Study Notes: Antennas | Electromagnetics - Electronics and Communication Engineering (ECE) PDF Download

Introduction

An antenna is a way for linking the electromagnetic waves from transmitter to receiver.
A resonant antenna is a transmission line whose length is exactly equal to the multiple of half wavelength, i.e.,
l = nλ/2
where, n = 1, 2, 3,….. positive real integer and λ is wavelength.
Basic Antenna Parameters: Antenna parameters are the factors that select the antenna for particular reason or application.
Directivity: Directivity is defined as the ratio of radiation intensity in particular direction to average radiation intensity

• U(θ, φ) = radiation intensity in a direction
• U_av = average radiation intensity

Dipole Antenna

• A dipole antenna may be defined as a symmetrical antenna in which the two ends are at equal potential relative to mid-point.
• A physical dipole consists of two equal and opposite charges i.e., in the literal sense, two poles.
• The dipole magnetic field lines are shown in the figure.
• A half-wave dipole λ/2 antenna is the fundamental ratio antenna of the metal rod on a thin wire, which has a physical length of half wavelength in free space.

Dipole magnetic field antenna linesNote: A λ/2 antenna is also known as Hertz antenna or half-wave doublet.
Antenna's Power and Field: Normalized power and field pattern can be obtained by dividing a power or field component by its maximum value respectively i.e.,
Normalized power:

Normalized field pattern:

• Radian is defined as the arc of length l on the circle from a centre of the circle of radius r since the circumference of a circle is 2πr, there are 2π radians in a full circle.
• Area of a sphere is 4πr², there is 4π steradian in a full sphere i.e., dω = 4π.

Radiation Pattern: The radiation pattern is basically a 3-D graph which indicates the variations in electromagnetic field or power as a function of spherical coordinates θ and φ.
Field pattern: Following Figure shows the radiation pattern of an antenna which includes generally three lobes as a main lobe, side lobe, and back lobe.
Main lobe: It contains the direction of maximum radiation.
Side lobe: The side lobe is adjacent to the main lobe.

Back lobe: In back lobe, the field goes to zero.
Field pattern of an antenna

Key Points

• The radiation pattern is different for different antennas and is affected by the location of an antenna with respect to earth.
• When radiation pattern is measured in terms of field strength E then it is called field strength pattern.
• When it is measured in terms of power unit solid angle, then it is called as power pattern.
• The field pattern and power pattern are related to each other.

Radiation Intensity: radiation intensity is defined as the radiated power per unit solid angle i.e.,

Radiation intensity(in watt/steradian):
U = W_r/4π
where W_r = Radiated power

Antenna Characteristics: The following are the basic parameters of an antenna which judge the characteristics of an antenna

• Antenna efficiency:
  η = Power radiated/Total power input = P_r/P_T
• Directivity:
  D = Maximum radiation intensity of test antenna/Average radiation intensity of test antenna = U (θ, ∅)_max/U_av
• Directivity, in terms of power and solid angle,
  
  (Beam solid angle or beam area)
• For isotropic antenna:
  
  where, U₀ = Radiation intensity of the isotropic antenna
• In terms of beam area:
  
• Gain of antenna can be related to directivity as G = kD; where, k = Efficiency factor (0 ≤ k ≤ 1
• The ratio of maximum radiation intensity in a given direction to the maximum radiation intensity from a reference antenna produced in the same direction with same power input:
  G₀ = U_m/U₀
  where, Um = maximum radiation intensity in a given direction and U₀ = maximum radiation intensity from a reference antenna
• Power gain: The power gain compares the radiated power density of actual antenna and an isotropic antenna on the basis of same input power o both:
  
  where PT = Transmitted power
• Directive gain: The directivity gain in a given direction is defined as the ratio of the radiation intensity in that direction to the average radiated power:
  
  where P_r = radiated power
• Power gain and directive gain can be related as GP = ηGd
• In a case of directivity gain, the total output power is maintained same.
• In the case of power gain, the total input power is maintained the same.

Effective Area:
Ae = Power received/ Power density of incident wave (W/m² = P_r/S

• It is also called antenna aperture.

Effective Height: The effective height of an antenna indicates that how effectively an antenna radiates or receives an electromagnetic wave energy.
h = Induced voltage (V)/Incident field (E)

• Relation between him and A_e
  
  where Z₀ = Intrinsic impedance = 377Ω
• Antenna aperture efficiency (ε_ap) for horn and parabolic antenna is in the range of 50% to 80%.

Beam Efficiency (εm): The beam efficiency is defined as the ratio of power transmitted with in cone angle (θ) to the power transmitted by the antenna. In terms of beam area (Ω_A)
ε_m = Ω_m/Ω_A = main beam area/Total beam area

• The resolution of an antenna is defined as equal to half the beam width between the first nulls.
• Resolution =
  FNBW/2

where, FNBW ≅ 2 HPBW; HPBW = Half Power Beam Width; FNBW = Full Null Beam Width

• Antenna beam area:
  
• Directivity is equal to the number of point sources in the sky that the antenna can resolve.
• Radiation in the dipole occurs due to moving charge in simple harmonic motion along the conductor i.e., acceleration or deceleration of charge along the conductor.

Antenna Beam Width: Antenna beam width is defined as the angular separation between two half power points on the radiation pattern of an antenna.

Practical Antenna

• RMS value of induced emf in loop antenna having N turns in volts is
  
• The far-field of the loop has only an Eφ component and Hθ component as,
  

Log-Periodic Antenna

In a log-periodic antenna, the design ratio (τ) or scale factor can also be written as

where, R = Spacing between dipoles, L = Length of the dipole and Apex angle is

Log - periodic antenna

• In helical antenna, the pitch angle can be calculated as
  

where, πD is the circumference of the helix, S is the spacing of the helix. If the pitch angle is zero, then the winding is flattened. In horn antenna, the flare angle can be calculated as

where a = Aperture of the horn in the horn antenna
L = Horn length in metre
S = Path length in the front face of the horn
and

• Optimum horn dimensions can be related by

Optimum S,

Optimum length,

• In the horn antenna, the value of S in E plane is usually 0.25 λ and in H plane is usually 0.4 λ.
• Directivity of a horn antenna can be expressed in terms of its effective aperture is
• For rectangular horn, the value of directivity is
  
• For pyramidal (rectangular) horn, the value of directivity can also be expressed as D ≅ 10 logs (7.5 aελ aHλ)
• In microstrip antenna, the characteristic impedance is
  Z_c = 26.7Ω
  where, Z₀ = intrinsic impedance
  η = w/t (width of the microstrip)/(Thickness of the microstrip)
  
  
• Maximum effective aperture of the loop in loop antenna is
  A_em = 3λ²/8π
• The expression for radiation resistance in the loop antenna is:
  R_r = 3720(α/λ)
  where a = Radius of the loop (circular)

Input Impedance versus Log f Plot: Figure below shows a plot of input impedance |Z_in| versus the logarithm of frequency.

The impedance |Z_in| goes through identical cycles of variations where each cycle is exactly like the preceding one.

• In helical antenna, BWFN (Beam Width of First Null)
  

where, C = Circumference = πD, L_a = Total length of the helical antenna

• Directivity:
  D = 15NC²S/λ³

where, S = Spacing between turns, N = Number of turns, λ = Wavelength, and C = Circumference of the helix.

Reflector Antenna

• Half power beam width of paraboloid is
  ∅ = 70λ/D_α
• Directivity of the paraboloid is
  D = 9.87(D/λ)²
• Power gain of the paraboloid is
  g_p = 6.4(D_a/λ)²
• Reflectors are used to produce desired shapes of the radiation pattern.
• A flat sheet reflector is the simplest reflector or which is used to guide electromagnetic energy in the desired direction.
• A corner reflector is a reflective object which consists of two or three mutually intersecting conducting flat surfaces.
• A reflector which has the directional feed which radiates all or most of the energy into parabola is called parabolic reflector.
• For flat sheet reflector, the gain and the spacing of the drive unit can be related as
  
  where S is the spacing of antenna from the flat sheet reflector.
• Offset feed is used to removing the problem of aperture blocking in the parabolic reflector.
• In corner reflector, a spacing of driven element modulates the bandwidth and gain of the main lobe.
• A cylindrical parabola converts a cylindrical wave radiated by an in-phase line source at the focus into a plane wave at the aperture.
• For rectangular aperture paraboloidal reflector, Beam Width First Null is given by BWFN
  = 115λ/L
  degree
• Due to the tapering in paraboloid reflector, the captured area is less as compare to actual area i.e., A₀ = k A_a
• where A₀ is capture area and A_a is the actual area of the mouth and k is constant whose value is 0.65 for a dipole antenna.
• The phases of all waves arriving at the aperture are the same i.e., a plane wave front is created in the aperture plane.
• In the parabolic reflector, all the waves are in phase, a very strong and concentrated beam of radiation is along the parabolic axis.
• The geometrical properties of a parabola provide very good microwave reflectors that lead to the generation of concentrated beam of radiation.
• Aperture and directivity can be related as
  D = 4πA_e/λ²
• Beam width between the first null for large circular aperture is (in degree)
  VWFN = 140λ/d
• Far field or Fraunhofer region can be expressed as (in metre)
  d_f = 2D²/λ
• Near field, a region is a region close to the transmitter, in some λ distance and the far field region is far away from the transmitter, after some λ distance.
• The height of the transmitting antenna and Antenna Under Test (AUT) can be related as
  H_AUT = λ.D/4H_r
  where D is the distance between source and AUT.
• Indoor measurement is controlled and interference free, so easy and accurate.
• For accurate measurement of far-field or Fraunhofer region, the distance between transmitting and receiving antenna should be
  r ≥ 2d²/λ
  where d is a maximum linear dimension of the aperture of either antenna.
• Gain and directivity can be related as
  D = G₀/λ
• In two antenna, absolute gain measurement, the gain can be expressed as
  
  where P_R = Receiving power, and P_T = Transmitting power