3.1 Introduction | unit 3 antenna fundamental and definitions

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Unit - 3

Antenna fundamentals and definition

3.1 Introduction

An antenna is a device used to transmit and/or receive electromagnetic waves. Electromagnetic waves are often referred to as radio waves. Most antennas are resonant devices, which operate efficiently over a relatively narrow frequency band. An antenna must be tuned (matched) to the same frequency band as the radio system to which it is connected, otherwise reception and/or transmission will be impaired. The device, which converts the required information signal into electromagnetic waves, is known as an Antenna. An Antenna converts electrical power into electromagnetic waves and vice versa.

For wireless communication systems, the antenna is one of the most critical components. A good design of antenna can relax system requirements and improve overall system performance.

The antenna serves to a communication system the same purpose that eyes and eyeglasses serve to a human.

An Antenna can be used either as a transmitting antenna or a receiving antenna.

• A transmitting antenna is one, which converts electrical signals into electromagnetic waves and radiates them.

• A receiving antenna is one, which converts electromagnetic waves from the received beam into electrical signals.

• In two-way communication, the same antenna can be used for both transmission and reception.

Antenna can also be termed as an Aerial. Plural of it is, antennae or antennas. Now-a-days, antennas have undergone many changes, in accordance with their size and shape. There are many types of antennas used for variety of applications.

3.2 Basic Antenna Parameters

Antenna pattern

Definition

The radiation pattern or antenna pattern is the graphical representation of the radiation properties of the antenna as a function of space.

That is, the antenna's pattern describes how the antenna radiates energy out into space (or how it receives energy).

It is important to state that an antenna radiates energy in all directions, at least to some extent, so the antenna pattern is actually three-dimensional. It is common, however, to describe this 3D pattern with two planar patterns, called the principal plane patterns.

These principal plane patterns can be obtained by making two slices through the 3D pattern through the maximum value of the pattern or by direct measurement.

It is these principal plane patterns that are commonly referred to as the antenna patterns.

Chart, radar chart

Description automatically generated

(a):dipole azimuth radiation pattern (b):dipole elevation radiation pattern

Figure 1. Antenna patterns

In discussions of principal plane patterns or even antenna patterns, you will frequently encounter the terms azimuth plane pattern and elevation plane pattern. The term azimuth is commonly found in reference to "the horizontal" whereas the term elevation commonly refers to "the vertical".

The fig.(a) shows horizontal pattern and fig.(b) shows vertical pattern.

Half power beam width

Definition

The 3 dB, or half power, beamwidth of the antenna is defined as the angular width of the radiation pattern, including beam peak maximum, between points 3 dB down from maximum beam level (beam peak).

Indication of HPBW

When a line is drawn between radiation pattern’s origin and the half power points on the major lobe, on both the sides, the angle between those two vectors is termed as HPBW, half power beam width. This can be well understood with the help of the following diagram.

Half Power Point

Figure 2 half-power points on the major lobe and HPBW.

Mathematical Expression

The mathematical expression for half power beam width is

Half power Beam Width = 70 λ /D

Where

λ is wavelength (λ = 0.3/frequency).

Dis Diameter.

Units

The unit of HPBW is radians or degrees.

Radiation Resistance

It is that part of an antenna's feedpoint electrical resistance that is caused by the radiation of electromagnetic waves from the antenna.

The radiation resistance {\displaystyle R_{\text{R}}}RR can be defined as the value of resistance that would dissipate the same amount of power as radiated as radio waves by the antenna with the antenna input current passing through it.

It is equal to the total power {\displaystyle P_{\text{R}}}PR radiated as radio waves by the antenna divided by the square of the rms current {\displaystyle I_{\text{rms}}}Irms into the antenna terminals:

The radiation resistance is determined by the geometry of the antenna and the operating frequency.

Front to back ratio

The Front to Back Ratio (F/B Ratio) of an antenna is the ratio of power radiated in the front/main radiation lobe and the power radiated in the opposite direction (180 degrees from the main beam)

This ratio tells us the extent of backward radiation and is normally expressed in dB. This parameter is important in circumstances where interference or coverage in the reverse direction needs to be minimized

Reflection coefficient

Definition:

In the context of antennas and feeders, the reflection coefficient is defined as the figure that quantifies how much of an electromagnetic wave is reflected by an impedance discontinuity in the transmission medium. The reflection coefficient is equal to the ratio of the amplitude of the reflected wave to the incident wave.

Calculating reflection coefficient

There are many ways in which the reflection coefficient can be calculated.

Using the basic definition of the reflection coefficient, it can be calculated from a knowledge of the incident and reflected voltages.

Diagram

Description automatically generated

Figure 3. Reflection coefficient

r =

Where,

r= reflection co-efficient

Vref= = reflected voltage

Vfwd = forward voltage

It is also useful to be able to calculate the reflection coefficient in terms of the forward and reverse power levels. As the power is proportional to V2 [ watts = V2 / R], we can deduce that:

r =

Where:

Γ = reflection coefficient

Pref = reflected power

Pfwd = forward power

Impedance bandwidth

The "impedance bandwidth" is just the ordinary bandwidth of the antenna. Normally this is defined as the range of frequencies over which the return loss is acceptable.

Bandwidth of an antenna is an important concept. The bandwidth of an antenna refers to the range of frequencies over which the antenna satisfies a particular parameter specification.

The parameters generally specified are gain, radiation pattern, the VSWR etc. Most commonly, the VSWR is chosen as the parameter for bandwidth considerations and this bandwidth is called the impedance bandwidth.

Pattern bandwidth

Bandwidth can be defined in terms of radiation patterns or VSWR/reflected power. The definition used is based on VSWR. Bandwidth is often expressed in terms of percent bandwidth, because the percent bandwidth is constant relative to frequency.

Polarization of an antenna

When the direction is not stated, the polarization is taken to be the polarization in the direction of maximum gain.‖ In practice, polarization of the radiated energy varies with the direction from the center of the antenna, so that different parts of the pattern may have different polarizations

Polarization may be classified as linear, circular, or elliptical.

If the vector that describes the electric field at a point in space as a function of time is always directed along a line, the field is said to be linearly polarized.

In general, however, the electric field traces is an ellipse, and the field is said to be elliptically polarized.

Linear and circular polarizations are special cases of elliptical, and they can be obtained when the ellipse becomes a straight line or a circle, respectively.

The electric field is traced in a clockwise (CW) or counterclockwise (CCW) sense. Clockwise rotation of the electric-field vector is also designated as right-hand polarization and counterclockwise as left-hand polarization.

Linear Polarization For the wave to have linear polarization, the time-phase difference between the two components must be

Circular Polarization Circular polarization can be achieved only when the magnitudes of the two components are the same and the time-phase difference between them is odd multiples of π/2.

||=||

Elliptical Polarization Elliptical polarization can be attained only when the time-phase difference between the two components is odd multiples of π/2 and their magnitudes are not the same or when the timephase difference between the two components is not equal to multiples of π/2 (irrespective of their magnitudes). That is

||||

Antenna Field Zones

The fields around an antenna may be divided into two principal regions, one near the antenna called the near field or Fresnel zone and one at a large distance called the far field or Fraunhofer zone.

The boundary between the two may be arbitrarily taken to be at a radius

R = (m)

where

L= Maximum dimension of the antenna in meters

λ=wavelength, meters

In the far or Fraunhofer region, the measurable field components are transverse to the radial direction from the antenna and all power flow is directed radially outward. In the far field the shape of the field pattern is independent of the distance. In the near or Fresnel region, the longitudinal component of the electric field may be significant and power flow is not entirely radial. In the near field, the shape of the field pattern depends, in general, on the distance.

Diagram

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Figure 4. Antenna region, Fresnel region and Fraunhofer region.

Key takeaways:

The radiation pattern or antenna pattern is the graphical representation of the radiation properties of the antenna as a function of space.

Beam width of the antenna is defined as the angular width of the radiation pattern, including beam peak maximum, between points 3 dB down from maximum beam level (beam peak).

The beam area or beam solid angle or ΩA of an antenna is given by the integral of the normalized power pattern over a sphere (4π sr)

4. The power radiated from an antenna per unit solid angle is called the radiation intensity U (watts per steradian or per square degree).

5. The ratio of the main beam area to the (total) beam area is called the (main) beam efficiency εM. Thus,

Beam Efficiency = (Dimensionless)

6. The directivity of an antenna is equal to the ratio of the maximum power density P (θ, φ)max (watts/m2 ) to its average value over a sphere as observed in the far field of an antenna. Thus,

D =

7. The resolution of an antenna may be defined as equal to half the beam width between first nulls (FNBW)/2.

8. The effective height h (meters) of an antenna is another parameter related to the aperture. multiplying the effective height by the incident field E (volts per meter) of the same polarization gives the voltage V induced.

9. The radiation resistance {\displaystyle R_{\text{R}}}RR can be defined as the value of resistance that would dissipate the same amount of power as radiated as radio waves by the antenna with the antenna input current passing through it.

10. The Front to Back Ratio (F/B Ratio) of an antenna is the ratio of power radiated in the front/main radiation lobe and the power radiated in the opposite direction (180 degrees from the main beam)

11. The reflection coefficient is equal to the ratio of the amplitude of the reflected wave to the incident wave.

12. Impedance Bandwidth is defined as the range of frequencies over which the return loss is acceptable.

13. If the vector that describes the electric field at a point in space as a function of time is always directed along a line, the field is said to be linearly polarized.

14. In general, however, the electric field traces is an ellipse, and the field is said to be elliptically polarized.)

3.3 Patterns

Isotropic Pattern - an antenna pattern defined by uniform radiation in all directions, produced by an isotropic radiator (point source, a non-physical antenna which is the only nondirectional antenna). Directional Pattern - a pattern characterized by more efficient radiation in one direction than another (all physically realizable antennas are directional antennas).

Omnidirectional Pattern - a pattern which is uniform in a given plane.

Principal Plane Patterns - the E-plane and H-plane patterns of a linearly polarized antenna.

E-plane - the plane containing the electric field vector and the direction of maximum radiation.

H-plane - the plane containing the magnetic field vector and the direction of maximum radiation.

3.4 Beam Area (Beam solid angle)

Beam Area (or beam solid angle)

In polar two-dimensional coordinates an incremental area dA on the surface of a sphere is the product of the length r dθ in the θ direction (latitude) and r sin θ dφ in the φ direction (longitude), as shown in Fig. Thus,

dA = (r dθ)(r sinθ dφ) = r 2 dΩ (1)

Where dΩ = solid angle expressed in steradians (sr) or square degrees ( ) dΩ = solid angle subtended by the area dA

The beam area or beam solid angle or ΩA of an antenna is given by the integral of the normalized power pattern over a sphere (4π sr)

3.5 Radiation Intensity

Definition

The power radiated from an antenna per unit solid angle is called the radiation intensity U (watts per steradian or per square degree).

The normalized power pattern of the previous section can also be expressed in terms of this parameter as the ratio of the radiation intensity U(θ, φ), as a function of angle, to its maximum value. Thus,

Whereas the Poynting vector S depends on the distance from the antenna (varying inversely as the square of the distance), the radiation intensity U is independent of the distance, assuming in both cases that we are in the far field of the antenna.

3.6 Beam Effeciency

Beam Efficiency

The (total) beam area ΩA (or beam solid angle) consists of the main beam area (or solid angle) ΩM plus the minor-lobe area (or solid angle) Ωm. Thus,

ΩA = ΩM + Ωm

The ratio of the main beam area to the (total) beam area is called the (main) beam efficiency εM. Thus,

Beam Efficiency = (Dimensionless)

The ratio of the minor-lobe area (Ωm) to the (total) beam area is called the stray factor. Thus

= stray factor

It follows that

+ = 1

3.7 Directivity D and Gain G

Directivity (D) AND Gain (G)

Directivity (D)

The directivity D and the gain G are probably the most important parameters of an antenna. The directivity of an antenna is equal to the ratio of the maximum power density P(θ, φ)max (watts/m2 ) to its average value over a sphere as observed in the far field of an antenna. Thus,

D =

The directivity is a dimensionless ratio ≥1. The average power density over a sphere is given by

P =

= dΩ (W )

Therefore, the directivity

D = =

And

D =

This is the diversity from beam area, where Pn(θ, φ) dΩ = P(θ, φ)/P(θ, φ)max = normalized power pattern.

Gain

The gain G of an antenna is an actual or realized quantity which is less than the directivity D due to ohmic losses in the antenna or its radome (if it is enclosed). In transmitting, these losses involve power fed to the antenna which is not radiated but heats the antenna structure. A mismatch in feeding the antenna can also reduce the gain. The ratio of the gain to the directivity is the antenna efficiency factor. Thus, G = kD

Where k= Efficiency factor (0< k< 1), dimensionless

3.8 Directivity and resolution

Resolution

Definition

The resolution of an antenna may be defined as equal to half the beam width between first nulls (FNBW)/2.

When the antenna beam maximum is aligned with one satellite, the first null coincides with the adjacent satellite. Half the beamwidth between first nulls is approximately equal to the half-power beamwidth (HPBW) or

The product of the FNBW/2 in the two principal planes of the antenna pattern is a measure of the antenna beam area. Thus,

3.9 Antenna Apertures

Antenna Apertures

The concept of aperture is most simply introduced by considering a receiving antenna. Suppose that the receiving antenna is a rectangular electromagnetic horn immersed in the field of a uniform plane wave as suggested in Fig.

Let the Poynting vector, or power density, of the plane wave be S watts per square meter and the area, or physical aperture of the horn, be Ap square meters. If the horn extracts all the power from the wave over its entire physical aperture, then the total power P absorbed from the wave is

Diagram

Description automatically generated

Figure 5. Plane wave incident on electromagnetic horn of physical aperture AP

P =

Figure 6. Radiation over beam area

Thus, the electromagnetic horn may be regarded as having an aperture, the total power it extracts from a passing wave being proportional to the aperture or area of its mouth. But the field response of the horn is NOT uniform across the aperture A because E at the sidewalls must equal zero.

Thus, the effective aperture Ae of the horn is less than the physical aperture Ap as given by

(Dimensionless) Aperture efficiency

where εap =aperture efficiency.

3.10 Effective height

Effective height

The effective height h (meters) of an antenna is another parameter related to the aperture. multiplying the effective height by the incident field E (volts per meter) of the same polarization gives the voltage V induced.

Thus, V = hE (1) Accordingly, the effective height may be defined as the ratio of the induced voltage to the incident field or h = V/E (m)

3.11 Radio communication link

The Friis transmission formula is used in telecommunications engineering, equating the power at the terminals of a receive antenna as the product of power density of the incident wave and the effective aperture of the receiving antenna under idealized conditions given another antenna some distance away transmitting a known amount of power

Pr = Received power, W

Pt = Received power, W

Aet = Effective aperture of transmitting antenna, m2

Aer = Effective aperture of receiving antenna, m2

r = Distance between antennas, m

= Wavelength, m

Key takeaways:

Friss transmission is given by

)

3.12 Fields from oscillating dipole

It is a normal dipole antenna, where the frequency of its operation is half of its wavelength. Hence, it is called as half-wave dipole antenna.

The edge of the dipole has maximum voltage. This voltage is alternating (AC) in nature. At the positive peak of the voltage, the electrons tend to move in one direction and at the negative peak, the electrons move in the other direction. This can be explained by the figures given below.

Working Half-Wave Dipole

Figure 8. Haly wave dipole.

The figures given above show the working of a half-wave dipole.

Fig 1 shows the dipole when the charges induced are in positive half cycle. Now the electrons tend to move towards the charge.

Fig 2 shows the dipole with negative charges induced. The electrons here tend to move away from the dipole.

Fig 3 shows the dipole with next positive half cycle. Hence, the electrons again move towards the charge.

The cumulative effect of this produces a varying field effect which gets radiated in the same pattern produced on it. Hence, the output would be an effective radiation following the cycles of the output voltage pattern. Thus, a half-wave dipole radiates effectively.

Radiates Effectively

Figure 9. Current distribution

The above figure shows the current distribution in half wave dipole. The directivity of half wave dipole is 2.15dBi, which is reasonably good. Where, ‘i’ represents the isotropic radiation.

Radiation Pattern

The radiation pattern of this half-wave dipole is Omni-directional in the H-plane. It is desirable for many applications such as mobile communications, radio receivers etc.

Omni-Directional

Figure 10. Dipole in H and V plane

The above figure indicates the radiation pattern of a half wave dipole in both H-plane and V-plane.

The radius of the dipole does not affect its input impedance in this half wave dipole, because the length of this dipole is half wave and it is the first resonant length. An antenna works effectively at its resonant frequency, which occurs at its resonant length.

3.13 Single to noise ratio

The system noise power is related to the system noise temperature as:

From Friis transmission equation:

one can calculate the signal power Pr . Thus, the SNR ratio becomes:

SNR = /

3.14 Antenna temperature

Antenna Temperature

It is a measure of the noise being produced by an antenna in a given environment. This is also called an Antenna Noise Temperature.

It is not the physical temperature of the antenna. This temperature depends of the gain, radiation pattern and the noise that the antenna picks up from the surrounding environment.

The Antenna Temperature can be represented by the following formula:

Antenna temperature (=

This equation shows that the antenna temperature is calculated by integrating over the entire sphere, based on the radiation pattern of the antenna and the temperature distribution of the antenna.

R() is the radiation pattern of the antenna.

T( )is temperature distribution of the antenna based on its surroundings. For example, the temperature of the night sky is 4 Kelvin, the value of the temperature pattern in the direction of the ground would be based on the physical temperature of the ground.

3.15 Antenna impedance

Antenna impedance relates the voltage to the current at the input to the antenna. This is extremely important as we will see.

Let's say an antenna has an impedance of 50 ohms. This means that if a sinusoidal voltage is applied at the antenna terminals with an amplitude of 1 Volt, then the current will have an amplitude of 1/50 = 0.02 Amps. Since the impedance is a real number, the voltage is in-phase with the current.

Alternatively, suppose the impedance is given by a complex number, say Z=50 + j*50 ohms.

Note that "j" is the square root of -1. Imaginary numbers are there to give phase information. If the impedance is entirely real [Z=50 + j*0], then the voltage and current are exactly in time-phase. If the impedance is entirely imaginary [Z=0 + j*50], then the voltage leads the current by 90 degrees in phase.

If Z=50 + j*50, then the impedance has a magnitude equal to:

√ 50 2 + 50 2 = 70.71

The phase will be equal to:

tan -1 Im(Z) / Re(Z) = 45

This means the phase of the current will lag the voltage by 45 degrees. That is, the current waveform is delayed relative to the voltage waveform. To spell it out, if the voltage (with frequency f) at the antenna terminals is given by

V(t) = cos(2πft)

The electric current will then be equal to:

I(t) = 1/ 70.71 cos (2πft - . 45)

Hence, antenna impedance is a simple concept. Impedance relates the voltage and current at the input to the antenna. The real part of the antenna impedance represents power that is either radiated away or absorbed within the antenna. The imaginary part of the impedance represents power that is stored in the near field of the antenna. This is non-radiated power. An antenna with a real input impedance (zero imaginary part) is said to be resonant. Note that the impedance of an antenna will vary with frequency.

References:

1. Antenna Theory: Analysis and Design Book by Constantine A. Balanis

2. Antenna and Wave Propagation Book by Deepak Handa and K. D. Prasad

3. Antenna and Wave Propagation Book by Ranjana Trivedi

4. ANTENNAS AND WAVE PROPAGATION Book by SACHIN D. DR RUIKAR

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