The centre of a half-wave dipole is placed at the origin of the standard spherical coordinate system with the wire parallel to the z axis. This centre-fed dipole is in resonance at 0.9 GHz and the total radiated power is 200 W.(a) Calculate the effective height vector in the xy plane (θ = 90°).(b) Find the electric field vector (peak value) radiated by the dipole in the far-field region.(c) A second similar dipole is also placed in the xy plane parallel to the first at a distance of 1500 m. Neglecting losses and assuming the free-space condition, calculate the voltage U (peak value) induced in the dipole, i.e. the voltage in the equivalent receiving circuit.(d) Based on the voltage U, calculate the maximum rms power available at the matched load

Consider a half-wave dipole that is radiating into free space when the origin is at the centre of the dipole and its axis is aligned with the z axis. The input power fed to the dipole is 300 W. If we assume that the dipole has an efficiency of 75%, calculate the power density at point P(r,θ,φ) of the spherical coordinate system with r = 300 m, θ=75° and φ=45°.

Consider an electric dipole on the x-axis and centered at the origin. At a distance h = 18.9 cm along the positive x-axis, the magnitude of electric field due to the electric dipole is given by k(2qd)h3𝑘(2𝑞𝑑)ℎ3 , where q = 3.07 μC and d = 2.57 cm. Find a distance perpendicular to the x-axis and measured from the origin at which the magnitude of the electric field is the same. (You may enter your calculation using scientific notation.)  m

The figure above shows the radiation pattern of an antenna in linear scale.a). If the main lobe magnitude is 4.1, calculate the magnitude of its half power point. b). If the main lobe magnitude is 7 dB, calculate the magnitude of this new half power

Time left 0:01:01Question 11Not yet answeredMarked out of 15.00Flag questionTipsQuestion textThe electric and magnetic fields of a short dipole (length L << λ) that is placed at the origin and oriented parallel to the z axis of the standard spherical coordinate system can be calculated in the general case at the point r,θ,φ from the following formulaeE⃗ =Erur+Eθuθ𝐸→=𝐸𝑟𝑢𝑟+𝐸𝜃𝑢𝜃 whereEr=j2ωμILcosθe−jkr4πr(1jkr+1(jkr)2)𝐸𝑟=𝑗2𝜔𝜇𝐼𝐿cos⁡𝜃𝑒−𝑗𝑘𝑟4𝜋𝑟(1𝑗𝑘𝑟+1(𝑗𝑘𝑟)2)Eθ=jωμILsinθe−jkr4πr(1+1jkr+1(jkr)2)𝐸𝜃=𝑗𝜔𝜇𝐼𝐿sin⁡𝜃𝑒−𝑗𝑘𝑟4𝜋𝑟(1+1𝑗𝑘𝑟+1(𝑗𝑘𝑟)2) andH⃗ =Hϕuϕ=uϕjkLIsinθe−jkr4πr(1+1jkr)𝐻→=𝐻𝜙𝑢𝜙=𝑢𝜙𝑗𝑘𝐿𝐼sin⁡𝜃𝑒−𝑗𝑘𝑟4𝜋𝑟(1+1𝑗𝑘𝑟)ω is the angular frequency, I is the amplitude of the electric current in the dipole, L is the length of the dipole, and k = 2π/λ is the wave number.(a) Simplify the expression for the wave impedance of a short dipole η=|E⃗ |/|H⃗ |𝜂=|𝐸→|/|𝐻→| as much as possible when θ = 90°. (Keep in mind part b)(b) Using the software of your choice, plot the wave impedance η as a function of the distance-to-wavelength ratio r/λ along the axis perpendicular to the antenna (θ = 90°). Choose, e.g., 0.05≤r/λ≤3 and 0 Ω≤η≤1000 Ω.(c) Mark on the plot i) the level where η = η0 =377 Ω, ii) the distance r/λ = 1/(2π), and iii) the distance r/λ at which η = 0.997η0.(d) What is the reactance of a short dipole like? Which field (E or H) dominates in the distance range r/λ = 1/(2π)? How is this related to the reactance of a short dipole?(e) What distance can be considered as the outer boundary of the reactive near fields of a short dipole?(f) What is the distance of the far field region of a short dipole?(g) How would you assume that the wave impedance curve changes for a small loop antenna? What is the reactance of a small loop, inductive or capacitive?

The question is in relation to the antenna analysis. Which of the statement below is correct?Select one:a.A half wave dipole antenna has a maximum directive gain of 2.15 dBb.A long antenna is required to reduce radiation resistancec.A half wavelength dipole has a maximum directive gain of 2.15 dBid. Image theory is use to increase antenna radiated power and directivitye.A half-wave length dipole antenna has a radiation resistance of 50 Ohms