JNTU B.Tech III Year ANTENNAS AND WAVE PROPAGATION Previous Question Paper (March - 2021 - R13/R15)

i) Beam Area (Ω_A): The beam area or beam solid angle is the integral of the normalized radiation pattern over a sphere of 4π steradians. It is defined as Ω_A = ∫∫ P_n(θ, φ) sinθ dθ dφ, representing the solid angle through which all power would be radiated if the radiation intensity were constant at its maximum value.
Radiation Intensity (U): Radiation intensity is defined as the power radiated from an antenna per unit solid angle. It is independent of the distance from the antenna and is measured in Watts per steradian (W/sr). It is given by U = r²W_rad, where W_rad is the time-average power density.

ii) Effective Height (h_e): The effective height of an antenna is a measure of the effectiveness of the antenna as a radiator or collector of electromagnetic waves. For a transmitting antenna, it is the ratio of the induced open-circuit voltage at the terminals to the incident electric field strength, h_e = V/E.
Antenna Temperature (T_A): Antenna temperature is a parameter used to describe the noise power received by an antenna. It represents the temperature of a resistor that would generate the same noise power at the antenna terminals as the noise received from the environment, calculated as T_A = (1/4π) ∫∫ T_B(θ, φ) G(θ, φ) dΩ, where T_B is the brightness temperature of the environment.

For a half-wave dipole of length L = λ/2 placed along the z-axis, the current distribution is assumed to be sinusoidal: I(z) = I₀ sin[k(λ/4 - |z|)]. The far-field radiation components are derived using the vector potential approach.

1. The far-field electric field component E_θ is given by:
   E_θ = j(η I₀ e^-jkr / 2πr) * [cos((π/2)cosθ) / sinθ]
2. The magnetic field component H_φ is related to the electric field by the intrinsic impedance of free space (η ≈ 120π Ω):
   H_φ = E_θ / η = j(I₀ e^-jkr / 2πr) * [cos((π/2)cosθ) / sinθ]
3. In these expressions, k = 2π/λ is the wavenumber, r is the distance from the center of the dipole, and θ is the elevation angle measured from the dipole axis. The term [cos((π/2)cosθ) / sinθ] represents the field pattern of the half-wave dipole, showing maximum radiation in the equatorial plane (θ = 90°) and zero radiation along the axis (θ = 0°, 180°).