Eskisehir Technical University
Electrical Eng. Dept.
EEM 502 Antenna Engineering
Spring 2021 Midterm Take Home Exam
1. In a space radio operations base, a 30 dB gain antenna radiates (in the positive z-direction) 5 W of power
at 2 GHz. It has an impedance of 40 ohm, and is connected to a transmission line with characteristic
impedance of 75 ohm. The field pattern is at the beam maximum given by Et = (aˆx + jaˆy )Ft (θ, φ) . A
satellite antenna is placed in medium earth orbit, roughly 4500 km away from the first antenna, and is used
to receive wave from the transmitting antenna, placing its beam maximum along the negative z-direction.
This antenna has an efficieny of 95% and its field pattern is given by Er = (2aˆx + jaˆy )Fr (θ, φ) . As shown in
the field pattern for both antennas, they are not perfectly matched in polarization. The received power from
the transmitting antenna needs to be at least 1 Femtowatt ( 10−15 W) when reaching the satellite antenna for
the signal to be picked up and decoded. Determine the minimum directivity (both dB and dimensionless)
that the receiving antenna needs to have that will enable it to decode the signal. Assume perfect conditions
in all other unmentioned parameters.
2. You are an antenna engineer and you are asked to design a high directivity/gain antenna for a space-
borne communication system operating at 10 GHz. The specifications of the antenna are such that its
pattern consists of one major lobe, and ideally no minor lobes. The pattern is also requested to be
symmetrical to the azimuthal plane. In order to meet the requirements, the antenna must have a half-
power beamwidth of 10 degrees. To expedite the design, the radiation pattern will be approximated by
the function U (θ, φ) = cosn (θ) and exists only on the upper hemisphere ( 0 ≤ θ ≤ π2 , 0 ≤ φ ≤ 2π ).
a) Determine the value of n (not necessarily an integer, keep 5 significant figures in your calculations)
b) Determine the exact maximum directivity, both unitless and in dB
3. A communications satellite is in synchronous (stationary) orbit around the earth (assume a stable
altitude of 22,370 miles), and it transmits with 8.0 W of power. The receiving antenna is a 210 ft
paraboloidal antenna at the NASA tracking station at Goldstone, CA. Assume the transmitter antenna is
isotropic, that both antennas are impedance matched, and resistive losses are negligible. The only
mismatch is in the polarization, which was calculated to have an 8-degree tilt between the 2 antennas.
a) Calculate the power density (in mW2 ) incident on the receiving antenna.
b) Calculate the power received by the ground-based antenna, if its gain is 60 dB .
4- A two dimensional current density on the x-axis is given below. Find the far-zone electric field.
∫ J(ρ ′) H 0(2)(k ρ − ρ ′ )dl ′ .
i
J = zˆ η2 sin ϕie jkx cos ϕ , x 1 < x < x 2 . Hint: E(J) = kη
4 C
5. A vertical half-wave dipole antenna is used as ground-to-air,over-the-horizon communication antenna at
the VHF band (f=200 MHz). The antenna is elevated at a height ℎ measured from its center feed to the
ground.Assume the ground, to be a perfect, flat, and infinite electric conductor.In order to avoid cross-talk
interference with other nearby communications systems,it is desired to place a null in the far-field amplitude
of the antenna at an angle of 60° from the vertical. Determine the three smallest non-trivial heights in meters,
at the mentioned frequency, in which the antenna can be placed to meet the specifications.
6. A circular loop, of radius λ 30 and wire radius λ 1000 , is used as a transmitting antenna in a back-pack
radio communication system at 10 MHz. The wire of the loop is made of copper with a conductivity of
5.7 × 107 ℧ m . Assuming that the antenna is radiating in free space. a) Determine the radiation resistance of
the loop, b) Determine the loss resistance of the loop (assume that its value is the same as if the wire were
straight), c) Determine the radiation efficiency.
