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.,
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 i.e.,
- U(θ, φ) = radiation intensity in a direction
- Uav = average radiation intensity
- 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.
Note: 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 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.
- 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.
- Antenna efficiency:
- Directivity, in terms of power and solid angle,
- For isotropic antenna:
- In terms of beam area:
- Gain of the 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 the same power input:
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 an actual antenna and an isotropic antenna on the basis of the 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 Pr = radiated power
- Power gain and directive gain can be related as GP = ηGd
- In the case of directivity gain, the total output power is maintained the same.
- In the case of power gain, the total input power is maintained the same.
- It is also called antenna aperture.
- Relation between him and Ae
where Z0 = Intrinsic impedance = 377Ω
- Antenna aperture efficiency (εap) 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 within cone angle (θ) to the power transmitted by the antenna. In terms of beam area (ΩA)
- The resolution of an antenna is defined as equal to half the beam width between the first nulls.
- Resolution =
- 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.
- 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,
- 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
L = Horn length in metre
S = Path length in the front face of the horn
- Optimum horn dimensions can be related by
- 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
Zc = 26.7Ω
where, Z0 = intrinsic impedance
- The maximum effective aperture of the loop in a loop antenna is
- The expression for radiation resistance in the loop antenna is:
where a = Radius of the loop (circular)Input Impedance versus Log f Plot: Figure below shows a plot of input impedance |Zin| versus the logarithm of frequency.
- In helical antenna, BWFN (Beam Width of First Null)
Reflector Antenna: The antennas which used for microwave frequency regions are called parabolic reflector antennas. Parabolic dish antennas are liked to generate narrow beams in the microwave region. Reflectors are used to adjust the radiation of the primary antenna and increase the directivity in any particular direction.
- The half-power beamwidth of the paraboloid is
- Directivity of the paraboloid is
- Power gain of the paraboloid is
- 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 reflectors, 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
- Due to the tapering in paraboloid reflector, the captured area is less as compare to actual area i.e., A0 = k Aa
where A0 is capture area and Aa 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 wavefront 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
- Beamwidth between the first null for large circular aperture is (in degree)
- Far-field or Fraunhofer region can be expressed as (in metre)
- 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
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
where d is a maximum linear dimension of the aperture of either antenna.
- Gain and directivity can be related as
- In two antenna, absolute gain measurement, the gain can be expressed as
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