(SEM VI) THEORY EXAMINATION 2023-24 ANTENNA AND WAVE PROPAGATION

ANTENNA AND WAVE PROPAGATION – KEC603

Section-wise Important Questions & Ready Answers

SECTION A

(Attempt all – 2 marks each)

(a) Gradient of a Vector in Cylindrical Coordinate System

The gradient operator in cylindrical coordinates is used to find the rate of change of a scalar field in radial, angular, and axial directions. It helps analyze electromagnetic fields where cylindrical symmetry exists, such as coaxial cables and antennas.

(b) Irrotational Fields

An irrotational field is one in which the curl of the vector field is zero. Such fields do not exhibit circulation and can be expressed as the gradient of a scalar potential. Electrostatic fields are irrotational in nature.

(c) Electric Field Intensity

Electric field intensity is defined as the force experienced by a unit positive charge placed at a point in an electric field. It is a vector quantity measured in volts per meter and indicates the strength and direction of the electric field.

(d) Maxwell’s Equation for Electric Field

Maxwell’s equations describe the relationship between electric and magnetic fields. The divergence of electric flux density is equal to the volume charge density, which explains how electric fields originate from charges.

(e) Solid Angle and Beam Area

A solid angle represents the three-dimensional angle subtended by an object at a point. Beam area is the total solid angle through which an antenna radiates power and is used to describe radiation pattern characteristics.

(f) Beam Area of an Antenna

The beam area of an antenna is the integral of its normalized power radiation pattern over all directions. It indicates how concentrated or spread the radiation is and is inversely related to antenna directivity.

(g) Major Advantage of Folded Dipole Antenna

The major advantage of a folded dipole antenna is its higher input impedance compared to a simple dipole. This makes it easier to match with transmission lines, improving power transfer efficiency.

(h) Maximum Range of Tropospheric Transmission

The maximum tropospheric range depends on antenna heights. It increases with taller antennas due to extended line-of-sight propagation, accounting for atmospheric refraction effects.

(i) Critical Frequency for Vertical Incidence

Critical frequency is the highest frequency that can be reflected back to earth by the ionosphere at vertical incidence. It depends on the maximum electron density of the ionospheric layer.

(j) Maximum Electron Concentration of D and E Layers

Electron concentration is directly related to the critical frequency of an ionospheric layer. Higher critical frequency implies higher electron density, which determines reflection capability for radio waves.

SECTION B

(Attempt any three – 10 marks each)

1. Vector Conversion from Cylindrical to Cartesian Coordinates

To convert a vector from cylindrical to Cartesian coordinates, the unit vectors are expressed in terms of x and y components. This conversion is essential in electromagnetic field analysis when changing reference systems for problem simplification.

2. Magnetic Field Due to a Finite Line Conductor

The magnetic field due to a finite current-carrying conductor is derived using Biot–Savart law. The resulting expression shows that magnetic field strength depends on current magnitude, distance from the conductor, and the angles subtended at the observation point.

3. Antenna Temperature and Relation with SNR

Antenna temperature represents the noise power received by an antenna due to its surroundings. It directly affects the signal-to-noise ratio, as higher antenna temperature increases noise and reduces communication quality.

4. Vertical Antenna and Folded Dipole Antenna

A vertical antenna radiates omnidirectionally in the horizontal plane and is widely used for broadcasting. A folded dipole consists of two parallel conductors and offers improved impedance matching and bandwidth compared to a simple dipole.

5. Critical Frequency, Multihop Propagation, and Skip Distance

Critical frequency determines ionospheric reflection. Multihop propagation occurs when signals are reflected multiple times between the ionosphere and earth, enabling long-distance communication. Skip distance is the minimum distance from the transmitter where the sky wave returns to earth.

SECTION C

Q3(a) Differential Length Element in Vector Calculus

A differential length element represents an infinitesimally small displacement in space. It is used in line integrals to calculate work done, electric potential, and magnetic fields along a path.

Q3(b) Divergence and Curl Evaluation

Divergence measures the net outward flux of a vector field from a point, while curl measures its rotational tendency. Evaluating both for a given vector helps determine whether the field is conservative or rotational.

Q4(a) Electric Field Due to a Charged Ring

The electric field on the axis of a uniformly charged ring is derived using Coulomb’s law. The field reaches maximum value at a certain distance along the axis. When the ring radius tends to zero, the expression reduces to the electric field of a point charge.

Q4(b) Design of a 3-Element Yagi-Uda Antenna

A Yagi-Uda antenna consists of a reflector, driven element, and director. The driven element length is approximately half wavelength, while the reflector is slightly longer and the director is shorter. Proper spacing improves directivity and gain.

Q5(a) Fields from Oscillating Dipoles and Directivity

An oscillating dipole produces both electric and magnetic fields that vary with distance. Directivity measures how concentrated the radiation is in a particular direction. Antenna gain is the product of directivity and efficiency.

Q5(b) Effective Aperture, Effective Height, and Antenna Temperature

Effective aperture represents the power-receiving capability of an antenna, while effective height relates received voltage to incident field strength. Antenna temperature accounts for thermal noise affecting receiver performance.

Q6(a) Electric Field Due to Two λ/2 Antenna Array

When two half-wave antennas carry currents of equal amplitude and phase, the resulting field is obtained using array factor theory. The radiation pattern shows enhanced directivity compared to a single antenna.

Q6(b) Fields of a Short Dipole

A short dipole produces electric and magnetic fields whose strength decreases with distance. These fields consist of near-field and far-field components, essential for understanding radiation mechanisms.

Q7(a) Skip Distance Considering Earth Curvature

Skip distance increases when earth curvature is considered because the ionospheric reflection point shifts. This affects coverage areas in sky wave communication systems.

Q7(b) Maximum Usable Frequency (MUF)

MUF is the highest frequency that can be used for communication between two points via ionospheric reflection. It depends on critical frequency, angle of incidence, and earth curvature.