1. Antenna Terminology
Antenna is a connecting link between Tx and free space or free space and Rx
Operational Characteristics of system are designed around directional properties of the antenna.
Can be used in
Omnidirectional Applications
Directional Applications
Point to Point communication

2. ISOTROPIC RADIATOR
An Isotropic Radiator is a fictitious radiator which radiates uniformly in all the directions. It is also called omnidirectional radiator.
It is a hypothetical lossless radiator with which practical radiators are compared.
It is used as a reference antenna.
A Point source of sound is an example of isotropic radiator.

3. RADIATION PATTERN
Radiated Energy from an antenna is not uniform in all the directions.It can be more in one direction and less or zero in other.
Energy radiated in a particular direction is measured in terms of field strength at a particular point which is at a particular distance from antenna.
R P of a short diploe is shown

4. DEFINITION OF RADIATION PATTERN
Radiation Pattern is a graph which shows the variation in actual field strength of electromagnetic field at all points which are at equal distance from the antenna.
The graph of radiation pattern will be three dimensional and can’t be represented on a plain paper.
Alternatively, The graphical representation of radiation of an antenna as a function of direction is given the name Radiation Pattern of an antenna.

5. Field Strength Pattern : If the radiation from an antenna is expressed in terms of field strength E (Volt/Meter) the R.P is called “Field Strength Pattern”.
Power Pattern : If the radiation from an antenna is expressed in terms of Power per unit solid angle the R.P is called “Power Pattern”.
FIGURES 6.2, 6.3 SHOWING TWO & THREE DIMENSIONAL R.Ps OF A SHORT DIPOLE

6. PRINCIPAL PATTERNS
E-PLANE PATTERN: The plane containing the electric field vector and the direction of maximum radiation.
H-PLANE PATTERN :The plane containing the magnetic field vector and the direction of maximum radiation.

7. RADIATION PATTERN LOBES
Different parts of radiation pattern are called as LOBES.
A RADIATION LOBE is a portion of the radiation pattern bounded by regions of relatively weak radiation intensity.

8. CLASSIFICATION OF LOBES
Major Lobe :It is also called as main beam. It is defined as “The radiation lobe containing the direction of maximum radiation”.
Minor Lobe :Any Lobe except a major lobe is a minor lobe.
Side Lobe :Radiation lobe in any direction other than the intended lobe.
Back Lobe :Radiation Lobe in a direction opposite to the major lobe.

9. POLAR AND RECTANGULAR PLOT OF LOBES
Minor Lobes represent radiation in undesired directions and they should be minimised.Side Lobes are usually the largest of minor lobes.

10. RADIAN AND STERADIAN
A radian is defined with the aid of Figure a). It is the angle subtended by an arc along the perimeter of the circle with length equal to the radius.
A steradian may be defined using Figure (b). Here, one steradian (sr) is subtended by an area r2 at the surface of a sphere of radius r.

11. RADIATION INTENSITY( )
Radiation Intensity is defined as “Power per unit solid angle”.
Unit of Radiation intensity is Watts/Steradian.
= Differential Power(dWr)
Differential Element of Solid Angle

12. Also for an isotropic radiator,total solid angle contains 4π steradians.Therefore,
Where φav is radiation intensity produced by an isotropic radiator radiating the same total power Wr

13. GAIN
The ability of an antenna to concentrate the radiated power in a given direction or conversely to absorb effectively the incident power from that direction is specified by various antenna terms like Gain, Directive Gain, Directivity, Power Gain etc.

14. DEFINITION OF ANTENNA GAIN
Gain (G) of an antenna is defined as:
Max Radiation intensity from subject or test antenna
Max Radiation Intensity from reference antenna with same power input.
When the reference antenna is isotropic,it will be lossless.
Gain (G0) of an antenna is defined as:
Radiation Intensity from Isotropic antenna with same power input.
Go = Φ’m Φo

15. When antenna efficiency is 100 % Gain = Directivity
In terms of signal power received by a rx-er at a distant point in the direction of max radiation,
Gain (G) of an antenna is defined as:
Max Power Received from subject or test antenna(P1)
Max Power Received from reference antenna(P2)
For the same input power in both the cases of test & reference antenna

16. In terms of field strength produced at a given distance
Gain (G) of an antenna is defined as:
Field Strength at a given distance from the practical antenna in most favoured direction(E1)
Field Strength at the same distance from the isotropic antenna(E2)
db gain= 10 Log10 G

17. DIRECTIVE GAIN
The extent to which a practical antenna concentrates its radiated energy relative to that of some standard antenna is termed as directive gain (Gd). It is expressed as
Radiation Intensity in a particular direction
Average Radiated Power

18. Directive Gain (Gd)=Radiation intensity in a particular direction
Average radiated power
Gd (θ,φ)= Φ(θ,φ) = Φ(θ,φ) = 4πΦ(θ,φ)
Φav Wr Wr 4π
Gd (θ,φ)= 4πΦ(θ,φ)
∫ΦdΩ
Φ(θ,φ) = Radiation intensity in a particular direction
Φav = Average radiation intensity in that direction Wr
Directive gain is expressed in decibels then :
dbGd (θ,φ) = 10 log10{ 4πΦ(θ,φ) }

19. Assuming both are radiating the same total power
2) Directive gain of an is defined, in a particular direction as :
Gd = Power density radiated in a particular direction by subject antenna
Power density radiated in a particular direction by an isotropic antenna
Assuming both are radiating the same total power

20. Power Gain The antenna power gain is defined as :
Gp = Power density radiated in a particular direction
by the subject antenna
Power density radiated in that direction by
isotropic antenna.
Assuming the same input power to both
Directive gain & Power gain is related as:
Gp = η Gd
η = Efficiency factor lies between 1 & 0
If η = 1,then Gp = Gd

21. Power Gain(Contd..) 2) Gp = Radiation intensity in a given direction
Average total input power
Gp = Φ(θ,φ) WT 4π
where WT = Wr+Wl = total input power
Wl = Ohmic Loss
3) Gp = Power input supplied to the subject antenna in the
direction max.radiation
Power antenna supplied to reference antenna
Gp = 4π Φ(θ,φ) WT

22. Average radiation intensity of
Directivity(D)
The maximum directive gain is called directivity of an antenna and is denoted by D. where D is constant.
1) Directivity(D) = Maximum radiation intensity of
test antenna
Average radiation intensity of Or
D = Φ(θ,φ)max both of test antenna
Φav

23. Directivity(D)(Contd..)
2) Directivity(D) = Maximum radiation intensity of subject test
antenna
Radiation intensity of an isotropic antenna
radiating the same total power Or
D = Φ(θ,φ)max.(test antenna)
Φ0(isotropic antenna)
3) Directivity of an antenna is in term of the radiated power is given as:
Directivity(D) = Power radiated from a test antenna
Power radiated from an isotropic antenna
D = W’ (from test antenna)
Wn (from isotropic antenna)

24. Directivity(D)(Contd..)
Since the average radiation intensity()is obtained by dividing total radiated W by 4π in steradian is given as:
D = Φ(θ,φ)max. W 4π
D = 4π Φ(θ,φ)max. W

25. D = 4π(maximum radiation intensity)
Directivity(D)…..
D = 4π(maximum radiation intensity)
Total radiated power

26. Relation b/w Gain & Directivity
G = KD
Where,
G=Gain
k=efficiency factor=1 for 100% efficiency
D=Directivity
In many antennas losses are extremely small and hence the value of gain is almost equal to directivity. That is why gain and directivity are interchangeably used.

27. Antenna Efficiency ( ) Antenna Efficiency= Power Radiated
Total Input Power
Antenna Efficiency represents the fraction of total energy supplied to the antenna which is converted into electromagnetic waves.
If WT => Total Input Power
Wr => Power radiated
Wl =>Ohmic Losses then
WT = Wr + Wl

29. If current flowing in an antenna is I then
Where,
Rr =Radiation Resistance
Rl =Ohmic Loss Resistance of antenna conductor
Rr + Rl =Total Effective Resistance

30. Effective Area or Effective Aperture or Capture Area
A Tx-ing antenna transmits electromagnetic waves and a rx-ing antenna receives the same.
An antenna is considered to have an effective area or aperture over which it extracts electromagnetic energy from em waves.
It is defined as the ratio of power received at the antenna load terminal to the poynting vector(or power density)in Watts/meter2 of the incident wave.Thus
Effective Area= Power Received
Poynting Vector of incident wave
Ae = W/P

31. Let a rx-ing antenna is placed in the field of plane polarised travelling waves having an effective area A and the rxing antenna is terminated at a load impedance ZL=RL+XL I
Direction
Of propagation of
Plane polarised wave ZL
Fig 1

32. V=>Equivalent Thevenin Voltage
If I be the terminal current then Rx-ed Power is
W=Irms2RL
Where RL =>Load Resistance
Irms =>Terminal rms current
Therefore A = W = Irms2RL
P P
The entire system can be replaced by an equivalent thevenin circuit as shown in Fig 2
V=>Equivalent Thevenin Voltage
ZA =>Equivalent Thevenin Impedance V ZL ZA
Fig 2

33. Irms= Equivalent Voltage
Equivalent Impedance
Irms = V
ZL + ZA
Where ZA= RA + jXA =>Complex Antenna Impedance
RA= Rr + Rl = Rr if Rl is assumed to be 0
Where Rr =Radiation Resistance
Rl =Loss Resistance
Putting the values of ZA and ZL in Eq 1 we get
Eq 1

34. Where,
XL=Load Reactance
XA=Antenna Reactance
W=Irms2RL
Eq 2

35. According to maximum power transfer theorem, maximum power will be
transferred from antenna to the antenna terminating load if
Eq-3
If Rl=0
Maximum Power received in antenna terminating load impedance ZL can be
Obtained by putting eq 3 in eq 2

36. Maximum Effective Aperture
Eq 4
The ratio of effective area and max effective area is known as effectiveness
Ratio and is denoted by α
The value of α lies between o and 1

37. Scattering, Loss Aperture (AS, Al)
Scattering and Loss Aperture corresponds to considerable losses in radiation resistance and antenna loss resistance respectively
Mathematically,

38. Putting the conditions of maximum transfer of energy from eq 3
From Eq 4 and Eq 5 it is clear that under the condition of maximum transfer
of energy maximum scattering aperture and maximum effective aperture are same
Further the ratio of scattering aperture to effective aperture is called as
Scattering ratio and is denoted by β.Thus

39. Collecting Aperture
Out of the power collected by antenna there are losses as heat in load resistance (RL), radiation resistance (Rr) and antenna loss resistance (Rl) and correspondingly these apertures are Effective, Scattering and Loss. By virtue of conservation of energy these three apertures are collectively known as Collecting Aperture (AC). Mathematically it is given as,
AC=Ae+As+Al

40. PHYSICAL APERTURE : This is related to actual physical size of antenna
and is denoted by Ap.In larger cross antennas like horn, parabolic reflector the physical aperture is greater than effective aperture.
In an ideal size when there are no thermal losses, the physical aperture and effective aperture are equal and under these conditions maximum directivity is achieved i.e
Ap=Ae when there are no losses
Further the ratio of maximum effective aperture to the physical aperture is given the name absorption ratio and is denoted by γ

41. Relation between max aperture and gain or directivity
It is found in practice that directivity of rx-ing antenna is directly proportional to the maximum effective apertures.
Let there be two antennas A and B whose directivities and maximum effective apertures are denoted by Da,Db and (Aea)max,(Aeb)max respectively.
Therefore,
Eq 1
Relation between gain and directivity is given by G=KD, k can be replaced by
Effectiveness ratio α. i.e G= αD

42. Let us assume Goa, αa,Da being the gain, effectiveness ratio and directivity of
Antenna A and Gob, αb,Db corresponding quantities for antenna B.
Eq 2
But from definition
Eq 3

43. Putting the values from eq 3 into eq 2
In eq 1 assume that antenna A is an isotropic antenna then its directivity Da=1
Putting this condition in eq 1
This eq indicates that if maximum effective aperture and directivity of an antenna
B is known then the ratio of two will give maximum effective aperture of an
Isotropic antenna.Further if max effective aperture of an isotropic antenna is
Calculated then directivity of any antenna can be calculated by following formula,

44. The above expression shows that directivity of any antenna is the ratio of its
maximum effective aperture and the maximum effective aperture of an isotropic
Antenna.
For e.g take the case of a short dipole whose max. effective aperture and directivity
If calculated will be given by (3/8π)λ2 and 3/2 respectively
Therefore

45. In general the relation between directivity and maximum effective aperture of
An antenna is given as below

46. Effective Length
The term effective length represents the effectiveness of an antenna as radiator or collector of electromagnetic wave energy. It indicates how far an antenna is effective in transmitting or receiving the electromagnetic wave energy.
Effective Length is the ratio of induced voltage at the terminal of the receiving antenna under open circuited condition to the incident electric field intensity (or strength) E. Thus,
Effective Length = Open Circuited Voltage
Incident Field Strength
le =V/E meter or wavelength

48. Under conditions for maximum effective aperture when
This is the relation between maximum effective aperture and effective length

49. For transmitting antenna the effective length is that length of an equivalent linear antenna that has the same current I(c) (as at terminals of the actual antenna) at all the points along its length and that radiates the same field intensity E as the actual antenna.
If I(c)=>Current at the terminals of actual antenna
I(z)=>Current at any point Z of antenna
le=>Effective Length
l=>Actual Length

50. RECIPROCITY THEOREM
STATEMENT: If an emf is applied to the terminals of an antenna no. 1 and the current measured at the terminals of another 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 emf is applied to the terminals of antenna no.2 OR
If a current I1 at the terminals of antenna no. 1 induces emf E21 at the open terminals of antenna no. 2 and a current I2 at the terminals of antenna no. 2 induces emf E12 at the open terminals of antenna no. 1 then E21=E12 PROVIDED I1=I2.
ASSUMPTIONS:1)emfs are of same frequency
2)Medium between two antennas are linear passive and isotropic
3)Generator producing emf and ammeter for producing current have zero impedance or if not both the generator and ammeter impedances are equal

51. Transfer Impedance=Z12=E12/I2
From Reciprocity it follows

52. Proof: To prove the reciprocity theorem the space between antenna 1 and antenna
2 is replaced by a network of linear ,passive and bilateral impedances.
Z11,Z22=>Self Impedance of antenna 1 and 2 respectively
Zm=>Mutual Impedance between two antennas I1 1 2
Z11
Z22
E12 Zm I2 1 2 2 1

53. I1 1 2
Z11
Z22
E21 Zm I1 1 2 2 1

54. Applying kirchoff’s mesh law to loop 2
Eq1
Applying kirchoff’s mesh law to loop 1

55. Eq2
Putting value of I1 from eq 2 in eq 1
Eq 3

56. Similarly the current I1 can be obtained by symmetry Suffix 2 may be replaced by 1
And vice versa
Eq 4
From Eq 3 and Eq 4 it is clear that if E21 and E12 are same then I1=I2

57. Radiation Resistance
The antenna is a radiating device in which power is radiated into space in the form of electromagnetic waves .Hence there must be power dissipation which may be expressed in usual manner as
W=I2R
If it is assumed that all this power appears as electromagnetic radio waves then this power can be divided by square of current i.e
Rr=W/I2
at a point where it is fed to antenna and obtain a fictitious resistance called as radiation resistance.
It is normally denoted by Rr or Ra or Ro

58. Total Power loss in an antenna is sum of the two losses
Thus Radiation Resistance can be defined as that fictitious resistance which when substituted in series with the antenna will consume the same power as is actually radiated.
Total Power loss in an antenna is sum of the two losses
Total Power Loss = Ohmic Loss + Radiation Loss
If R=Rr+Rl

59. The value of Radiation Resistance depends on
Configuration of Antenna
The Point where radiation resistance is considered
Location of antenna with respect to ground and other objects
Ratio of length of diameter of conductor used
Corona Discharge-a luminous discharge round the surface of antenna due to ionization of air etc.

60. Self Impedance
Self Impedance is the impedance at a point where the transmission line carrying RF power from the transmitter is connected.
Since at this point input to the antenna is supplied so it is also called as antenna input impedance
Also at this point RF power from the transmitter is fed so this is also called as Feed Point impedance
Also at this point the transmission line operates
so it is also called as driving point impedance or terminal impedance

61. Antenna Input impedance is very important because it is generally desired to supply maximum available power from the transmitter to the antenna or to extract maximum amount of received energy from the antenna.
Transmission Line
Antenna Terminals ZL
Transmission Line
Antenna Terminals
Equivalent Load

62. If the antenna is lossless and isolated then the antenna terminal impedance is same as the self impedance of the antenna. Mathematically,
For a linear half wave centre fed antenna the self impedance is calculated to be

63. Thus for a lossless antenna self impedance and terminal impedance are equal which is a complex quantity the real part of which is known as self resistance or radiation resistance and imaginary part as self reactance
But if antenna is in nearby of other objects then terminal impedance gets modified because besides self impedance mutual impedance comes into existence due to current flowing in neighboring antennas
This is why self impedance of an antenna is defined as its input impedance when all other antennas are completely removed i.e away from it.

64. Mutual Impedance
Mutual Impedance is defined as negative ratio of the voltage induced in one circuit (by a current flowing in the second circuit) to the current in the second circuit with all the circuits open circuited except second circuit
Ckt 1 P
Ckt 2 S
E21 I1

65. By Definition
E21=>Open Ckt Voltage across ckt no. 2 due to current I1 in ckt no 1
E12=>Open Ckt Voltage across ckt no. 1 due to current I2 in ckt no 2
Mutual Impedance depends upon
Magnitude of Induced Current
Phase Relationship between induced and original currents
Tuning Conditions of nearby antennas

66. Front to Back Ratio
It is defined as the ratio of power radiated in desired direction to the power radiated in opposite direction.
Higher the front to back ratio better it is.
FBR depends upon tuning conditions or electrical length of parasitic elements
Higher FBR can be achieved by diverting the gain in opposite direction to the desired direction by tuning the length of parasitic elements
For Receiving purposes adjustments are made to get maximum FBR rather than maximum gain.

67. Antenna Bandwidth
Antenna Bandwidth is the range of frequency over which the antenna maintains certain required characteristics like gain, front to back ratio or SWR pattern (shape or direction), polarization and impedance
It is the bandwidth within which the antenna maintains a certain set of given specifications.

68. fr=Centre or Resonant Frequency
Q= 2π Total Energy Stored by antenna
Energy Radiated or Dissipated per cycle
Lower the Q of antenna higher is the bandwidth and vice versa

69. In frequency independent antennas like log periodic antennas etc
In frequency independent antennas like log periodic antennas etc. which have unlimited bandwidth where lower and upper frequency limits are specified independently ,the bandwidth is specified as the ratio of highest to lowest operating frequency

70. Antenna Beam width
Antenna Beam width is an angular width in degrees measured on the radiation pattern (major lobe) between points where the radiated power has fallen to half its maximum value. This is called as “beam width” between half power points or half power beam width (HPBW) because power at half power points is just half.
Half Power Beam width is also known as 3 db beam width because at half power points the power is 3 db down of the maximum power value of major lobe.
Further at half power points the field intensity (voltage) equals 1/21/2 or times its maximum value

71. Sometimes radiation pattern is described in terms of angular width between first nulls or first side lobes known as beam width between first nulls or first side lobes known as beam width between first nulls (BWFN).
Directivity is given as

72. B= HPBW in horizontal plane x HPBW in vertical plane …….square radians
= HPBW in E plane x HPBW in H plane

73. For direction finding applications a narrow beam is desirable and accuracy of direction finding is inversely proportional to beam width

74. Antenna Beam Efficiency
The parameter is defined as the ratio of main beam area (ΩM) to the total beam area (ΩA)
Total Beam area=Main Beam Area + Minor Lobe Area
= Stray Factor
= Beam Efficiency