E8 204: ANTENNA THEORY AND PRACTICE
Assignment-1 (Total Marks = 25, Deadline: 29/02/2024)
February 9, 2024
Exercise 1
For an electric dipole in static (time-invariant) scenario having length 𝑑 and placed as shown
in Fig. 1, determine the expressions for potential 𝑉 and electric field 𝐄 at P. Consider the
Figure 1: An electric dipole in static scenario.
observation region: 𝑥 = 𝑑, −5𝑑 ≤ 𝑦 ≤ 5𝑑, −5𝑑 ≤ 𝑧 ≤ 5𝑑. Plot 𝑉 /𝑞 and |𝐄|/𝑞 along the
observation region, considering spatial resolution of 0.01𝑑.
Exercise 2
Consider an infinitesimal 𝑥-directed Hertzian dipole of length 𝑙 and current amplitude 𝐼0 at the
√
origin. The wave-number is 𝑘 = 𝜔 𝜇ϵ = 2𝜋/𝜆, where 𝜆 = 2𝜋𝑐/𝜔 is the operating wavelength.
• Determine the phasor form of magnetic field 𝐇 and electric field 𝐄 at a far-field point ‘P’
with coordinates (𝑟, 𝜃, 𝜙).
̃ = 𝐇(𝑟,
̃ 𝜃, 𝜙, 𝑡) and electric
• Determine the expression for instantaneous magnetic field 𝐇
̃ 𝜃, 𝜙, 𝑡) at ‘P’.
field 𝐄̃ = 𝐄(𝑟,
• Determine the expressions for corresponding Poynting vector in phasor as well as
instantaneous form.
1
Exercise 3
The power radiated by a lossless antenna is lossless antenna is 10 watts. The radiation intensity
𝑈 (in watts/solid angle) of the antenna has the following expression:
𝑈 = 𝑈0 cos7 𝜃 where 0 ≤ 𝜃 ≤
𝜋
, 0 ≤ 𝜙 ≤ 2𝜋.
2
1. Find the maximum power density (in watts/square meter) at a distance of 1,000 m (assume
farfield distance). Specify the angle where this occurs.
2. Determine the exact values for the maximum directivity 𝐷0 (both dimensionless and in
dB), using analytical formulae as well as numerical integration.
3. Note that, Half-Power Beamwidth (HPBW) is defined (by IEEE) for an antenna as: “In
a plane containing the direction of the maximum of a beam, the angle between the
two directions in which the radiation intensity is one-half value of the beam.” Now,
for antennas with one narrow major lobe and very negligible minor lobes, one defines
beam solid angle approximately equal to the product of the HPBWs in two perpendicular
planes. If Θ1 and Θ2 are the respective HPBWs (in radian) in one plane and in the plane
at a right angle to the other, we can use the approximate Kraus’s formulae as:
Ω𝐴 ≈ Θ1 Θ2 and 𝐷0 ≈
4𝜋
.
Θ1 Θ2
For the given 𝑈 , first determine the values of Θ1 and Θ2 (choose any two mutually
orthogonal planes), and then compute approximate values for Ω𝐴 and 𝐷0 .
2
0
