Unit - 3

Antenna fundamentals and definition

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.

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.

(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.

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

Units

The unit of HPBW is radians or degrees.

Radiation Resistance

Front to back ratio

.

Reflection coefficient

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

Figure 3. Reflection coefficient

r =

Where,

r= reflection co-efficient

Vref= = reflected voltage

Vfwd = forward voltage

r =

Where:

Γ = reflection coefficient

Pref = reflected power

Pfwd = forward power

Impedance bandwidth

Pattern bandwidth

Polarization of an antenna

||=||

=

=

||||

=

Antenna Field Zones

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.

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

Key takeaways:

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 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.)

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.

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)

Definition

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

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.

ΩA = ΩM + Ωm

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

Directivity (D) AND Gain (G)

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

Resolution

Definition

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

Antenna Apertures

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

P =

Figure 6. Radiation over beam area

(Dimensionless) Aperture efficiency

where εap =aperture efficiency.

Effective height

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

)

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.

Figure 8. Haly wave dipole.

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

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.

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.

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.

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 = /

Antenna Temperature

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.

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