Antennas
Mid1Syllabus
Unit-1: ANTENNA FUNDAMENTALS: Introduction, Radiation Mechanism – single wire, 2 wire, dipoles, Current Distribution on a thin wire antenna. Antenna Parameters - Radiation Patterns, Patterns in Principal Planes, Main Lobe and Side Lobes, Beam widths, Polarization, Beam Area, Radiation Intensity, Beam Efficiency, Directivity, Gain and Resolution, Antenna Apertures, Aperture Efficiency, Effective Height; illustrated Problems. Antenna Theorems – Applicability and Proofs for equivalence of directional characteristics
Unit-2: THIN LINEAR WIRE ANTENNAS: Retarded Potentials, Radiation from Electric Dipole, Quarter wave Monopole and Half wave Dipole – Current Distributions, Evaluation of Field Components, Power Radiated, Radiation Resistance, Beam widths, Directivity, Effective Area and Effective Height, Small Loops – Characteristics, Comparison of far fields of small loop and short dipole.
Unit-3(1): ANTENNA ARRAYS: 2 element arrays – different cases, Principle of Pattern Multiplication, N element Uniform Linear Arrays – Broadside, End-fire Arrays, Derivation of their characteristics and comparison- Illustrative problems Folded Dipoles and their characteristics, Arrays with Parasitic Elements, Yagi-Uda Array, Illustrative problems.
Mid2Syllabus
Unit-3(2):
NON-RESONANT RADIATORS: Introduction, Long wire TWA-patterns, Broadband Antennas: Helical Antennas –Significance, Geometry, basic properties, Design considerations for monofilar helical antennas in Axial Mode and Normal Modes (Qualitative Treatment).
Unit-4:
VHF, UHF AND MICROWAVE ANTENNAS: Reflector Antennas - Flat Sheet and Corner Reflectors, Paraboloidal Reflectors – Geometry, characteristics, types of feeds, F/D Ratio, Spill Over, Back Lobes, Aperture Blocking, Off-set Feeds, Cassegrain Feeds. Micro strip Antennas-Introduction, Features, Advantages and Limitations. Rectangular Patch Antennas –Geometry and Parameters, Impact of different parameters on characteristics. Horn Antennas – Types, Optimum Horns, Design Characteristics of Pyramidal Horns; Lens Antennas – Geometry, Features, Dielectric Lenses and Zoning, Applications.
Unit-5:
WAVE PROPAGATION: Concepts of Propagation – frequency ranges and types of propagations. Ground Wave Propagation–Characteristics, Wave Tilt, Flat and Spherical Earth Considerations. Space Wave Propagation – Mechanism, LOS and Radio Horizon. Tropospheric Wave Propagation – Radius of Curvature of path, Effective Earth‘s Radius, Effect of Earth‘s Curvature, Field Strength Calculations.
TextBooks
1. Antennas for All Applications – John D.Kraus and Ronald J.Marhefka, TMH, 3rd Edition,2003.
2. Antenna Theory - C.A. Balanis, John Wiley and Sons, 2nd Edition, 2001.
3. Antennas and Wave Propagation, G. S. N. Raju, Pearson Education, 2006.
4. Antennas and wave propagation- Sisir K Das, Annapurna Das, TMH,2013
5. Electromagnetic Waves and Radiating Systems – E.C.Jordan and K.G.Balmain,PHI,2nd Edition, 2000.
Frequently Repeated Terms
1. Radiating Zones / Fields /regions around an antenna
⊙ from r1 to r2 is Radiating Near field region (Fresnel Field) where r1 < r2 ⋜ 2 D2/ λ
⊙ above r2 is Far-Field region(Fraunhofer Field) r2 > 2 D2/ λ
Example: E(θ,φ) = ( )1/r3 + ( )1/r2 + ( )1/r indicates the regions discussed above.
Coffecient of 1/r3: is the Reactive near field region
Coffecient of 1/r2: is the Radiating near field region (Fresnel field)
Coffecient of 1/r: is the Far-field region (Fraunhofer field)
2. D= 4π/ΩA = 41,253 degSq/(θHP φHP) ≅ 40,000 degSq/(θHP φHP)
Antenna Fundamentals
1. Radiation Mechanism:
single wire:
Consider a wire of circular cross-section 'A' and volume V. The volume charge density is qV. let the charge be Q distributed uniformly along the wire of length 'L'. The charge is flowing along z-direction of velocity vz.
The current density is given by Js=qs vz
Iz= qL vz; ----------(1)
if its time varying, taking derivative on both sides gives below equation
dIz/dt= qL dvz/dt
| 1. If a charge is not moving, current is not created and there is no radiation.
2. If charge is moving with a uniform velocity: a. There is no radiation if the wire is straight, and infinite in extent. b. There is radiation if the wire is curved, bent, discontinuous, terminated, or truncated.
3. If charge is oscillating in a time-motion, it radiates even if the wire is straight.
| |
2 wire:
Dipoles:
Animated Video showing generation of EM waves from a Dipole Antenna
credits: Learn Engineering
2. Current Distribution on a thin wire antenna.
3. Antenna Parameters:
· Radiation Patterns:
a. field pattern( in linear scale) typically represents a plot of the magnitude of the
electric or magnetic field as a function of the angular space.
b. power pattern( in linear scale) typically represents a plot of the square of the
magnitude of the electric or magnetic field as a function of the angular space.
c. power pattern( in dB) represents the magnitude of the electric or magnetic field,
in decibels, as a function of the angular space.
· Patterns in Principal Planes:
The E-plane is defined as “the plane containing the electric field vector and the direction of maximum radiation.”
The H-plane as “the plane containing the magnetic-field vector and the direction of maximum radiation.”
· Main Lobe and Side Lobes:
A major lobe (also called main beam) is defined as “the radiation lobe containing the direction of maximum radiation
A minor lobe is any lobe except a major lobe.
A side lobe is “a radiationlobe in any direction other than the intended lobe.”
A back lobe is “a radiationlobe whose axis makes an angle of
approximately 180◦ with respect to the beam of an antenna.
· Beam widths:
Half Power Beam width (HPBW) : power pattern (in dB) at −3 dBvalue of its maximum OR power pattern (in a linear scale) at its 0.5 value of its maximum OR field pattern at 0.707 value of its maximum.
Beam width between first Nulls (BWFN) or (FNBW): Power or Field pattern where power or field is zero adjacent to major lobe.
· Polarization: Polarization of a radiated wave is defined as “that property of an electromagnetic wave describing the time-varying direction and relative magnitude of the electric-field vector.
Linear Polarization- Types of linear polarization are
(i) Horizontal Polarization (ii) Vertical Polarization
Non- Linear Polarization – (i) Elliptical Polarization (ii) Circular Polarization
· Beam Area: It is the Solid angle through which all power would flow if radiation intensity of antenna is constant. Major beam area, Minor Beam area.
· Radiation Intensity: Radiation intensity ina given direction is defined as “the power radiated from an antenna per unit solid angle.” The radiation intensity is a far-field parameter.
U = r2 Wrad
· Beam Efficiency: Parameter used to judge the quality of transmitting and receiving antennas is the beam efficiency (BE)
where θ1 is the half-angle of the cone within which the percentage of the total power is to be found.
Directivity: directivity of an antenna defined as “the ratio of the radiation intensity in a given direction from the antenna to the radiation intensity averaged over all directions. The average radiation intensity is equal to the total power radiated by the antenna divided by 4π
· Gain and Resolution: Gain of an antenna (in a given direction) is defined as “the ratio of the intensity, in a given direction, to the radiation intensity that would be obtained if the power accepted by the antenna were radiated isotropically. The radiation intensity corresponding to the isotropically radiated power is equal to the power accepted (input) by the antenna divided by 4π.
· Antenna Apertures:
capture area is defined as the equivalent area, which when multiplied by the incident power density leads to the total power captured, collected, or intercepted by the antenna.
The scattering area is defined as the equivalent area when multiplied by the incident power density is equal to the scattered or reradiated power
loss area is defined as the equivalent area, which when multiplied by the incident power density leads to the power dissipated as heat through RL
Physical Area or Aperture Physical area or opening available for radiation
Effective area or Aperture Area or opening part of antenna producing maximum radiation
Capture Area = Effective Area + Scattering Area + Loss Area
· Aperture Efficiency: Ratio of the maximum effective area Aem of the antenna to its physical area Ap
· Effective Height: he= Iavg/Im hp
4. Antenna Theorems:
Applicability and Proofs for equivalence of directional characteristics.
Reciprocity Theorem: The current due to a source in the network is equal to the current through that branch in which source was originally placed when the source is again put in the branch in which the current was originally obtained.
Assuming Z12=Z21 it can be proved that if I1=I2, then E12=E21
WireAntennas
1. λ/2 dipole - (Current Distributions, Evaluation of Field Components, Power Radiated, Radiation Resistance, Beamwidths, Directivity, Effective Area and Effective Height)
2. λ/4 monopole - (Current Distributions, Evaluation of Field Components, Power Radiated, Radiation Resistance, Beamwidths, Directivity, Effective Area and Effective Height)
NOTE: Retarded Potentials
3. Natural current distributions, fields and patterns of Thin Linear Center-fed Antennas of different lengths
4. Radiation Resistance at a point which is not current maximum.
5. Retarded Potentials, Radiation from Small Electric Dipole
6. Loop Antennas: Small Loops - Field Components, , D and Rr relations for small loops
7. Comparison of far fields of small loop and short dipole
8. Concept of short magnetic dipole
NOTE:
i) Thin => thickness of wire << λ i.e., thickness, d< λ/100
ii) Linear wire => Straight wire (straight line)
iii)Retarded Potentials:
· I=IO ejωt is a sinusoidal current representation
- t’ = t – (r/c) => Retarded time
- [ I ] => retarded current
- [ I ] = IO ejω(t-r/c) is the retarded current.
- IO ej(ωt-ωr/c)
- IO ej(ωt-2πf r/c)
- IO ej(ωt-2πr f/c)
- IO ej(ωt-2πr (1/λ))
- IO ej(ωt-r (2π/λ))
- IO ej(ωt-r β)
- Therefore [ I ]=> IO ej(ωt-βr) is the retarded current.
- Similarly, [ J ]=> JO ej(ωt-βr) is the retarded current density.
- Magnetic vector potential
- Electric scalar potential
1. λ/2 dipole:
(Current Distributions, Evaluation of Field Components, Power Radiated, Radiation Resistance, Beamwidths, Directivity, Effective Area and Effective Height)
1a) current distributions:
Let I(z) = A’ cosβz + B’ sinβz z>0+
I(z) = A” cosβz + B” sinβz z<0-
At the ends of dipole, current cannot flow; so I(+h)= I(-h)=0.
I(+h)=0= A’ cosβh + B’ sinβh
if A’ = I1 sinβh, B’ = − I1 cosβh
I(z) = I1 sinβh cosβz − I1 cosβh sinβz
=> I(z)= I1 sin(β(h-z)) ------------------------------------------(1)
similarly, I(-h) = 0= A” cosβ(-h)+ B” sinβ(-h)
=> 0= A” cosβh -B” sinβh
if A” = I2 sinβh, B” = I2 cosβh
I(z) = I2 sinβh cosβz + I2 cosβh sinβz
=> I(z)= I2 sin(β(h+z)) ------------------------------------------(2)
Since (1) and (2) are currents flowing in same element, |(1)|=|(2)|
=> I1 = I2 =Im
Therefore I(z)= Im sin(β(h-z)) z>0+ ------------------------------------------(3)
I(z)= Im sin(β(h+z)) z<0- ------------------------------------------(4)
1b) Evaluation of Field Components: AZ, HΦ, Eθ :
3. Natural current distributions, fields and patterns of Thin Linear Center-fed Antennas of different lengths:
Current distributions:
 |
| A= λ/2 B= 3λ/4 C= λ D= 3λ/2 E=2λ |
λ/2 dipole:
L= λ
3λ/2 Dipole:
4. Radiation Resistance at a point which is not current maximum:
* At the ends/ tips of the antenna, current is zero
* At the centre of the antenna, the current is non-zero which results in some resistance
* antennas resistance appear at the ends of transmission line as RO
5. Retarded Potentials, Radiation from Small Electric Dipole:
6. Loop Antennas:
Small Loops -Field Components, Rr and D relations for small loops:
- A wire of thickness d << λ connected to form a loop through a source are called Loop Antennas.
- Shapes rectangular, circular, Elliptical, triangular, square, etc.
- Used in HF, VHF, and UHF bands
- Loop length => Circumference << λ/10 => SMALL LOOP
- Loop length => Circumference is about λ => ELECTRICALLY LARGE LOOP
7. Comparison of far fields of small loop and short dipole
8. Concept of short magnetic dipole:
- An electric dipole is a separation of positive and negative charges; A permanent electric dipole is called Electret.
- A magnetic dipole is a closed circulation of electric current.
- An example is a single wire loop with current flowing through it.
- Short magnetic dipole is the equivalent of small loop antenna.
APPENDIX-1
Rr and D of wire antenna of different lengths:
APPENDIX-2
1/r -Far field (Fraunhofer field/ zone)
1/r2 -Radiating Near field component (Fresnel field / zone)
1/r3 -Reactive Near field component
Arrays
N- element ULA:
1. |AF|=|(sinNΨ/2)/(sinΨ/2)|
------------------------------------------------------------------------------------------------------
2. if Ψ=0, apply L’Hospital rule => [d(num)/dx]/[d(den)/dx]
then, |(sinNΨ/2)/(sinΨ/2)|Ψ=0 =>
|[(N/2) (cosNΨ/2)]/[(1/2)(cosΨ/2)] |Ψ=0 => (since cosΨ=cos0=1)
(N/2)/ (1/2)=>
|AF|Ψ=0 =N
------------------------------------------------------------------------------------------------------
3. Normalized array factor
|AF|n=1/N|(sinNΨ/2)/(sinΨ/2)| =>
1/N (sinNΨ/2)/ (Ψ/2) => (for small x, sinx ≈ x)
(sinNΨ/2)/ (NΨ/2)
Therefore |AF|n=(sinNΨ/2)/ (NΨ/2)
------------------------------------------------------------------------------------------------------
4. * For Major lobe (Max radiation) => Ψ=0,
* for Minor lobe maxima => AF=1
* for Minor lobe minima => NULLS => AF=0 (Ex: nλ/L)
* for BWFN => for n=1 (in previous point (Ex: nλ/L))
* for HPBW => BWFN/2
NOTE-1:
In AF, denominator is neglected (approximating Denominator, sinΨ/2≈1)
Hence, AF= (sinNΨ/2)
NOTE-2:
Length of array, L= (N-1)d ≈ Nd
β=2π/λ
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5. Characteristics of Arrays:
(i) BSA (α=0):
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Major lobe (Maxima)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
=> Ψ=βd cosθ =0
=> (2π/λ) d cosθ =0
=> cosθ =0
=> θ= ±π/2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Side Lobe Maxima
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
AF=(sinNΨ/2)=1
=> NΨ/2 =±(2n+1)π/2
=> N ((2π/λ) d cosθ )/2= ±(2n+1)π/2
=> N ((2π/λ) d cosθ )/2= ±(2n+1)π/2
=> N(2/λ )d cosθ = ±(2n+1)
=> cosθ = ±(2n+1) λ/ (2Nd)
=> θ = cos-1[(±(2n+1) λ/ (2L)]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Side Lobe Minima
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
=>
AF=(sinNΨ/2)=0
=> NΨ/2 = ±nπ
N ((2π/λ) d cosθ )/2= ±nπ
=> cosθ= ±nλ/Nd
=> cosθ= ±nλ/L
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
BWFN
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
n=1, BSA=2γ
From figure, θ=90 – γ
so, => cosθ= ±λ/L
cos(90 – γ)= ±λ/L
sin (γ)= ±λ/L
=> γ ≈ ±λ/L
BWFN=2 γ ≈ ±2λ/L
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
HPBW
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
=>
HPBW= BWFN/2
HPBW= ± λ/L
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Directivity
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
D= 2 (L/λ)
------------------------------------------------------------------------------------------------------
5. Characteristics of Arrays:
(ii) EFA (α≠0)
=> Ex: α=+βd or -βd
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Major lobe (Maxima) => Ψ=0
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Ψ=-βd+βd cosθ =0
=> βd(-1+cosθ) = 0
=> -1+cosθ = 0
=> cosθ = 1
=> θ= 0
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Side Lobe Maxima => AF=(sinNΨ/2)=±1
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
AF=(sinNΨ/2)=1
=> NΨ/2 =±(2n+1)π/2
=> N(βd(-1+cosθ))/2 =±(2n+1)π/2
=> N((2π/λ)d(1+cosθ)) =±(2n+1)π
=> (-1+cosθ)= ±(2n+1) λ/(2Nd)
=> cosθ= [±(2n+1) λ/(2Nd)] +1
=> θ= cos-1{[±(2n+1) λ/(2Nd)] +1}
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Side Lobe Minima AF=(sinNΨ/2)=0 => NΨ/2 = ±nπ
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
=>
N(βd(-1+cosθ))/2= ±nπ
=> N ((2π/λ) d(-1+cosθ))/2= ±nπ
=> (-1+cosθ)= ±nλ/L
=> -2 sin2θ/2 = ±nλ/L
=> sin2θ/2= -/+ nλ/2L
=> θ/2= sin-1√( nλ/2L)
=> θ= 2 sin-1√( nλ/2L)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
BWFN => n=1, EFA=2θ
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
From above figure, BWFN= 2θ
but sin2θ/2= -/+ nλ/2L
=> sin θ/2= -/+ √(nλ/2L)
=> θ/2 ≈ -/+ √(nλ/2L)
=> θ ≈ 2 √(nλ/2L)
=> θ ≈ √(2 nλ/L)
BWFN= 2 θ = 2 √(2 nλ/L)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
HPBW => HPBW= BWFN/2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
HPBW= √(2 nλ/L)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Directivity
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
D= 4 (L/λ)
NOTE: (HPBW)EFA > (HPBW)BSA
------------------------------------------------------------------------------------------------------
6. EFAID: End Fire Array with Increased Directivity
To increase the EFA directivity, phase of current is partly varied when compared to EFA as follows:
α = +(βd + 2.98 /N) ≈ + (βd + π /N)
α = -(βd + 2.98 /N) ≈ - (βd + π /N)
The directivity is given by,
D= 1.789 ( 4 (L/λ))
HPBW= 52° / √(L/λ)
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7. Scanning Arrays OR Phased Arrays:
Just by varying the angle component in cos function, the direction of radiation of the array can be varied. Thus these are called as Steered arrays or Scanning arrays or Phased arrays.
Yagi-Uda Array
Consists of TWO element types:
- Parasitic Elements- Directors and Reflector
- Driven Element- Folded Dipole
Directivity depends on the number of elements (N) in the array
| N | D (dB) |
| 3 | 7.1 |
| 5 | 9.2 |
| 7 | 10.2 |
| 12 | 12.25 |
| 17 | 13.4 |
| 15 | 14.2 |
d/ λ= 0.0085
Sd= 0.2λ (N=3,5,12,17)
= 0.25λ (N=6)
= 0.308λ (N=15)
Length of the elements in the array:
l1=0.48 λ
l2=0.46 λ
l3= l4=0.44 λ
l5=0.43 λ
l6=0.4 λ
l7= l8= …= 0.4 λ
Non-Resonant Radiators
NOTE: in this unit c= velocity of EM wave in free space,
C= circumference of a circle/loop
Band | Hz | |
MF | 300K | 3M |
HF | 3M | 30M |
VHF | 30M | 300M |
UHF | 300M | 3G |
--------------- TOPIC-1-----------
Introduction to long wire TWA
- Long wire means one to many wavelengths
- In non-resonant antennas, only forward waves exist; So waves travel. Hence the name Travelling Wave Antennas.
- Since waves travel only towards load, these produce unidirectional radiation pattern.
- Used in MF, HF range of frequencies
- Linear polarization
- EM waves are slow waves (these have phase velocity) υp= ω / β
- Two types of TWA:
- surface wave antenna defined as “an antenna which radiates power flow from discontinuities in the structure that interrupt a bound wave on the antenna surface. Ex: Most of the surface wave antennas are end-fire or near-end-fire radiators
- leaky-wave antenna defined as “an antenna that couples power in small increments per unit length, either continuously or discretely, from a traveling wave structure to free-space. Ex: slotted rectangular waveguide
fig: long wire TWA
- Above radiation pattern is for l= 5λ (thick lines), l= 10λ (dotted lines)
Comparison of resonant and non-resonant antennas:
Resonant Antennas:
Not Terminated by load
Produce bidirectional patterns
Also called as Standing wave antennas
Ex1: vertically placed Dipole, gives sleeping 8pattern.
Ex2: 
the above figure gives Resonant radiation pattern (Only thick lines represent standing wave pattern in above figure for l= 5λ)
Ex3:
-------------------------------------------------------
Non-Resonant Antennas
Usually terminated by load
Produce unidirectional patterns
Also called as Travelling wave antennas
Ex1: Helical antenna; it gives uni directional pattern
Ex2:
the above figure gives Non-Resonant radiation pattern(Only dotted lines represent travelling wave pattern in above figure for l= 5λ)
Ex3:
--------------- TOPIC-2-----------
Helical Antenna
- D= diameter of one turn
- N= no. of turns
- Length of wire between each turn, Lo = √(S2+C2)
- S= spacing between each helix
- Length of helical antenna, L= N S
- Length of the wire= N Lo
- diameter of the ground plane should be at least 3λ/4 => 0.75λ
- pitch angle,
- circumference of each helix, C = π D
- if α=0, then HELIX becomes LOOP antenna of N turns
- if α=90, then HELIX becomes linear wire
- so HELIX designed 0<α<90
- Helix radiates in many modes
- Two are principal modes
Two principal modes: Normal mode(Broadside mode), Axial mode(End fire mode)
Normal mode
- To achieve the normal mode of operation, the dimensions of the helix are usually small compared to the wavelength (N Lo << λo)
 |
| Pitch angle=α= 0, 90 |
 |
| Radiation |
- α=0 => geometry of Helix reduces to LOOP
- α=90 => geometry of Helix reduces to linear wire; by limiting geometries to a Dipole
- Axial Ratio=> AR= Eθ / EΦ= 4S/πβD2 = 2λS/ (πD)2. (For proof check Appendix-2)
- By varying D and S => AR varies from 0 to ∞
AR=0 => Horizontal PolarizationAR=∞ => Vertical PolarizationAR=1 => Circular Polarization=> 2λS/ (πD)2 =1=> C= √(2λS)
- The current throughout the length of the helix is of constant magnitude and phase
Axial mode
- the diameter D and spacing S must be large fractions of the wavelength
- α= 12° to 14°
 |
| Radiation |
- often the antenna is used in conjunction with a ground plane, whose diameter is at least 3λO/4, and it is fed by a coaxial line
- AR=
- To achieve circular polarization, primarily in the major lobe, the circumference of the helix must be in the 3/4 < C/λO < 4/3 range; Optimum => C/λO =1, S= λO/4
- other types of feeds (such as wave guides and dielectric rods) are possible, especially at microwave frequencies
- Input impedance,
Design of Helical antenna in axial mode:
Generally ‘f’ frequency and AR will be given.
From given data: (step1,2 can be done)
step1: AR= (2N+1)/2N=> number of turns =N=
step2: f= ( )Hz => wavelength= λ =c/f =3x108/f =
step3: distance between helix proper and ground plane= r= λ/8
step4: thickness of wire= d= 2a = 0.02λ
step5: Diameter of helix turn or loop= D= 0.32λ
step6: Spacing between each loop=S= 0.22λ
step7: Diameter of ground plane= Dg ≥ 0.8λ
step8: circumference of loop or turn= C= πD
step9: pitch angle =
step10: length of wire used to form helical antenna = Lo = √(S2+C2)
step11: length of helical antenna= L = N S
(n=1) Monofilar helical antenna=> Single wire looping
(n=2) Bifilar helical antenna=> Two wire looping
(n=4) Quadrafilar helical antenna=> Four wire looping
(n) Multifilar helical antenna=> Multi wire looping
θm= cos-1 [1 ± (λ/2L) (2m+1)] where m=0,1,2,3,4,5,...
Null (n=0 is must)=> θn = 0 degrees
θn = cos-1 [1 ± (nλ/L)] where n=1,2,3,4,5,...
Step2: calculations required for θm and θn are N. (for each)
Step3:
Solve θm for m=0,1,2,3,.... (if we try to solve m=N, we get cos-1( ) value greater than 1; its an indicator to stop calculations)
Step4:
Solve θn for n=1,2,3,4,... (if we try to solve n=N+1, we get cos-1( ) value greater than 1; its an indicator to stop calculations)
Step5: Now Plot the calculations. for easy plot, follow the below steps as shown in Rough work. Then draw final plot in step5
- Draw a circle, in that plot max (with 'o' mark) and Nulls (with 'x' mark)
- now join the lobes( in between nulls) (remember that only two major lobes, remaining all are minor lobes)
- erase the circle parts
Follow steps from 1 to 5;
Generally ‘f’ frequency and AR will be given.
From given data: (step1,2 can be done)
step1: AR= (2N+1)/2N=> number of turns =N=
step2: f= ( )Hz => wavelength= λ =c/f =3x108/f =
step3: distance between helix proper and ground plane= r= λ/8
step4: thickness of wire= d= 2a = 0.02λ
step5: Diameter of helix turn or loop= D= 0.32λ
step6: Spacing between each loop=S= 0.22λ
step7: Diameter of ground plane= Dg ≥ 0.8λ
step8: circumference of loop or turn= C= πD
step9: pitch angle =
step10: length of wire used to form helical antenna = Lo = √(S2+C2)
step11: length of helical antenna= L = N S
Design a monofilar Helical antenna to operate at 2.4GHz with AR=2.5
#3 Model problem on Design of Rectangular Microstrip patch antenna.
Design a Rectangular microstrip patch antenna to operate at 2GHz with substrate value of 2.2 and height of 1cm.
Sol: follow the steps described above to solve W, L, x.
VHF UHF and Microwave Antennas
Rearranging the syllabus:
Reflector Antennas=> Flat sheet, Corner, Paraboloidal
Patch Antennas
Horn
Lens
Meaning: Tapering = Narrowing, becomes gradually thinner at one end
ex: Christmas tree; Its tapered
unit-5 Contents
Frequency bands (info purpose only)
I. Flat sheet reflector
II. Corner Reflector
III. Paraboloidal reflector
IV. Horn Antenna
V. Lens Antenna
Unit overview:
I. Flat sheet reflectors
II. Corner Reflectors
III. Paraboloidal reflector:
- Geometry, characteristics
- types of feeds
- F/D Ratio
- Spill Over
- Back Lobes
- Aperture Blocking
- Off-set Feed
- Cassegrain Feed
IV: Patch Antenna
V. Horn antennas:
ii. Optimum Horns
iii. Design Characteristics of Pyramidal Horns
VI. Lens Antennas
- Geometry
- Features
- Dielectric Lenses- Zoning, Applications.
Wavelength-ranges
 |
| credits for above image: http://solar-center.stanford.edu/about/uvlight.html |
Band | Hz | Wavelength | |
VLF | 3K | 30K | 100km to 10km |
LF | 30K | 300K | 10km to 1km |
MF | 300K | 3M | 1km to 100m |
HF | 3M | 30M | 100m to 10m |
VHF | 30M | 300M | 10m to 1m |
UHF | 300M | 3G | 1m(100cm) to 0.1m (10cm) |
SHF | 3G | 30G | 10cm to 1cm(10mm) |
EHF | 30G | 300G | 10mm to 1mm |
Microwave bands
Band name | Frequency range (Hz) |
L | 1G to 2G |
S | 2G to 4G |
C | 4G to 8G |
X | 8G to 12G |
Ku | 12G to 18G |
K | 18G to 27G |
Ka | 27 to 40G |
Millimetre wave | 40G to 300G |
- Reflectors direct energy in a desired direction; Optics Ex: Candle and mirror
- Reflectors-Based on shape: Rod, flat sheet OR plane sheet(different shapes), corner, paraboloidal (different shapes, feeds), elliptical, etc.,
I. Flat sheet reflector:
- Plane sheet or Flat sheet reflector
- It is a perfect conducting infinite plane sheet reflectors
- Applying image theory and geometric theory of diffraction to above figure, its working can be studied.
- For wide spacing G▼ and BW ▲
- If antenna has Rloss= 1Ω, a spacing of λ/8 gives maximum gain
- a large flat sheet reflector converts a bidirectional into a unidirectional radiation
- for narrower reflecting sheet, more radiation exists in the region above and below at the sides of the sheet
- This diffraction can be minimized, by using a rolled edge and absorbing material
- s= 0.1λ to 0.3λ
- Using image theory, a flat sheet reflector can be approximated as follows:
- forms an image for a sheet at 180° from the source
- this causes partial shadow zones at the edges (sides of reflectors)
- forms a complete Shadow behind the reflector
II. Corner reflector:
To better collimate the energy in the forward direction, also prohibit radiation in the back and side directions. The new model consists of two plane reflectors joined, to form a corner. Hence the name.
Legend: l= length of the sheet
h= height of the sheet
s= distance between vertex of corner and source
α= INCLUDED Angle= angle between two sheets
Da= length of the aperture for the corner (in the direction of α)
- n= 180/α° where n must be an integer
- No. of images formed= 2n-1
- Ex: α=1°,2°,..5°,....10°,20°,30°,....45°,....,60°,90°,.....120°,.....180°
- Ex: α=180 => corner becomes FLAT Sheet reflector
- Ex: α=90, then it is called Square corner reflector
- If a source exists at the corner=> ACTIVE corner reflector
- If a source DOESN’T exist at the corner=> PASSIVE corner reflector
- a 3D corner reflector => RETRO reflector
- Formation of images:
- The magnitude of current in all images is same. The phase only varies.
- Example: All dots have same phase; All crosses have same phase;
- Ex: 90° corner or Square corner reflector:
- α=90°
- n=180/90= 2
- no. of images = 2n-1= 3
- applying method of images (Image theory)
- x= are having same phase (current)
- o = are having same phase (current)
o, x out of phase
- 4-lobed pattern of source and images (1= source; 2,3,4= images)
- Spacing of source, s= 0.25λ to 0.7λ
- s varied to show the variation of Directivity in case of a square corner:
s ▲=> Beamwidth ▼, Bandwidth ▼ , Gain ▲
- To reduce the wind resistance of a corner, a grid structure of height ‘R’ (across the dipole) is used. The grids are spaced λ/8 apart.
- Grids are conductors
- supporting boom may be conductor or insulator.
- Spacing between grids (centre to centre) ≤ λ/8
- If dipole length= 0.5λ, and reflector length≥0.7λ;
- then only, grids work as REFLECTORS
- If dipole length= 0.5λ, and 0.3λ<reflector length<0.6λ;
- then radiation at the sides increase => G▼
- If dipole length= 0.5λ, and reflector length<0.3λ;
- then grids work as DIRECTORS
 |
Grid corner with Bowtie-dipole |
Passive (retro corner reflector):
- A corner antenna without a source
- 3D square corner reflector => Eight Quadrants
- Each quadrant occupies 4π/8 => π/2 Sr.
- Any wave incident (within the solid angle)will be reflected back in the same direction
- Application: small water-craft make their presence more visible on RADAR screen by using a retro reflector on the top of the mast
III. Paraboloidal reflector:
(TAPER=diminish or reduce in thickness towards one end)
Parabola= 2D => y=mx2 or x=my2
Paraboloid= 3D => r= 2f/(1+cosθ)
Geometry:
Characteristics:
Compared to corner: Corner doesn’t require directional antenna, but paraboloid does.
Since path lengths are same, All reflected rays emerging from an isotropic source reach AA’ at same time(equi-phase)
All reflected rays are parallel to each other i.e., collimated rays
f/d = focal to diameter ratio:
f/d=0.5 for prime focus
f/d ▲ => paraboloid is more like a saucer; f/d ▼ => paraboloid is more like a cup
- if f=2λ/4, 4λ/4, 6λ/4,... => even multiple of λ/4 the direct radiation gets cancelled by reflected
- if f=nλ/4 => odd multiple of λ/4, the direct radiation from source will be in same phase
- Feeding element (Primary antenna) radiation pattern is called Primary pattern
- Reflected radiation from paraboloid is called Secondary pattern.
Feed illumination taper - The maximum gain for any aperture antenna is only achieved when the intensity of the radiated beam is constant across the entire aperture area. However the radiation pattern from the feed antenna usually tapers off toward the outer part of the dish, so the outer parts of the dish are "illuminated" with a lower intensity of radiation. Even if the feed provided constant illumination across the angle subtended by the dish, the outer parts of the dish are farther away from the feed antenna than the inner parts, so the intensity would drop off with distance from the center. So the intensity of the beam radiated by a parabolic antenna is maximum at the center of the dish and falls off with distance from the axis, reducing the efficiency.
Taper at the edge of reflector for ultra-low spillover sidelobes
NOTE: Relative Field Intensity = Eθ/Eo derivation, refer Appendix_1
types of feeds:
f/d ratio:
- deep-dish reflectors=> f/d is small
- shallow-dish reflectors=> f/d is large
- shallow-dishes => Easy support and move
- for shallow-dishes=> narrow primary patterns
- for shallow-dishes=> feed has to be larger also
- f/d= 0.3 to 0.5 (general)
- f/d= 0.5 to 1(monopulse tracking radars)
- f/d= 0.5 (optimum)
- f/d ▲ => paraboloid is more like a saucer; f/d ▼ => paraboloid is more like a cup
Derivation: f/d= 1/4 cotθ/2
from paraboloid equation, r+ (r cosθ)=2f
General parameters for paraboloid:
D= 4π Ae/ λ2 ≈> 4π Ap/ λ2
for circle (diameter=d),Ap= πr2= π d2/4
for rectangle (La= length, Lb= breadth), Ap= L2= La x Lb
so for Circular cross-section, D= 4π (π d2/4)/ λ2 = π2 d2 / λ2 = 9.87(d/λ)2
so for rectangular cross-section, D= 4π (L2)/ λ2 = 4 π L2 / λ2 = 12.6(L/λ)2
Cassegrain feed:
* focal point away from two dishes
* f larger
* convex sub reflector
* for good radiation, subreflector must be at least few wavelengths in diameter
* used for applications that require gain of 40dB or more
* primary dish must be too large to avoid shadowing
* virtual feed concept is not accurate, so equivalent parabola concept is used.
+ telescopic design => scanning or broadening of beam by moving one of the reflecting surfaces
+ ability to place feed in a convenient location
+ reduction of spillover => less minor lobes
+ fe >fp (effective focal length greater than physical focal length)
+ greater flexibility
+ shorter transmission lines
+ to reduce aperture blocking, sub reflector is made of horizontal wires
- losses in TXn line => sensitivity of antenna reduces
IV: Microstrip Antenna- Rectangular patch
Introduction:
- consist of a very thin ‘t’ metallic strip (patch) (t<< λO)
- this metallic strip is placed above a ground plane at height ‘h’(h<<λO) (0.003λO to 0.05λO)
- in between ground plane and metallic strip is the dielectric material (called Substrate)
- Microstrip antennas are also referred to as Patch antennas
- The radiating elements and the feed lines are usually photo etched on the dielectric substrate
- Rectangular patch of length ‘L’ (λO/3 < L <λO/2)
- substrate dielectric constant values 2.2 ≤ εr≤ 12
- Better efficiency, larger bandwidth, loosely bound fields for thick substrate & lower εr values (=> Antenna size will be bigger)
- Less efficient, Smaller bandwidth, tightly bound fields for thin substrate (=> Antenna size will be smaller) => Minimize undesired radiation; Application: Microwave circuitry
- The radiating patch may be square, rectangular, thin strip (dipole), circular, elliptical, triangular, or any other configuration
- Linear and circular polarizations can be achieved with either single elements or arrays of microstrip antennas
- Arrays of microstrip elements, with single or multiple feeds, may also be used to introduce scanning capabilities and achieve greater directivity
- Feeding types: Microstrip line, Coaxial probe, Aperture coupling and Proximity coupling
Advantages:
Light weight, low volume, low profile, planar configuration, which can be made conformal
Low fabrication cost and ease of mass production
Linear and circular polarizations are possible
Dual frequency antennas can be easily realized
Feed lines and matching network can be easily integrated with antenna structure
Limitations:
Narrow bandwidth (1 to 5%)
Low power handling capacity
Practical limitation on Gain (around 30 dB)
Poor isolation between the feed and radiating elements
Excitation of surface waves
Tolerance problem requires good quality substrate, which are expensive
Polarization purity is difficult to achieve
Size is large at lower frequency
Applications:
Pagers and mobile phones
Doppler and other radars
Satellite communication
Radio altimeter
Command guidance and telemetry in missiles
Feed elements in complex antennas
Satellite navigation receiver
Biomedical radiator
Geometry & Parameters:
- Fringing (form a border around something)fields develop around the patch
- Ex: capacitor, C = εO εr A/ d; due to fringing fields, A inc => C inc
- Best EX: standby water pond; A= LxW; With tides=> Anew= Lnew xWnew
- More the fringing fields => more radiation (NOT desirable for microstrip line )
- tanδ is called Loss tangent ex: εr= εr’ +j εr’’; Now δ = tan-1(εr’’/ εr’)
Design of Microstrip Patch Antenna:
Impact of different parameters on characteristics:
▲means increase, ▼ means decrease
1. With increase in the feed location ‘x’, input impedance will be HIGHER
EX: Microstrip line feed; it is edge feed; x=L/2
2. With increase in W, aperture area, εreff and fringing fields(ff) INCREASE, hence frequency DECREASE and input impedance plot shifts towards LOWER impedance values
From the formula 
=> W α 1/fr
From the formula 
=> εreff α W
3. As h increases, fringing fields and probe inductance INCREASE, frequency DECREASE
∆L= h / √εe ; 
so if ∆L inc, h inc => fr dec => h α 1/fr
4. As probe diameter decreases, its inductance increases, so resonance frequency DECREASES
5. With increase in tan δ, dielectric losses INCREASE; Efficiency and Gain DECREASE.
 |
6. With decrease in εr, both L and W increase, which increases fringing fields and aperture area, hence both BW and Gain INCREASE
Above impact parameters simply:
1: if x▲ => i/p impedance ▲
2: if W▲ => Ae, ff ▲ and freq, i/p impedance▼
if εreff ▲=> W ▲
3: if h ▲ => ff, probe inductance ▲ => freq ▼
4: if probe diameter ▲ => probe inductance ▲ => freq ▼
5: if tan δ ▲ => dielectric losses ▲ =>G, Efficiency ▼
V. Horn Antennas:
Types:
Optimum Horns:
Design Characteristics of Pyramidal Horns:
Steps for design: (Given data will be: f, G(dB), a, b) (to find: h, W, Pe and Ph)
▼ Side view ▼
▼ Top View ▼
to solve from given data:
(i) λ=c/f
(ii) if G is given in number Ex: G=100 =GO=> go to calculations procedure directly
OR
else if G(dB) => GO= 10 (G given /10)
Calculations procedure:
VI. Lens Antennas:
Lens antennas used to collimate incident divergent energy to prevent it from spreading in undesired directions.
Material based classification:
Natural lens-Lens material is lucite or polystyrene (default)
Artificial lens- Lens material is metallic or artificial dielectrics
Shape based classification:
Delay lens: Electrical path length more (Default)
Fast lens: Electrical path length less compared to delay lens.
Geometry & Features:
Dielectric Lenses-Zoning:
- Bulky lens => less focal length(‘f’ is shorter); θ is larger; Tapered illumination is used to suppress minor lobes; Bulky means heavy; not suitable for applications like Satellite communication etc; {Adv}: FREQUENCY INSENSITIVE
- Thinner lens => long focal length(‘f’ is longer); θ is smaller; Near uniform illumination possible; Light weight; Not suitable for practical applications like Satellite communication where volume of satellite is limited{Adv}: FREQUENCY INSENSITIVE
- A compromise of both above cases is a Zoned lens i.e. with a short focal length and mechanically light weight. {Disadv}: FREQUENCY SENSITIVE
- Zoning: Weight of the lens is reduced by removing sections or Zones, such that lens performance is unaffected at desired frequency. Zone step within the lens and outside the lens is different;
for 1λ i.e. unity wavelength,
Disadvantage of zoning: Zoned lens becomes frequency sensitive
Uses of lens:
- Optimum performance with narrow beamwidth
- reduce quadratic phase error in conical horns
- Narrow radiation pattern as flare angle increases in horn antenna
- collimation with dielectric lens
Applications:
- Lens antennas used in conical horn to reduce quadratic phase error
- Placed at horn aperture to narrow radiation pattern as flare angle increases (for horn)
Disadvantages of lens:
- Reflection property by lens => this is sufficient to mismatch of the primary antenna to feed line
- Reflections at convex surface not serious; flat surface reflections enter source refocussed;
- lens beam axis tilts from antenna major beam axis.
Appendix_1
Relative Field Intensity
Eθ/Eo derivation (Parabolic dish)
WavePropagation
SYLLABUS:
WAVE PROPAGATION: Concepts of Propagation – frequency ranges and types of propagations. Ground Wave Propagation–Characteristics, Parameters, Wave Tilt, Flat and Spherical Earth Considerations.
Space Wave Propagation – Mechanism, LOS and Radio Horizon. Tropospheric Wave Propagation – Radius of Curvature of path, Effective Earth’s Radius, Effect of Earth’s Curvature, Field Strength Calculations
Unit overview:
I. Concepts of Propagation – frequency ranges and types of propagations.
II. Ground Wave Propagation
-Characteristics
- Parameters
-Wave Tilt
-Flat and Spherical Earth Considerations.
III. Space Wave Propagation
-Mechanism
-LOS and Radio Horizon
(Tropospheric Wave Propagation)
-Radius of Curvature of path
-Effective Earth’s Radius
-Effect of Earth’s Curvature
-Field Strength Calculations
1. Concepts of propagation:
- Ground Wave Propagation (Surface) (up to 2MHz): Ground wave propagation refers to the wave that glide along the surface of the Earth
- Sky Wave Propagation (Ionospheric) (2MHz to 30MHz): Sky Wave Propagation refers to the waves that get reflected back to the Earth after reflection from Ionosphere
- Space Wave Propagation (Tropospheric) (above 30MHz): Space Wave Propagation refers to the waves that travel in optical or radio horizon.
 |
| frequency bands use for various propagations |
- Earth's radius, r= 6370Km
- Effective Earth's radius is r‘=4r/3
2. Ground Wave Propagation:
2.1 Characteristics:
- Ground wave guide along the surface of the earth
- Upto 2MHz
- Vertically polarized wave preferred=> Vertically polarized antennas used
Horizontal component in contact with earth gets short circuited- This EM wave induces charges in earth constituting a current
- At this point Earth acts like a leaky capacitor
- ground wave is weakened due to earth’s absorption
- Suitable for VLF, LF and MF bands
- Requires high power for Tx
- Ground waves not affected by changes in atmosphere
- App: Ship to Ship comm, Maritime Mobile Comm, Ship to shore comm
2.2 Parameters:
- Field strength is
- E0 = field strength of the wave at the surface of the earth at a unit distance from the transmitter
- d = distance from the transmitting antenna to the point at which E is to be estimated
- A= reduction factor which accounts for ground losses and is a function of the conductivity σ, permittivity ε, frequency f and distance d in terms of the wavelength λ
‘A’ is expressed in terms of p and b; p is called the numerical distance and b phase constant and is a measure of the power factor angle of the earth.
p, b = f(σ, f)
2.3 Wave tilt: Change of orientation of the E i.e vertically polarized wave; Wave tilt changes vertically polarized wave to Elliptically polarized wave.
Space Wave Propagation
3.1 Mechanism
Direct ray+ Ground reflected ray+ Reflected and Refracted from troposphere + Diffracted rays around the curvature of Earth
MAJOR PART:
This comprises of
(i) Direct Wave (Space)
(ii) Indirect Wave (Reflection)
3.2 LOS and Radio Horizon
5.2.1 Line of Sight (LOS):
LOS= d=d1+d2
=> d1=(( ht+r)2- r2)1/2 ; d2=((hr+r)2-r2)1/2
=>d= √[ ( ht2+ r2 + 2 ht r)-r2 ] + √[ ( hr2+ r2 + 2 hr r)-r2 ]
=>d= √[ ( ht2 + 2 ht r)] + √[ ( hr2 + 2 hr r) ] Ex: hr r =100m x 6370km; but hr2 = 100m2
So hr2 << 2 hr r and ht2 << 2 ht r
=>d= √[ ( 2 ht r)] + √[ ( 2 hr r) ] taking √ (2 r ) common from the two terms
=>d= √ (2 r ) √[ ht ] + √[ hr ] √ (2 r ) = √ (2 x 6370 km) = 3.47 Km
=>d= 3.47 { √[ ht ] + √[ hr ] } Km
3.2.2 Radio Horizon (RH):
Earth is bulged at the centre. But not elliptical.
So, Effective Earth's radius is r‘=4r/3, where r= 6370Km
RH= d=d1+d2
=> d1=(( ht+r' )2- r' 2)1/2 ; d2=(( hr+r' )2-r'2)1/2
=>d= √[ ( ht2+ r'2 + 2 ht r')-r'2 ] + √[ ( hr2+ r' 2 + 2 hr r' )-r' 2 ]
=>d= √[ ( ht2 + 2 ht r' )] + √[ ( hr2 + 2 hr r' ) ]
Ex: hr r' =100m x 4/3 x 6370km; but hr2 = 100m2
So hr2 << 2 hr r' and ht2 << 2 ht r'
=>d= √[ ( 2 ht r')] + √[ ( 2 hr r') ] taking √ (2 r' ) common from the two terms
=>d= √ (2 r' ) √[ ht ] + √[ hr ]
√ (2 r' ) = √ (2 x 4/3 r)= √ (2 x 4/3 6370 km) = 4.12 Km
=>d= 4.12 { √[ ht ] + √[ hr ] } Km
3.3 Radius of Curvature of path
Angle=arc/radius
dθ= v dt/R
R dθ= v dt -----------(1)
At a different region on Earth, h and v will vary.
(R+dh)dθ = ( v+dv) dt -----------(2)
(2)-(1)
(dh)dθ = ( dv) dt
dθ/dt = dv/dh v=c/μ
dθ/dt =-c/μ2 dμ/dh
dθ/dt ≈ -c/μ dμ/dh v=c/μ
dθ/dt = -v dμ/dh
(v dt/R)/dt = -v dμ/dh
R = -dh/dμ
3.4 Effective Earth’s Radius
r‘=4r/3, where r= 6370Km
3.5 Effect of Earth’s Curvature
- More reflections due to spherical earth
- Shadow zones (Diffraction zones)
- Possible distance of txn reduced
3.6 Field Strength Calculations
Part1: to find path difference, phase difference
d12=(ht-hr)2+d2 , d22=(ht+hr)2+d2
=> d1=d(√ {[(ht-hr)/d]2+1} )
=>d1≈ d(1+ (ht-hr)2/2d2) = d + (ht-hr)2/2d
=>d2≈ d(1+ (ht-hr)2/2d2) = d + (ht+hr)2/2d
Path difference (pd)= > d2-d1= 2hthr/d
Phase difference = α =β (pd)
=> α =2π/λ (2hthr/d) = 4π ht hr/ λ d
Part2: find ER
ER= EO (1+K e-jθ) e-jθ = cosθ-jsinθ
where ER is resultant (net) electric field intensity
k is constant , for perfect Earth (K=1)
=>|ER|= EO √{(1+cosθ)2+( sinθ)2}
=>|ER|= EO √(2+2cosθ} 1+cosθ =2 cos2 (θ/2)
=>|ER|= EO 2 cos(θ/2)
where EO= 7√P /d P= effective radiated power
Part3: simplify ER
|ER|= EO 2 cos(θ/2)
θ =α+β= α+π
=> |ER|= EO 2 cos((α+π) /2)
=> |ER|= EO 2 sin(α/2)
=> |ER| ≈ EO 2 (α/2) = EO α
=> |ER| ≈ EO (4π ht hr/ λ d )
=> |ER| ≈ (7√P /d) (4π ht hr/ λ d )
=> |ER| ≈ (7√P) (4π ht hr/ λ d2 )
=> |ER| ≈ (88√P ht hr/ λ d2 )
PreviousQP and Key 2019
Question Paper
Key
PART-A
1a)
1b) Rr and D:
Name of Wire Antenna: Shape : Length : Rr ( Ω ) : Directivity
Quarter wave length monopole : Single wire: λ/4 : 36.55Ω : 3.28
Small dipole/Short dipole : Two wire: λ/50 < L < λ/10 : 20 p2 (L/λ)2 : 1.5
1c) Arrays are group of similar elements (antennae);
If the elements are on a straight line, then that array is called Linear Array.
1d) * Global Positioning Satellites * Data-Relay satellites
* Weather Satellites * Telephone
* Television
1e) Principle is “Fermat’s principle” means equality of path length;
All paths from the source to the plane are of equal electrical length. This is the principle of equality of electrical (or optical) path length (Fermat’s principle)
1f) Maximum frequency that gets reflected back from Ionosphere to the Earth when incident at an angle other than normal.
PART-B
2a) Effective height =he= (Iavg / Im) hp
P=(1/4) V2/Rr
he= 2 √(Rr Ae / ZO) where Gd= (4π Ae )/λ2
he= 2 √(Rr Gd λ2/4π ZO)
2b)
Isotropic pattern: Antenna radiates uniformly in all directions (θ and φ)
Omni-directional pattern: Antenna radiates completely in θ and partially in φ directions or vice-versa.
Directional Pattern: Antenna radiates partially in θ and φ directions
3a)
3b) Comparison of far fields of small loop and short dipole
4a)
d= λ/3;
N=4;
L=(N-1)d= 3 λ/3 = λ meters;
D= 2 (L /λ)=2 or 3.01dB
BWFN=±2λ/L=2 radians= 2x57.3°=114.6°
HPBW= ± λ/L=1 radian= 57.3°
4b)
Assume(BSA) α=0; d= λ/2
AF= cos{α/2 +(βd/2) cosθ}
AF=1 means Major lobe radiation => ((2π/λ)/( λ/2) cosθ)/2=0 => cos θ = 0=> θ=±π/2
AF=0 means NULL=> ((2π/λ)/( λ/2) cosθ)/2=±π/2 => θ = 0 or π
5a) Travelling Wave radiators:
Long wire antennas, Helical antennas, etc.,
l Long wire means one to many wavelengths
l In non-resonant antennas, only forward waves exist; So waves travel. Hence the name Travelling Wave Antennas.
l Since waves travel only towards load, these produce unidirectional radiation pattern.
l Used in MF, HF range of frequencies
l Linear polarization
l EM waves are slow waves (these have phase velocity) υp= ω / β
l Two types of TWA:
n surface wave antenna defined as “an antenna which radiates power flow from discontinuities in the structure that interrupt a bound wave on the antenna surface. Ex: Most of the surface wave antennas are end-fire or near-end-fire radiators
n leaky-wave antenna defined as “an antenna that couples power in small increments per unit length, either continuously or discretely, from a traveling wave structure to free-space. Ex:slotted rectangular waveguide
fig: long wire TWA
l When a TEM wave travels parallel to an air-conductor interface, it creates a forward wave tilt. If the conductor is a perfect electric conductor (PEC), then the Wave Tilt is zero because the tangential electric field vanishes along the PEC. The wave tilt increases with frequency and with ground resistivity.
5b)
6a)
Functionality or Working:
The horn can be treated as an aperture antenna. It’s a waveguide flared in all directions(Pyramidal Horn) or sometimes vertically or horizontally which are called H-plane or E-plane horn. . When the horn is not mounted on an infinite ground plane, the fields outside the aperture are not known and an exact equivalent cannot be formed. The fields within the horn can be expressed in terms of cylindrical TE and TM wave functions.
Design:
Steps for design: (Given datawill be: f, G(dB), a, b) (to find: h, W, Pe and Ph)
▼ Side view ▼
▼ Top View ▼
to solve from given data:
(i) λ=c/f
(ii) if G is given in number Ex: G=100 =GO=> go to calculations procedure directly
OR
else if G(dB) => GO= 10 (G given /10)
Calculations procedure:
step8: if Pe=Ph then the pyramidal is realizable physically
6b)
(i) f/D Ratio: f/d= 1/4 cot(θ/2)
Cross section of Paraboloid (eq is circle) =>
xO2+yO2= (d/2)2
=> xO2+yO2= d2/4
Also xO2+yO2= 4f (f-zO)
tanθ= d/2 / ( f- d2/16f)
Rearranging
tanθ= d/2f / ( 1- d2/16f2) Using analogy tanθ= 2 tanθ/2 / 1-tan2θ
cotθ/2 = 4f/d
=>
f/d= 1/4 cotθ/2
(ii) Spill Over: Part of energy radiated by feed not intercepted by reflector.
Aperture Efficiency:
The aperture efficiency is generally the product of the
1. fraction of the total power that is radiated by the feed, intercepted, and collimated by the reflecting surface (generally known as spillover efficiency)
2. uniformity of the amplitude distribution of the feed pattern over the surface of the reflector (generally known as taper efficiency)
3. phase uniformity of the field over the aperture plane (generally known as phase efficiency )
4. polarization uniformity of the field over the aperture plane (generally known as polarization efficiency)
5. blockage efficiency
6. random error efficiency over the reflector surface
Thus in general
(iii) Front-to-back ratio:
FBR is the ratio of power radiated in desired direction to that of in the opposite direction.
FBR = G+T+K-G(horn)
G is gain of dish
T is feed’s average pattern edge taper
K is constant obtained from f/D
7a)
Applying Pythagoras theorem to above figures,
d12=(ht-hr)2+d2
and d22=(ht+hr)2+d2
Simplifying above d1 and d2
• d1≈ d(1+ (ht-hr)2/2d2) = d + (ht-hr)2/2d
• d2≈ d(1+ (ht-hr)2/2d2) = d + (ht+hr)2/2d
Path difference (pd)=> d2-d1= 2hthr/d
Phase difference = α =β (pd) => α =2π/λ (2hthr/d) = 4π hthr/ λ d
Relative field strength, ER= EO (1+K e-jθ)
where e-jθ= cosθ-jsinθ
ER is resultant (net) electric field intensity
k is constant , for perfect Earth (K=1)
ð |ER|= EO √{(1+cosθ)2+( sinθ)2} where EO= 7√P /d and P= effective radiated power)
ð |ER|= EO √(2+2cosθ} since 1+cosθ =2 cos2 (θ/2)
ð |ER|= EO 2 cos(θ/2)
ð |ER|= EO 2 cos(θ/2)
ð θ =α+β= α+π
ð |ER|= EO 2 cos((α+π) /2)
ð |ER|= EO 2 sin(α/2)
ð |ER| ≈ EO 2 (α/2) = EOα
ð |ER| ≈ EO (4π hthr/ λ d )
ð |ER| ≈ (7√P /d) (4π hthr/ λ d )
ð |ER| ≈ (7√P) (4π hthr/ λ d2 )
ð |ER| ≈ (88√P hthr/ λ d2 )
Therefore |ER| ≈ (88√P hthr/ λ d2 )
7b)
Effect of Earth’s curvature:
Ø More reflections due to spherical earth
Ø Shadow zones (Diffraction zones)
Ø Possible distance of txn reduced
Feb2020 Supple
Quiz/ Model Bits
Antenna Fundamentals
In reference to an Antenna answer the following:
1. The Directivity is related to Radiation Intensity as ______________
2. The beam efficiency is the ratio of _______ to _______
3. Aperture efficiency is the ratio of _______ to ________
4. The Directivity of an isotropic antenna is ____
5. The Directivity of an isotropic antnenna is _____ dB
6. The BWFN is related to resolution as ________
7. The total angle subtended by an isotropic antnenna is ____ Steredians
8. 1 Steredian = ________ degree square
9. An isotropic antenna radiates ______ Steredians
10. An antenna has electric field E=cos2θ V/m, the BWFN=
11. An antenna has electric field E= cos2θ V/m, HPBW=
12. An antenna has U=cosθ; Prad=10; Maximum Directivity,Dmax= ________ dB
13. The Gain and Directivity are related as _______
14. Stray factor is (formula) _____
15. Antenna lobes are primarily classified as _____ and _______ lobes.
16. An antenna has BWFN =6 degrees; Resolution is _____
17. Basic Radiation equation of an Antenna is _______
18. Based on patterns, antennas are classified as _____________ and ____________
19. The effective height of an antenna is given by _________
20. An antenna has Directivity of 20; Directivity in dB = ________
21. An antenna has effective aperture of 20m^2; Its aperture efficiency is 0.86; Its physical aperture is __________
22. An antenna has efficiency of 0.79; If its gain is 40; Directivity, D= _____ dB
23. Mention any five types of antenna:
_______________,
_________________,
_______________,
________________,
_______________
24. An antenna has a power pattern of P= cos2θ Watts, HPBW =______and BWFN= _______
25. The lobes that exist immediately after the nulls of a major lobe are called _________ lobes.
Thin-linear wire antennas
In reference to an Antenna answer the following:
1. Retarted current is given by ___________
2. Retarded Potential of an antennna is given by V= ____________
3. Directivity of a dipole = ________
4. Radiation resistance of a dipole = __________
5. Directivity of a monopole = ________
6. Radiation resistance of a monopole = __________
7. Beam area of Dipole= ________
8. Beam area of monopole= ________
9. The elevation angle (range) in case of a monopole= _____________
10. The elevation angle (range) in case of a dipole= _____________
11. The azimuthal angle (range) in case of a monopole= _____________
12. The azimuthal angle (range) in case of a dipole= _____________
13. The radiation resistance of a center fed antenna at which current is not maximum is ________
14. Formula for directivity of a short dipole is ___________
15. A lambda/4 monopole is called as _____________
16. A lambda/2 dipole is called as ____________
17. Rr of a small dipole is given by ____________
18. Rr for a infinitesimal dipole is given by ____________
19. In Relation to antennas, the equation representing the Reciprocity theorem is _____ =_____
20. Directivity of a small loop antenna = ________
21. Rr of a small loop antenna = ________
Antenna Arrays
In reference to an Antenna answer the following:
1. An array is a group of similar _____________in respect to AWP
2. Dipoles used for calculation of ULA properties is ___________
3. ULA acronym is
U_____ L______ A______
4. BSA acronym is __________ ___________ ___________
5. EFA acronym is __________ ___________ ___________
6. EFA-ID is also called as _________________________________
7. The electric field component representing an infinitesimal dipole is ______________
8. If an Antenna array has elements placed on a straight line, such array is called as __________ __________
9. If an Antenna array has elements on a straight line spaced equally and phase between the elements is same or progressive, such array is called as __________ ___________ ___________
10. The Directivity of EFA is given by ______________
11. The Directivity of BSA is given by ______________
12. The HPBW of BSA is given by ____________
13. The HPBW of EFA is given by ____________
14. The principle of pattern multiplication is given by
____ = ______ x _____
15. In BSA, the radiation pattern is ________________to array axis.
16. In EFA, the radiation pattern is ________________to array axis.
17. An antenna array pattern shape can be controlled by various methods like
(a) Spacing of elements (b) Excitation levels (c) Phase control (d) Shape of array (e) Pattern of individual element
(i) Both a and b (ii) a,b,c (iii) a,b,c,d (iv) a,b,c,d,e (v) except a and b, all are correct
18. A Parasitic element radiates on its own T/F
19. In a Yagi-Uda array, lengths of elements are l1=0.5m, l2=0.49m, l3=0.48m, l4=0.47m, l5=0.46m;
The element l1 is called ______
The element l2 is called ______
The element l3,l4,l5 are called ______
20. A two-folded half-wave dipole has impedance of _______
Antennas in GATE Exam
Antenna:
Gate2017, 2018, 2019
(i) Antenna Types
(ii) Radiation Pattern
(iii) Gain and Directivity
(iv) Return loss
(v) Antenna Arrays
Gate2020:
Basics of Antennas:
(i) Dipole antennas
(ii) radiation pattern
(iii) antenna gain.
Gate2021, 2022, 2023:
(i) Dipole and monopole antennas
(ii) Linear antenna Arrays
ACE coaching- Link
PreviousPapers and Key
Gate Pattern for ECE:
Marks (Questions)= 100M (65Q) = 15M (10Q on GA) + 85M (55Q on EC)
NOTE: 15M for GA + (12 to 15M for Engg Maths) +( 73 to 70M for EC)
Questions pattern= MCQ, MSQ, NA
Negative marking = Mark/3; Example: if its 2M question, then negative marking is 2/3.
NOTE: Negative marking for MCQ only.
GATE / Tutorial Questions
1. Determine the type of Polarization of the EM wave travelling in +Z direction with field components as:
E = 4 cos(ωt) ax + 4 cos(ωt-90°) ay;
2. Determine the directivity, if an antenna has E(θ,φ) = (sinθ cos2φ ) 1/2
0 ⋜ θ ⋜ π;
0 ⋜ φ ⋜ π/2 ;
3π/2 ⋜ φ ⋜ 2π
3. Determine the polarization of the along with AR.
(i) Ex =Ey, ∆φ=φy−φx =π/2
(ii) Ex =0.5Ey, ∆φ=φy−φx =-π/2
(iii) Ex =Ey, ∆φ=φy−φx =π/4
4. A hypothetical isotropic antenna is radiating in free-space. At a distance of 100 m from the antenna, the total electric field (Eθ) is measured to be 5 V/m. Find the
(a) Power density (Wrad)
(b) Power radiated (Prad)
5. The normalized radiation intensity of an antenna is rotationally symmetric in φ, and it is represented by
Uu(θ,φ) = 1 ; 0 ⋜ θ ⋜ 30
0.5 ; 30 ⋜ θ ⋜ 60
0.1 ; 60 ⋜ θ ⋜ 90
0 ; 90 ⋜ θ ⋜ 180
What is the direcitivity of antenna in dBi ?
Assignments
Antenna Fundamentals
1. If E(θ) = cosθ cos2θ for an antenna; Caclulate its HPBW
2. A lossless antenna radiates 10 W of power. The raidation intensity of antenna is
U= Qo (cosθ)3 W/Sr.
Calculate its
(a) Maximum power density at 1Km
(b) Beam Area
(c) Directivity
(d) Gain
3. Caclulate the Directivity for an antenna that has
U(θ,φ) = sinθ sinφ for 0≤θ≤π, 0≤φ≤π
= 0 elsewhere;
4. Determine the type of Polarization of the EM wave travelling in +Z direction with field components as:
Ex = 4 cos(ωt) ax and Ey= 4 cos(ωt+90°) ay;
5. Define and formulate the following:
(a) Directivity
(b) Gain
(c) Resolution
(d) Radiation Inetnsity
6. State and prove equality of directivities.
7. Explain about the radiation mechanism of two-wire.
8. With reference to antenna, explain the following terms:
(i) Beam area
(ii) Lobes
(iii) HPBW and BWFN
9. illustrate With neat sketches, the current distribution on the following dipoles of various lengths:
(i) l= λ/2
(ii) l=λ
(iii) l= 2λ
10. Explain about basic radiation equation (OR) Radiation mechanism of single wire.
NOTE: Q1,2,3,4 are K3 level; Q5,6 at K1 level; Q7,8,9,10 are at K2 level;
Thin Linear-wire antennas
1.Show that the radiation resistance of λ/2 dipole is nearly 73 Ω
2. Explain about retarded potentials of an electric dipole
3. A halfwave dipole is radiating 1KW and has a gain of 2.15dBi. Find the input power to the isotropic antenna, that will radiate same field strength of the dipole.
4. A small circular loop antenna has diameter of 1.5λ. Calculate its radiation resistance.
5. Compare far-fields of Small loop and Short dipole antenna.
Antenn Arrays
1. For an N-element ULA , Obtain AF.
2. What is pattern mutlitplication? Draw the pattern of two point-sources separated by λ/2.
3. A broad side array operating 100cm wavelength consists of four dipoles spaced 50cm apart. All the elements carry same magnitude and phase current of 0.5A. Calculate the radiated.
4. Obtain the BSA characteristics (i) Sidelobe maxima (ii) side lobe minima (iii) BWFN (iv) HPBW
5. What is a pararisitc element? What is the need of a folded dipole in Yagi-Uda array? Design a Yagi-Uda array of directivity 9.2dB.
Assignment- Solutions for Problems
Assignment-1:
#1. E(θ) = cosθ cos2θ = 1/√2 at HPBW points
Solving θ= 1/2 cos-1 (1/√2cosθ)
using iterative method, in RHS θ=0; then LHS=22.5
now in RHS θ=22.5°, LHS=20.03°;
in RHS, θ=20.03°; LHS=20.59°;
in RHS θ=20.59°; LHS= 20.47°
in RHS θ=20.472°; LHS= 20.497°
in RHS θ=20.497°; LHS= 20.491°
in RHS θ=20.491°; LHS= 20.493°
As LHS and RHS are approximately equal; θ=20.49° ≈ 20.5°
HPBW = 2θ = 2 x 20.5 = 41°
NOTE: if you want to calculate BWFN, then E(θ) = cosθ cos2θ = 0;
so either cosθ=0 or cos2θ = 0
--->
θ=90° or θ=45°; as it is asked to calculate first nulls; θ=± 45° is the first Nulls;
BWFN = 2θ= 2x 45°=90°
#2.
(a)
Prad = ∬ U(θ,φ) dΩ
-->
Prad = ∬ U(θ,φ) sinθ dθ dφ
-->
10 = ∫θ ∫φ Qo (cosθ)3 sinθ dθ dφ
-->
10 =π ∫θ=0 2π∫φ=0 Qo (cosθ)3 sinθ dθ dφ
-->
10 =Qo π ∫θ=0 (cosθ)3 sinθ dθ 2π∫φ=0 dφ
-->
10 =Qo (1/4) (2π)
-->
10/ (0.25x2π) =Qo
-->
Qo = 6.366
∴ U= 6.366 (cosθ)3 W/Sr
S= U/r2
= 6.366 (cosθ)3 / (1000)2 = 6.366 x 10-6 (cosθ)3 W/m2
Smax= 6.366 x 10-6 W/m2
(b)
D= 4π Umax/ Prad
= 4π (6.366)/ 10 = 7.999 = 10 log7.999= 9.03dBi
(c) beam area = ΩA = Prad/ U = 10/(6.366 (cosθ)3)
≈ 10/6.366 = 1.5708 Sr.
(d)given, antenna is lossless; so efficiency=k=1;
G=kD = 1 x 7.999 = 7.999 = 9.03 dBi
#3. D= 4π Umax/Prad;
U = sinθ sinφ;
Umax= 1
Prad = ∬ U(θ,φ) dΩ
-->
Prad = ∬ U(θ,φ) sinθ dθ dφ
-->
Prad = π ∫θ=0 sin2θ dθ 2π∫φ=0 sinφ dφ
-->
Prad = (π/2) x2 = π
∴ D= 4πx1/ π = 4 = 6.02dB
#4. Ex= Ey;
Δφ = φy-φx= 90-0 = 90°
From the below Figure, its LHP;
On every axis, E has same magnitude==> Circular polarization; So its LHCP.
Assignment-2:
#3.Given dipole radiates power, Prad =1KW. Given Dipole of half wavelength;So D=1.64
Given Gain=2.15dBi; ==>
102.15/10 = 1.64
Here for this dipole, G= D;
Hence Pin = Prad =1KW;
#4. Given Small circular loop antenna diameter =1.5λ
Area of loop antenna = πr2 = π d2/4 = 1.767 λ2
For small loop antenna, Rr=320 π4 ( A2/ λ4)
solving above two, Rr= 97.3KΩ
Assignment-3:
#2. Pattern Multiplication is: Array Pattern = Element Pattern x Array Factor
For BSA α=0;
given d= λ/2;
AF= cos{ α/2 + (βd/2) cosθ }
if AF=1 ==> Major Lobe Radiation ==> θ=± π/2
if AF=0 ==> Null ==> θ = 0 or π
Given BSA => l=100cm= 1m
N=4
Half -wave dipole used => Rr = 73 Ω
D=50cm=0.5m
I=0.5A
Prad = N I2 Rr
Prad= 4 x 0.52 x 73 = 73W
Special Formulae
1.
Ae=η|le|2 4* Rrad
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