Middle East Technical University Department of Electrical and Electronics Engineering

Spring Semester 2012

EE 426 HW2 Due: April 5, 2012 Thursday

To be submitted to Room D-304 untill 17:00

HW Problems: 1-5 Supplementary Problems: 6,7

1. The phasor electric field which is incident upon the antenna shown in the figure below is

given by

( ) jkzyx

ieaajEE −−= ˆ2ˆ20 , where 0E is constant

Calculate the polarization loss factor when the receiving

antenna is

i. LP in x-direction

ii. LP in y-direction

iii. RHCP

iv. LHCP

2. A radar with a circularly polarized antenna cannot “see” a large conducting screen placed in

front of it. Why?

3. Two infinitesimal dipoles of length dl is placed at the origin of the

coordinate system as shown in the figure. Each dipole has the same

current I.

a) Determine the electric field in the far zone.

b) Determine the polarization of the radiated field when

2

πφθ == .

c) What is the total radiated power?

4. The electric field intensity of a transmitting antenna, in the direction of the main beam,

when radiating into free space, is given by ( )r

eajaIE

jkr−

+= φθ ˆ4ˆ330 0 where I0 is the

peak value of the antenna terminal current. The radiation resistance of the antenna is

Rr=75Ω. Find the directivity, Dmax, of the antenna and its maximum effective aperture, Aem, if

it is operating at f=5GHz.

z

x

y

iE

x

y

z

Middle East Technical University Department of Electrical and Electronics Engineering

5. (problem 2.49, Balanis 3rd Edition) An antenna with a radiation resistance of 48 ohms, a

loss resistance of 2 ohms, and a reactance of 50 ohms is connected to a generator with

open-circuit voltage of 10 V and the internal impedance of 50 ohms via λ/4 long

transmission line with characteristic impedance of 100 ohms.

a. Draw the equivalent circuit.

b. Determine the power supplied by the generator.

c. Determine the power radiated by the antenna.

6. A line of sight communication link has the following parameters

Transmitter Receiver

Zs: Source impedance = 50 Ω ZL: Load impedance = 50 Ω

ZA,t: Antenna impedance = 30+j10 Ω ZA,r: Antenna impedance = 40+j50 Ω

Rr,t: Radiation resistance = 10 Ω Rr,r: Radiation resistance = 30 Ω

Dt: Antenna directivity = 15.6 Dr: Antenna directivity = 10

The main beams of the antennas are aligned in the direction of each other and they are

polarization matched. The distance between the antennas is 30 km and the atmospheric

attenuation is 0.1dB/km. If the transmitter source voltage is Vs=130 V peak operating at

f=6GHz, find

a. The total power radiated by the transmitter, Pt

b. The electric field intensity , Einc at the receiver site

c. The effective length of the receiver antenna, leff, and the volatge, Voc that would

be induced at the terminals of the receiving antenna, if its terminals were left

open-circuited

d. The power delievered to the load at the receiver, Pr.

7. A radar that uses the same antenna both for reception and transmission has the following

specifications:

Transmitter power, Pt=10 kW

Antenna Directivity, D= 30 dB

Operating frequency, f=6GHz

Receiver sensitivity, Prmin=10-14

W

Efficiency of the antenna is 70%

Assume that there is a 3dB polarization loss. What must be the minimum radar cross section

of a target that this radar can detect from a distance of 50 km?