JNTU B.Tech III ANTENNAS AND WAVE PROPAGATION Previous Question Paper (August - 2022 - R13)

The principle of radiation in antennas is based on the fact that time-varying electric and magnetic fields produce electromagnetic waves that propagate through space. According to Maxwell's equations, an accelerating charge creates electromagnetic radiation.

Consider a simple dipole antenna, which is essentially a straight conductor carrying an alternating current. As the current oscillates, charges on the conductor accelerate back and forth.

1. Accelerating Charges: When an alternating voltage is applied to the dipole, charges (electrons) are forced to move back and forth along the conductor. This back-and-forth motion is an acceleration.

2. Time-Varying Current: The movement of charges constitutes an alternating current flowing through the conductor. This current is maximum at the center and zero at the ends of the dipole.

3. Creation of Electric and Magnetic Fields:

• A time-varying current produces a time-varying magnetic field around the conductor, circulating in loops.
• A time-varying electric field exists due to the charge distribution on the conductor. The charge density is maximum at the ends and zero at the center, leading to an electric field that varies in magnitude and direction.

4. Electromagnetic Wave Generation: According to Maxwell's equations, these time-varying electric and magnetic fields are mutually perpendicular and in phase. As these fields oscillate, they generate each other and detach from the antenna, propagating outwards as electromagnetic waves at the speed of light. The fields are strongest perpendicular to the conductor.

Diagrammatic Representation:

Imagine a short dipole antenna. At any instant, there's a distribution of charge and current. As the current reverses direction, the polarity of the electric field reverses, and the magnetic field lines also change direction. These disturbances propagate away from the antenna as transverse electromagnetic waves, where the electric field (E), magnetic field (H), and direction of propagation (k) are mutually perpendicular.

The radiation pattern shows the spatial distribution of radiated power. For a short dipole, it's typically toroidal (doughnut-shaped), with maximum radiation perpendicular to the antenna axis and nulls along the axis.

The effective length ($L_e$) of an antenna is related to its radiation resistance ($R_r$) and physical length. For a short dipole antenna, the effective length is defined such that the open-circuit voltage induced in the antenna is $V_o = E_z L_e$, where $E_z$ is the electric field strength at the antenna's location.

The relationship between radiation resistance and effective length for a short dipole is given by:

where $\lambda$ is the wavelength.

Given radiation resistance $R_r = 73 \ \Omega$. We need the wavelength $\lambda$ to calculate $L_e$. Assuming a standard frequency like 300 MHz, $\lambda = \frac{c}{f} = \frac{3 \times 10^8 \ m/s}{300 \times 10^6 \ Hz} = 1 \ m$.

Rearranging the formula to solve for $L_e$:

Substituting the values:

The effective aperture area ($A_e$) of an antenna is related to its radiation resistance and directivity. For a lossless antenna, the effective aperture area is given by:

where $G$ is the directivity of the antenna.

For a short dipole, the directivity is $G = 1.5$.

Using $\lambda = 1 \ m$ and $G = 1.5$:

Note: The calculation of effective length assumes a short dipole. The frequency was assumed to be 300 MHz to determine the wavelength. If a different frequency is implied, the wavelength and consequently the effective length and aperture area would change.