasitic elements.

Consider an array in free space having one driven element and one parasitic element spaced at distance d.. Both elements

are vertical. The Driven element is supplied with power. Currents are induced in parasitic elements by fields from driven

element. The circuit relations are

V1=I1Z11+I2Z12

0=I2Z22+I1Z12 that is I2=-I1(Z12/Z22)

The driving point impedance Z1of driven element is

Considering any losses present, adding a term R1L to represent losses

If P is the power input

The electric field intensity in far field in direction Ф is

27

Considering a λ/2 antenna with same power input P

Gain in field intensity of array with respect to half wave antenna is

Where it is taken ROO=R11 and ROL=R1L

If Z22 I smade very large by detuning parasitic element ( make X22 large) G=1

The magnitude of current in parasitic element and its phase relation to the current in the driven element depends on tuning. Parasitic element can have fixed length of λ/2 and tuning is achieved by inserting lumped reactance in series with antenna at its center. Alternately tuning can be done by varying the length of parasitic element. When parasitic element is longer than λ/2 it is inductive in nature and acts as reflector. If the length is less than λ/2 it is capacitive in nature and acts as director. The Yagi-Uda antenna

The basic unit of a Yagi-Uda antenna consists of a number of linear dipole elements. A resonant half-wave dipole is enerzised by feed transmission line and is called driven element . Other elements arranged parallel to the driven element act as parasitic radiators. Parasitic elements in the vicinity of radiating antenna are used either to reflect or to

direct the radiated energy so that a compact directional antenna

system could be obtained. The length of parasitic element determines its reactance. If the length is greater than λ⁄2 , it will be inductive and less than λ⁄2 it will be capacitive. Properly spaced elements shorter than /2 acts as director and

reinforce the fields of driven element in the direction away the

driven element. On other hand an element of length r greater

than /2 acts as reflector. The spacing between elements and the

length of the parasitic elements determine the phases

The parasitic element in the back of the driven element act as reflector and those in front of the driven element act as

directors. The driven element is to be resonant that is 0.5 λ long but usually0.45-0.49 λ long. The directors are 0.4 to 0.45λ long and spaced 0.3 to 0.4λ apart. The impedance of directors is capacitive in nature and current in them lead induced emf. The reflector is slightly longer than driven element and is spaced 0.25 λ from it. The impedance of reflector is inductive in nature and current in it lag induced emf. By suitable dimensioning the lengths of parasitic

elements and spacing between two elements, the radiated energy is added up in front and tends to cancel the backward

radiation.If a parasitic element is positioned very close it is excited by the driven element with equal amplitude, so that

field on the parasitic element is drivenincident EE A current is excited on the parasite and the resulting radiated electric

field is equal in amplitude and opposite in phase to the incident wave drivenparasite EE

If more than one director is employed, then each director will excite the next.

The general expressions to find element lengths for 3-element Yagi-Uda antenna Reflector length =[152 /(f MHz)] meters Director length = [137 /(f MHz)] meters Driven element length = [143/(f MHz)] meters Yagi-Uda antenna is very popular because of light weight, simple to build and has relatively high

gain

Folded dipole antenna

An extremely practical wire antenna is the folded antenna. It consists of two parallel dipoles

connected at the ends forming a narrow wire loop as shown in fig.

28

The dimension "d" is much smaller than a wavelength. The feed point is at the center of one side. The folded dipole is an

unbalanced transmission line with unequal currents.

Its operation is analyzed by consideration the current to be composed of two modes:

The transmission line mode and The antenna mode

The input impedance for the transmission line mode Zt is given by the equation of Zin of a transmission line of

characteristic impedance Zo and with short circuit load

The Transmission line mode current It= V/2Zt

In the antenna mode, the fields from the current in each vertical section reinforce in the far

field since they are similarly directed. In this mode the charges go around the corner at

the end, instead of being reflected back toward the input as in an ordinary dipole, which

leads to a doubling of the input current for resonant length. The result of this is that the

antenna mode has an input current that is half that of a dipole of

resonant length. Antenna current Ia= V/2Zd .

Zd is input impedance of ordinary dipole of same length.

Total current on left is It+Ia/2 and total voltage is V

Therefore input impedance of folded dipole is ZA=V/( It+Ia/2 )

Substituting for It and Ia and simplifying we get

ZA=[(4ZtZd)/(Zt+2Zd)]

In case of folded half wave dipole L=λ/2 and Zt=∞ .

So ZA=4Zd =4x73= 292 or≈300 Ohms.

In case of tri-pole Rr=(3)2 x 73= 657 ohm

Helical antenna: If a conductor is wound into a helical shape and fed properly, it is referred to as helical antenna, or simply as a helix. The typical geometry for a helix is shown in fig.

2tan Lot

jZZ

Transmission line mode

Antenna mode

29

Geometry of helical antenna

If one turn of helix is uncoiled, the relation among the various helix are revealed, as shown in fig The symbols used to describe the helix are defined as follows: D = diameter of helix (between center of coil material)

C = circumference of helix = ,

S = spacing between turns = C tan()

= pitch angle = tan-1 (S/C); L= Length of one turn = (C2+S2 )1/2 N = number of turns, Lw = length of helix coil = NL h = height = axial length =NS,; d = diameter of helix conductor

Note that when S = 0( = 0), the helix reduces to a loop antenna,

and when D = 0 (= 90), it reduces to a linear antenna . There are two modes of helix operation: Transmission mode and Radiation mode

Transmission mode or T mode.

Describes manner of em wave propagation along infinite helix,

T0 is lowest mode where in charges are separated by several turns.

In T1 mode the charges are separated by 1 turn. In T2 mode charges are 900 apart,

in T3 mode 600 apart , and in Tm mode (180/m)0 apart.

Radiation mode indicate the far field pattern and here two modes are significant .

(i) The axial or beam mode R1 . When dimensions of helix are comparable to wavelength ,radiation will be

maximum in direction where the radiation beam is parallel to helix axis.

single turn helix

30

2222

4

2

/221

2120

4

4 sin

4 4 sin

C

S

C

S

D

S

rID

rISj

E

E

(ii)The normal mode R0 where the radiation beam is perpendicular to helix axis. When dimensions of helix

are small compared to wavelength that is diameter of helix D<<λ and length of helix L<<λ the radiation will

be maximum in a direction normal to helix axis. The radiation efficiency and directive gain are low for this

mode.

In normal mode of operation one turn can be approximated as a small loop and ideal

dipole of length S. The total far zone electric field radiation for one turn is vector sum of field due to dipole [ED in θ direction] and field due to loop [EL in Ф direction] Total radiation field is

Or

E=

sr

IjaA

r

Ia mm

sin60sin120ˆ

2

2

S the spacing between helical turns is the length of the ideal dipole, D2 /4 or π r2 =A is the area of the loop. Both are having sin θ pattern and are 900 out of phase. The ratio of Eθ to EФ gives the axial ratio of Polarization ellipse ARP.

2222

2 )(2

2

2

2sin120

sin60

C

s

r

s

r

s

IA

rs

r

Ior

m

m

ARP varies between zero to infinity. When ARP is zero, Eθ will be zero and polarization is linear horizontal and helix is equivalent to loop. When ARP is infinity E φ=0 and polarization is linear vertical and helix is equivalent to dipole. When C=πD=√2Sλ then the ratio E θ/EФ = 1 and circular polarization is obtained. For all cases as α increases 0< α<1, polarization becomes elliptical with major axis horizontally polarized. 1< α<infinity, polarization becomes elliptical with major axis vertically polarized. The radiation resistance of this helix antenna is 640(h/λ)2 as compared to 395(h/λ)2 of short monopole. This antenna is widely used for small trans receivers like hand held radios. A wire of length LW=λ/4 operated as monopole fed against ground plane. This is called normal mode helix antenna NMHA or resonant stub helix. Axial mode operation: When circumference of turn and the spacing between turns of a helix are comparable to a wavelength, the antenna behaves in an entirely different manner. The main beam of radiation will be in the end-fire direction. This is axial-mode of operation. This type of helical antenna is used with communication satellites and space vehicles as well as on earth station. Axial mode helix antenna is used when moderate gain up to about 15 dB and circular polarization are required. These antennas are widely used at UHF frequencies, for satellite communications. The radiation pattern of the axial mode helix can be modeled using array theory, with each turn being an element of the array. The sense of winding determines the sense of polarization of the antenna namely left hand sensed helix and right hand sensed helix. Practical design considerations for monofilar Axial mode helical antenna: The important parameters for design of axial mode helical antenna are Beam width, Gain, Impedance and Axial ratio. Gain and beamwidth are interdependent (gain is inversely proportional to square of HPBW). Impedance and axial ratio are functions of number of turns ,pitch angle or inter turn spacing and frequency.For a given number of turns these four decide useful bandwidth. The parameters are also functions of Ground plane size and shape, helical conductor diameter, helix support structure and feed arrangement.Ground plane may be flat , circular or square with side dimension or diameter at least 3λ/4.Conductor size may range from 0.005λ to 0.05λ. Helix may be fed axially or peripherally from any convenient location or ground plane launching structure with inner conductor of co-axial line connected to helix and outer one bonded to ground planes.

asinIDasinISjEr4

e2

4

2

r4e rjrj

31

Terminal resistance R = 140 (C/λ); for axial feed and R = 150/

C , Baker relation for peripheral feed.

Quasi empirical relations valid for 120 < < 140 ; (3/4) < C/λ < (4/3) ; n≥ 4 or 0.8< C/λ (or Cλ)<1.15 and120 < < 140; n>3 HPBW =[(52λ3/2)/C(nS)1/2] or [52/Cλ(nSλ)1/2 degrees FNBW =[(115λ3/2)/C(nS)1/2] or [115/Cλ(nSλ)1/2 degrees Directivity D= [15 n C2S/λ3] or 15 Cλ 2 n Sλ . considering effect of minor lobes a more realistic relation is D

nSC 212

ARP =1+ (1/2n), Normalized far field pattern E= sin (π/2n) cos θ [sin (nψ/2)/sin (ψ/2)] Illustrative examples 1.calculate directivity of helical antenna with N=20, =12,and C=λ ans 63.6 or 18.03 dBi 2. calculate directivity of helical antenna with N=20,S=0.3λ,C=10cm, f=3GHz ans 90 or 19.54dBi D= 15 Cλ 2 n Sλ

Sol1. here C=λ or Cλ=1; from Helical geometry S=C tanα= λ tan 120=0.212λ;Sλ=0.212

Substituting, D=15x(1)2x20x0.212=63.6 or 18.03dBi

Sol 2. f=30GHz, λ=(3x108)/(3x109)=0.1m or 10cms, C=λ, S=0.3λ ; Cλ=1, Sλ=0.3

D=15x(1)2x20x0.3=90 or 19.54dBi

32

Horn Antenna: A Horn Antenna is similar to the opened out waveguide. It is excited at one end and kept opened at the other radiated energy. Depending upon the flaring, horn antennas are classified as, 1. Sectoral horn antenna 2. Pyramidal horn antenna and 3 Conical horn antenna. Horn antennas are generally used at microwave frequencies with moderate power gain. Horn antennas are also used as a standard for calibration and gain measurement of other antennas.They are also used as primary radiators for reflector antennas. Sectoral Horn Antenna When the flaring is done in only one particular direction, it is known as sectoral horn antenna, depending upon the direction of flaring, sectoral horn antenna can be, H-plane sectoral horn antenna, (ii) E-plane sectoral horn antenna. Or (iii) pyramidal horn If the flaring is done to the walls of circular waveguide result will be Conical Horn as shown

The main function of electromagnetic horn antenna is to produce uniform phase front with a larger aperture to provide greater directivity. and better impedance matching . Principle of equality of path length-Fermat’s principle Fermat’s principle: or principle of equality of path length is applicable in horn design. Light or radiation travelling between two points takes that path which takes least time. Light waves travel from point A to B by all possible routes ABj . These various paths vary by amounts greatly in excess of λ. So waves arriving at B have large range of phases and tend to interfere destructively. But if there is a short route ABo a considerable number of neighboring routes close to ABowill have optical paths differing from ABo by second order amounts only and will therefore interfere constructively. Thus instead of having constant phase across the horn mouth it is enough if phase deviation is less than a specified amount equal to path length difference between rays travelling along the axis and along the side of horn.

33

Cos(θ/2)= L/(L+δ); Sin(θ/2) = a/2(L+δ); Tan (θ/2)=a/2L Θ is flare angle in degrees: θE for E plane and θH for H plane. a is aperture: aE for E plane and aH for H plane L is horn length, is path difference. For <<<L From L2+a2/4=(L+ )2 we can approximate L=a2/8

θ = 2tan-1(a/2L) =2cos-1(L/ L +δ) In E plane horn is held 0.25λ or less and in H plane horn can be up to 0.4λ.These are the design equations of horn antenna. If the value of flare angle is very large, the wave front on the mouth of the horn antenna will be curved rather than plane. Optimum Horn design: To obtain as uniform an aperture distribution as possible a very long horn with small flare angle is required. For practical convenience horn should be as short as possible.Optimum horn is, in between these two extremes, design to provide minimum beam width without excessive side lobe level. For given length L as aperture a and flare angle θ are increased D increases and BW decreases.

However if they become very large may become equivalent to 180 electrical degrees and field at aperture edge will be in phase opposition to field along axis. Now Directivity decreases and side lobe increases. For all but very large flare angles [L/(L+ ) ]≈ 1. Maximum directivity occurs at largest flare angles for which does not exceed a certain value 0. ( usually 0.1 to 0.4λ). The optimum horn dimensions are found from relations For a given L, Optimum = 0=[L/cos(θ/2)-L] For a given 0, Optimum L= [ 0cos(θ/2)/1-cos(θ/2] For example for 0 =0.25λ and L=10 λ we get θ=250 flare angle for maximum directivity. Directivity D=[(7.5 Ap)/λ2] Ap= aE x aH for rectangular Horn =π r2for conical horn where r is aperture radius. Half Power Beam Width (HPBW) of optimum flare horn in E and H directions, are given by the approximate relations θE = (56λ/h) and θH= (67λ/ω). The pyramidal horn is most widely used microwave antenna. It is simple to construct, versatile, has large gain and easy to excite. Used as feed element for radio astronomy. Widely used as standard to make gain measurements of other antennas. Design of optimum pyramidal horn: Specify required gain G, operating wavelength λ, connecting wave guide dimensions a,b

34

Useεap=0.51. Solving A4-aA3+[(3bGλ2A)/(8πεap)]= [(3G2λ4)/(32 π2+ εap2)] - find value of A.

From the relation A=√(3λR1) find R1 From (R1/RH)=A/(A-a) find RH &

From 𝓁H2=R12+(A/2)2 find 𝓁H Using the relation G=0.51(4π/λ2)AB , Find the value of B From B=√(2λR2) find R2 From (R2/RE)= B/(B-b) find RE From 𝓁E2=R22+(B/2)2 find 𝓁E

Example Design Specifications: G=20dB=100, f=9.5GHz; WR90 waveguide a=2.286cms , b=1.016 cms

Instead of solving A4-aA3+[(3bGλ2A)/(8πεap)]= [(3G2λ4)/(32 π2+ εap2)] to find value of A , a simple procedure

followed is use first an approximate value of A, A=0.45λ = 0.45x3.158x√100=14.21 , find other parameters. Change value of A and repeat till RE = R H

A B R1 R2 RE RH RE-RH

𝓁E 𝓁H

14.21 10.94 21.31 18.96 15.91 19.31 -3.4

14.3 10.87 21.59 18.72 15.72 19.55 -3.83

14 11.1 20.69 19.53 16.34 18.78 -2.44

13.8 11.26 20.11 20.1 16.77 18.28 -1.51

13.6 11.43 19.53 20.69 17.21 17.78 -0.56

13.4 11.6 18.96 21.31 17.68 17.28 0.4

13.5 11.51 19.24 21 17.44 17.53 -0.08

13.49 11.52 19.21 21.03 17.47 17.5 -0.04

13.48 11.53 19.19 21.06 17.49 17.48 0.01 21.83 20.34

35

UNIT-III: UHF, VHF and MW antennas- II , Lens antennas

Microsrtip antennas- introduction, features, advantages and limitations, Rectangular patch antennas- geometry, parameters, Characteristics of microstrip antennas, impact of different parameters on characteristics. Reflector antennas- introduction, -Flat sheet and corner reflectors, Paraboloidal reflectors-geometry ,pattern characteristics, feed methods,Reflector types, related features Lens antennas- Introduction, Non-metallic dielectric Lenses, Zoning , tolerances , applications. Illustrative problems

Microstrip patch antennas or Patch antenna or printed antenna The antenna consists of dielectric substrate with radiating patch on one side and ground plane on other

sisde. A thin conducting sheet or metal patch of (λ0x0.5λ0) is positioned on top surface of dielectric substrate. Th ebottom surface of dielectric substrate is coated with continuous metal layer of suitable metal to form the ground plane. A hole is formed through ground plane and dielectric to access the lower surface of patch.Center conductor of co axial cable (surrounded by metallic housing within the substrate) is directly connected to patch. Copper or Gold is the material for patch. A plastic radome protects the structure.

The patch can be square, rectangular,circular,triangular elliptical or any shape. Rectangular patch is widely used as analysis is simple.

The microstrip antenna is widely used in situations where size weight,cost, performance are constraints and low profile antennas are required in high performance air craft, space craft, satellite and missile applications. Also used in mobile radio and wireless communications.

Advantages: • Light weight, • smaller size, • less volume, • Ease to mould to any desired shape . • Can be attached to any host surface • Low fabrication cost, • Suitable for mass production. • Can support linear and circular polarization • Compatible with microwave monolithic and opto electronic IC

technologies (MMIC, OEIC) • Easy to form large arrays with λ/2 or smaller spacings. Limitations • Narrow bandwidth (<5% for single substrate and upto 35% with second substrate dual band design), • Low efficiency, • low gain, • low power handling capacity. • Suffers from effects of radiation from feeds and junctions

Rectangular Patch antennas Let L be the mean long dimension or length which causes resonance at its λ/2 frequency and W width of patch. ( L>W). Let h be the substrate thickness where h<<<λ and εr be relative permittivity of substrate material. The radiating edges are at the ends of L dimension of rectangle and they set up radiation of single polarization. Radiation if any at ends of W dimension is called cross polarization. Since W/h >>>>1and εr>1 electric field lines concentrate mostly in substrate. Fringing in this case makes micro strip line look wider and longer electrically than its physical dimensions. Since some of the waves travel in substrate and some in air effective dielectric constant εr eff will be considered to account for fringing and wave propagation in line. At low frequencies the effective dielectric constant is fairly constant and is called its static value. At intermediate frequencies the value begin to increase monotonically and approach the value of dielectric constant of substrate. The static values are W/h >1 and

36

2/1

h 121

2

1

2

1

W

rrreff

Due to fringing the patch looks bigger than physical dimensions. The dimensions along length is extended by ∆L on each side and

8.0 258.0

264.0 3.0

412.0h

L

h

W

h

W

reff

reff

The effective length of patch is Leff=L+2∆L. For dominant mode that is TM010 mode resonant frequency is

00

0102

1

r

rL

f

.

The resonant frequency corrected including edge effects is

0000

0102

1

2

1

reffreffeff

rcLLL

f

As substrate height increases fringing also increases and leads to larger separations between radiating edges

and lower resonant frequencies.

Design Example:

Design a rectangular patch using substrate with dielectric constant 2.2, h=0.1588 cms so as to resonate at

10GHz.

i.Find width of patch

cmscmsf

x

fW

rrrr

186.11

2105.1

1

2

2

1 10

00

ii. Find effective dielectric constant

W

121

2

1

2

1 hrrreff

=1.972

iii. extended incremental length ∆L = 0.081 cms from

8.0 258.0

264.0 3.0

412.0h

L

h

W

h

W

reff

reff

iv. Actual length

Lf

L

reffr

22

1

00 =0.906 cms

v. Effective length Le= L+2∆L =1.068 cms

Characteristics of Microstrip:

Radiation pattern Infinitely long ground plane prevents back lobes. But real antenna has fairly small finite

ground plane. So power in back ward direction is only 20dB down from that in main beam.

Beam width is very wide in azimuth and elevation

Gain is around 7-9dB

Directivity for TM10 mode is given by the relation

0

20

2'20

22

rP

kWEhD

Where h= substrate thickness; Pr= radiated power; k0= wave number;

37

yxL

mEEhWW z

W

n cos cos and ; 0

'

Impedance bandwidth is influenced by spacing between patch and ground plane (h). As patch is moved

towards ground plane, less energy is radiated and more energy is stored that is Q increases and BW=(S-

1)/[Q0S1/2] where Q0 is unloaded Q value. If S increases impedance- bandwidth increases.

Patch antenna has high quality factor. Large Q leads to narrow bandwidth and low η.

Q can be reduced by increasing h, thickness of dielectric substrate but increasing h results in large portion of

power travelling as surface wave and more unwanted power loss.

Using array configuration low gain and low power handling capacity can be overcome

Efficiency η=Pr/(Pc+Pd+Pr) ; Pc ic power loss in conductor, Pd is power loss in dielectric, Pr is radiation power

loss

Polarization: Patch antenna can have Polarization diversity.It can be easily designed to have vertical,

horizontal,RHC and LHC polarizations.

Return loss is ratio in dB of power reflected by antenna to power fed to the antenna and is given by 20 log

(S/S-1)

GPS guidance system need low radar cross section platform. But RCS of patch antenna is high.To reduce

patch antenna is covered with magnetic absorbing material.But this reduces gain.

Impact of different parameters on characteristics:

The parameters that influence the radiation characteristics are L, W, h and εr

Length L and width W control resonant frequency fr.

Width W also controls input impedance and as W increases Zin decreases.

W also helps in maximizing efficiency. Best choice for W is

cms

f

xW

rr )1(2

103 10

εr Controls the fringing field . if εr is lower more wide fringing , better radiation increased bandwidth,

increased efficiency. On the other hand higher εr results in increased impedance, shrinking of patch . In cell

phones where space is little and to have λ/2 antenna use substrate with high permittivity.

From the relation of L we find L 1/√εr, hence if εr is increased 4 times length will become half or reduce by

factor 2.

Height of substrate h controls bandwidth since BW B h and B 1/√εr . Increase in h increases volume and

hence bandwidth, improves efficiency. However increase in h induce surface waves that travel within

substrate.

Reflectors Reflectors are used to modify the radiation pattern of radiating element. The different types of reflectors are Plane sheet, active corner, passive corner, parabolic, elliptical, circular and hyperbolic reflectors etc. Plane sheet reflector corner reflector parabolic reflector

Reflector antennas- Introduction, -Flat sheet and corner reflectors, Paraboloidal reflectors-geometry ,pattern characteristics, feed methods, Reflector types- related features-Illustrative examples

38

Hyperbolic reflector truncated paraboloid Cheese antenna Flat sheet reflector: consider an antenna at a distance d from perfectly conducting plane sheet reflector. To use method of images analysis, replace reflector by image of antenna Gain in field intensity of λ/2 dipole at distance d from infinite flat reflector is

/2d where

cossin2

r

1211

11

d

dRRR

RRG r

L

Lf

Plotting patterns for different spacing d , with RL=0, it is observed that small

spacing are effective but results in narrow bandwidth. Wide spacing results in

wider bandwidths but now gain will be less. Hence selection of spacing d will be a compromise between gain

and bandwidth.

There will be 3 principal angular regions namely

Region 1 : above & infront of reflector: the total radiated field is resultant of direct field of dipole and reflected

field from sheet.

Region2: above and below at sides of sheets: there will be only direct field from dipole

Region 3: below or behind the sheet: the sheet acts as a shield and there will be no direct or reflected fields but

only diffracted field.

An array of 16, half wave dipoles spaced λ/2 apart when backed by large sheet reflector provides a gain of

17dBi. To reduce wind resistance the reflector can be replaced by a back curtain of 16 half wave dipoles, still

gain is 17dBi. Adding another set of curtain arrays along side this array both at front and back making total of

64 dipoles gain is 20dBi. Doubling again to 128 dipoles gain is 23dBi, with 256 dipoles gain is 26 dBi and with

512 dipoles gain is 29dBi.

Example: A station transmitter delivers 25000 watts to 512 dipole array.

What is the ERP effective radiated power. Find the field strength at a distance of 7500 kms assuming the signal

to be trapped between ionosphere at a height of 250 kms and earth.

For 512 dipole gain is 29 dBi . Taking antilog(29/10) ; gain =794

ERP = 25000 x 794= 19.9x106 =19.9 M w

39

Power density=S = ERP/ area =(19.9x106 )/[2πx(7500x103)x(250x103)]=1.68 x10-6 w/m2

Field intensity E=√Sxη0 =(1.68x10-6x377)1/2 =25 mV/m Corner Reflector

Two flat reflectors joined to form a corner with some angle is called corner reflector. The sheets intersecting at angle less than 1200yields sharper radiation pattern than flat sheet reflector. For many applications angle is 900. A corner reflector with exciting antenna in between is called active corner reflector while a reflector without exciting antenna is called passive corner reflector or target for radar waves. In case of passive reflector angle is always 900.

The efficiency depends on spacing d between vertex of corner reflector and feed element.when icluded angle decreases d has to be increased and vice-versa. Generally the aperture of corner reflector DA is taken to be between λ and 2λ. Spacing between vertex and feed point d is kept between λ/3 and 2 λ/3. Length of reflector is s elected as Ĺ=2d for =90.For smaller values of , Ĺ is made larger than 2d.

To analyze corner reflector for =(180/n) method of images is used. Consider a λ/2 driven elemnet and 90 degree corner reflector.There will be 3 image elments that are λ/2 long. Driven element and 3 images have currents of equal magnitude. Phase of currents in elemnts 1& 4 is same.Phase of currents in 2& 3 is same but 180 degrees out phase with respect to current in element 1. At any point P at large distance D in direction Ф the field E(ф)=2 k I[ cos (drcosф) - cos(dr sinф)], where I is current in each element, k is aconstant involving distance D.

The emf V1 at center of driven element is V1=I1Z11+I1R1L+I1Z14 -2I1Z12 Z11: Self impedance of driven element; R1L:equivqlent loss resistance of element 1 Z14 : mutual impedance of elements 1,4; Z12 : mutual impedance of elements 1,2 If P is power delivered to driven element, then the current I1

is sincoscoscos2R

P2E and

2R

PI

12141111214111

1 rr

LL

ddRRR

kRRR

The pattern will have 4 lobes , however only one is real. In order to reduce wind resistance offered by solid reflectors a grid of parallel wires or conductors can be used. The spacing between reflector conductors is ≤ λ/8. When driven elemnet is λ/2 long , reflectors ≥ 0.7λ are used and a square corner reflector provides gain of 11-14dBi.

Paraboloidal Reflector To provide highly directional radiation parabolic reflectors ar used. The parabolic reflector transforms curved wave front from feed antenna at focus into a plane wave front.Paraboloid is the surface generated by revolution of parabola around its axis. Parabola is locus of a point which moves in such a way that its distance from a fixed point (focus) plus distance from a straight line (directrix) is constant. The radiation from large paraboloid with uniformly illuminated aperture is equivalent to that from circular aperture of same diameter D in a infinite metal plate with uniform plane wave incident on plate The ratio of field intensity at radius ρ from axis is given by

2

1

E

E

0

COS

40

The radiation from large paraboloid E( Φ ) as a function of Φ isWhere D is diameter of reflector antenna, Φ is angle with respect to normal to aperture, J1 first order Bessel function,J1(x)=0 when x=3.83

BWFN for large circular apertures= 140λ/D deg HPBW for large circular apertures = 70 λ/D deg Directivity D=9.87[D/λ]2 considering aperture efficiency Gain= 6[D/λ]2 For rectangular or square apertures

BWFN= 115λ/L; Directivity D=12.6[L/ λ]2 ;Power gain over λ/2 dipole= 7.7[L/λ]2 Reflector surfaces may be made of Solid sheets ,Wire screens,Metalgrating ,(Aluminum) expanded metal sheets Advantages of spherical , parabolic, cassegrain reflector surfaces Light weight;Low wind pressure ;Low cost;Easy to fabricate Spherical reflector Provides wider scanning angle than paraboloid Drawbacks: permit energy leak;Result in back lobe, side lobes.With increasing side lobe levels,efficiency decreases Feed methods for parabolic reflectors: 1.dipole: A parabolic reflector can be fed using a dipole antenna. 2.dipole with parasitic reflector: In addition to a simple dipole in the feed system few parasitic elements like another dipole or plane sheet can be added 3.open ended wave guide: when an open ended wave guide is used for feed more energy is directed in forward direction. A circular paraboloid can be fed by circular wave guide in TE11 mode 4. wave guide horn: this method gives better directivity. This is similar to a point source with large reflector. for uniform illumination the ratio of f/D( ) should be large 5. In addition to above the parabolic reflector also can be fed by front feed using horn, rear feed using horn, and offset feed using horn. In case of offset feed only half of the parabola is used 6.Cassegrain antenna. the feed radiator is mounted at or near the surface of a concave main reflector and is aimed at a convex secondary reflector slightly inside

the focus of the main reflector. Energy from the feed unit illuminates the secondary reflector, which reflects it back to the main reflector, which then forms the desired forward beam Used in monopulse tracking with radar work permits in reduction of axial dimensions of antenna. The feed radiator is more easily supported and the antenna is geometrically compact. It provides minimum losses as the receiver can be mounted directly near the horn. The subreflectors of a Cassegrain type antenna are fixed by bars. These bars and the

secondary reflector constitute an obstruction for the rays coming from the primary reflector in the most effective direction. Lens antennas Lens, antennas are suitable for frequencies above 3000 MHz .If the frequency is less than 3000 MHz, then the lens antenna will have more thickness. The thickness of lens antennas can be reduced with the help of zoning. This process reduces the weight of lens considerably. The zoned dielectric lens antenna ensures that signals are in phase after emergence, despite difference in appearance. The zoned lens is having less power dissipation. But the zoned lens antennas are frequency sensitive.Zoning is classified into two types Curved surface zoning Plane surface zoning.

41

Differences between Natural Dielectric Lenses and Artificial Dielectric Lenses 1. Artificial dielectric lenses have less weight compared to natural dielectric lenses. 2. Artificial dielectric lenses are made up of discrete metal particles whereas natural dielectric lenses consist of molecular particles. 3. Natural dielectric lenses, does not have any resonant effect Characteristics 1. Both type of lens can be used to speed up (or) delay the travelling wave front. 2. Artificial and natural dielectric lenses are not much dependent on the wavelength. 3. The variation in thickness front ideal contour and variations in refractive index causes change in path length. 4. Lenses may be turned frequency sensitive with the help of zoning.

42

5. The thickness of lens antenna depends upon the refractive index μThickness can be increased by reducing the refractive index. 6. The design conditions of artificial and natural dielectric lens antennas are same for same refractive index. Merits and Demerits 1. Artificial dielectric lenses have less weight compared to the natural dielectric lenses. 2. Disadvantage of artificial dielectric lens is that they may have resonance effects. 3. Power dissipation is more in natural dielectric lenses.

43

UNIT-IV: Antenna Array, Antenna measurements

Point sources-definition, patterns, Arrays of 2 isotropic sources- Different cases Principle of pattern multiplication N element uniform linear arrays, BSA,EFA, EFA with increased directivity , Derivation of their characteristics and comparison. BSA with non uniform amplitude distributions-general considerations and bio-nominal arrays Antenna measurements– Introduction, concepts reciprocity, near and far fields, co-ordinate systems, sources of errors, Patterns to be measured. Pattern measurement arrangement, Directivity measurement , gain Measurement (comparison, absolute, 3 antenna methods)

Antenna Arrays A point source radiator is a fictitious volume less emitter. At a sufficient distance in the far field of an antenna, the radiated as at the point O at a distance R on the observation circle in Fig. 5-1. It is convenient in many analyses to assume that the fields of the antenna are everywhere of this type. Several antennas can be arranged in space and interconnected to produce a directional radiation pattern. Such a configuration of multiple radiating elements is referred to as an array antenna, or simply, an array. Many small antennas can be used in an array to obtain a level of performance similar to that of a single large antenna. Arrays offer the unique capability of electronic scanning of the main beam. By changing the phase of the exciting currents in each element antenna of the array, the radiation pattern can be scanned through space. The array is then called a phased array. Phased arrays have many applications, particularly in radar. The concept of phased arrays was proposed in 1889, but the first successful array (a two-element receiving array) did not appear until about 1906. Arrays are found in many geometrical configurations. The most elementary is that of a linear array in which the array element centers lie along a straight line. The elements in an array can form a planar array. A popular planar array is the rectangular array in which the element centers are contained within a rectangular area. Arrays Examples 1.Two Isotropic Point Sources with Identical Amplitude and Phase Currents, Spaced λ/2 apart Consider two isotropic point sources located symmetrically about the origin along X axis. They carry equal amplitude ,in phase currents, and spaced one-half wavelength apart.

The origin is taken as reference for phase calculations At distant point in direction θ, field from source 1 is retarded by β(d/2) cos Φ while field from source 2 is advanced by β(d/2) cos Φ Total field at distant point

ET = 22

00EE

jj

ee

where Ψ=βd cosΦ

cos2

cosE2

)2/cos(E22

)(E2

)(EE

0

00

0T

22

22

d

ee

ee

jj

jj

Normalize the field that is make 2E0=1 and En= cos[(βd cos Φ)/2]. cos[(βd cosΦ)/2] is called array factor normalized AFn. Since the two sources are half wave length apart ,d=λ/2. βd/2=π/2. The array factor becomes AFn= cos (π/2) cosΦ The pattern or variation of field with Φ will be a bidirectional figure of 8 with maxima along Y axis. If source 1 is at origin and source 2 at distance d from source 1, take field from source 1 as reference. ET= E0 + E0 cos (Ψ)=E0(1+cosΨ) and we get AFn=cos(Ψ/2)LΨ/2. Cos(Ψ/2) gives variation of amplitude. The

44

angle factor gives variation with respect to source1 as reference as shown.

When phase is referred to point midway between sources there is no phase change around array –solid line. Observer at distance observes no phase change when array is rotated about its mid point. A phase change will be observed if array is rotated with source 1 as center of rotation. NOTE: If the two isotropic sources are placed symmetrical to origin along Z axis as shown then Ψ=βd cosθ and

cos2

cosE2

)2/cos(E2

2

)(E2

)(EE

0

0

0

0T

22

22

d

ee

ee

jj

jj

When sources are half wave length apart ,d=λ/2. βd/2=π/2.and array factor becomes AFn= cos (π/2) cosθ

The polar plot of array factor magnitude will be as shown with maximum along Y axis. 2.Two isotropic Point Sources with Identical Amplitudes and Opposite Phases, and Spaced λ/2 apart Consider two isotropic point sources located symmetrically about the origin along X axis. They carry equal amplitude and out of phase currents, and spaced one-half wavelength apart. Now Total field at any distant point P in direction Φ will be

2222

0000TEEEEE

jjjjj

eeeee

where

Ψ=βd cosΦ (The negative sign indicating opposite phase of currents)

coscos22

ddjj

neeE

;Using 22

d , the array

factor AF becomes )cossin( 2 n

AF

The pattern is relatively broad figure of 8 with maximum field in same direction as line joining the sources that is X axis.

3 Two Isotropic Point Sources with Identical Amplitudes and in phase quadrature Spaced λ/2 apart Taking origin as reference for phase source 1 is retarded by 450 and source 2 advanced by 450. Total field in direction Φ at large distance r is given by

Polar plot of array

fator magnitude

45

Normalizing and with d=λ/2

Most of radiation is in 2 and 3rd Quadrants. If the spacing between sources is reduced to λ/4, then

The field pattern is cardioid shaped unidirectional pattern with maximum field in x direction. 4 Two isotropic sources of equal amplitude and any phase difference Consider two isotropic point sources of equal amplitude and any phase difference . The total phase difference ψ between fields from source 2 and source 1 at distant point in direction Φ is Ψ=dr cosΦ+ . The+sign indicates that if source 1 is taken as reference for phase , source 2 is advanced in phase by . If source 2 is retarded in phase then use - . If we take the center point of array as reference for phase then phase of field from 1 at distant point is –ψ/2 and that from 2 is +ψ/2. The total field is E=E0(ejψ/2+e-jψ/2)=2E0 cos(ψ/2). The normalized field will be En= cos(ψ/2). The first three cases are special cases of this with =0,1800 and 900 respectively

5 Two isotropic point sources of unequal amplitude and any phase difference : Most general case

Let amplitude of Source 1 be E0 and of source 2 be a E0 where 0<a<1 and Ψ=(βd cosФ+δ) ,phase angle

referred to source 1.In far field resultant E=E0[(1+a cosψ)2+a2sin2ψ]1/2 and phase ξ= arc tan [asinψ/(1+acosψ)] Pattern multiplication we have discussed only arrays of isotropic point sources. Actual arrays have element antennas that, of course, are not isotropic. In this section, we discuss how to compute the radiation pattern of actual arrays. An array factor plays a major role in pattern calculations. When the elements of an array are placed along a line and the currents in each element also flow in the direction of that line, the array is said to be collinear. The total field pattern of an array of non-isotropic but similar sources is the product of the individual source pattern and the pattern of an array of isotropic point sources each located at the phase center of the individual source and having the same relative amplitude and phase, while the total phase pattern is the sum of the phase patterns of the individual source and the array of isotropic sources. Let E1 and E2 the far fields at distance P of two point sources with equal amplitude and phase. The total far

field at point P, in the direction of is given by )cos(22

2/2/ o

jo

joT EeEeEE

Now let the field pattern of each non- isotropic similar point source be given by sinEE 1o

Thus, )cos( sin 221

EET

and normalized far field is given by )cos(sinE

2

From this expression, we can identify :Result is same as multiplying pattern of individual source (sin )by pattern of 2 isotropic sources(Cos(Ψ/2))

Examples of pattern multiplication Array of two half-wavelength spaced, equal amplitude, equal phase, collinear short dipoles Consider two collinear short dipoles spaced a half-wavelength apart and equally excited

The element pattern is sin for an element along the z-axis

46

and the array factor was found to be )cos( 2

.

Ψ/2=(1/2)(β d cosθ ). With d=λ/2 and β=(2π/λ) we get Cos(ψ/2) = cos[ (π/2) cos θ]The patterns are illustrated.

Two Parallel, Half- Wavelength Spaced Short Dipoles: The complete pattern for the array of two parallel short dipoles in Fig. -a is found by pattern multiplication as indicated in Figs.b and c. Array of two half-wavelength spaced, equal amplitude,equal phase parallel short dipoles. (a) The array ( b) The xz-plane pattern

(c) The yz-plane pattern

47

Uniform Linear array of n isotropic point sources of equal amplitude and spacing

Suppose that we have linear array of several elements. The elements are equally spaced along Z axis

The angle is that of an incoming plane wave relative to the axis of the receiving array. The isotropic sources respond equally in all directions, but when their outputs are added together (each weighted according to In), a directional response is obtained. The phase of the waves arriving at the origin is set arbitrarily to zero. The incoming waves at element 1 arrive earlier than those at the origin since the distance for these is shorter by an amount “d

cos()”. The corresponding phase lead of waves at element 1

relative to those at 0 is ψ= d cos(). Equally spaced linear array of isotropic point sources This process continues and total field (assuming amplitude of each source E’=1) is E=(1+ ejψ + ej2ψ +ej3ψ +ej4ψ….+ej(n-1)ψ)….i Multiplying both sides by ejψ E ejψ= ejψ(1+ ejψ + ej2ψ +ej3ψ +ej4ψ….+ej(n-1)ψ)….ii Subtracting i from ii and simplifying we get E =(1- ejnψ )/(1-ejψ)

= = ,where referred to field of source 1 and normalized field

En=(1/n) In general we can write for far field observations the array factor as

an = amplitude of n th source , Ψ=βd cosγ +α where α is the progressive phase shift in excitations , d is spacing between elements and γ is angle between the array line and direction of field measurements. When elements are along Z axis cos γ= cos θ or γ=θ When elements are placed along X axis cos γ= sin θ cos Φ or γ= cos -1(sin θ cos Φ) When elements are along Y axis cos γ= sin θ sin Φ or γ= cos -1(sin θ sin Φ)

(i)Broadside Array (sources in phase)

The first case is a linear array of “n” isotropic sources of the same amplitude and phase. Therefore, = 0 and

)cos(d .To make = 0 requires that 2

1k2

, where k = 0, 1, 2, 3, …… The field is therefore, a

maximum where 2

and

2

3 .That is, the maximum field is in a direction normal to the array. Hence this

condition, which is characterized by in-phase sources ( = 0), results in a broadside type of array.

For an n element array the resultant field is E=(1-ejnψ)/(1-ejψ)

The null directions occur when E=0 and denominator is≠0 that is

48

ejnψ =0 or ejnψ=1 or nψ= 2k or ψ = 2k where k=0,1,2,3… . (however avoid value of k=mn where m is an

integer1,2,3….because then then ψ= = 2 denominator will become zero) .In case of broad side array =0

and Фmin=Cos-1 2k /(nβd)= Cos-1 k /(nd)

Example : consider 4 element array with λ/2 spacing ie n=4 and d= λ/2 ;

Фmin=Cos-1(±k/2)

For k=1; Фmin= Ф01=±600 and± 1200 and for k=2; Фmin= Ф02=00 and± 1800 that is total 6 nulls.

In place of Фmin if we use complimentary angle γmin=900- Фmin. γmin= sin-1 ±kλ/nd.

When the array is very long nd>>>>>kλ then γ0= γmin≈ (kλ/nd).

Further the first nulls on either side of maximum occur for k=1;γ01=γmin=±λ/nd

BWFN orFirst Null Beam Width FNBW =2 γ01≈ (2λ/nd)= (2λ/L) whereL=nd length of array. (ii) Ordinary End-Fire Array

Let us now find the phase angle between adjacent sources that is required to make the field a maximum in the

direction of the array 0 . An array of this type may be called an end-fire array. For this we substitute the

condition = 0 and 0 in )cos(d , from which d .Hence, for an end-fire array, the phase

between sources is retarded progressively by the same amount as the spacing between sources in radians.

For an n element array the resultant field is E=(1-ejnψ)/(1-ejψ)

The null directions occur when E=0 and denominator is≠0 that is 1- ejnψ =0 or ejnψ=1 or nψ= 2k or ψ =

2k where k=0,1,2,3… . (however avoid value of k=mn where m is an integer1,2,3….because then then ψ=

= 2 denominator will become zero) .In case of end fire array =-βd and ψ=βd ( CosФ0-1)=(± 2k /n)

CosФ0-1=[(± 2k )/(nβd)]=±(kλ/nd) or 2 sin2(Ф0/2)= ±(kλ/nd) or sin2(Ф0/2)= ±(kλ/2nd) Ф0/2 =sin-1

( or Ф0= 2 sin-1 (

First nulls occur on either side of main lobe for k=1 and Ф01=(

FNBW for long end fire array = 2Ф01=2√(2λ/nd) (iii) End-Fire array with increased directivity:

When the phase angle d it results maximum field in direction 0 but doesnot give maximum

directivity. Hansen and Woodyard proposed that larger directivity is obtained by increasing phase change between sources to satisfy )/( nd and

ndndd /)1(cos/)cos( For an n element array the resultant field is E=(1-ejnψ)/(1-ejψ)

The null directions occur when E=0 and denominator is≠0 that is 1-e jnψ =0 or e jnψ =1 or nψ= 2k that is

ψ = 2k where k=0,1,2,3… . (however avoid value of k=mn where m is an integer1,2,3….because then then

ψ= = 2 denominator will become zero) .In case of end fire arrays with increased directivity

=-(βd+π/n) and Ψ=βd CosФ0-βd-π/n . on simplification

Cos Ф0-1=±[(2k-1)π/(nβd)]=±[(2k-1)λ/2n d],Sin2(Ф0/2)=±[(2k-1)λ/4n d]

Ф min= Ф0= 2 Sin -1±[ (2k-1)λ/4nd]1/2 When array is long nd>>>>kλ; Ф0 ≈ ±[λ(2k-1)/nd]1/2

First nulls occur on either side of main lobe for k=1 Ф01=√(λ/nd) and FNBW= 2 Ф01=2√(λ/nd)≈2λ/2nd ≈λ/L (iv)Array with maximum field in any arbitrary direction: To have an array that gives maximum field in some arbitrary direction Ф1 not equal to multiples of π/2

usethe relation 0 cos 1 d , find d and hence calculate using )/( nd . For example if we

consider 4 sources separated by λ/2 and wish to have maximum radiation in 600direction then

2-60 cos- 0)60cos

2

2(

or

49

Note Length of array =L=(n-1)d≈nd when n is large.

parameter BSA EFA EFA increased D

Nulls γ0=±[λk/nd] Ф0=±[λ(2k)/nd]1/2 Ф0=±[λ(2k-1)/nd]1/2

First null beam width (2λ/nd)

2√(2λ/nd)

2√(λ/nd)

Half power beam width (λ/nd)

√(2λ/nd)

√(λ/nd)≈

(v)Linear broadside arrays with non uniform amplitudes : In this section we consider the properties of a linear array of 5 isotropic sources with λ/2 spacing and having

amplitude distributions (a) uniform (b) binomial (c) edge and (d) optimum A uniform distribution where all sources are of equal amplitude that is relative amplitude is 1,1,1,1,1 gives maximum directivity or gain of 6.98dBi with 230 half power beam width. But in this case the side lobe levels are more. First side lobe is nearly 24% of main lobe or side lobe level is -12dB To reduce the side lobe level Johm Stone Stone proposed the amplitudes of sources to be proportional to

the coefficients of binomial series .Accordingly in case of 5 source array relative amplitudes will be 1.4.6.4.1. This is called binomial array. There will be no minor lobes but half power beam width is 310 while gain is 5.63dBi and side lobe level is -∞dB.

In case of edge distribution only end sources are excited . For 5 element array the relative amplitudes will be 1,0,0,0,1.The main lobe half power beam width is 150but minor lobes also have same amplitude as main lobe . The directivity is 3.02dBi and side lobe level is -0dB that is same as main beam. An ideal array would be one that provides sharp beam width like edge array and zero side lobe level like bionomail array.Applying Doplh –

Tchebysceff distribution polynomial coefficents the realtive amplitudes for optimum arraycan be evaluated. In this case if side lobe level is specified BWFN is minimized. If BWFN is specified the side lobe level is minimized.For a side lobe level 20dB below main lobe the relative amplitudes rae 1,1.6,1.9,1.6,1. The gain will be 6.72 dBi, beam width between half power points is 270. Illustrative examples

1. A linear broad side array of four equal isotropic sources with spacing λ/3 is arranged . find the directivity and BW.

2. A BSA consists of 4 identical half wave dipoles spaced 50cm apart. Wave length is 0.1m.Each element carries rf current of equal magnitude of 0.25 A and same phase. Calculate power radiated and HPBW of major lobe. 3. Find length and BWFN for broad side and end fire arrays with directive gain 15. 4. Calculate the directivity in dB for broad side as well as end fire array consisting of 8 isotropic elements separated by λ/4 distance. What will be the directivity if it is an end fire array with increased directivity 5. An end fire array with elements spaced λ/2 and with axes of elements at right angles to line of array is required to have directivity of 36. Determine array length and width of major lobe. 6. A broad side array of 8 isotropic radiators separated by λ/2 is placed along z axis. Find the directions of maximum, nulls and side lobe maxima. 7. A linear array has 12 isotropic sources with λ/4 spacing between elements and successive phase difference of 900 . Find HPBW, Directivity, Beam solid angle and effective aperture.

50

Antenna measurements The basic parameters to describe an antenna:

1. Far field patterns (amplitude and phase) 2. Gain and directivity 3. Polarization 4. Efficiency 5. Input impedance 6. Current distribution

The ideal condition for measuring the far-field pattern and antenna gain is its illumination by a uniform plane wave. This is a wave, which has a plane wave front with the field vectors being constant across it.. In practice, antennas generate far fields in 3-D space which are closely approximated by spherical wave fronts when the observation point is sufficiently far from the source. Also, at large distances from the source antenna, the curvature of the phase front is small at the aperture of the test antenna and it is well approximated by a uniform plane wave. the antenna far-field characteristics must be measured at a sufficiently large distance between the source antenna and the AUT. This distance must be larger than the sum of the inner limits of the far zones of both antennas. The above requirement leads to a major difficulty in antenna measurements – large separation distances are required between the source antenna and the AUT. The larger the AUT, the larger the measurement site. While the size of the site may not be a problem, securing its reflection-free, noise-free, and EM interference-free environment is extremely difficult. Special attention must be paid to minimizing unwanted reflections from nearby objects (equipment, personnel, buildings), from the ground or the walls of the site. This makes the open sites for antenna measurements (open ranges) a rare commodity since they have to provide free-space propagation. Such ideal conditions are found only in unpopulated (desert) areas of predominantly flat terrain. The other alternative is offered by indoor chambers (anechoic chambers), which minimize reflections by special wall lining with RF/microwave absorbing material. They are much preferred to open ranges because of their controlled environment. Unfortunately, the anechoic chambers are very expensive and often they cannot accommodate large antennas. Thus summary of the challenges in antenna measurements: · affected by unwanted reflections; · often require too large separation distances; · very complicated when a whole antenna system (e.g., on-craft mounted antenna) is to be measured; · outdoor sites have uncontrollable EM environment, which, besides all, depends on the weather; · indoor sites cannot accommodate large antenna systems; · the instrumentation is expensive. Most antennas are measured in their receiving mode.

• According to reciprocity principle the antenna under test(AUT)can act as either transmitting or receiving since the transmitting and receiving patterns are same and power flow is same in either way. • The ideal condition for measuring the far-field pattern and antenna gain is its illumination by a uniform plane wave. • To satisfy far region criteria the distance between transmitter and receiver should be r > 2D2/λ • Maximum phase error from an ideal plane wave : 22.50 • The largest phase difference between the spherical wave and the plane wave appears at the edges of the AUT, which corresponds to the difference in the wave paths δ . • This must fulfil the requirement: kδ≤π/ 8. • The antenna measurement equipment includes: antenna ranges, antenna positioners, pattern recorders, vector network analyzers, signal generators, antenna gain standards, etc. Later on, sophisticated computer systems were developed to provide automated control of pattern measurements as well as fast calculations related to antenna directivity, 2-D to 3-D pattern conversion, near- to-far field transformations (in compact antenna ranges), etc.

The antenna measurement sites are called antenna ranges (AR). They can be categorized as outdoor ranges and indoor ranges (anechoic chambers). According to the principle of measurement, they can be also categorized as reflection ranges, free-space ranges, and compact ranges

• The reflection ranges are designed so that the direct and ground reflected waves add constructively and form a uniform wave front in the region of the test antenna.

51

• Reflection ranges are usually of the outdoor type. They are used to measure antennas of moderately broad patterns operating in the UHF frequency bands of 500 MHz to 1000 MHz. • The free-space ranges are designed to provide reflection-free propagation of the EM waves. • Outdoor free-space ranges: elevated ranges and slant ranges. • Indoor ranges: anechoic chambers, near-field ranges.

Elevated ranges • Elevated ranges are used to test physically large antennas. • Both antennas (the transmitting and the receiving) are mounted on high towers or buildings. The terrain beneath is smooth. The transmitting antenna has very low side lobe level. The line-of-sight is always clear.

slant ranges • are more compact than the elevated ranges. • The test antenna is mounted at a fixed height on a non-conducting tower while the source antenna is mounted near the ground. The first null is pointed toward ground to suppress the reflection..

Anechoic chambers • Anechoic chamber are mostly utilized in the microwave region. • provide convenience and controlled EM environment, an all-weather capability and security. • Inner surface are covered with special RF/ microwave absorbers.

Anechoic chambers are of two types: rectangular chambers and tapered chambers • The design of both chamber types is based on the principles of geometrical optics. The goal is to minimize the amplitude and phase ripples in the test zone (the quiet zone), which are due to the imperfect absorption by the wall lining. The tapered chamber has the advantage of tuning by moving the source antenna closer to (at higher frequencies) or further from (at lower frequencies) the apex of the taper. Thus, the reflected rays are adjusted to produce nearly constructive interference with the direct rays at the test location

Antenna pattern measurements:

The radiation pattern or antenna pattern is the graphical representation of the radiation properties of the antenna as a function of space. It describes radiation of energy from antenna into space (or how antenna receives energy from space).The antenna pattern is actually three-dimensional. It is common to describe this 3D pattern with two planar principal plane patterns namely azimuth plane pattern and elevation plane pattern. The term azimuth refers to horizontal and elevation refers to vertical. Considering Antenna Measurement Coordinate System as shown in figure -the x-y plane (θ = 90 deg) is the azimuth plane. The azimuth plane pattern is obtained when

the measurement is made traversing the entire x-y plane around the antenna under test. The elevation plane is a plane orthogonal to the x-y plane, say the y-z plane (φ = 90 deg). The elevation plane pattern is made traversing the entire y-z plane around the antenna under test.

For the component EФ (a) E-plane pattern E Ф(θ = 90°, Ф) and (b) H-plane pattern E Φ = (θ, Φ = 90°) For the component Eθ (a) Eθ (θ=90°, Φ) -H-plane pattern. (b) Eθ(θ, Ф= 90°) -E-plane pattern. For circularly or elliptically polarized antennas, these four patterns should be measured. Antenna pattern measurement and directivity estimation 1.The primary antenna is fixed, and the secondary antenna is equipped for free rotation around the primary antenna in circular fashion. The field strength and direction of secondary antenna with respect to primary is noted at different points on

52

the circular path of secondary antenna. Then, the required antenna pattern plot is made. 2. Then the field strength is recorded at different point on the vertical rotation path.. Then, with recorded values, plot is made. The half power beam widths θ1in E plane and θ2 in H plane in degrees are determined from radiation pattern. The directivity is computed from the two principal plane patterns .Then directivity D is calculated from the relation D=(41253)/(θ1θ2) .The Draw back of this method is low accuracy Measurement of Gain

Gain is the most important figure-of-merit parameter of an antenna. There are two methods: i absolute-gain ii gain-transfer ( or gain-comparison) Absolute-gain measurements : The methods are based on Friis transmission formula. There are two basic methods: two-antenna method and three-antenna method

Two antenna method Two identical test antennas with gain G are used, one as transmitting and the other as receiving Antenna. Assuming that the antennas are well matched in terms of impedance and polarization. Gain is calculated using Friss formula G=[(4πR/λ)]√(Pr/Pt) Three-antenna method If the two antennas are not identical, three antennas must be employed and three measurement must be made with all three combinations: ANT 1,2, ANT2,3 & ANT1,3 and three equations are formed.

With Antenna 1Tx and 2 Rx

Antenna 2 Tx and 3 Rx

Antenna 1 Tx and 3 Rx

Solving these the gains of three antennas can be evaluated.

G1=[(A+B-C)/2] and G2=[(A-B+C)/2] and G3=[(-A+B+C)/2] Gain-Transfer (Gain-Comparison) measurements This technique needs apart from transmitting and test antennas one more standard antenna whose gain G S is known. Two sets of measurements are performed. The test antenna is used as receiving antenna, and the received power PT is recorded.The geometrical arrangement is kept intact and the transmitted power is maintained same and the test antenna is replaced by standard gain antenna and its received power Ps is measured. Using the relation GT dB= GS dB + 10 log 10(PT/PS ) the gain of test antenna G T can be calculated. If the test antenna is circularly or elliptically polarized, two orthogonal linearly polarized gain standards must be used in order to obtain the partial gains corresponding to each linearly polarized component. The total gain of the test antenna is GT dB = 10 log10 (GTV + GTH ) GTV : the partial gain with respect to vertical polarization GTH : the partial gain with respect to horizontal polarization

53

UNIT-V: Wave propagation – I , Wave propagation – II

Introduction, definitions, categorizations and general classifications, different modes of wave propagation, Ray/Mode concepts GWP- qualitative treatment: introduction, plane earth reflections, space and surface waves, wave tilt and curved earth reflections. Space wave propagation-introduction ,Fundamental equation for free space propagation, Basic transmission losses ,field strength variation with distance and height, Effect of earth’s curvature, absorption, Super refraction, M curves and duct propagation, Scattering phenomena, Tropospheric propagation, Sky Wave Propagation- introduction, structure of ionosphere,Reflection and Refraction of sky waves by ionosphere,Ray path, Critical frequency, MUF, LUF,OF, Virtual height and Skip distance,

Relation between MUF and Skip distance. Multiple hop propagation

WAVE PROPAGATION-I Introduction : The most important application of radio waves is in long distance communication. Radio wave arbitrarily refers to em waves in the frequency range 0.001 to 1016Hz. VLF 3-30KHz waves used in submarines. LF 30-300KHz in beacons, MF 300-3000KHz in AM broadcast,HF 3-30 MHz in shortwave broadcast, VHF 30-300MHz in FM,TV;UHF 300-3000MHz in TV LAN, cellular, GPS; SHF 3-30GHz in Radar, GSO satellites, data and EHF 30-300GHz in Radar, automotive ,data. The radio waves from the transmitting antenna reach the receiving antenna following any of the following modes of propagation depending upon several factors like frequency of operation, distance between transmitting and receiving antennas etc. 1. Ground wave or surface wave propagation. (Upto 2 MHz) 2. Sky wave or ionospheric propagation.(2MHz-30MHz) 3. Space wave propagation.(30MHz-3GHz) The space wave dominates at large distances above earth and surface waves are stronger nearer to earth’s surface. In addition to these, special propagation types are: Tropospheric scatter ,Duct propagation ,Stationary satellite communication. a)Relation between E at any point & power transmitted Pt. Let Ptwatts be the power radiated into free space from transmitter. ER v/m be the electric field intensity at any point at distance R from the transmitter. The Poynting vector or the power density is given by

HxES

watts/m2

For a uniform plane wave the E and H are related by H

E

where is the intrinsic impedance of medium =120 or 377 ohms for free space.

The average poynting vector at distance R from transmitter is 2

t

RR4

PS

=

2RE =

120

E2R

Therefore 2

t2R

R4

x120PE

=

2

t

R

30P and

R

30PE

tR volts/meter.

ER is the rms value of electric field intensity.

If transmitting antenna has a gain Gt, then R

30ER

ttGP volts/meter…

In case of half wave antenna it has a gain of 1.64 and ER= mvR

Pt/7

b)Relation between E at any point & power radiated Pt by earthed vertical antenna

In case of linear antennas the current distribution is either triangular or sinusoidal and in such case one has to

54

use effective length .Consider a grounded vertical antenna of physical length L or effective length L e. Due to

image effect apparent effective length will be 2 Le. Power radiated by antenna is W=(1/2) Im2 Rr=Irms2 Rr

Rr the radiation resistance for short dipole with uniform current is 2

2280

L

rR

Using the apparent effective length the radiation resistance will be 2

22320

2

22280

e

Le

L

rR

But since the vertical grounded antenna radiates through one hemi-sphere Power radiated will be half as that

of dipole and

2rms

I

22160

e

radP

. . . . (1)

The Electric field intensity due to short dipole is give by R

rmsI 60

rmsE

R

mI 60

mE

or

For Vertical grounded antenna using apparent effective length R

rmsI 120

rmsE

e

L

….. (2)

From (1) and (2)

mv/m 300rms

E then,1KmR distance and

Kw 1 ispower radiated theIf v/m.90

E Therefore

90

2R

2R 2

22rms

I 2120

2rms

I

22160

2

R

radP

rms

eL

eL

rmsE

radP

GROUND WAVE OR SURFACE WAVE PROPAGATION In ground wave propagation the electromagnetic wave is guided along the surface of the earth. Surface wave permits the propagation of electromagnetic wave around the curvature of the earth. This mode of propagation exist when the transmitting and receiving antennas are close to the surface of earth and is supported at its lower edge by the presence of the ground. is of practical importance at broadcast and lower frequencies i.e. for medium waves, long waves and very long waves. used invariably in local broadcasting. All the broadcast signals received during daytime are due to ground wave propagation. When the surface wave glides over the surface of the earth energy is abstracted from the surface wave to supply the losses in the earth. The surface wave looses some of its energy by absorption. Energy lost so, however, is recovered to a certain extent, by the energy diffracted downward from the upper portion of the wave front present some what above the immediate surface of the earth. The ground wave suffers varying amount of attenuation while propagating along the curvature of the earth, depending upon frequency, surface irregularities, permittivity and conductivity the mode of propagation is suitable for low and medium frequencies up to 2 MHz only. Besides ground attenuation, there is still another way in which surface wave is attenuated i.e. due to diffraction and tilt in the wave front. As the wave progress over the curvature of the earth, the wave front starts gradually tilting more and more. This increase in the tilt of wave causes short circuit of the electric field component and hence the field strength goes on reducing.

55

Ultimately, at some appreciable distance in wavelength from the transmitting antenna, the surface wave dies because of the losses mentioned above.

Earth surface is considered flat for distances 3/1

MHzf

80d kms. Beyond this distance effect of earth’s curvature

is to be taken to into account. The wave propagation is divided into two cases namely propagation over (i) flat earth and (ii) spherical earth. The reflection coefficient of earth depends on surface roughness factor given by Roughness factor R=(4πσisinθ/λ) where σiis standard deviation of surface irregularity relative to mean surface, V is angle of incidence. When R‹ 0.1 surface is considered smooth and when R› 10 it is taken as rough. Reflections from rough surface cause scattering of waves and amplitude of reflected wave reduces. When wave is incident at near grazing angle on smooth earth reflection coefficient is 1at an angle 1800 for both vertical and horizontal polarizations. According to Somerfeld analysis ground wave field strength for flat earth at distance d from transmitter is E=(AE0/d) V/m; E0 is the field strength at unit distance from transmitter and will be 300 mV/m for a transmitted power of 1Kw at a distance of 1Km. For any other power PtKw E0=300(√Pt) mV/m. The factor A is attenuation factor which depends on frequency f,dielectric constant and conductivity of earth. A is expressed in terms of two auxiliary parameters numerical distance p and phase constant b. The relations are For vertical polarized wave: p=(π/x)(d/λ) cos b and tan b=(εr+1)/x For horizontal polarization: p=(π x d)/(λcos b1) and tan b1=(εr-1)/x X=(1.8x1012σ)/f(Hz), where σ is conductivity of earth in mho/cm A=[(2+0.3p)/(2+p+0.6p2)] –sin b (√p/2) e-(5/8)p For p<1: the value of A slightly differ from unity,while for p> 1: A decreases rapidly and for p>10: A varies inversely as d2 Earth offers resistive impedance for vertical polarized waves when b=0 and for horizontal polarized waves when b=1800.It offers capacitive reactance for both polarizations when b=900. The conductivity of earth varies widely from 10 for cities, 20 for rocky soil, 100 for fresh water and 45000 for sea water. The relative permittivity εr values are 5 for cities, 10 for rocky soil, 80 for fresh water and 81 for sea water. At broadcast and lower frequencies earth is regarded as pure resistance. At high frequencies 10 MHz and above it is considered as capacitive reactance. Curved earth reflection: Bulge of earth prevents surface wave reaching receiver by straight line path. The surface wave reaches receiver by diffraction around earth or by refraction in lower atmosphere above the earth. In space wave propagation also the wave gets reflected from curved surface instead of flat surface. As a result the wave will be more diverged and will be weaker at receiver. The effective antenna heights will be less than actual antenna height .The effect of curved earth in space wave propagation is studied in next topic.

56

Space wave propagation-introduction ,Fundamental equation for free space propagation, Basic transmission losses ,field strength variation with distance and height, Effect of earth’s curvature, absorption, Super refraction, M curves and duct propagation, Scattering phenomena, Tropospheric propagation Space wave Propagation : The space wave propagation of practical importance atVHF, UHF bands and microwave frequencies (between to 30 MHz to 300 MHz or 3 G Hz). The major use is communication between a fixed base station and several mobile units located on vehicles, ships or air craft. Typical applications are in control tower to air craft communication at air ports, ship control within harbour, police department. Also television, radar, frequency modulation schemes utilize this mode of propagation. In this mode of propagation, electromagnetic waves from the transmitting antenna reach the receiving antenna either directly or after reflections from ground in the earth's troposphere region. Troposphere is that portion of the atmosphere, which extends up to 16 km from the earth surface. The composition of Troposphere remains approximately the same as at the surface of the earth. Although in the troposphere, the percentage of the gas components remains almost constant with increase of height, the water vapor decrease with height. The other important property of the troposphere is that temperature decreases with increases in height and falls to a minimum. After the top of the troposphere, tropopause starts and ends at the beginning of stratopause or region of calm. Above certain critical height (tropopause) the temperature remains uniform and begins to increase afterwards. Space wave consists, of at least two components e.g. direct component and indirect or ground reflected component. Both waves (direct and indirect) leave the transmitting antenna atthe same time with the same phase but may reach the receiving antenna either in phase or out of phase, because the two waves travel along different length paths. The strength, of the resultant waves, thus, at the receiving point may be stronger or weaker than the direct path alone depending upon whether the two waves are adding or opposing in phase. At receiving point the signal strength is the vector addition of direct and indirect waves. Space waves propagate through troposphere and hence this is also called as Tropospheric propagation. Space wave propagation is used mainly in VHF, and higher frequency range because at these frequencies sky wave and ground wave propagation both fail. Beyond 30 MHz sky Wave fails as the wavelength becomes too shorts to be reflected from the ionosphere and ground waves propagating close to the antenna only, as attenuation is very high. Therefore just after few hundred feet ground waves die due to attenuation and wave tilt. Space wave propagation is also called as line of sight propagation because at VHF, UHF and microwave frequencies, this mode of propagation is limited to the line of sight distance and is also limited by the curvature of the earth. Although in actual practice space waves propagate even slightly beyond the line of sight distance due to refraction in the atmosphere. In line of sight distance transmitting antenna and receiving antenna can usually "see" each other. Increasing the heights of transmitting and receiving antennas can increase the line of sight distance that is range of communication. The curvature of the earth and the height of the transmitting and receiving antennas determine the maximum range of communication through direct waves. The line of sight distance has now been extended by what is known as Space Communication or Satellite Communication, which has facilitated transoceanic propagation of microwaves with the potentiality of large bandwidth. Space communication means radio traffic between a ground station and satellite, between satellites, and also between ground stations. Fundamental Equation for free space propagation-Friss transmission formula The free space propagation is governed by Friis transmission formula and is derived below

Figure -Free space communication link The two antennas shown in Fig. 1 are part of a free-space communication link, with the separation between the antennas, R, being large enough

57

for each antenna to be in the free-field region of the other. The transmitting and receiving antennas have

effective areas At, and Ar and radiation efficiencies t and r, respectively. Assume that both antennas are impedance matched to their respective transmission lines. The two antennas are oriented such that the peak of the radiation pattern of each antenna points in the direction of the other. The average power density at receiver for maximum reception is

Sr= Smax= Gt24 R

Pt

=

24 R

PD ttt

= 22R

PA ttt

Power intercepted by the receiving antenna with an effective area Ar

Pint = SrAr = 22R

PAA trtt

The receiving power Pr delivered to the receiver is equal to the intercepted power Pint multiplied by the

radiation efficiency of the receiving antenna, r. orPr = rPint.

Therefore 22R

AA

P

P rtrt

t

r

=

2

4

RGG rt

and

tr

2

tr GGR4

PP

…… is the Friis transmission formula.

Pr = power received. Gt=gain of transmitting antenna, Gr = gain of receiving antenna, R= distance between

transmitter and receiver. wavelength of signal. Free space propagation loss As the signal propagates there will be loss due to spreading of the wave outward from the source. Relation between transmitted and received power of space wave

tr

28

tr

2

tr

2

t

r GGR f 4

103GG

R4 fGG

R4P

P

xc

Or Kmsin R and MHzin is f when GGR f 4

3.0

P

Ptr

2

t

r

Taking log on both sides

tr

t

r

tr

tr

tr

t

r

logGGloglog2log225.310P

Plog 10

logGGloglog2log225.3

logGGloglog2log29943.2041.10457.1

logGGloglog2log2log24log23.0log2P

Plog

Rf

Rf

Rf

Rf

The equation can be expressed as

dBdBdB

dB

flog 20 Rlog 2032.5GGPt

P1010RT

r

The freespcae propagation loss is given by the last term Lf (dB) = [32.5 + 20 log R + 20 log f] dB In the above equations R is the distance between transmitter and receiver in kilometers. f is frequency in M Hz. GT gain of Tx antenna GR gain of Rx antenna At microwave frequencies, the loss will be greater because of atmospheric absorption.

58

Radio Horizon: The radio horizon of an antenna is related to its

height by the relation d=4.12 h where d is distance from antenna in kilometers and h is height of antenna in meters. Range of space wave propagation will be the sum of radio horizon distances of transmitting and receiving antennas and is given by

Kms )(h )(h4.12rt

mm where ht and hr are heights of

transmitting and receiving antennas respectively in meters. Proof: With Tx antenna of height h1 and Rx antenna of height h2the range or LOS distance d0 is given by

Kms )(h )(h3.57d

get wegsimplifyin and meters6.37x10aearth of radius Using

22

rto

6

2222'

2

'

1

mm

ahahaahaahdddrtrto

When the distance d between Tx and Rx is less than do, the total field at Rx is sum of direct ray field strength+ reflected ray field strength. In working propagation problems it is convenient to assume straight line ray path and compensate for curvature of earth using effective radius of earth r’=ka k=R/(R-a)=1/[1+a(dn/dh)] where R= (-1)/(dn/dh) and dn/dh is variation of refractive index with height Substituting a=6370,000 meters and (dn/dh)=-0.04x10-6/m, for standard atmosphere we get k=4/3.

Hence we get LOS distance = Kms )(h )(h4.12Kms )(h )(h3.573

4rtrt

mmmm

However considering spherical earth the reflection at convex surface will result in divergence of reflected ray path and hence will reduce power.

Example: Find radio horizon distance of a transmitting antenna of height 80meters and receiving antenna of height 40 meters. Find the maximum space wave communication distance possible using these two antennas.

Solution: Radio horizon of transmitting antenna dt=4.12 th =4.12 80 = 35.8 km

Radio horizon of receiving antenna dr= 4..12 rh =4.12 40 = 25.3 km

Range of communication = dt+ dr= 61.1 kms

Field strength of space wave: d12=d2+(ht-hr)2 and d22=d2+(ht+hr)2 d1=[ d2+(ht-hr)2]1/2=d[1+(ht-hr)/d2]1/2

≈d[1+(ht-hr)2/2d2]=d+[(ht-hr)2/2d] , similarly d2=d+[(ht+hr)2/2d] and path difference(d2-d1)=(2hthr/d) phase difference due to path difference α=(2π/λ) (2hthr/d) =4πhthr/λd radians Further considering perfect earth with reflection coefficient 1, the ground reflected wave will have additional phase difference of

1800 or radians.total phase difference Φ= +4 hthr/λd. If the field strength due to direct wave is E1

total field strength ER=E1+E1e-jΦ =E1(1+e-jΦ) =E1(1+cosΦ+j sinΦ)

ER= )2/cos(2)2/(cos42cos22sincos1 12

1122

1 EEEE

=2E1cos[π/2+(4πhthr/2λd)]=2E1sin(4πhthr/2λd)≈2E1(4πhthr/2λd)=E14πhthr/λd But E1=7(√P)/d where P is power radiated and d is distance between Tx and Rx Substituting and simplifying we get ER=[88(√P)hthr/(λd2)] v/m

Effects of curvature of earth: and field strength variation Due to curvature of earth the actual and effective heights of antennas differ. Reflected wave at receiver is

59

weak. This effect is less for moderate to large incident angles and more for small angles. At large distance, for small incidence angles resultant field at receiver is more than that if earth were flat. These two effects neutralize to some extent. Due to curvature there will be a change in number and location of maxima and minima. These locations depend on ht, hr, f and distance between Tx and Rx. Accordingly the field strength varies. Absorption: Rain attenuates very high frequency signals partly by absorption and partly by scattering. Attenuation is a function of λ, ε, raindrop diameter, drop concentration and losses due to scattering. Attenuation is more at λ=3 cm for heavy rains and at λ=1 cm for moderate rains. Attenuation due to snow is very small. Due to molecular interaction absorption of energy takes place at certain wave lengths due to water vapor and gases. Super refraction : M curves -Duct propagation: VHF, UHF and high frequency signals are neither reflected by ionosphere nor propagate along earth surface, but they undergo refraction in the troposphere( region 15 Kms from earth surface). In the troposphere with increase in height above ground air density decreases and refractive index increases. Normally the change in refractive index is linear and gradual. But under some conditions the refractive index decreases rapidly.In normal or standard atmosphere dielectric constant is assumed to decrease uniformly with height to a value 1where air density is essentially zero. When refracting conditions are different from normal, super refraction or duct propagation occurs. Between layers of air a duct is formed that guides e m waves.This happens nearer to the ground and within 30 meters. As a result radio waves are continuously refracted by the duct and reflected by ground. They are propagated around the curvature of earth for distances above 1000 km. This is called duct propagation. Atmospheric ducts are of the order of tens of meters and the duct propagation occurs mostly at UHF and microwave frequencies. In this case to explain super refraction and duct propagation concept of modified refractive index is used.Due to change of water vapour content with height of troposphere at high frequencies the effective refractive index varies with height.

The refractive index

T

WP

Tn r

480010

801 6 where T= absolute temperature of air, P= air pressure

in milli- bars, W= partial pressure of water humidity in milli –bars. Modified refractive index is defined as modified refractive index N=( n +h/a) Where n= actual refractive index, h =height above earth surface, a= radius of earth. Though N is close to unity its actual value is important .Differentiating the relation of modified refractive index with respect to h and multiplying by 106 we get

adh

dW

T

x

dh

dT

T

WP

Tdh

dP

Tx

adh

dnx

6

22

66 104800809600808010

110

dh

dN

The first term on RHS is always positive last term also is always positive. The 2nd and 3rd terms sign may be + or - depending on atmospheric conditions. For standard atmosphere they both are -ve with values such that (dN/dh) is positive and is equal to 0.118X10-6/m. Excess modified index or refractive modulus M is defined as M=(N-1)x106=(n-1+h/a)x106

The value of gradient (dM/dh) and its sign + or - depends on troposphere conditions. With change in atmospheric conditions (dT/dh) and (dW/dh) vary rapidly and some times (dM/dh) may become negative over a region close to sea surface resulting in surface duct and a little higher in atmosphere resulting in elevated duct. Duct is formed only when (dM/dh) is negative that is M decreases with increase in

60

Ground based duct Elevated duct

.

height h. From measurements if M is plotted against h that is h vs M we get M curves. When h-M curve has a negative slope rays entering with small angles are trapped between upper wall and lower wall of duct and oscillate. This is called super refraction. The signal of wavelengths above λc=0.084 hd3/2 cm (where hd is height of duct in meters) are trapped. The wave length where duct propagation ceases is given by λmax=2.5 hd√(∆Mx10-6) Example: Calculate maximum frequency which can be transmitted by a duct of height 1000m if total change in M is of the order 0.036. λmax=2.5 x1000x√(0.036x10-6)=0.475, fmax= (3x108)/0.475= 631MHz Scattering phenomena The troposphere and ionosphere are in continuous state of turbulence. This causes local variation of refractive index of atmosphere. Waves passing through such regions get scattered. It has been established that it is possible to achieve a very reliable communication much beyond LOS distance by using high power transmitter and high gain antennas . Scatter propagation is of practical importance at VHF, UHF and microwaves. Reliable scatter propagation is possible in the VHF and UHF band. The name scatter propagation (beyond the horizon propagation) is given to it due to mechanism involved in the phenomenon. There are two different theories involved in the interpretation of scattering. Antennas must be of high gain and must be oriented such that their beams overlap in a region where forward scatter takes place

Turbulent scattering theory : According to this there is turbulent variation of refractive index with height that causes scattering. Layer reflection theory: There are large number of randomly distributed layers with different refractive indices resulting in scattering. Signals of frequency 500 MHz onwards get scattered in troposphere and maximum range is 300-600 Kms. Signals in the range 30-50 MHz get scattered from the Lower E layer of the ionosphere and has maximum range of 2000 Kms. In case of free space propagation received power is given by Friis

formula tr

2

tr GGR4

PP

In scatter propagation the received power can be calculated using the relation

volumescattering theis vandsection -cross scattering effective is σ(θ)

; σ(θ)vπR

2F and

factor n attenuatio theis F wheret

Gr

G2

R 4

λ

tFP

rP F '

rP

llustrative examples 1.Two space craft are separated by 100Mm. each has a n antenna with D=1000 operating at 2.5 GHz. If craft A receiver requires 20dB over 1 pW find the transmitter power of craft B.

61

2.What is the maximum power received at a distance of 0.5 km over free space 1 GHz circuit consisting of transmitting antenna with input 150 W,gain 25dBi and receiving antenna with gain 20dBi. 2.A transmitting aerial has Rr=50 ohms and power gain of 20dB in direction of receiver 64km apart. With aerial supplied with a current of 0.5 Afind intensity in W/m2 and electric field strength at receiver. If receiving aerial has E=1.5and Rr=75 ohmsfind maximum power available to receiver and overall transmission loss in dB. 3. Determine the height of receiving antenna to obtain maximum transmission distance of 48.7 km from transmitting antenna of 40 meter height. Sky Wave Propagation- introduction, structure of ionosphere,Reflection and Refraction of sky waves by ionosphere,Ray path, Critical frequency, MUF, LUF,OF, Virtual height and Skip distance, Relation between MUF and Skip distance. Multiple hop propagation

Sky waves or ionospheric wave propagation The sky wave propagation is of practical importance at medium and high frequencies for very long distance radio communications. In this mode of propagation electromagnetic waves reach the receiving point after reflection from the ionized region in the upper atmosphere called ionosphere. The ionosphere is situated between 50 km to 400 km above earth surface. The ionosphere acts like a reflecting surface and is ableto reflect back the electromagnetic waves of frequencies between 2 to 30 MHz. Electromagnetic waves of frequency more than 30 MHz penetrate through the ionosphere and are not reflected back. This mode of propagation is also called as 'Short wave propagation'. Further, since sky wave propagation takes place after reflection from the ionosphere, it is also called as ionospheric propagation. Since long distance point to point communication is possible with sky wave propagation it is also called point to point communication. The sky waves are reflected from some region of the ionized layers of ionosphere and return back to earth either in single hop or in multiple-hops of reflections. Thus for a sky wave of suitable frequency it is possible to cover any distance round the earth. The signals received due to sky wave propagation are, however, subjected to fading due to which the signal strength varies with time. It is because sky waves follows different paths in the ionosphere and at receiving point, the received signal is the vector sum of all. So fading occurs which can be minimized by using diversity reception technique. The structure of ionosphere The upper part of the earth's atmosphere absorbs large quantities of radiant energy from the sun. This not

only heats the atmosphere but also produces ionization .The ionized region consists of free electrons, positive ions and negative ions. The most important ionizing agents are ultra-

violet radiation (UV), , rays, cosmic rays and meteors. These ions can easily be effected under electric forces. Further, the ions, electrons and atoms in a gas are constantly in motion so frequent collisions occur between them and consequently the process of recombination continued all the time. Thus once a molecule is ionized, does not remain ionized indefinitely. The time of recombination depends on many factors and one factor is the average distance between the particles of the gas. In the lower part of the earth atmosphere collisions are very frequent and

hence air molecules do not remain ionized for a longer time. Besides the ultraviolet rays from the sun are greatly absorbed by the upper parts of the atmosphere and so there is relatively little ionization in the lower part of the earth's atmosphere and very little ionization below about 50 km. On the other hand, above the height of 400 km the air particles present are so few that the density of ionization is again very low. Considerable ionization exists between 50 km to 400km. This region has most influence on the sky wave propagation. Sky waves of different frequencies are found to return to earth from different heights. This means that ionosphere consists of several layers. The number of layers, their heights and the amount of sky wave that can be bent by them, will vary from day to day, month to month and year to year. For each layer there is a critical frequency, above which vertically upward transmitted radio wave, will not return back to the earth but will penetrate it. There are four principal layers called D,E, F1, and F2 layers as shown in Fig. The D layer lies between 50 to 90 km and is responsible for the daytime attenuation of high frequencies waves. This layer refracts signals of low frequencies . Due to recombination of ions D layer disappears after sunset. E layer also known as Kennely - Heaviside layer is generally found at the 110 km but may vary between 90 km to 140 km. The ionisation of this layer is weak and the layer may disappear at night. The E layer reflects some high frequency waves in day time . Sometimes along with E layer there is a sporadic E layer Es .It persists at

62

night also. It sometimes permits good reception. The F1 layer exists at a height of 150 to 240 km. F2 layer has typical height range of 250-400 km with little seasonal variations. During night the F1 and F2 layers combine and form one layer called F layer. The disappearance of D, E layers and combination of the two F layers is a reason for better high frequency reception at night. Reflection and refraction of sky waves by ionosphere In an ionized medium having free electrons and ions when the radio wave passes through, it sets these charged particles in motion. Since the mass of the ions are much heavier than the electrons so their motions are negligibly small and neglected for all practical purposes. The electric field of radio waves set electrons of the ionosphere in motion. These electrons vibrate simultaneously along paths parallel to the electric field of the radio waves and the vibrating electrons represent an a.c. current proportional in the velocity of vibration. The actual current flowing through a volume of the space in the ionosphere consists of two components;

the usual capacitive current, which leads the voltage by 90 and the electron current, which lags the voltage by

90 and opposes the capacitive current. Thus free electrons in space decrease the total current. The dielectric constant of the space is also reduced below the value that would be in the absence of electrons. The reduction in the dielectric constant due to presence of the electrons in the ionosphere causes the path of radio waves to bent towards earth (refraction from high electron density to lower electron density). The dielectric constant is given by

2mo

2Ne1

r

where N = electron density of the layer , m = Electron mass = 9.11x 10-31 Kg, e = Electron charge = 1.6x 10-19 C;

= Angular frequency of waves rad/sec, o = 8.854 10-12 F/m

The angular velocity of the wave can have a value that makes r equal to zero, and is termed plasma

angular velocity, p. From the above equation is seen that for r to be zero

o

mpfor

22

2Ne2m

o

2Ne2p

.

Putting in the numerical values for the constants, we get N9 f p and

the dielectric constant can be rewritten as 2

2p

rf

f -1 =

2f

81N- 1

So the index of refraction of ionosphere 2

2i

f

N 81 - 1 n .

The equation shows that ni cannot be greater than 1 since N and f are always positive. • Real values of refractive index of the ionosphere is always less that unity and the deviation of ni from

unity becomes greater, if the electron density is higher and frequency is lower. • If f2< 81N, the refractive index becomes imaginary which means under such condition the radio waves

are attenuated at this frequency and the ionosphere is not able to transmit or bend the radio waves.

• As electron density N increases the refractive index ni decreases and when 1f

N 81

2 ,

ni=0 and the frequency at this point is called critical frequency fc. • From an ionosphere layer signal of frequency f ‹fc will be reflected back irrespective of the incident angle.

Signal of frequency f ›fc will return back only when the angle of incidence θi satisfies the relation ni= sinθi. Critical frequency : is the highest-frequency wave that will be reflected from a given layer a vertical incidence

and is determined by the maximum electron density of that layer. It and is given by maxc N9 f

The bending of radio waves by the ionosphere is governed

by Snell's law. The angle of incidence i and refraction r at any

point in ionosphere is given by v

c

sin

sin n

pr

i i

where vp is

phase velocity of wave in ionosphere and c velocity in free

63

space.[note ni= r and vp=r00

c11

r

The phase velocity vp at any given height can be determined by application of Snell's law of refraction.When a

wave enters an ionized layer at an oblique angle of incidence i, it follows a curved ray path as shown in fig.

At the apex of the path, r = 90, and therefore

2

2p

i2

f

f - 1 sin or ip sec f f . secant law.

MUF , Optimum frequency and lowest usable frequency The highest frequency that can be used for sky wave communication between two given points for angle of incidence θi other than vertical is known as the maximum usable frequency (MUF) of a layer . It is related to

the critical frequency of the layer by MUF = fc sec i

For sky wave to return to earth angle of refraction r = 90.

With N=Nmax, f will be fMUF. Using fc2=81Nmax the relation f

81N-1

sin

sin n

2

r

i i

will become

ic

i

c

MUF

iiii

ff

sec cos

f and

cossin1f

for

f

f-1sinor

f

f-1sin n 2

MUF

c

2

MUF

c2

2

MUF

c

i

Maximum F MUF = 3.6 fc that corresponds to incident angle of 740 Optimum working frequency : The frequency where optimum return of wave energy is present is known as the optimum working frequency (OWF) and is normally used for ionospheric transmission . It is chosen to be about 15% less than the MUF. Lowest usable frequency is the frequency below which the entire power gets absorbed Virtual height: In ionosphere as the wave is refracted from a layer, it is bent down gradually rather

sharply. The actual path of the wave in the ionized layer TACR is a curve and is due to the refraction of the wave. Since it is more convenient to think of the wave being reflected rather than refracted, the path can be assumed to be straight lines TB and RB as shown in figure. The height OB is called the virtual height of the ionized layer, as it is not the true height. The true height is the height shown in figure. The virtual height is always greater than the actual height. If the virtual height of layer is known, then it is easy

to calculate the angle of incidence required for the wave to return to earth at a desired point. The Virtual height of an ionospheric layer may be defined as the height to which a short pulse of energy sent vertically upward and travelling with the speed of light would reach the receiving point taking the same two way travel time as does the actual reflected pulse from the layer. The virtual height has the greatest advantage of being easily measured, and it is very useful in transmission-path-calculations. For flat earth assumption and assuming that the ionospheric conditions are symmetrical for the incident and reflected waves, the transmission-path distance TR is .

tan

2

2

tanh

TRorTR

h

TO

BO

Measurement of virtual height is normally carried out by means of an instrument known as an Ionosonde. The basic method is to transmit vertically upward a pulse-modulated radio wave with pulse duration of about 150 microseconds. The reflected signal is received close to the transmission point, and the time T required for the round trip is measured. The virtual height is then h =cT/2 where c is speed of light

Skip distance Radio waves radiated horizontally from a transmitter near the earth's surface is quickly absorbed due to large

64

ground losses and hence only short distance communication is carried out by this horizontal radiation of ground or surface wave.Radio wave radiated at high angle may not be bent sufficiently at the ionospheric layers to earth at all and hence escapes rather penetrates the layer, see fig. Between the distance at which surface wave becomes negligible and the distance at which the first wave returns to earth from the ionospheric layer, there is a zone, which is not covered by any wave (i.e. neither ground nor sky).This is called skip zone or area and the distance across it is the "skip distance". Although,it is more usual to consider skip distance from the transmitter to the point where the first sky wave is received. Hence skip distance may be defined as the minimum distance from the transmitter at which a sky wave of given frequency is returned to earth by the ionosphere. Relation between MUF and skip distance (i)Thin layer and flat earth ( for distances upto 500 Kms)

1f

(2h)D 2

1f

gRearrangin 4

14

4

f

4

4

f

fcos ,

f

f-1sin n

,,90 MUFFor 4

2

4h

h cos

22

2

2

2

222

22

22

MUF

c2

2

MUF

c i

max

0

r222

2

c

MUFcMUF

c

MUF

ii

i

fand

h

Df

h

D

h

Dh

f

Dh

h

NNDh

h

DAB

BO

(ii) Thin layer curved earth ( for distances beyond 500 Kms) In the figure AC=D distance between transmitter and receiver, BE= h height of ionosphere layer, OA=OE=OC=a (radius of earth) From the geometrical relation angle=arc/radius , 2 = D/a or D=2a From the figure AT =a sin ,

OT = a cos ,

BT=OE+EB-OT=a+h-acos

AB=22AT BT

= cossin

222 aaha

Cos θi=BT/AB =

cosasin

cos a-ah

22

aah

Cos2θi=

cosasin

cos a-ah22

2

aah

=

2

MUF

c

f

f

The distance D will be maximum when .Curvature of

earth limits fMUF and skip distance. This limit is obtained when wave leaves transmitter at grazing angle ie angle OAB=900. Then cos =(OA/OB)=[a/(a+h)]≈[1+(h/a)]-1≈ (1-h/a);

since is very small and h/a is <<<1 for small angles

sin ≈

cos = 1-2 sin2( /2)=1-2 sin( /2) sin ( /2)=1- 2/2.

=(1-h/a) or 2=2h/a.

Since D=2aθ or D2=4a2 2 ; D2=8ah or ah 8D and h=(D2/8a),

65

From cos =1-(h/a) , substituting h=(D2/8a), and using for small values of angles, = sin = (D/2a)

=[1-(D2/8a2)] and Substituting for cos and simplifying

cosasin

cos a-ah22

2

aah

=2

MUF

c

f

f

we get

1f

f

8

Dh2D and

8

842

c

MUF

2

22

222

a

a

Dh

a

Dh

D

ff cMUF

Multi hop propagation: The transmission path distance is limited by curvature of earth and skip distance. When a wave originating from transmitter reaches the receiver in one go without touching ground it is called single hop propagation. Some times signals may reach receiver from different paths that is separate layers of ionosphere may contribute to the propagation. In such case link between transmitter and receiver

may be maintained in many ways like single hop single layer, single hop multi layer, multi hop single layer and multi hop multi layer schemes. The maximum distance covered by sky wave in single hop is 2000 Kms for E layer and 4000 Kms for F layer. Multi hop paths are occurring generally and provide coverage over earth semi circumference.

66

Special topics:(Ref wikepedia) Smart antennas –introduction- A smart antenna system consists of an antenna array, associated RF hardware, and a computer controller that changes the array pattern in response to the radio frequency environment, in order to improve the performance of a communication or radar system. Switched-beam antenna systems are the simplest form of smart antenna. By selecting among several different fixed phase shifts in the array feed, several fixed antenna patterns can be formed using the same array. The appropriate pattern is selected for any given set of conditions. An adaptive array controls its own pattern dynamically, using feedback to vary the phase and/or amplitude of the exciting current at each element to optimize the received signal The smart antenna system estimates the direction of arrival of the signal, using techniques such as MUSIC (Multiple Signal Classification), estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithms, Matrix Pencil method or one of their derivatives. They involve finding a spatial spectrum of the antenna/sensor array, and calculating the DOA from the peaks of this spectrum. These calculations are computationally intensive.Matrix Pencil is very efficient in case of real time systems, and under the correlated sources. Beamforming is the method used to create the radiation pattern of the antenna array by adding constructively the phases of the signals in the direction of the targets/mobiles desired, and nulling the pattern of the targets/mobiles that are undesired/interfering targets. This can be done with a simple FIR tapped delay line filter. The weights of the FIR filter may also be changed adaptively, and used to provide optimal beamforming, in the sense that it reduces the MMSE between the desired and actual beampattern formed. Typical algorithms are the steepest descent, and LMS algorithms Two of the main types of smart antennas include switched beam smart antennas and adaptive array smart antennas. Switched beam systems have several available fixed beam patterns. A decision is made as to which beam to access, at any given point in time, based upon the requirements of the system. Adaptive arrays allow the antenna to steer the beam to any direction of interest while simultaneously nulling interfering signals. Beamdirection can be estimated using the so-called direction-of-arrival (DOA) estimation methods. The technology of smart or adaptive antennas for mobile communications has received enormous interest worldwide in recent years. Base station antennas with a pattern that is not fixed, but adapts to the current radio conditions. The principle reason for introducing smart antennas is the possibility for a large increase in capacity: an increase of three times for TDMA systems and five times for CDMA systems has been reported. Other advantages : increased range and the potential to introduce new services. Major drawbacks : increased transceiver complexity and more complex radio resource management. Also read ENCYCLOPEDIA FOR ELECTRICAL ENGINEERING, JOHN WILEY PUBLISHING CO., 2000 Smart Antennas for Mobile Communications :A. J. Paulraj, D. Gesbert, C. Papadias :