assignment 02

7/21/2019 Assignment 02

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May 3, 2006

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Assignment 2: Antenna Fundamentals

Problem 2.1

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 y E E = and 0φΔ = ,

b) x y E E ≠ and 0φΔ = ,

c) x y E E = and /2φ πΔ = ,

d) x y E E = and /2φ πΔ = − ,

e) x y E E = and /4φ πΔ = ,

f) x y E E = and /4φ πΔ = − ,

g) 0.5x y E E = and /2φ πΔ = ,

h) 0.5x y E E = and /2φ πΔ = − .

In all cases justify the answer.

Problem 2.2

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.



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Problem 2.3

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 by4

17x y

a

a ja ρ

+=

Find the polarization loss factor (PLF) dimensionless and in dB.

Problem 2.4*

A right-hand circularly polarized antenna has normalized electric far-field pattern

given as:

( )sin cos 0 180 , 90 90

,0 elsewhere

E θ 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.

* Problem taken from a previous exam.



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Problem 2.5

The normalized E-field pattern of an antenna, independent of frequency, varies as

follows:

0

1 0 45

0 45 90

1 90 180

2

E

E

θ

θ

θ

⎧⎪⎪ ≤ ≤⎪⎪⎪⎪= ≤ ≤⎨

⎪⎪⎪⎪ ≤ ≤⎪⎪⎩

a)

What is the directivity of this antenna?

b) What is the radiation resistance of the antenna at 200 m from it if the field is

equal to 10 V/m (rms) for 0θ = at the distance and the terminal current is

5 A (rms)?

Problem 2.6

A /2λ dipole, with a total loss resistance of 1 Ω , is connected to a generator whose

internal impedance is 50 25 j + Ω . Assuming that the peak voltage of the generator is

2 V and the impedance of the dipole, excluding the loss resistance, is 73 42.5 j + Ω ,

find the power.

a)

supplied by the source (real),

b)

radiated by the antenna,

c) dissipated by the antenna.



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Problem 2.9*

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 R 45R = Ω and the loss resistance is L 5R = Ω . The

maximum directivity of the antenna appears in the z + -direction and is 0 12dBiD = .

y

x

z

RL= 5

Rr = 45

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 4 VV = is connected to the antenna. Calculate the peak

electric field strength at 1kmz = .

c)

A lossless dipole antenna is located at 1kmz = 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 taken from a previous exam.

assignment 02

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