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Lecture 3, 1/27/11
ECE 3101, Copyright P. B. Luh
1
•
Reading Assignment: Sects. 1.61.81, 1.9, 1.10, 10.110.21
•
Problem Set 1: Due
Thursday
•
Last Time:
1.4
Some Useful Signal Models
•
Elementary Signals: Step, Ramp, and Sign Functions/Sequences
•
Trigonometric Functions and Sequences
•
Complex Functions and Sequences
•
Unit Impulse Function
and Unit Impulse Sequence
1.5
Even and Odd Functions and Sequences
ECE 3101 Signals and Systems
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ECE 3101, Copyright P. B. Luh
2
•
Today:
Systems
1.6
Systems
1.7
Classification of Systems: RLC Circuits with Input
Output Description
•
Liner vs. nonlinear; Time invariant vs. time varying
•
Additional system properties: Instantaneous vs. dynamic;
Causal vs. noncausal; Finite dimensional vs. infinite dim.
1.10 and 10.1, 10.2
StateSpace Description
•
Next Time:
Sections 1.82 to 1.11
1.8
System Modeling: Integrators/Differentiators, OpAmps,
and Mechanical Systems
3.4 and 3.5
DiscreteTime Systems
Lecture 3, 1/27/11
ECE 3101, Copyright P. B. Luh
3
•
Broadly speaking, a system is anything that responds
when stimulated or excited
•
Systems accept
excitations
or
input signals
at their inputs
and produce
responses
or
output signals
at their outputs
•
The above is a singleinput singleoutput system
1.6
Systems
u(
t
)
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ECE 3101, Copyright P. B. Luh
4
A multipleinput multipleoutput system
u
1
(
t
)
u
2
(
t
)
We have seen several examples of systems in Lecture 1
Lecture 3, 1/27/11
ECE 3101, Copyright P. B. Luh
5
•
What are the key system characteristics?
Using, for
example, a savings account in a bank
–
With a fixed interest rate. A linear and timeinvariant
system
–
Interest rate is time varying.
A time varying system
–
Interest rate depends on the amount of money in the
account.
A nonlinear system
–
Future interest rates are uncertain.
An uncertain system
•
Depending on the characteristics
–
System properties could be quite different
–
Methods of analysis and synthesis could be quite different
•
We shall study system classification next
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1.7
Classification of Systems: RLC Circuits
Elements:
R, L, C, and voltage and current sources
•
How to describe these elements?
The systems?
+
+



u(t)
R
C
L
+
y
R
v

+
i
v = Ri
L
v

+
i
dt
di
L
v
=
C
v

+
i
dt
dv
C
i
=
•
Linearity
–
i
1
→
v
1
= R i
1
−
2i
1
→
2v
1
;
Homogeneity
–
i
2
→
v
2
= R i
2
−
i
1
+ i
2
→
v
1
+ v
2
;
Additivity
–
u
1
→
y
1
2
→
y
2
, then k
1
u
1
+ k
2
u
2
→
k
1
y
1
+ k
2
y
2
;
Linearity
•
Are R, L, and C linear elements?
−
Yes.
Differentiation is a linear operation
Lecture 3, 1/27/11
ECE 3101, Copyright P. B. Luh
7
i
v
•
Linearity: A straight line passing through the origin
•
Timeinvariance:
The characteristics of an element do not
change over time
–
v = Ri ~ Linear timeinvariant element
–
v =
R(t)
i
~ Linear timevarying element
–
Similar v = L di/dt (
LTI
) vs. v =
L(t)
di/dt (
LTV
)
–
u(t)
→
y(t), then u(tt
1
)
→
y(tt
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This note was uploaded on 03/29/2011 for the course ECE 3101 taught by Professor Luh during the Spring '11 term at UConn.
 Spring '11
 Luh

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