Busitema University
Antennas & Wave propagation
Take Homework Test
Due: 11:59pm, 20.07.2022
Question 1
You have been tasked to design a 40 km microwave link that should operate at 10 GHz.
Unfortunately, there is a 12 m tall apartment block along the link path, 15 km from the receiver.
Answer the following:
a) What height of the earth’s curvature do you have to contend with?
[3 Marks]
b) What is the radius of the first Fresnel zone?
[3 Marks]
c) What is minimum height of towers to hold both antennas? (Assume that both towers have
the same height.)
[4 Marks]
Question 2
Briefly explain the three basic propagation mechanisms which impact propagation in mobile &
wireless communication systems.
[5 Marks]
Free space loss is (FSL) defined as the loss incurred by an electromagnetic wave as it propagates
in a straight line through a vacuum with no absorption or reflection of energy from nearby objects.
Prove that that FSL =32.4 +20log f(MHz) +20logd(km) [dB].
[5 Marks]
(Note: d=T-R separation, f =frequency of operation)
Question 3:
Consider the diameter of a parabolic dish antenna to be 2m. If the application operates at 5 GHz
and transmits a power of 10 dB, answer the following:
What is the far-field distance? [ 1Marks]
If you consider a minimum close-in reference distance, what is the power received at that distance?
[2 Marks]
Given that the path loss exponent is n=4, find the path loss suffered at a distance of 5 km.
[2 Marks]
Question 4.
You are tasked to design a microwave link. You can use channels at either 2.4 GHz or 5.2 GHz.
You have two parabolic dish antennas which have gains of 20 dB and 30 dB. You will find the
effective radii of the antennas.
(a) Show that the effective radius of the parabolic dish antenna, denoted as 𝑅𝑒, is expressed as
𝑅𝑒 =3√𝐺/20𝜋𝑓𝑔 , [10 Marks]
where 𝐺 is the antenna gain and𝑓𝑔 , is the frequency in GHz.
(b) What is the effective radius at both frequencies and gains?
Express your answers as in the table below: [12 Marks]
Gain
20
30
2.4 GHz
(c) Comment on the relationships between:
i. Gain and effective radius. [1 Mark]
ii. Frequency and effective radius. [2 Marks]
5.2 GHz