Examples of Antenna Array | Solved Examples based on Parameters of Antenna Array | Engineering Funda

Summary

In this video, the presenter tackles two complex antenna array problems, following up on a previous video where three similar questions were solved. The first problem involves calculating the distance between two half-wave dipole antennas, considering a phase shift and radiation angle. The second problem deals with finding the minimum height for a dipole above a conducting plane to achieve maximum far-field radiation at a specific angle. The presenter explains key concepts, such as phase shifts, array factors, and errors commonly made by students, providing step-by-step solutions for better understanding.

Takeaways

• 📡 In this video, two interesting questions related to antenna arrays are solved, following a previous video on the same topic.
• 🧐 In question 4, two half-wave dipole antennas are excited with a 3 MHz frequency, and the phase shift of the origin element is -π/2.
• ✏️ Key concept: If the reference element has a phase shift, that phase is negative. This is crucial for solving antenna problems.
• 📐 The distance between the antennas, denoted as 'd,' is derived using the formula for ψ: βd cosθ + α. At the maximum radiation point (θ = 60°), d is λ/2, or 50 meters.
• 🔍 The wavelength (λ) is calculated using c/f, where c is 3×10^8 and f is 3 MHz, yielding 100 meters.
• 💡 Question 5 discusses an infinitesimally small dipole (Hertzian dipole) placed at a height (h) above a conducting plane and determining the minimum height (h) for maximum radiation at a 60° angle.
• 🧲 A Hertzian dipole has an α value of 0, while a dipole of λ/2 would have an α value of π. This is essential for solving the radiation pattern.
• 🔗 The Array Factor for two elements is given by cos(ψ/2), where ψ = βd cosθ + α. Using this, the problem is solved for maximum value of h.
• 🔢 The correct minimum value of h for maximum radiation at 60° is λ, with n = 1, meaning h = λ.
• ⚠️ Common mistake: Students often assume α = π, which leads to incorrect results (h = 0.5λ), but for a Hertzian dipole, α = 0.

Q & A

Question 1: What is the primary focus of the video?

The primary focus of the video is to solve two interesting questions related to antenna arrays.

Question 2: What is the frequency given in question 4?

The frequency given in question 4 is 3 MHz.

Question 3: What phase shift is observed between the two half-wave dipole antennas in question 4?

The phase shift between the two half-wave dipole antennas is given as pi by two (π/2), but the reference element at the origin has a phase shift of -π/2.

Question 4: How is the distance 'd' between the two antennas calculated in question 4?

The distance 'd' is calculated using the formula psi = βd cos θ + α, where ψ = 0, β = 2π/λ, cos θ = cos 60°, and α = -π/2. After simplifying, the distance is found to be λ/2, which equals 50 meters.

Question 5: What concept does the speaker emphasize about the phase shift in antenna arrays?

The speaker emphasizes that if the reference element (origin) is given a phase shift, that shift should be treated as negative.

Question 6: In question 5, what is the minimum value of 'h' for the maxima in the far-field radiation pattern at 60 degrees?

The minimum value of 'h' is equal to the wavelength λ for the maxima in the far-field radiation pattern to occur at 60 degrees.

Question 7: What is the role of the array factor in solving question 5?

The array factor helps in determining the condition for maxima in the far-field radiation. It is expressed as cos(ψ/2), where ψ = βd cos θ + α, and the maxima occur when the argument of the cosine function is a multiple of π.

Question 8: How is the distance 'd' related to the height 'h' in question 5?

The distance 'd' between the dipole and its image is equal to 2h, where 'h' is the height of the dipole above the conducting plane.

Question 9: What common mistake do students make when solving for the minimum value of 'h' in question 5?

Students often mistakenly assign α = π for a Hertzian dipole, but for an infinitesimally small dipole (Hertzian dipole), α should be 0.

Question 10: Why is it important to distinguish between different types of dipoles in the problem-solving process?

It is important because the value of α depends on the type of dipole. For example, for a Hertzian dipole, α = 0, whereas for a dipole of λ/2, α = π. Incorrect assumptions about the type of dipole can lead to errors in calculations.