Assignment 3 – Fundamentals Antennas and Propagation, Frühjahrssemester 2010

Problem 3.1 : A uniform plane wave is propagating in direction of the positive z-axis. Find the polarization (linear, circular, or elliptical), sense of rotation (CW or CCW), axial ratio (AR), and tilt angle τ (in degrees) for

a) x yE E= and 0φΔ = ,

b) x yE E≠ and 0φΔ = ,

c) x yE E= and /2φ πΔ = ,

d) x yE E= and /2φ πΔ = − ,

e) x yE E= and /4φ πΔ = ,

f) x yE E= and /4φ πΔ = − ,

g) 0.5x yE E= and /2φ πΔ = ,

h) 0.5x yE E= and /2φ πΔ = − .

In all cases justify the answer. Problem 3.2 : Write a general expression for the polarization loss factor (PLF) of two linearly polarized antennas if a) both lie in the same plane, b) both lie in different planes. Problem 3.3 : A linearly polarized wave traveling in the negative z-direction has a tilt angle τ of 45°. It is

incident upon an antenna whose polarization characteristics are given by 417

x ya

a jaρ

+=

Find the polarization loss factor (PLF) dimensionless and in dB. Problem 3.4 : Problem taken from a previous exam A right-hand circularly polarized antenna has normalized electric far-field pattern given as:

( )sin cos 0 180 , 90 90

,0 elsewhere

Eθ φ θ φ

θ φ⎧ ⋅ ≤ ≤ − ≤ ≤⎪⎪= ⎨⎪⎪⎩

a) Calculate the direction (θ,φ) of maximum radiation and the exact maximum directivity in dB.

b) Find the 3-dB beamwidths in azimuthal and elevation planes. c) A CW elliptically polarized plane wave propagates along –x-direction towards the

antenna. The major axis of the ellipse is positioned along the y-axis and is twice as large as the minor axis. Find the polarization loss factor (PLF). Note: It is assumed that the antenna is placed at the center of the coordinate system.

Assignment 3 – Fundamentals Antennas and Propagation, Frühjahrssemester 2010

Problem 3.5 : A /2λ dipole, with a total loss resistance of 1 Ω , is connected to a generator whose internal impedance is 50 25j+ Ω . Assuming that the peak voltage of the generator is 2 V and the

impedance of the dipole, excluding the loss resistance, is 73 42.5j+ Ω , find the power.

a) supplied by the source (real), b) radiated by the antenna, c) dissipated by the antenna. Problem 3.6 : Problem taken from a previous exam Assume a horn antenna located at the origin of the coordinate system. Its E-plane lies in the yz-plane and its H-plane lies in the xz-plane. The antenna is operated at 3 GHz. The figure below shows the orientation of the antenna and its equivalent circuit. The radiation resistance is RR = 45 Ω and the loss resistance is RL = 5 Ω. The maximum directivity of the antenna appears in the +z-direction and is D0 = 12 dBi. a) Calculate the maximum effective aperture of the antenna with the assumption of a

matched load and a matched polarization. b) A generator with an internal impedance of G 50 20Z j= + Ω and a peak generator

voltage of G 4VV = is connected to the antenna. Calculate the peak electric field

strength at 1kmz = .

c) A lossless dipole antenna is located at z = 1 km and lies in the plane parallel to the xy-plane. The E-field of the antenna is parallel to the xy-plane and assumes an angle of 45° with respect to the x-axis. Calculate the polarization loss factor (PLF).

Problem 3.7 : The effective antenna temperature of an antenna looking towards zenith is approximately 5 K. Assuming that the temperature of the connected transmission line (waveguide) is 72 °F, find the effective temperature at the receiver terminals when the attenuation of the transmission line is given as 4 dB / 100 ft, and its length is : a) 2 ft, b) 100 ft. Problem 3.8 : In a long-range microwave communication system operating at 9 GHz, the transmitting and receiving antennas are identical, and they are separated by 10 000 m. To meet the signal-to-noise ratio of the receiver, the received power must be at least Pr = 10 μW. Assuming the two antennas are aligned for a maximum reception to each other, including being polarized matched, what should the gains (in dB) of the transmitting and receiving antennas be when the input power to the transmitting antenna is 10 W ?