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City University of Hong Kong
Department of Electronic Engineering
Course:
EE3118 – Linear Systems and Signal Analysis
Year:
Semester A 2008/09
This laboratory module consists of two main parts: MATLAB programming and LabView
Programming. For MATLAB, you are asked to do it individually. For LabView, two
students are grouped together.
Part 1:
Individual work – MATLAB Programming
Programming Media:
Matlab 6.0 or above with control system toolbox.
Background:
1) Before you start, you have to be familiar with the following functions:
•
tf
•
impulse
•
step
•
lsim
•
bode
•
plot
•
title
•
xlabel, ylabel, grid
[The detailed description of functions can be obtained by typing “help xxx”, where ‘xxx’ is the
function name.]
2)
A frequency transfer function is Fourier Transform of the impulse response of a system,
expressed as
() ()
()
ω
φ
j
e
A
H
=
equivalent to the ratio of the complex exponential time waveform at the input of the system to the
complex exponential time waveform causing it at the output port.
In Matlab, the gain and the phase shift, i.e.
( )
ω
A
and
( )
ω
φ
, can be obtained by the function “bode”.
Note: The xaxis of
Bode Diagram obtained is in
ω
.
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I.
Passive filters
(A) Firstorder Low Pass filter
Figure 1 show the first order lowpass filter based on a RC circuit. Its frequency transfer function can
be expressed as
()
()
()
( )
()
ωτ
ω
j
C
j
R
C
j
V
V
H
in
out
+
=
+
=
=
1
1
/
1
/
1
where
RC
=
τ
is called the time constant.
Paper Work
Prove that the cutoff
frequency (3dB) is
π
2
1
0
=
f
.
Programming Work
If R=2k
Ω
, determine the value of C so that the cutoff
frequency is
(100+
X
) Hz (
X
is the last 2 non
zero digits of your student ID). Plot the bode diagram for verification.
(Please refer to Appendix I for the design procedure)
(B)
Firstorder highpass filter
Figure 2 shows a first order highpass filer based on a RC circuit in Fig. 2 is constructed. Its
frequency transfer function can be expressed as
()
()
()
j
j
C
j
R
R
V
V
in
out
+
=
+
=
1
/
1
where
RC
=
is called the time constant, and the cutoff
frequency is again
2
1
0
=
f
.
Programming Work
If R=2k
Ω
, determine the value of C so that the cutoff frequency is
(1000+
X
) Hz (
X
is the last 3
nonzero digits of your student ID). Plot the Bode diagram for verification.
(C)
Second order bandstop filter
Figure 3 shows a bandstop filer based on a RLC circuit. Its frequency transfer function is given as:
()
()
()
()
()
C
R
j
LC
LC
C
j
L
j
R
C
j
L
j
V
V
H
in
out
+
−
−
=
+
=
=
2
2
1
1
/
1
/
1
where the bandwidth is
L
R
BW
2
=
Programming Work
Let R=1.8k
Ω
, C=56nF, L=47mH, plot the Bode diagram
and describe its characteristics of the filter.
Figure 3. RLC bandstop filter
Figure 2. RC highpass filter
Figure 1. RC lowpass filter
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This note was uploaded on 01/11/2011 for the course EE 3118 taught by Professor Kitsangtsang during the Spring '08 term at City University of Hong Kong.
 Spring '08
 KITSANGTSANG

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