JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech III Year ANTENNAS AND PROPAGATION Previous Question Paper (August - 2022 - R18)

The relationship between electromagnetic potentials and their sources is derived from Maxwell's equations. We define the Magnetic Vector Potential (A) and the Electric Scalar Potential (Φ) to simplify the solution of wave equations.

• From Gauss's Law for magnetism, ∇ · B = 0, we can define B as the curl of a vector potential:
  B = ∇ × A
• Substituting this into Faraday's Law, ∇ × E = -∂B/∂t, we obtain ∇ × (E + ∂A/∂t) = 0. Since the curl of a gradient is zero, we define the scalar potential Φ such that:
  E = -∇Φ - ∂A/∂t
• Applying the Lorenz Gauge Condition, ∇ · A = -με(∂Φ/∂t), to decouple the wave equations, we arrive at the non-homogeneous wave equations for the potentials in terms of source current density (J) and charge density (ρ):
  ∇²A - με(∂²A/∂t²) = -μJ
  ∇²Φ - με(∂²Φ/∂t²) = -ρ/ε

A Loop Antenna consists of a wire formed into a closed loop, typically circular or rectangular. Its operation depends on the ratio of its circumference (C) to the wavelength (λ).

• Small Loop (Electrically Small): When the circumference is much smaller than the wavelength (C < λ/10), the current is essentially uniform throughout the loop. The radiation pattern is similar to a short electric dipole, with maximum radiation in the plane of the loop and a null along the axis perpendicular to the loop.
• Large Loop (Resonant): When the circumference is approximately equal to the wavelength (C ≈ λ), the current distribution is non-uniform. The radiation pattern changes, exhibiting maximum radiation along the axis perpendicular to the loop.
• Applications: Due to their compact size and directional properties, small loops are widely used in radio direction finding (RDF), portable receivers, and RFID tags.
• Characteristics: They are characterized by low radiation resistance, which often necessitates impedance matching networks to improve efficiency.