a question a bout Matlab
PPPan
Tutorial05PhasedArray-New.docTutorial 05 – Phased Array
MECH 5720: SENSORS & SIGNALS
TUTORIAL: PHASED ARRAY
VALUE: 4%
THIS TUTORIAL SHOULD TAKE A TOTAL OF 4 HOURS TO COMPLETE
Notes:
· Answer questions briefly and clearly
· Tutorials must be completed and a PRINTED COPY handed in prior to the start of the following tutorial
· A soft copy (including MATLAB listings) must also be submitted through Blackboard for processing through Turnitin
· Tutorials returned after the due date will lose 20% per day (or part thereof) unless accompanied by a valid doctor’s certificate.
· The title page should include the following information:
· Sensors: Tutorial XX
· Name
· Student Number
· E-mail address
Tutorial 05
Read “Introduction to Sensors for Ranging and Imaging”, Ch 12 – High Angular Resolution techniques.
Question 1.
The output of an N element phased array in which the phase front is defined as passing through the geometric centre of the array can be determined using the following sum
å
=
÷
÷
ø
ö
ç
ç
è
æ
÷
ø
ö
ç
è
æ
+
-
+
=
N
k
N
k
t
SumOutput
1
2
1
sin
y
y
w
(1.1)It can be shown that equation (1.1) reduces to:
(
)
(
)
(
)
2
/
sin
2
/
sin
sin
y
y
w
N
t
SumOutput
=
(1.2)a) Use equation (1.2) to plot the non-steered field intensity pattern as a polar plot.
( SumOutput vs.
q
) for -(/2 < ( < (/2. Identify the main lobe, the side lobes and grating lobes (5)Use the values:
· v = 1450 m/s speed of sound.
· f = 175 kHz operating frequency
· N = 4 elements
· d = 12 mm array spacing.
Hint:
· Remove the time dependency of the signal by choosing an instant in time where the signal amplitude is a maximum.
· Plot the abs value of equation (1.2). This is the field intensity pattern
· For polar plots:
· See help polar
· Immediately following the polar command, Use: set(gca,'CameraUpVector',[1 0 0]) to view zero degrees as upright.
b) Replot the intensity pattern using conventional rectangular axes to allow you to perform the following measurements. (5)
c) From the plot measure the width of the main beam (this will be at 0.707( the peak amplitude) (2)
d) Compare to the theoretical value for a fully illuminated aperture of the same size.
Hint: Read section 5.3.3 Antennas to understand where eqn 12.31 comes from (3)
Question 2.
a) Plot for N = 40. (5)
b) From the plot, measure the angle of the grating lobes and compare to the theoretical value. (3)
c) Plot the array response for the same total aperture D = Nd with a new array spacing, d, to remove the grating lobes. (5)
Question 3.
The array is steered to
0
q
by applying a phase-shift to each element in the array. The applied phase-shifts pattern is linear with successive elements differing by
(
)
0
0
sin
2
q
l
p
y
d
=
a) Explain graphically or in words why this successfully steers the main beam to
0
q
.Hint: Consider the phase-shifts due to geometry and the applied phase-shifts (5)
b) Extend equation (1.1) and (1.2) to incorporate the steering phase shifts. (3)
c) Use b) or equivalent from lecture notes to plot the steered array response in both polar and Cartesian space for:
· v = 1450 m/s speed of sound.
· f = 175 kHz operating frequency
· N = 4 elements
· d = 12 mm array spacing.
·
0
q
= 5 degrees steering angle (5)d) Label the main beam and grating lobes. (2)
e) Check the position of the grating lobes against theoretical values. (2)
f) Plot the steered array response in both polar and Cartesian space for:
· v = 1450 m/s speed of sound.
· f = 175 kHz operating frequency
· N = 4 elements
· d = 12 mm array spacing.
·
0
q
= 25 degrees steering angle (5)g) Explain what is happening to the main beam and grating lobes. (2)
h) Find the maximum non-ambiguous field of view by plotting the function at a range of angles. (This is defined as the full angular extent of the region covered only by the main beam when steered, but never by a grating lobe) (10)
Question 4.
Assume that the array can be removed from the water and operated in air where the speed of sound in 330m/s, plot the results for the configuration. (5)
Discuss the differences between the two patterns and explain why they are so different (5)
� The beamwidth is measured at 0.5 ( the peak of the power pattern which equates to 0.707 of the peak of the voltage pattern
MECH5720 SENSORS & SIGNALS 3of3
