Departamento de Engenharia Electrotécnica e de Computadores – Instituto Superior Técnico _________________________________________________________________________________________

_________________________________________________________________________________________

2nd Exam of Antennas –17 July 2020

Antenas

2nd Exam 17 July 2020

Remote Exam Submission deadline: 11am _________________________________________________________________________________________

Instructions:

Please submit your resolution through Fenix as a project (2nd Exam). The submission

deadline is 11am.

If possible the resolution should be returned in a single .pdf file.

Together with the exam, you should return a signed declaration of honor stating the

following:

Declaration of honor:

For Portuguese students: Declaro por minha honra que a resolução que apresento foi preparada

exclusivamente por mim sem auxílio de terceiros. Em particular, declaro por minha honra que não

recebi auxilio nem auxiliei outros colegas.

For non-Portuguese speaking students:

I hereby declare by my honor that the present work was prepared exclusively by me without the

assistance of third parties. In particular, I declare on my honor that I have not received assistance or

helped other colleagues.

Departamento de Engenharia Electrotécnica e de Computadores – Instituto Superior Técnico _________________________________________________________________________________________

_________________________________________________________________________________________

2nd Exam of Antennas –17 July 2020

Problem 1 (15%).

The power radiated by an antenna with efficiency of 90% is 10W. The radiation intensity of the

antenna is described by

3

0 cos , 0 90º ,0 360º

0, otherwise

BU

Find the power gain, the maximum gain and sketch the radiation pattern of the antenna.

Problem 2 (10%).

Indicate which of the following antennas is more suitable for TV broadcasting. Justify your answer.

Problem 3. (25%) An array of two half-wavelength dipole antennas

is fed as shown in the figure. The spacing between the antennas is

0 / 2d and the length of the feeding lines is 0 / 2l . The

frequency of operation is 1GHz.

a) By analyzing the feeding circuit, justify that the two dipoles are

fed with symmetric currents (i.e., currents with the same amplitude

and phase-shifted by 180º).

b) Suppose the self-impedance and the mutual impedance of the

antennas is 11 22 73 42.5Z Z j e 12 13 29Z j . Find the

input impedance of the antenna array (after the connection point of

the lines with length l).

Departamento de Engenharia Electrotécnica e de Computadores – Instituto Superior Técnico _________________________________________________________________________________________

_________________________________________________________________________________________

2nd Exam of Antennas –17 July 2020

c) Suppose that the array is matched to the main feeding line using an impedance transformer (as

illustrated in the picture). The power of the transmitter is 10kW. Find the maximum of the electric

field radiated by the array at a distance of 10km from the antennas.

Problem 4. (20%)

A uniform planar array consists of 10 10 elements placed along the xoz plane with the distance

between elements 0.5 .

a) Find the current phaseshifts along the x and z directions, x and z , that maximize the

transmission towards a point P with coordinates P= 0, 20 km,10 km .

b) Using a computational tool, calcule the array radiation pattern in the yoz plane. Explain the

structure of the radiated beam.

Problem 5. (15%)

Two identical E-sectoral horn antennas with axial length 10E and dimensions 4a B

are used in an indoor (short distance) microwave link at 10GHz. Suppose that the feeding power is

1Watt. Find the maximum distance between the antennas that guarantees that the power captured

by the receiving horn is at least 0.1mW. Suppose that the receiving antenna is matched to the load.

Departamento de Engenharia Electrotécnica e de Computadores – Instituto Superior Técnico _________________________________________________________________________________________

_________________________________________________________________________________________

2nd Exam of Antennas –17 July 2020

Problem 6 (15%).

Consider an electric charge q under the influence of an external electric field. The total force acting

on the charge is given by ext Ab-LF qE qE F , where extE is the external field (created by other

charges) and Ab-L selfF qE is the so-called Abraham-Lorentz force due to the self-field selfE of the

charge itself.

a) Recall that the instantaneous power transferred to a point particle is given by p Fv with v the

charge velocity. Using this property explain the physical meaning of each of the terms of the

formula:

ext Ab-Lp qE v F v

b) The Abraham-Lorentz force can be written in terms of the charge acceleration /a dv dt as

2

Ab-L 0 6

q daF

c dt

. Using this result prove that if the charge trajectory is periodic in time, the time-

averaged radiated power is given by:

22

rad 306

qp a

c

In the above, the brackets represent a time-averaging. The above formula confirms that an

accelerated motion leads to the emission of electromagnetic radiation.