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Random antenna notes
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mohammedhamza6174Copyright
© © All Rights Reserved
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/ 234
“en va CHAPTER
Antenna Basics
1.1 PRINCIPLES OF RADIATION
Antenna is a device used to feed the maximum power in the required direction or to
receive maximum power from the required direction. Antenna is required only for wireless
communication like mobile communication, broadcast systems, cellular phones, microwave
linking, satellite linking etc. The signal operation between transmitter and receiver is in
the form of electromagnetic waves. 4
Different antennas radiate maximum power in different directions depending upon
the shape, size and orientation of the system. The names are specified based upon the
shape and dimensions like, dipole, monopole, V antenna, loop antenna, Helical, parabolic;
horn antenna etc,
4-2 0-=
Dipole Monopole Loop antenna Helical antenna
Hom antenna Paraboloid
Figure 1.1
Antenna is basically constructed by extending a feeding terminal in a plane normal to
the power flow. Antenna to defined as a transmedia of power between atmosphere and the
feeding terminal. _
Antennas and Wave Propagation
Principle of Operation
The guided wave travelling along a transmission line continues to travel after the
transition region. The free space wave expands spherically in 3-dimensions. The transition
region between the transmission line and free space is called an antenna.
Transition
‘Transmission Fegion,
line 1
Free space wave
radiating in 3-dimensions
. Figure 1.2
The free space electromagnetic wave consists of field components E, and H, for a
‘wave propagating in a direction along z-axis. The space time relationship for a plane wave
re :
E, [zt] = E, sin [2nft~ Bz +9]
‘ = #,sin[ (1-2) +9]
o
27
where B=
>|8
Figure 1.3 Antenna Basics
v being the velocity of the wave.
2
H, [2 t] = Hy sin [oe (-2}+9]
Boundary sphere
‘Antenna region
Equatorial plane
(Transparent)
1 Antenna
'
1
Polar plane
(Opaque)
Figure 1.4
Most of the energy is reflected at the terminals along polar plane which acts like
opaque. Energy along equatorial plane continued to enter the outer region as though the
boundary acts like transparent. Usually the radiated power that is of interest and antenna
patterns are obtained from far field regions.
The basic parameters of an antenna system are:
1. Radiation pattern 7. Radiation resistance
2. Power density 8. Beam width
3, Radiation intensity 9, Band width
4, Directivity 10. Input impedance
5. Gain : 11. Polarization
6. Directive gain 12. Radiation efficiency
System performance depends upon the above parameters. The antenna design and
construction depends upon the specified parameters and specified applications.
1.2 BASIC ASPECTS - POWER DENSITY (P)
Power density or Poynting vector P is the power flow through unit area, the area is
being considered in a plane normal to the direction of power flow. fe A
4 Antennas and Wave Propagat,
@)
‘Areafzormal to the power flow
Figure 15
If E and H are the electric and magnetic field components existing in the plane
containing the area, the power density
P=ExH
[Pl = [E).|H].-sind since @= 90°,
= 2 wee (1)
The relation between E and H is
lH
je
which is the impedance of the medium through which the waves are propagated.
For free space propagations,
W2Omor377Q 0, (2)
Substituting (2) in (1) and considering only magnitude.
Er
. P= EW= oy =H W200 sveee (3)
The average value or rms value of power density is
1
Pe ERR ale at 4)
<<. Unit Area
‘, |
\
@)
Antenna a
System
1
Je Sphere
Figure 1.6 Antenna Basics 5
The power density at a distance from a source is defined as the total power radiated
through unit area measured on the surface of a sphere of radius equals to the distance
under consideration enclosing the source at the centre.
Power Theorem
The surface integral of power density covering the entire surface of a sphere with the
source at the centre results the total power radiated.
W = [[P.ds www (5)
Figure 1.7
The polar coordinates r, @, and @ are as shown along with their respective unit vectors
4 a, and a,, 0 plane refers to vertical plane and @ plane refers to horizontal plane.
:
|
8 Antennas and Wave Pg
“an,
Inverse Square Law
‘The wave front isa surface of the constant phase, The phase angle of » fiety
distance R is uy
Qn
=a (®)=BR
LS
Point Rs
source
Wave front Wavefront
(a) @)
2) (Py)
Figure LI
The phase of fields considered along the surface ofa sphere with source atthe con
Temains same as the distance from the source remains same,
Consider two wavefronts (A) and (B) as shown, Ifthe power densities along thes.
wave fronts are P, and P, respectively.
|
oar eer
» (Re)
mR
Power density is inversely proportional to the distance referred to as inverse square
Jaw. This law is applicable for any antenna assuming the velocity of the wave is same in all
directions.
1.4 RADIATION PATTERNS
1. Power patterns
Test antenna Receiving
: { ymeana
Rotating
table oo
Power
Meter (P)
Source
Figure 1.12 Antenna Basics» 9
A test antenna whose pattern is to be obtained is used as transmiiter mounted on a
2 .
rotating table, A receiving antenna is mounted at,a distance r> 2 where / is maximum
dimension of antenna system and 2 is the operating wavelength. The received power is
power ‘tensity (P) if the area through which the power is received is unit area.
Table 1.1 Main lobe
[oye PIP, 20 lox,,(P/P,)
o | Pp,
5 Side lobes _-/
10° |
: / iN
Back lobe
360°
Figure 1.13
A plot of P w/s @ (vertical plane) or (horizontal plane) is called absolute power
pattern. A plot of P/P,, w/s 0 or @ is called relative power pattern and a plot of
20 logl0(P/P,,) v/s 6 or @ is called dB plot. Practically dB plot is preferred. The pattern
shape is identical when the system is used as transmitter or receiver. This is known as
directional property,
Beam Width
The lobe corresponds to maximum power is called main lobe or major lobe or principal
lobe. The lobe opposite to main lobe is called back lobe. Any other lobe in between two
nulls is called side lobe.
The angle through which maximum power is radiated or received is called beam
width, Beam width always refers to main lobe. The beam width between nulls is the angle
between nulls adjacent to major lobe. The beam width between half power cut-off points
is the angle between half power cut-off points obtained for main lobe.
0,
Half power
beam width
‘Beam widih
beam nulls: 4
O60) es
[JQ
Figure 1.14 fanans AN WAS Pree a9.
Pies
The catistion pattern can aise be plotted mm rectangular CHOFGITIAIES 48 Shee op
estimation of heam width is as shows
Ip, Hy
ean wt
rae aie
Figee IS
Siren tons wich antennae ae pecteres for poinn te grime communication
ithe, ioe wikis ators wees geboreass Loot Meng,
Ke $
PADS A AE LIE RE PIB ; fox ahsspte gattea, hog haste patter
ah SME len Be G8.
ERO ABE LRG SEVP AE WILE LENER. ISG He Kel pois in
6,
4; = 7 om -% we 14,
| Fer x ech sys te At Che, gym: Gress basins ia waiters teatagfe Ct he
| SA ALBUA Sie Wife, PERE ING 5. BEG tt, LEW PRIGE SNE OBE FEES,
4, =&, abs, =b,
Ee Setoseltyy Gator ne,
& eee bles ie os intone grttean. Halt paver 15
Sia 1? GS AONE GORE, he seiasre yatttat Gauls ~% Oe Neat Oghns,
by Gath Gib KE
Bgpoe fh on Faith wteneaty Eafe ay 50 CHICA Git pattern, Wall garner ric
MPRA gt CA MING PERS, B ton vehatons yoetnaras, woth ~ 4 OB Nene ONG per
| fenseagie. guerre i Sisaisn font a rie voweie, Vee gattesn ts syfetical in“:
iano Be HLRKAE 6 TL bunntiinin. Sivertitands pattern in obtained $e
WERALAB ALIEN BNMB SILA. RSE WA I ORs tte lite Oh Cote hE pesarca BAVOe
t ile e
Onmidirectional pattern ja obtaines for 2 systern which Gieectional in one plane an
Oranidivestional im 4 RAG cs
Caually side (abe levels ace congress a4 4 rai 8 goer denaity in tatinkete that of
ie fabes of lecvh ~ 2) OB ox lessen ave ras harretal te rast of the applications.
yy tlt vide bones of ~ 2G dB level. Low side She level ratios are
gee Calne tat ge Incas
lar plane,
poner lobe
Carehal design
1G inpet
te ghaar 1 t
Apa
pane prs
shape, ine
tion, angle Gor 9 16 called
iaicn depends upon the
ations of ante ws depends
LE DIMECTIVISY OD)
Disectivity is defined 2s a ratio of mm
intemity,
un radiation intensity and average radiation
Maximum radiztion intensity Un
D = “Nverage radiation intemity ~ Uy
The averaye value U, signifies the power that can be received if the system radiates
uniformly in all the directions. F
oY
12 Aniannas and Wave Propagation
Directivity is also defined as a ratio of maximum radiation intensity and intensity of
isotropic antenna feeding the same power.
Maximum radiation intensity
Ds
Intensity of isotropic feeding same power
U,
Deo”
0 v,
Directivity for isotropic antenna is unity,
Practically there is no antenna which is a perfect
unidirectional. Hence, minimum directivity that can
be obtained is one.
Directivity in aB's = Dy = 10 log,, (D)
Relative directivity = Pattern for
‘sotopic antenna
Where D,,, is the directivity of any reference antenna,
Relative directivity in dB's = D',, = 10 log, (D’) Figure 117
Directivity in terms of power density is
Py
pe
P,
where P, is the maximum power density and P, is average power density or powey
density of isotropic antenna feeding the same power.
1.6 POWER GAIN (G)-
‘When directivity is estimated the system under consideration is assumed to be 100%
efficient. Whereas the power gain is estimated based upon the system efficiency.
Power gain is defined as a ratio of maximum radiation intensity U,, and intensity of
isotropic antenna U,, taking into account the system efficiency.
If Kis efficiency factor, U,'=K.U,,
U,
Hence G = K—" or G=K,
U,
Gain in dB's = G,, = 10 log,,(G)
Relative gain=G 13
Antenna Basics
ny reference antenna
Where G,, is the gain of "
= 10 log, (6)
Relative gain in dB's = Gy,
Gain for isotropic antenna is unity.
Signifieances of D or G.
a Cuau
Tr]
D>D,
Figure LIS
antenna micasures the maximum power that can be obtained
Directivity or Gain of an 1 powe ;
j directivity increases, the received
related to isotropic source. As
ata particular distanc
power also increases.
(i) b,
ct : flu
1
Li | {lu
Try
"Ded,
Figure 1.19
Directivity or Gain of an antenna measures the distance of communication. As
directivity increases, a required power can be received through longer distance.
Directivity or Gain of an antenna measures the capability of feeding the power in
soe direction or to receive the power from the required direction.
irectivity of any antenna can be increased by
(a) Increasing the input power.
(b) Properly matching the impedances.
(©) Converting the antenna into unidirectional.
(d) Reducing the side and back lobes.
(©) Reducing the beam width. oY
14 Antennas and Wave Propagation
Total power radiated by a transmitter of 1000 watts power and a gain 10 dB is same a,
that of a transmitter of 500 watts and a gain of 20 dB. Hence, it is less expensive to double
the power gain than it would be for doubling the transmitted power.
iq paneer GAIN (D, or D))
Figure 1.20
Directive gain is defined as a ratio of radiation intensity in required direction anc
intensity of isotropic antenna feeding the same power. If U, and U, are the intensities in
the directions @ and 9 respectively, the directive gains in the corresponding directions ar
Yo
Uy
Directive gain for isotropic antenna in any direction is unity. Practically the directive
gain ranges between 0 and D.
Relation between directivity and beam width
6-plane $plane
Figure 1.21
Consider an ideal unidirectional system having the intensity patterns as shown.
Total solid angle = 09.
If U,, is the radiation intensity, the total power radiated is
W =U,(00) ‘Antenna Basics 15
By definition, directivity is
Un _ 4nUy
Et ga a (16)
4nU, = W = Power radiated by isotropic antenna.
Substituting (5) in (16),
D= = 06
Beamarea = Ti =0o= a ejirads (ter ert tia hic (17)
For uniform radiation in both the planes
O=6
Hense @ = gf rad 18
jense B= Gay rd ha (18)
Practically the directivity is obtained from
where 0, and 6,) are half power beam widths expressed in radians.
Beam Efficiency (€,,)
In any given plane the total beam are: of any antenna system is
lobe te Qyae lobe.
= Q,+2,
MT Fin,
Beam efficiency is defined as a ratio of the beam area of main lobe and total beam
area.
Qu
Beam efficiency &, =
A
The stray factor is defined as a ratio of the beam area of side lobe and total beam area.
: 2,
Stray factor €,, = Q,
e+e, =1 C
Estimation of Directivity
G
The accurate value of directivity is obtained from D = XK where G is the gain and K is.
efficiency factor. fies
i I
Antennas and Wave Propagat,
16
The gain of three dimensional antenna pattern is
=a
~ Sfp, (0,0) 40
where P, (6,6) = Normalized power pattern = (E, (0. 0)]°
E, (0,9) = Normalized field pattern.
dQ = sin d0 do
‘The approximate directivity is obtained from
where 0, and 6, are half power beam widths obtained in vertical and horizont
planes respectively.
_esolution
The resolution of antenna system is defined as half of the beam width between fir
nulls (BWEN)
. BWEN
Resolution = =~
(Borg)
Resolution is approximately Half power-beam width.
Resolution = HPBW
(80rd) - (0, or ¢,)
(ae). (am)
Antenna beam area = Q, = C3
Number of antennas or transmitters required for a particular resolution is
ae
=a,
where 2, should be in square radians.
7 4a
Since D= a
approximately N=D
Ideally the number of point sources required to resolve the given beam area is
approximately the directivity of the antenna, hy Antenna.Basics .
1.8 ANTENNA IMPEDANCE
The antenna self impedance or terminal impedance is defined by
Ry +iX,
- 1
= (R,+R,) +i] wl, ---
‘i * aly
s upon the shape and
where Ry, Ly and Cy are antenna paramet
s ance offered by the
dimensions cf antenna system. R,
system responsible to radiate or r
responsible for heat dissipations.
ving the pow
uy
x.) 0
ig 7, T> frequency
-J
Figure 1.22 : Reactance Characteristic
1
oC,
‘The resonance frequency f, is obtained when X,
= OL, -
X, = Oly
where,
12H
f — frequency
Figure 1.23 Figure 1.24 SEE
M.R.P.< | 50.00 | 60.00 | 70.001 80.00 | 90.001
Ma ananprinorateen GOWgUBA Haman, HYVERAL)
B
‘Antennas and Wave Propagat,
At resonance frequency fy |Z,]i8 minimum equals to R,.
fy > frequency
Figure 1.25
At resonance frequency f, the current is maximum equals to [I]...
Band Width
There is no unique definition of antenna band width. All antennas are limited in the
frequencies over which they will operate satisfactorily. This frequency range is referred to
as the bandwidth of antenna.
If the antenna is capable of operating between 295 MHz to 305 MHz, its band width
i s
305 - 295 = 10 MHz.
Designing a wide band antenna is complicated as compared to narrow band antennas.
The bandwidth is specified in two ways. (i) Band width over which the gain is higher than
the specified acceptance value, (ii) Band width over which the SWR is below a specified
value.
The band width is inversely proportional to Q factor.
fy
BW= (19)
where f, is centre frequency, and Q is the quality factor.
The band width also depends upon the dimensions and shape. As an example the
band width for cylindrical antenna as shown is given by
fat =
Band width = 5 antenna Basics
7 a
(a) Maximum band width (b) Narrower band width
(©) Minimum band width
Figure 1.26
e
1.9 FIELDS FROM OSCILLATING DIPOLE \
(a) Field lines and its detachment
tat Detached
8 17 field lines
\
ie f
b (
D
ar Dipole
J field tines
ene
= T v=Max
Me
Figure 1.27 Antennas and Wave Propagatior
20
surrent distribution for dipole is as shown. Afte;
Jhanges and the field line detaches from th
The velocity of charge flow and the ©
ipon the direction of current flow.
every half a cycle the direction of current c
dipole as shown. The orientation of ficld depends u
(b) Near and Far/fields
E-field
lines
“7, 1
2 Antenna 1
reguont
__ Equatorial
plane
'
Polar or
antenna aus
Figure 1.
Basically the space around antenna is distinguished as antenna region and outer regi
‘Antenna region is a sphere of radiuin 1/2, where J is the maximum antenna dimension
To infinity
Antenna
Farsficld
(Fraunhofer region)
Boundary sphere
of antenna region
*\ Fresnel-Fraunhofer
boundary sphere
Figure 1.29
The electric fields form concentric circles in outer region as shown in Fig. 1.29.
Fines are normal to both E lines and direction of power transmission. E line of princiy
mode must end on conductors and hence. the free space fields consists of higher mode~
Radial component is maximum along antenna axis and zero along equatorial plat
The fields are transverse in Fraunhofer regions and the field patterns are independent
radius of sphere. In Fresnel zone the racial component is quite applicable and the patter
a function of the radius. ‘Antenna Basics a
Nearfields > E,,E,and E,
Far fields > E,and E,,
The electro magnetic wave radiated from an antenna is found to be proportional to
ta ia FEAR
Fre? AM gs MHereR is the distance from the s
urce. Large part of the field represents
power stored in space during one part of the sine wave and return to the antenna during the
rest of the cycle known
a :
he jg component represents power travelling
outward from antenna dnd never returns to antenna called radiated power. Hence, far field
is aiso called radiated field and near field is called induction field.
clive power. 1
1 3
Re 7 Stat
1 .
ye > Induction field
1
rR” Radiation field.
’ 2 oR
Figure 1.30 E
1.10 RECIPROCITY TI REM FOR ANTENNA been
The reciprocity theorem applicd to antennas is sta
ied as
“If an emf is applicd to the terminals of an antenna A and the current measured at the
terminals of another antenna B, then an equal current (in both amplitude and phase) will
be obtained at the terininals of antenna A if the same emf is applied to the terminals of
antenna B™.
Proof :
Consider two antennas A and B as shown. The reciprocity theorem says that
@ IKVL=V, Lal,
(ii) Transfer impedances Z,,
y,
Le, tae
I,
From fig. (a),
esos (20) 22
Energy
fw
I,
v, . is
Antenna - A Antenna - B
Energy
flow
Vv,
1 . ,
Antenna- A Antenna - B
Figure 1.31
y
1A APERTURES
Antennas and Wave Propagation
Z. Zs
Fig. (a)
%]
Fig. (b)
Equivalent circuit of antenia system
Aperture of an antenna is the area through which the power radiated or received. -
Hom antenna, parabolics, lenses etc., are called aperture type of antenna in which the
power operation is through a particular area.
(A)
@)
Figure 1,32
==
——7
(Wy)
(Wi)
(Wy
Load Antenna Basics 23
Aperture of an antenna is basically defined as a ratio of the power under consideration
and power density. Depending upon the Power considered, different apertures are defined
like effective aperture, scattering aperture e
Consider an antenna used as a receiver as shown in Fig. 1.32. From the total received
power, a portion is scattered or radiated (W.), a portion is wasted as heat dissipations (W,)
and remaining power is supplied to the load known as effective power or useful power
(wy. :
Load SS
Figure 1.33
Antenna
The equivalent circuit of the receiving antenna is as shown. V is the induced potential
difference across antenna terminals and i is the induced current.
Vv
Ey +Zy * (RR, #Ry)FTRAIX)
Vv
VR FR. FRY HK, XG)
Effective Aperture (A,)
Effective aperture is defined as the ratio of effective power W, and power density P.
WwW. _ PR,
A= pp
Substituting I from equation (21),
Be eee 22)
6 PLR + RL +Ry) +X, +Xz)']
For an ideal system, R, = 0, R, = R, and X, =— X,. Substituting these in the above
equation
Max.Effective ave
Aperture
em 4PR,
r 2 mtn ermine Ca Wile Rowan AVE
24 Antennas and Wave Propagatior,
Effectiveness ratio & is defined as a ratio of effective aperture A, and Max. effective
aperture A...
* Aww
cranges between 0 and | and itis | for ideal system. o signifies the ability of antenno
system to feed power to the load as related to ideal system.
Scattering Aperture (A)
Scattering aperture is defined as a ratio of power scattered or radiated W, and }
density P.
WR,
or A, = +, 124
PLR, + RL # Rr) +(K, + Xs) ]
Scattering ratio f is defined as a ratio of scattering aperture and effective pci ‘ure.
A _R,
Bon =R,
fs ranges between 0 and <>, und it is | for ideal system.
Loss Aperture (A, )
Loss aperture is defined as a ratio of power losses as heat di
density.
ations and tie powe
PR,
P
ee
OF DUR ER, FRG) #(Xq +Xr) |
The ohmic power losses depend upon the material used, shape and disn. sions «
antenna system. Ohmic resistance can be reduced by using conductors of large ero
sectional area and small Jength.
Collective Aperture (A,)
Collective aperture is defined as a ratio of total received power and power density
_ W_P(R,+R,+R,)
co Pp Pp
V? (R, +R, +R)
P[(R, +R, + Ry) + (Ky +X) ] Antenna Basics
physical Aperture (A,)
Physical aperture depends upon the shape, size and dimensions of antenna system
and is independent of power operation.
v
G BY
Paraboloid
Feral
Ayala A,
Figure 1.34
Physical aperture is defined as a mouth area for aperture type of antennas and length
for linear antennas only when the system is oriented to operate maximum power in the
required direction.
A, is very la:ge for aperture type of antennas and very small for thin linear antennas.
Absorption ratio v is a ratio of maximum effective aperture and physical aperture.
Kem
Ay
v
v signifies the capability of antenna system to receive the power as compared to physical
dimensions. v is more than | for thin linear antennas is less than | for aperture type of
antennas.
Vis also known as Aperture efficiency. For parabolic reflector the efficiency is approx
between 50% to 80%. For dipoles the aperture efficiency is 100%.
4
Relation between D and A, Diese Ati e peter a ae ay
4n 7
ii ivity i = wee (2
Also the directivity is D Q, )
where Q, is the solid angle of antenna system.
Equating (1) and (2) 2
1.12A_, FOR SHORT DIPOLE
Figure 1.35
Consider a short dipole of length I placed along y-axis with centre at the origin ¢
‘When the system is oriented to receive the maximum power, the field distribution w.r,
origin is given by
€ = E,cos(at)
=E, cos 2 (stance fom*o)]
Assuming the field magnitude e, remains constant through out the elemental lengii
dy, the potential difference across dy is
av = e,dy
Total potential difference across the antenna terminals is
v = fave Jessy
23
fe. co(28y) a
A’
2 so)
7 a
‘ 7”
For a short dipole ! <<). or I/A << 1. Hence approximately
EA nl
Ven R
or V = EJ volts
Power density for maximum power reception is
ER.
P= Ton phenna Basics 7
Radiation resistance of a short dipole is
eon22 2
R=
pee eed,
om 4PR, ES Ea
1200" 7?
342
=== 2 i
or AL, Bn 0.119 4? sq.units (25)
(.13A,,, FOR A 1/2 DIPOLE
Figure 1.36
Consider a 2/2 dipole placed along y-axis with centre at the origin O. The field
listribution w.r.t. origin is
e = E, cos(wt)
=E, cos| 2 (distance from ‘o)|
Assuming e, constant through out the elemental length dy, the potential difference
cross dy is
dV = e,dy
Total potential difference is
Ve fav = Jey-ay
%
5 abs y)}-8y
E,h
"
volts
R, for a A/2 dipole is 73 2. ‘Antennas and Wave Propayar,
28
vi (E,Aay’
Sen = GPR, ER oy
1 403
120m
or A, = oo 20138 squnis sone (2G
eo 3a
1.14RELATION BETWEEN A,,, AND D
Consider an antenna used as a transmitter. The power U,, increases as radiatio
resistance R, increases. Hence directivity D is directly proportional to R,.
Dak,
(0)
Figure 1.37
‘When the system is used as a receiver, the power supplied to the load increases as }
increases. Hence aperture A.,, is directly proportional to R,.
Aug &R,
Based upon the aboveresults, the directivity and aperture are directly proportional f
any antenna system.
A,, «D
or A.,, = KD
The proportionality K' remains same for any antenna.
Consider two separate antennas of apertures A,,, , A,,,. Directivities D,, D, ar
Gains G,, G, respectively. oid
ce a @
From the above relation, the aperture of any antenna can be obtained by comparit
the system with any antenna whose aperture is known.
‘ n 3
Consider a short dipole used as reference antenna whose parameters are A... = Bn :
: em
and D, = 1.5. Antenna Basics
>
"
2
= D squnits
4n
Ingeneral = Ag
Aen fOr isotropic source
2
eEeaD:
em 4n
2
# :
sinceD= 1, Agg = ez Sq-units
Aperture and directivities
Antenna Ac, Directivity
Isotropic wl4n 1
Short dipole 302/80 15
2 dipole 300/730 1.64
Figure 1.38
Consider an electric field E, at a far-off distance r in a direction normal to the power
flow as shown.
The aperture through which the power is radiated is A and the beam area isQ,.
E,) j
Radiated Power W = fl, watts weve (29)
where 120z is intrinsic impedance of free space. ’
‘i Antone and Wave Propagiyg,
a My
Alyo Ruuliated
sone
Power 10)
Q.
BAaHAP ARN, Gy
‘The fields B, and &, are related by
os (yy
For maximum power transmission the physical aperture A can be taken as effective
aperture,
AQ eM te Gu)
lio De 2 2
also D = Q (dy
From (34) and (35),
x ; n
Buy = aq Muanits oF D = gi den soe (30)
G=KD andifK = (approx.)
anf
x
D, A
Por two separate antennas —! = Gy fem
2G. Aw,
be
|
i
115 EFFECTIVE LENGTH (1)
Effective length referred to linear antennas is the length of an antenna responsible for
power radiation or reception, For a vertical linear antenna it also measures the effective
height (H.) which contributes to the radiations significantly,
J, or HH, depends upon the type of current distributions, 31
Antonna Basics
(a) Uniform Circuit
"I
Lt £
average current I,,,
Figure 1.39
Foran uniform current distribution throughout the length
Isl
_ Antenna,
(b)
Figure L40
Fora current distribution as shown,
1
he =
‘The magnetic field for a current element is
For any distributed current,
Tel
= oe (40)
Substituting 1, in equation (40),
us e(t
t= xd see GD)
From (39) and (AO), the effective length or effective height is half. of that of actual
length or designed length,
Lets
(©) Sinusoidal Current
ne
i
ft
; 2
Tronne d0 = 2
4 n Antennas and Wave Propagation,
From (39) and (42),
uw
1 sH= e
If1=0.1 A, the current almost tapers linearly from centre feed points to zero at the
ends in a triangular distribution as shown. The average current is half of maximum.
Effective height H, = 0.5/=0.5H
J
0.12,
Average
(05)
Figure 1.42
1.16 EFFECTIVE HEIGHT AND RADIATION RESISTANCE
Another way of defining effective height is to consider transmitting case and equate
the effective height to the physical height of length, multiplied with normalized average
I
H, = .H,
coe
Consider the case of receiving antenna
Effective length (H, or /,) is given by _ V _ Open circuited voltage
2” Incident electric field.
‘The effective aperture of an antenna is given by
[RRL Ry) +X, +%7)']
oy Vi120n
ince P= LO AS Sp oe
Since P= 195 E {®. +R, +R, J (Xa +Nr)]
For ideal or matched conditi
R= 0,R,=RpXy=-Xy
VFR, 120n
Am = 2 OR,)
NS,
Effective height (he) A
The height of the antenna responsible for the power operation is called effective height.
Practically effective height is less than actual height.
‘The voltage induced across the antenna terminals is v=h,E or h,=
; 0.64
S410
fet ele
t .
| A | el _/Uniform
1
{ Triangular /—
Sinusoidal 1-012
Figure 1.43
(@ For uniform current distribution
Lal
or h=l since approxh=1 or h,=1,
- 2
(ti) For x dipole Tye = 5 Iq = 0+ 64 Ty
hence h, = 0.641 i Antennas and Wave Propagation
(iii) For 0.1 4 dipole, the current distribution is approximately triangular.
1.7051, hence h=051
In general the effective height is given by
h i fetodre wa
where | is actual length or actual height power delivered to the load is
ve
sare wn (43)
Also W,=PA,
where P is the power density is A, is effective aperture
since poE
2,
5 woe (44)
0
Equating (43) and (44)
R, A, hiz,
FRIIS TRANSMISSION FORMULA
The Friis formula basically specifies the capacity of an antenna system to feed th:
required power to a given distance for a given input power. The formula is a “powe
transfer ratio” which is a ratio of received power and total transmitted power.
Rec-antenna
Isotropic = Pp (ens Dy)
antenna
T =
wy, 2)
Load
‘Trans, antenna
(Acer DD Rec-antenna
~> (on DL)
ros
Wy, @)
Load
Figure 1.44 Po
‘antenna Basics
35
Consider an iSotropic antenna used as a transmitter with total input power or radiated
power as W,, Consider a receiving antenna of aperture A, and directivity D, mounted at
a distance r oriented to receive maximum power, =
a If P, is the power density, received power is.
when isotropic is replaced by any other source of aj
. iperture A. and directivity D,, the
received power is
W,=PA,, sue (45)
Directivity of transmitting antenna is De= .
or,P = D.P, Pov 068 cua Soe (46)
W,
RE Se aspect ieee shah ea ge 7)
substituting (46) and (47) in (45),
Ww,
Ww,
Sia pate A ee Oe (48)
fi
Using the relation between D and A.,,,
S22 4n
= 32 Mem (49)
2
ene Gg De eth ee Pig es a 6 SR ee (50)
Substituting (49) in (48),
w, _ A
Winget ee (51)
fi
From (48) and (50),
W, _ DD.
WW, 16n?r?
(52)
The above relations (51) and (52) are called Friis transmission formula. They relate
the power W, received at a distance r with the total transmitted power W,.
Wr can be increased by increasing either directivity or aperture of either transmitting,
antenna or receiving antenna. If the apertures satisfy the condition A... Agae= 22, all the
transmitted power can be received at a distance r. Practically this can not be achieved since
the aperture is limited, distance to be covered is very large and system efficiency is limited. é Antennas and Wave Propagation,
1.18 RADIATION RESISTANCE
‘The radiation resistance isan ac resistance offered by the system responsible for power
radiation or reception. R, is calculated based upon the power radiated or received.
Practically R, depends upon the following parameters.
1. Antenna shape, size and orientation
2. Height of the antenna above earth surface.
3. Distance from the antenna at which the power is measured.
4. Earth's surface conditions and its constants 1, €, and o.
5. Atmosphere conditions.
6. Efficiencies of source and receiving antennas.
(a) Antenna as a transmitter
AN
e
Source
Figure 145
Efficiency of transmitter is defined esa ratio of power radiated and total input powe:
en=—
eh == ae
As R, increases the radiated power PR_ increases and hence 1 increases.
@b) Antenna as 2 receiver
antenna is defined as a ratio of power supplied to the !0
As R, increases the power available across antenna terminals increases and her.
power supplied te the load fncreases.
Practically antenna having large R. is prefered either as a transmitter or receiver. rs,
‘Antenna Basics 37
The radiation resistance ranges from a fraction of an ohm to hundreds of ohms. If
radiation is small, the power losses are more and reduces the system efficiency.
*
Induced '
po. = : SR,
i Load
RZ i x
x i
Antenna :
Figure 1.46
1.19 BABINET'S PRINCIPLE
A B
Plane of
screens —| ra Antennas and Vhave Propingain,
Habinets principle can be tise to reditee the probleins of slot
antennas t6 sittiation
involving coinpleniontary linear antennas fer which solutions h
rave already heen obstainer|
The Babinels principle states that “The field at any point behind a plane having
screen if added to the field at the same point when the complemen
is eqinal to the field at the point when no seteen is used",
lary sercen is Sibstitnted,
Consider an example as shown above with a plane af sereen (Ay
(B).
For case (1) let the field obtained at (x, Ye 7) is
“R= f (eye)
For case (2) let the field is
F=f ixyn
and for case (3) F=f) (x.y, 2)
andl plane of obvervati,
Using Babinets principle the field at (x,. ,.7,) is
Koei ar,
HO yA) = NOK yet LO yay
‘The sonree may be a point source (as shown) ora distribution of sources. "The priney
is applicable at any point behind the sereen. ‘The sercen should be a plane petter i
conducting and infinitesimally thin, If the sc
complementary screen must have infinite perme
conductor of clectrici
inagnetism.
is perfectly conducting (6 =, 4)
hility (a =). the sereen as a peste
Ys its complementary sercen should be a perfect conductor «
Bd
Ky Ey
B= B+ eon
Ks E ek, or 4
= iil
Slot
sq
Sour
Figure 1 Aasanin facies 4
EXAMPLES
Keample 1. A diveetional antenna has a macimum eloctrival dimension of SO m and its
npesating freqency 1s TOO MMe. A fietit is measured at 1 kan from the antenna Ws it near oe
fur fell?
Ans!
2d? 2(50)" 5710"
R a ~ 37108,
} 7 nee m
= 167 em
Since the distance at which the field is rneasured is less than 1.67 km, itis a near field
Example 2, For a microwave antenna operating at a frequency of 3 Gila, Obtain the
distance beyond which only far field exists.
Aus:
3x 108
Az g 201
3x10" 7
2a? ;
Re 200m
‘The far ficlds exist when the distance from the source is more than 20d? where d is
the maximuin dimension of antenna system,
Example 3. Find the directivity for the following intensity patterns.
Ans:
(a) Unidirectional cosine patierns,
OO
U = U,, cos
Total power radiated is -- U
w= ffude
%
2
a Ff fu,,.cov0 sind dd do
ao
mY Figure 1.49
Ob: Joo fieoso sin dO
04
1
= u,an(t) =nu, rk a)
IFU, is intensity of isotropic antenna the total power radiated is
W = 4nU, saon (2) Antennas and Wave Propagatig
Equating (1) and (2),
nU, = 4nU,
(b) Bidirectional cosine pattern,
U = U,cos0
me
W = Un. fdd f cos6 sind 40 6-0
0} .
= U,2n) Q) Teno sind d0 ——
°
1
=U, Qn) 2) (3) =U,
Equating to 4nU,
p= vm,
0
‘The directivity for unidirectional operation is half of that of bidirectional operation
(c) Bidirectional sine pattern.
U =U, sind
2
w= J JU,-sind sino d9 49 0
00
no
= U,,- [9 fsin?0 40
en)
4
= U,g(2n) | 28829 ao
, 2
©
=U (any | el ent
= u,e=(2) PU,
Equating to 4nU,,
WU, = 4nU,
Un _4
= o™ = =127
Deak
(d) Unidirectional sine pattern.
U =U, sind = Os
‘Antenna Basics zi an
an
W = Un. fag fsin?9 40
oo
= =) _ wu,
~ u,cn (8) «us
Equating to 4nU,
y,
D=—" =2:
Up 2.54
(e) Bidirectional sine squared pattern
U = U, sin’6
ee
We U,,- fag [sin® 9 sing a9
a0
(4
=U, Cm (5) =
Equating to 4nU,,
p= Um ens
= ype
() Uni-directicnal cosine squared pattern.
U = U, cos’0
a %
We Up. fad Joos? sino do
0
= 2nU_ Foosto sine dd
5
Letx=cord, do = —%
sind
when 0=(, x=1
n
§=5. x0
w = 2nu, fx?
0
2n Um Antonnas and Wave Propngatiy,
Equating to dU,
v
Deis
wo?
(g} Bidirectional cosine squared pattern,
VU = Ulcostd
yg AtUy
Wes
Equating to 4nU,,
Un
Up
(h) Show that the directivity for unidirectional operation is 2 (n + 1) for an intensiry
variation of
De
v
= U,cos'0
%
We Uy. feo {ecs* sino ao
0
0
4
= 2x Up Jos" O sind dO
0
Letcos0 =x, d0=—
~sin8
Wend =0, x=
O= 5. x20
Dl xn !
W = 2nU, u, J" dx = =2nU,, ntl,
Equating to 4nU,,
Yn
D= u, 2040
Example 4, Find the directivity for the following power patterns,
Ans:
(a) U=U, sin0 sin'g; 0S 0S
Ososn ‘ntonna Boslos is
1 ,
5 Up sin? 6 do fsino sin0 do
a
o
=u.(™)(7).7U,
u.(3) (3) 4
Equating to 4nU,,
D=
(b) Unidirectional pattern
U =U, cos'0
a %
W = Uy. fad feos? 0 sino ao
0 3
1)_ 2,
= U, Qn) (4)= i
Equating to 4nU,,
u
D=—"s
Wane
Example $. Find the directivity by approximate method.
Ans:
(a) U = U, cos"
Half power], _ 4,
Haw ow 20
O'is obtained when
U,,cos'0"
Lys
or 6' = cos (3) = 37.46"
0,' = 2.37.46) = 74.92"
Approximately $,'= 74.92°
Be Bib (7492)
x
U,, sin’ sin’® OSOS 3
O antenna, A,,, = ae
4n 30
=oraVe=
73n" = 164
Example 9. What to the maximum effective aperture (approximate value) ) fora beam antenna
having half power points of 3? and 35° in perpendicular planes intersecting in the beam
axis, Minor lobes are smetli and hence neglected.
Ans:
#
Ben = J, Where 2, = 8,6,
= 0.3198 sq. rad.
A, =
em 0.3198
Example 10. The maximum effective aperture of an antenna was observed to be 10 sq.m at
a frequency of 100 MHz. Calculate the directivity of the antenna.
Ans:
=3.3107
Example 11. Find the directivity of an antenna having a radiation resistance of 72.2, loss
resistance of 12 Q and a gain of 20.
Ans:
Dea 7 Antennas and Wave Propagetior
zemple 12. &.omal! dipole antenna carrying a uniform rms current of 10.4 is having «
force ms eid cta distance r'm ina direction making an angle 8 withthe conduct,
shen by B= sis9 Vin, Find the total radiated pointer
Ans:
2
Power desity P = <= for fre space
Terai radiated power W = [[P ds
22 © (20%)sinO/r)”
J ‘aria F sind dO do.
oo
;
= 20)" 5, (sin? 0.40
= & 2x]
2
= oa (43) = 888.86 watts
Example 13. A low frequency transmitting aerial has a radiation resistance of 0.5 Q ws |
total loss resistance of 2.5 Q. If the current fed to the aerial is 100 A, calculate 1)
radiated power input power and aerial efficiency.
Ans:
Radiated power W, = FR, = (100) x05
S kwatts
Input power P (R, + R= (106)? (0.5 + 2.5)
30 kwatts
w,
‘Aerial efficiency 1 = a ¥1O = 166%
Example 14, What is the maximum power received at a distance of 0.5 km over a fr
space } GHz circuit consisting of a transmitting antenna with 25 dB yain and a receiv
antenna of gain 20 dB. The gain is with respect to isotropic source. The transmit
antenna input is 150 watts.
Ans:
1=05 km = 500m
eens
aga
03m
SG,
Gj = tone,{ S-) as
irr aT “7
Anti log, (2.5) = 3162
Similarly, D, = Anti log, (2) = 100
DD,
lon
(316.2)(100)(0.3)?
= 150 16m? (500)? 10.8 mw
Wwew, (Friis formula)
Exaniple 1S. Two space crafts A and B ave separated by a distance 100 % 10° m. each has
anentenne with D = 1000, operating ui 2.5 GHz. Iferaft'A's receiver required 20 dB over
I picowatt, what Wansmitter power is required on craft ‘B' to achieve this signal power,
510"
D, = 1000 5 0.12
. “* 25x10" mt
(™ |
10 log,,| = = 20
W, = 100 pico watts
lent? (100 710°?) 161? (10")*
W, = Ww, = ! =
D.D22 1000 1000 (0.12)?
= 10.98 % 10" watts
= 10.98 k watts
Example 16. An antenna has a field pattern
E(0) = cos 0 Os50590
Find the HP BW.
; 1 :
Ans: AU HP, 0, E(0,) = Jy = eos? (0,), 0, = 33°
HPBW = 2% 33 = 66°
Example 17. E(0) = cos 0cos2 0 for 050590 find (i) HPLW (ii) BWEN.
1 1 (oe
Ans: E (0) = cos (0,) co 20) = Jee 0, = 5 0' 15 Cg |
for 0,=0, 6, = 225 = 205
0, = 22.5, 20.03
= 20.03, 0, = 20.47
HPBW = 20, = 41° e PRO HH Rie Seppe,
Sele Pr we By ATG AO AMG
wo His +
eter IO IAA GE PA AEA A te SEMEL Ae AREAL A ght WL tpneg
fie DEP GAM AG OF in 5 I : ae
fie 2 her) IBD 2 M4 mos
Gert tfen,
SIF BBO ST ADS, Sf npg,
SPRY Bit pies 8 Boor UO 00 VLRLYD tuk bar bony
Pipe tn, * b4
MEG» b EO 4 EL wh,
O + Uh fen? F tepthe
DYE ES iit ipo bah, LOW DIE LYE YE WALEED AAG by
HOPED GION YREEL be EL
C4 ALB
i n° Ga) anon,
E Bite 4 *AMOEG Vy £ Ae ae
g
I A Fuh be pel
i 8, IMAI ILL EIDE
! 02 WAAAY MYT E-
the
.
j OF ys) MOF
w # [oiye ¥,- 0, BOP
CLR Do
ey
Ay fore ue
nee
w ee
pyserd
e* OU MI |
Busan” 6.4, * Kray
(6
tw ee
Aaa The 4 Cahits 0d Hine BIG CANE cramewiitaee Ame, i ant qocarrig A
AGA OGAWA SE AO NCR ALS ER! SEG ESTED O00 SE PEE
survatis. taih We yet! Aeivarale ty YO AL WHEE MLSS ERE
Fe Foye ne
she oe oe Li wats
Aynge Li ate Nt hie wernt f dane Bigsde SEGA spew te fievesbortys DE
Any
ba # GRO Ne
deample UA thin Nae the wyecawe f 7 Aighe SEE A pew te firoccborr 6 BE
Abe
t= be ibe AE
LAMY LS WAL BINA GAA VAL BTA OAM BDL ONG At pert ELE aa
thee yw . Antennas and Wave Propagation
~ Nulls : For cas (@,) cos 2 O)=0, 0, =45°
FS BWEN = 90°.
Example 18, Find the solid angle in sq. degrees on a surface of a space which extends
from 0 = 20°10 8 = 40" and = 30° 10 O= 70"
: 6 a0 ad = 40 [-
‘Ans: Q= ffan= [foo @ = 40 [- cos 6] x =
= 0.121 steradian = 397 sq.deg,
Approx. = 06=40 x 20x sin (20°) = 400 sq.deg.
Example 19. The field pattern of an anterma is E (8) = cos? 8, 0090. Find the bean:
area.
‘ yah
[E @]sin 6 a0 do =a ie cos’ “ol
Ans: ef
a
2
Approx Q, = 0, 6,
- 1 7 a 7
cos? (0,) = FR 0,=33, or 6, =66° =¢,
Q, = 4356 sq.deg = 1. 33 sq.rad,
Example 20. A loss less end fire array of 10 isotropic point sources has a spacing of 1/4
having a field pattern as shovin
(m) ) sin (noh)
E> an(Z sin (9h)
where v = d,(cos 9-1)-*,
(i) Find the gain G
(ii) Find the Apollo and gain
(iii) What is the difference,
Ans:
4n
i = 2
@ Ge [re.oaa P= IE, 6, Oo
17.8 or 12.5 dB,
: 40,000
(ii) G = “(aq 25 or 14dB
"
(iii) AG = 78" 1.4 or 1.5qB ‘Antenna Basics 49
)
Example 21. The normalized field pattern ; enith angle, uth
angle. and @ range between O and x. Find (i) exact directivity (ii) Difference in dB.
Ans: mA +f Se
e 4n S S
@ ne .
J J(sin 0 sin 9) si
Se ao
4253 41.25.
ii D eo ee
a (appro) ~ 0, 8, = 90x 90 =!
6
Gi) Dit = 10log oS) =0.7dB
Example 22. A radio link has a 15 watt tansmitter connected to an antenna of 2.5 net
effective aperture of 0.5 ur and is located at a 15 Om LOS distance from the transmiuing
antenna. Find the power delivered to the load under ideal conditions,
Nea Nene,
Ans: Ww, = W, = 23 watts
Example 23. Show that the aperture of short dipole is 0.119 2?
Ans:
iven its directivity 1.5.
Example 24. Show that the aperture of A,-dipole is 0.13 2 given its directivity 164.
Ans: > ‘ : eae
BR. 8 !
“x L64 = 0.1
dn an a :
Example 25. What would be the beam area for an antenna having an aperture 2.5 2? sq.m.
Ans: F
wo l
LAG sie-eo= =
7 FQ, Ooh 2
= 04 sq. rad. j CHAPTER
_ Point Sources
2.1 INTRODUCTION 3
An antenna which does not have any specified shape is called a Point source. Poin;
source is also said to be isotropic antenna. Point source isa perfect omni-directional systen
in any plane passing thro’ the system. Since it is just a theoretical system its efficiency jx
considered as 100% either as a transmitter or receiver.
Point
\ 7 a
—>-
JIN
, Figure 2.1 aS He S Unit ares
Point
Power Pattern source. <— CX, (P)
« The power density P, remains same at any point / 1
on the surface of a sphere with point source at the WN Shere
centre. Either absolute power pattem (P, v/s 6 ord)
or relative power pattern (@yP,, ¥/s8-0rd) is circular %
as shown in polar plot. Applying power theorem, Po)
the total power radiated is
W = ffPoas
= Poff as
W = P,- dar? watt
Ww 7 e e Power pattern
P, = — 7 watt/sq. units
oF Bo ume? Wasa Figure 22
50 point Sources 4
Intensity Pattern
The radiation intensity U, remains same at any point on the surface of a sphere with
point source at the centre.
Applying power theorem, th total radiated power is.
Ww = ffU,a2 Serene
4 ‘solid angle
= Upff da vain Eo
0 source / NS : 7
W = U,* 4nwatt ia ‘*
Tw Sphere
y
or Use WY wattiste
‘are Intensity
; LoL patter
The antenna system may be unidirectional, ... ., circular
Bidirectional or omnidirectional. Fora given power
or intensity pattern the directivity for unidirectional
js twice as that of bidirectional pattern.
Consider as an example
U =U,,sind
(i) For unidirectional, power radiated is Figure 2
w = ffu,, 42 Hie
apa?
= J JU. sino sind doae, . * ;
ont slit ‘
= Un Jao Jsin? 6 ao
ao
=U, (2m 2 ) = Eee sate eh a
4 2 i
uating this the power ra¢ feoe isotropic antenna
crating this to the power i ER PS A Mos) othe ¢ aba
directivity D.
(ii) For bidirectional operation
ane
We iin sin sind 40 do a
ao ay BS dae “ oe
= Uy [9 fsin*o a8
0 8
7 veel)